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S  N<bW+bW+ BEH  \*@: : : WWtt  NbW+bW+ B$gEH   ^*@: : : WWtt  NԤbW+bW+ BK(dH  ^*@: : : WWttH  0<܍ ? 3380___PPT10.M`]< Default Design1 H@  0L D(  R  C *APicture1] qhH 4 TA" MOE_Screenshot"`H>%4EH  B ?"6@ NNN?Ni$0CW, $ s *3"` 'zL  PAbstract 2 $:  & s *3"`&'z( dA bit of Ligand Field Theory 2$: g ' s *X3"` 4 KL  Iron(II) Hexammine [Fe(NH3)6]2+ 2'$/$'$/$'$/$$ : 'F Tbl  1 xnb S  0t3"`Tb qFinding optimal parameters for spin-state changes in Iron(II) amine complexes in Ligand Field Molecular Mechanics r(2rP56:    6XZb  Prakash Patel1 , Rob Deeth2X(2 6 6 6 66: c + 6 XM bl  1MOAC Doctoral Training Centre, and the 2Inorganic Computational Chemistry Group, Department of Chemistry, ý.J(2 ' Y:  8 0P 4 The geometries and energies of six-coordinated amine complexes of Fe2+ at both spin states were explored using the DommiMOE program. Then the model parameters were refined using simulated annealing to give the correct geometries and predict the correct spin state of the metal, initially with [Fe(NH3)6]2+, then with three other amine complexes. The parameters found were applied to about 80 imine complexes, and after a slight modification, approximated the geometries reasonably well and most of the time predicted the correct spin state.xD    : B . # A"`-  9 s *lX3"`'z T Introduction 2 $:  : <4CX ?"6@`NNN?Ng'.4 ,The importance of organometallic proteins in biochemistry has long been recognised, which the metal instrumental in many of these protein s catalytic or binding functions. At the moment there are very few methods that model transition metal-containing organometallic proteins effectively, either using quantum or classical mechanical methods. Here is outlined a very promising new Molecular Modelling approach to deal with transition metal complexes which can be used to model biological macromolecules.:  < s *OX3"`'z Molecular ModellingB 2 $, $:  ? B ?"6@ NNN?Nmi A B ?"6@ NNN?Nmi = <8TX ?"6@ NNN?N"'.4 VMolecular Modelling (MM) of Force-Field (FF) methods of finding molecular structures determine the relationship between the energy and structure by application of empirical rules based on classical mechanics. To find an optimal structure in MM, we optimise the total strain energy: D B <fX ?"6@ NNN?N'\4& \where the terms correspond to the deviation from the optimal bond lengths, bond angles, torsions, non-bonded interactions and electrostatic interactions from those given by the a particular forcefield. Modelling transition metals using conventional MM has always been difficult as they can have variable oxidation states, spin states and electronic effects, and can coordinate from 4 to 12 different ligands in a complex. Rob Deeth has addressed this problem by developing this Ligand Field Molecular Mechanics model of dealing with transition metal centres using an approach called Ligand Field Theory.]]:  D B ?"6@ NNN?NF$miF$j C S A ??"? &  T <tvX ?"6@ NNN?N}('am7 ' In a free transition metal ion, the preference of the d-electrons is to occupy each of the five d-orbitals, and when there are more than five d electrons, spin-pairing occurs. In an octahedrally-coordinated complex, the dxy, dyz and dxz orbitals become lower in energy than the dx2-y2 and dz2 orbitals and are filled first. Ligand Field Theory states that this is because the former orbitals repel the ligand electron densities less than the latter (the d-orbitals are mostly antibonding and repel ligand electron clouds). Depending on the ligands (the so-called ligand field strength), the d-electrons may desert the dx2-y2 and dz2 orbitals completely as the electron pairing becomes energetically more favourable than the electron repulsion of ligand bonding orbitals.    ,  M  >: V W C .Adorbitals2%m4+ \ < ?"6@ NNN?N.4 _ < ?"6@ NNN?N.4 b < ?"6@ NNN?N.4  < ?"6@ NNN?N.4  < ?"6@ NNN?N.4  < ?"6@ NNN?N.4F 2)p*2 3   +`)2v4N  S A 2)p*2-N  S fA 2)_-2n0  TA ?"6@ NNN?N2)L02 3 F `B*23   +K34  H8^X=J?"6@`NNN?N{(*023 @: Wt  BXX?"6@`NNN?N`*0{(3 :(2) High Ligand Field strength (e.g. CN-, phenantroline) J;(&.&+ : Wt  HX=J?"6@`NNN?N{(6-2*0 @: Wt  B*X?"6@`NNN?N`6-{(*0 7(1) Low Ligand Field strength (e.g. Cl-, I-, F-, H2O) 8'&.&.&.&.&: Wt  HX=J?"6@`NNN?N{(B*26- @,: WtA  BX?"6@`NNN?N`B*{(6- Free Fe2+ ion (high spin)> : WtB  Bo ?"0@NNN?N`B*2B*B  <1 ?"0@NNN?N`6-26-B  <1 ?"0@NNN?N`*02*0B  Bo ?"0@NNN?N`323B  Bo ?"0@NNN?N`B*`3B  <1 ?"0@NNN?N{(B*{(3B  Bo ?"0@NNN?N2B*23/F $   u> ?i   X$  + High Spin: h   hX4 *Low Spin: j  S A   ??"??%yB  _  HX ?"6@ NNN?NFB'L%G yDeeth has implemented LFMM into the Molecular Operating Environment (MOE), a popular MM dynamics program, to form DommiMOE, which uses the forcefield MMFF94 for non-transition metals. DommiMOE can optimise the geometry a complex for a given spin state, and so can give hypothetical structures of transition metal complexes for both spin states with the same set of parameters.zz  H|Y ?"6@ NNN?N~ 4^: @This is an octahedral high-spin complex where the Fe  N bond lengths were 2.20  (from X-ray crystallographic data). To obtain data on the a hypothetical low-spin structure, QM techniques were used, which predict that the Fe  N bond lengths to be around 2.00 . An estimate of 11 kcal/mol was also imposed on the energetic favourability of the high spin state to the low spin state. As with all MM-based methods, some model parameters have to be found which fit the required geometries and energies. Parameters modified included the Morse function parameters (Fe N bond length potential was modelled by a Morse function), octahedral-field splitting term, the ligand-ligand repulsion term and some electron-pairing energy terms. To measure the  fit of the parameters, a cost function was constructed such that the smaller its value, the better the parameters fit the data.mm0P  gt  c >A m Fe_hexammine"` 0_g  s *X3"`z4J [Simulated Annealing 2$: "  BhY ?"6@ NNN?N7D\4N? rThe difference between low spin and high spin states is the metal-ligand bond lengths of low spin states are much smaller than those of high spin. For example, the Fe  N bond length in low spin and high spin amine complexes are about 2.00 and 2.20 respectively. This is because of the smaller repulsion of the ligands from the d-electron cloud at low spin. Deeth summarises this effect by the Ligand Field Stabilisation Energy (LFSE), and incorporated into the MM framework by adding to the MM equation:." : v  BY ?"6@ NNN?N4p287 r(1) is known as the high-spin state of Fe2+ as the total spin is greater than in (2), known as the low spin state.*s) H: j   S A  '??"?17` > '(  HL$Y ?"6@ NNN?N4gs rSimulated Annealing (SA) is a method of finding the maximum or minimum of a distribution (x) by using Markov Chain Monte Carlo (MCMC) to sample the parameter space, in this case the distribution needed to be minimised is the cost function A Markov chain (a  random walk ) is constructed whose limiting distribution is (x) - the target distribution. d`[""""""",Y  B ?"6@ NNN?N+$mi+$  HX ?"6@ NNN?N%46g* `BIn simulated annealing, the target distribution (x) is changed to (x)1/T (T is known as the  temperature ), which has the same maxima and minima as (x) but is rather  steeper as T decreases from 1 to 0, and this makes the Markov chain less likely to escape local minima. If the temperature is carefully reduced, then (hopefully) at the end of the procedure the Markov chain will reside near the global minimum. 2"""""**""K""""",0c   s *HY3"`*4 K1, WAmine Complexes 2$:   HXJY ?"6@ NNN?N5,4:\2 66The simulated annealing procedure yielded some good parameters for the iron hexaammine complex, which were applied to three other amine complexes. From the bond lengths in their X-ray crystallographic structures, (1) and (2) were low spin complexes, while (3) was a high spin complex, which illustrates the sensitivity of the spin state of Fe2+ with nitrogen ligands. The parameters found for [Fe(NH3)6]2+ were found to reproduce the geometry of the complexes very well in their native spin states, and also the spin states of the complexes were correctly predicted.7""  S"*7"*"*"*"L   s *8cY3"`24 KW4 WImine Complexes 2$: y  HdY ?"6@ NNN?N\446g; Can these parameters transfer to imine complexes? Unlike amine nitrogens, imine nitrogens are aromatic, and most Fe2+ imine complexes are low-spin. It was found that after some modification of the parameters, although the bond lengths were not very accurately reproduced, DommiMOE correctly predicted the spin state for most of the complexes (but not all). The most striking result was the predicted spin states of the low spin complex [Fe(1-10-phenantroline)3]2+ and the high spin [Fe(2-methyl-1-10-phenantroline)3]2+. Although the ligands in these complexes were very similar, DommiMOE correctly deduced their spin states, which correspond to a large change in geometry.i= t"*"f"*"*3"*"*",@  L  6?"6@ NNN?Nt!.:t!B  <?"0@NNN?N@DP@B  <?"0@NNN?NGDPGB  6?"0@NNN?N@DDGB  <?"0@NNN?N@PPGF dY<hE F  ;dYhD^   ByY?"6@ NNN?Nk`@DhE $[Fe(2-methyl-1-10-phenantroline)3]2+f% ememAe   BHY?"6@ NNN?NdY@Dk`E e(1-10-phenantroline)3]2+v%ememA   BdY?"6@ NNN?NdY< h@D >: Wtt   D# "A .?BUHKAQY<`7Dt   DF5 "A 5?CEPZOM`<|g7D  s *@Y3"`<4 Kq> T Applications 2 $:  3 H Y ?"6@ NNN?Nu>4YD B(The next step is to model iron(II) porphyrins, which are planar complexes with the Fe2+ surrounded by four aromatic nitrogens (chemically similar to imine nitrogens). The most important example of an iron(II) porphyrin is the O2 -binding site for haemoglobin, heme. Fe2+ in heme changes from high spin to low spin when it binds to an oxygen molecule, which changes the shape of the whole molecule. This change is important in the uptake and transport of oxygen. It would be very interesting to find out if DommiMOE can model this %U    "b G  $F: |~ 3   < 3  c"$) \g3N =  S X99?3  J >  # "`3  b ?  c 2A , .DETTOL3 b @  c 2A, .PAZXAP  b A  c 2AO f&PURYIK3  B  3 xY"` -  P1.$ :  C  3 Y"`m D-  P2.$ :  D  3 XY"`  - P3.$ : N8 4E7YaH N E47YaH 9  N?"6@`NNN?N4E7YaH 7  NtY?"6@`NNN?N81EQG The author would like to thank the MOAC Doctoral Centre staff and colleagues for their guidance and the Engineering and Physical Sciences Research Council Life Sciences Interface Programme for their generous support.:  5  HA moacc"`l51El8OH J  X3AdDownloads_Images_Logos_Version1Colour_EPSRC1RGBHI"`=Q^EX7Hj L C BA*the_warwick_uni_bluex 28 4SAv&  p4B%@ 7$D% m 4SAv&z   < A?sa"`7$D%B    `D??"0@NNN?Nr;sW? B  B  `D??"0@NNN?N; W? !B   `D??"0@NNN?N;@ !B  B  `D??"0@NNN?N9@V B    `D??"0@NNN?N:V <f!B ! 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Then the model parameters were refined using simulated annealing to give the correct geometries and predict the correct spin state of the metal, initially with [Fe(NH3)6]2+, then with three other amine complexes. The parameters found were applied to about 80 imine complexes, and after a slight modification, approximated the geometries reasonably well and most of the time predicted the correct spin state.xD    : B . # A"`-  9 s *lX3"`'z T Introduction 2 $:  : <4CX ?"6@`NNN?Ng'.4 ,The importance of organometallic proteins in biochemistry has long been recognised, which the metal instrumental in many of these protein s catalytic or binding functions. At the moment there are very      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFG&KLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~ few methods that model transition metal-containing organometallic proteins effectively, either using quantum or classical mechanical methods. Here is outlined a very promising new Molecular Modelling approach to deal with transition metal complexes which can be used to model biological macromolecules.:  < s *OX3"`'z Molecular ModellingB 2 $, $:  ? B ?"6@ NNN?Nmi A B ?"6@ NNN?Nmi = <8TX ?"6@ NNN?N"'.4 VMolecular Modelling (MM) of Force-Field (FF) methods of finding molecular structures determine the relationship between the energy and structure by application of empirical rules based on classical mechanics. To find an optimal structure in MM, we optimise the total strain energy: D B <fX ?"6@ NNN?N'\4& \where the terms correspond to the deviation from the optimal bond lengths, bond angles, torsions, non-bonded interactions and electrostatic interactions from those given by the a particular forcefield. Modelling transition metals using conventional MM has always been difficult as they can have variable oxidation states, spin states and electronic effects, and can coordinate from 4 to 12 different ligands in a complex. Rob Deeth has addressed this problem by developing this Ligand Field Molecular Mechanics model of dealing with transition metal centres using an approach called Ligand Field Theory.]]:  D B ?"6@ NNN?NF$miF$j C S A ??"? &  T <tvX ?"6@ NNN?N}('am7 ' In a free transition metal ion, the preference of the d-electrons is to occupy each of the five d-orbitals, and when there are more than five d electrons, spin-pairing occurs. In an octahedrally-coordinated complex, the dxy, dyz and dxz orbitals become lower in energy than the dx2-y2 and dz2 orbitals and are filled first. Ligand Field Theory states that this is because the former orbitals repel the ligand electron densities less than the latter (the d-orbitals are mostly antibonding and repel ligand electron clouds). Depending on the ligands (the so-called ligand field strength), the d-electrons may desert the dx2-y2 and dz2 orbitals completely as the electron pairing becomes energetically more favourable than the electron repulsion of ligand bonding orbitals.    ,  M  >: V W C .Adorbitals2%m4+ \ < ?"6@ NNN?N.4 _ < ?"6@ NNN?N.4 b < ?"6@ NNN?N.4  < ?"6@ NNN?N.4  < ?"6@ NNN?N.4  < ?"6@ NNN?N.4F 2)p*2 3   +`)2v4N  S A 2)p*2-N  S fA 2)_-2n0  TA ?"6@ NNN?N2)L02 3 F `B*23   +K34  H8^X=J?"6@`NNN?N{(*023 @: Wt  BXX?"6@`NNN?N`*0{(3 :(2) High Ligand Field strength (e.g. CN-, phenantroline) J;(&.&+ : Wt  HX=J?"6@`NNN?N{(6-2*0 @: Wt  B*X?"6@`NNN?N`6-{(*0 7(1) Low Ligand Field strength (e.g. Cl-, I-, F-, H2O) 8'&.&.&.&.&: Wt  HX=J?"6@`NNN?N{(B*26- @,: WtA  BX?"6@`NNN?N`B*{(6- Free Fe2+ ion (high spin)> : WtB  Bo ?"0@NNN?N`B*2B*B  <1 ?"0@NNN?N`6-26-B  <1 ?"0@NNN?N`*02*0B  Bo ?"0@NNN?N`323B  Bo ?"0@NNN?N`B*`3B  <1 ?"0@NNN?N{(B*{(3B  Bo ?"0@NNN?N2B*23/F $   u> ?i   X$  + High Spin: h   hX4 *Low Spin: j  S A   ??"??%yB  _  HX ?"6@ NNN?NFB'L%G yDeeth has implemented LFMM into the Molecular Operating Environment (MOE), a popular MM dynamics program, to form DommiMOE, which uses the forcefield MMFF94 for non-transition metals. DommiMOE can optimise the geometry a complex for a given spin state, and so can give hypothetical structures of transition metal complexes for both spin states with the same set of parameters.zz  H|Y ?"6@ NNN?NP 4>_  @This is an octahedral high-spin complex where the Fe  N bond lengths were 2.20  (from X-ray crystallographic data). To obtain data on the a hypothetical low-spin structure, QM techniques were used, which predict that the Fe  N bond lengths to be around 2.00 . An estimate of 11 kcal/mol was also imposed on the energetic favourability of the high spin state to the low spin state. As with all MM-based methods, some model parameters have to be found which fit the required geometries and energies. Parameters modified included the Morse function parameters (Fe N bond length potential was modelled by a Morse function), octahedral-field splitting term, the ligand-ligand repulsion term and some electron-pairing energy terms. To measure the  fit of the parameters, a cost function was constructed such that the smaller its value, the better the parameters fit the data.mm0P  gt  c >A m Fe_hexammine"` 0_g  s *X3"`z4 K [Simulated Annealing 2$: "  BhY ?"6@ NNN?N7D\4N? rThe difference between low spin and high spin states is the metal-ligand bond lengths of low spin states are much smaller than those of high spin. For example, the Fe  N bond length in low spin and high spin amine complexes are about 2.00 and 2.20 respectively. This is because of the smaller repulsion of the ligands from the d-electron cloud at low spin. Deeth summarises this effect by the Ligand Field Stabilisation Energy (LFSE), and incorporated into the MM framework by adding to the MM equation:." : v  BY ?"6@ NNN?N4p287 r(1) is known as the high-spin state of Fe2+ as the total spin is greater than in (2), known as the low spin state.*s) H: j   S A  '??"?17` > '(  HL$Y ?"6@ NNN?N4gs rSimulated Annealing (SA) is a method of finding the maximum or minimum of a distribution (x) by using Markov Chain Monte Carlo (MCMC) to sample the parameter space, in this case the distribution needed to be minimised is the cost function A Markov chain (a  random walk ) is constructed whose limiting distribution is (x) - the target distribution. d`[""""""",Y  B ?"6@ NNN?N+$mi+$  HX ?"6@ NNN?N%4dg* `BIn simulated annealing, the target distribution (x) is changed to (x)1/T (T is known as the  temperature ), which has the same maxima and minima as (x) but is rather  steeper as T decreases from 1 to 0, and this makes the Markov chain less likely to escape local minima. If the temperature is carefully reduced, then (hopefully) at the end of the procedure the Markov chain will reside near the global minimum. 2"""""**""K""""",0c   s *HY3"`*47K1, WAmine Complexes 2$:   HXJY ?"6@ NNN?N5,4\2 66The simulated annealing procedure yielded some good parameters for the iron hexaammine complex, which were applied to three other amine complexes. From the bond lengths in their X-ray crystallographic structures, (1) and (2) were low spin complexes, while (3) was a high spin complex, which illustrates the sensitivity of the spin state of Fe2+ with nitrogen ligands. The parameters found for [Fe(NH3)6]2+ were found to reproduce the geometry of the complexes very well in their native spin states, and also the spin states of the complexes were correctly predicted.7""  S"*7"*"*"*"L   s *8cY3"`247KW4 WImine Complexes 2$: y  HdY ?"6@ NNN?N\44g; Can these parameters transfer to imine complexes? Unlike amine nitrogens, imine nitrogens are aromatic, and most Fe2+ imine complexes are low-spin. It was found that after some modification of the parameters, although the bond lengths were not very accurately reproduced, DommiMOE correctly predicted the spin state for most of the complexes (but not all). The most striking result was the predicted spin states of the low spin complex [Fe(1-10-phenantroline)3]2+ and the high spin [Fe(2-methyl-1-10-phenantroline)3]2+. Although the ligands in these complexes were very similar, DommiMOE correctly deduced their spin states, which correspond to a large change in geometry.i= t"*"f"*"*3"*"*",@  L  6?"6@ NNN?Nt!.:t!B  <?"0@NNN?N@DP@B  <?"0@NNN?NGDPGB  6?"0@NNN?N@DDGB  <?"0@NNN?N@PPGF dY<hE F  ;dYhD^   ByY?"6@ NNN?Nk`@DhE $[Fe(2-methyl-1-10-phenantroline)3]2+f% ememAe   BHY?"6@ NNN?NdY@Dk`E e(1-10-phenantroline)3]2+v%ememA   BdY?"6@ NNN?NdY< h@D >: Wtt   D# "A .?BUHKAQY<`7Dt   DF5 "A 5?CEPZOM`<|g7D  s *@Y3"`<47Kq> T Applications 2 $:  3 H Y ?"6@ NNN?Nu>4YD B(The next step is to model Iron(II) porphyrins, which are planar complexes with the Fe2+ surrounded by four aromatic nitrogens (chemically similar to imine nitrogens). The most important example of an Iron(II) porphyrin is the O2 -binding site for haemoglobin, heme. Fe2+ in heme changes from high spin to low spin when it binds to an oxygen molecule, which changes the shape of the whole molecule. This change is important in the uptake and transport of oxygen. It would be very interesting to find out if DommiMOE can model this %U    "b G  $F: |~ 3   < 3  c"$) \g3N =  S X99?3  J >  # "`3  b ?  c 2A , .DETTOL3 b @  c 2A, .PAZXAP  b A  c 2AO f&PURYIK3  B  3 xY"` -  P1.$ :  C  3 Y"`m D-  P2.$ :  D  3 XY"`  - P3.$ : N8 4E7YaH N E47YaH 9  N?"6@`NNN?N4E7YaH 7  NtY?"6@`NNN?N81EQG The author would like to thank the MOAC Doctoral Centre staff and colleagues for their guidance and the Engineering and Physical Sciences Research Council Life Sciences Interface Programme for their generous support.:  5  HA moacc"`l51El8OH J  X3AdDownloads_Images_Logos_Version1Colour_EPSRC1RGBHI"`=Q^EX7Hj L C BA*the_warwick_uni_bluex 28 4SAv&  p4B%@ 7$D% m 4SAv&z   < A?sa"`7$D%B    `D??"0@NNN?Nr;sW? B  B  `D??"0@NNN?N; W? !B   `D??"0@NNN?N;@ !B  B  `D??"0@NNN?N9@V B    `D??"0@NNN?N:V <f!B ! 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Then the model parameters were refined using simulated annealing to give the correct geometries and predict the correct spin state of the metal, initially with [Fe(NH3)6]2+, then with three other amine complexes. The parameters found were applied to about 80 imine complexes, and after a slight modification, approximated the geometries reasonably well and most of the time predicted the correct spin state.xD    : B . # A"`-  9 s *lX3"`'z T Introduction 2 $:  : <4CX ?"6@`NNN?Ng'.4 ,The importance of organometallic proteins in biochemistry has long been recognised, which the metal instrumental in many of these protein s catalytic or binding functions. At the moment there are very few methods that model transition metal-containing organometallic proteins effectively, either using quantum or classical mechanical methods. Here is outlined a very promising new Molecular Modelling approach to deal with transition metal complexes which can be used to model biological macromolecules.:  < s *OX3"`'z Molecular ModellingB 2 $, $:  ? B ?"6@ NNN?Nmi A B ?"6@ NNN?Nmi = <8TX ?"6@ NNN?N"'.4 VMolecular Modelling (MM) of Force-Field (FF) methods of finding molecular structures determine the relationship between the energy and structure by application of empirical rules based on classical mechanics. To find an optimal structure in MM, we optimise the total strain energy: D B <fX ?"6@ NNN?N'\4& \where the terms correspond to the deviation from the optimal bond lengths, bond angles, torsions, non-bonded interactions and electrostatic interactions from those given by the a particular forcefield. Modelling transition metals using conventional MM has always been difficult as they can have variable oxidation states, spin states and electronic effects, and can coordinate from 4 to 12 different ligands in a complex. Rob Deeth has addressed this problem by developing this Ligand Field Molecular Mechanics model of dealing with transition metal centres using an approach called Ligand Field Theory.]]:  D B ?"6@ NNN?NF$miF$j C S A ??"? &  T <tvX ?"6@ NNN?N}('am7 ' In a free transition metal ion, the preference of the d-electrons is to occupy each of the five d-orbitals, and when there are more than five d electrons, spin-pairing occurs. In an octahedrally-coordinated complex, the dxy, dyz and dxz orbitals become lower in energy than the dx2-y2 and dz2 orbitals and are filled first. Ligand Field Theory states that this is because the former orbitals repel the ligand electron densities less than the latter (the d-orbitals are mostly antibonding and repel ligand electron clouds). Depending on the ligands (the so-called ligand field strength), the d-electrons may desert the dx2-y2 and dz2 orbitals completely as the electron pairing becomes energetically more favourable than the electron repulsion of ligand bonding orbitals.    ,  M  >: V W C .Adorbitals2%m4+ \ < ?"6@ NNN?N.4 _ < ?"6@ NNN?N.4 b < ?"6@ NNN?N.4  < ?"6@ NNN?N.4  < ?"6@ NNN?N.4  < ?"6@ NNN?N.4F 2)p*2 3   +`)2v4N  S A 2)p*2-N  S fA 2)_-2n0  TA ?"6@ NNN?N2)L02 3 F `B*23   +K34  H8^X=J?"6@`NNN?N{(*023 @: Wt  BXX?"6@`NNN?N`*0{(3 :(2) High Ligand Field strength (e.g. CN-, phenantroline) J;(&.&+ : Wt  HX=J?"6@`NNN?N{(6-2*0 @: Wt  B*X?"6@`NNN?N`6-{(*0 7(1) Low Ligand Field strength (e.g. Cl-, I-, F-, H2O) 8'&.&.&.&.&: Wt  HX=J?"6@`NNN?N{(B*26- @,: WtA  BX?"6@`NNN?N`B*{(6- Free Fe2+ ion (high spin)> : WtB  Bo ?"0@NNN?N`B*2B*B  <1 ?"0@NNN?N`6-26-B  <1 ?"0@NNN?N`*02*0B  Bo ?"0@NNN?N`323B  Bo ?"0@NNN?N`B*`3B  <1 ?"0@NNN?N{(B*{(3B  Bo ?"0@NNN?N2B*23/F $   u> ?i   X$  + High Spin: h   hX4 *Low Spin: j  S A   ??"??%yB  _  HX ?"6@ NNN?NFB'L%G yDeeth has implemented LFMM into the Molecular Operating Environment (MOE), a popular MM dynamics program, to form DommiMOE, which uses the forcefield MMFF94 for non-transition metals. DommiMOE can optimise the geometry a complex for a given spin state, and so can give hypothetical structures of transition metal complexes for both spin states with the same set of parameters.zz  H|Y ?"6@ NNN?NP 4>_  @This is an octahedral high-spin complex where the Fe  N bond lengths were 2.20  (from X-ray crystallographic data). To obtain data on the a hypothetical low-spin structure, QM techniques were used, which predict that the Fe  N bond lengths to be around 2.00 . An estimate of 11 kcal/mol was also imposed on the energetic favourability of the high spin state to the low spin state. As with all MM-based methods, some model parameters have to be found which fit the required geometries and energies. Parameters modified included the Morse function parameters (Fe N bond length potential was modelled by a Morse function), octahedral-field splitting term, the ligand-ligand repulsion term and some electron-pairing energy terms. To measure the  fit of the parameters, a cost function was constructed such that the smaller its value, the better the parameters fit the data.mm0P  gt  c >A m Fe_hexammine"` 0_g  s *X3"`z4 K [Simulated Annealing 2$: "  BhY ?"6@ NNN?N7D\4N? rThe difference between low spin and high spin states is the metal-ligand bond lengths of low spin states are much smaller than those of high spin. For example, the Fe  N bond length in low spin and high spin amine complexes are about 2.00 and 2.20 respectively. This is because of the smaller repulsion of the ligands from the d-electron cloud at low spin. Deeth summarises this effect by the Ligand Field Stabilisation Energy (LFSE), and incorporated into the MM framework by adding to the MM equation:." : v  BY ?"6@ NNN?N4p287 r(1) is known as the high-spin state of Fe2+ as the total spin is greater than in (2), known as the low spin state.*s) H: j   S A  '??"?17` > '(  HL$Y ?"6@ NNN?N4gs rSimulated Annealing (SA) is a method of finding the maximum or minimum of a distribution (x) by using Markov Chain Monte Carlo (MCMC) to sample the parameter space, in this case the distribution needed to be minimised is the cost function A Markov chain (a  random walk ) is constructed whose limiting distribution is (x) - the target distribution. d`[""""""",Y  B ?"6@ NNN?N+$mi+$  HX ?"6@ NNN?N%4dg* `BIn simulated annealing, the target distribution (x) is changed to (x)1/T (T is known as the  temperature ), which has the same maxima and minima as (x) but is rather  steeper as T decreases from 1 to 0, and this makes the Markov chain less likely to escape local minima. If the temperature is carefully reduced, then (hopefully) at the end of the procedure the Markov chain will reside near the global minimum. 2"""""**""K""""",0c   s *HY3"`*47K1, WAmine Complexes 2$:   HXJY ?"6@ NNN?N5,4\2 66The simulated annealing procedure yielded some good parameters for the iron hexaammine complex, which were applied to three other amine complexes. From the bond lengths in their X-ray crystallographic structures, (1) and (2) were low spin complexes, while (3) was a high spin complex, which illustrates the sensitivity of the spin state of Fe2+ with nitrogen ligands. The parameters found for [Fe(NH3)6]2+ were found to reproduce the geometry of the complexes very well in their native spin states, and also the spin states of the complexes were correctly predicted.7""  S"*7"*"*"*"L   s *8cY3"`247KW4 WImine Complexes 2$: y  HdY ?"6@ NNN?N\44g; Can these parameters transfer to imine complexes? Unlike amine nitrogens, imine nitrogens are aromatic, and most Fe2+ imine complexes are low-spin. It was found that after some modification of the parameters, although the bond lengths were not very accurately reproduced, DommiMOE correctly predicted the spin state for most of the complexes (but not all). The most striking result was the predicted spin states of the low spin complex [Fe(1-10-phenantroline)3]2+ and the high spin [Fe(2-methyl-1-10-phenantroline)3]2+. Although the ligands in these complexes were very similar, DommiMOE correctly deduced their spin states, which correspond to a large change in geometry.i= t"*"f"*"*3"*"*",@  L  6?"6@ NNN?Nt!.:t!B  <?"0@NNN?N@DP@B  <?"0@NNN?NGDPGB  6?"0@NNN?N@DDGB  <?"0@NNN?N@PPGF dY<hE F  ;dYhD^   ByY?"6@ NNN?Nk`@DhE $[Fe(2-methyl-1-10-phenantroline)3]2+f% ememAe   BHY?"6@ NNN?NdY@Dk`E e(1-10-phenantroline)3]2+v%ememA   BdY?"6@ NNN?NdY< h@D >: Wtt   D# "A .?BUHKAQY<`7Dt   DF5 "A 5?CEPZOM`<|g7D  s *@Y3"`<47Kq> T Applications 2 $: n  s 8AG (\?Image1"`r;:NjWoC 3 H Y ?"6@ NNN?Nu>4YD B(The next step is to model Iron(II) porphyrins, which are planar complexes with the Fe2+ surrounded by four aromatic nitrogens (chemically similar to imine nitrogens). The most important example of an Iron(II) porphyrin is the O2 -binding site for haemoglobin, heme. Fe2+ in heme changes from high spin to low spin when it binds to an oxygen molecule, which changes the shape of the whole molecule. This change is important in the uptake and transport of oxygen. It would be very interesting to find out if DommiMOE can model this %U    "b G  $F: |~ 3   < 3  c"$) \g3N =  S X99?3  J >  # "`3  b ?  c 2A , .DETTOL3 b @  c 2A, .PAZXAP  b A  c 2AO f&PURYIK3  B  3 xY"` -  P1.$ :  C  3 Y"`m D-  P2.$ :  D  3 XY"`  - P3.$ : N8 4E7YaH N E47YaH 9  N?"6@`NNN?N4E7YaH 7  NtY?"6@`NNN?N81EQG The author would like to thank the MOAC Doctoral Centre staff and colleagues for their guidance and the Engineering and Physical Sciences Research Council Life Sciences Interface Programme for their generous support.:  5  HA moacc"`l51El8OH J  X3AdDownloads_Images_Logos_Version1Colour_EPSRC1RGBHI"`=Q^EX7Hj L C BA*the_warwick_uni_bluex 28 4SAv&  p4B%@ 7$D% m 4SAv&z   < A?sa"`7$D%B    `D??"0@NNN?Nr;sW? B  B  `D??"0@NNN?N; W? !B   `D??"0@NNN?N;@ !B  B  `D??"0@NNN?N9@V B    `D??"0@NNN?N:V <f!B ! B  `D??"0@NNN?N;xAB "   `D??"0@NNN?N;h@ !B #   `D??"0@NNN?N?!:@!B $  `D??"0@NNN?N?8! @!B %   `D??"0@NNN?N? !:@f!B &  `D??"0@NNN?NW?FxAB '   `D??"0@NNN?NxAF-BB ( B  `D??"0@NNN?NABB )   `D??"0@NNN?NAB) B * B  `D??"0@NNN?N?) -B B +  `D??"0@NNN?N>? B ,   `D??"0@NNN?N;f!T<I"B -  `D??"0@NNN?N;"T<I"B .  `D??"0@NNN?N; !<"B /  `D??"0@NNN?N; <9!B 0 B  `D??"0@NNN?N4: ; B h B TD?"0@NNN?N? !h@!B i TD?"0@NNN?NX?;@f!B j TD?"0@NNN?Nr;s=B l TD?"0@NNN?N = !="8 QGqT% p C^E~Rf% 7  B A sa"`QGqT% o  B ?"6@ NNN?NuL!LI" 8 Vp d%  CDWddf% R  D A sa2"`Vp d%B r TD?"0@NNN?N[!g\!B s TD?"0@NNN?N[f!g\!B t B TD?"0@NNN?N[f!g\"B u  TD?"0@NNN?N["g\I"B v TD?"0@NNN?N[9!g\I"B w TD?"0@NNN?N[ !\9!B x B TD?"0@NNN?N[ !\!B y  TD?"0@NNN?N[!]!B {  TD?"0@NNN?N]!w]!B | B TD?"0@NNN?N]!w]!B }  TD?"0@NNN?N]!w]!B ~ TD?"0@NNN?Ng\!w]!B  B TD?"0@NNN?N[!g\v"B   TD?"0@NNN?N[v"["B   TD?"0@NNN?N["g\"B  B TD?"0@NNN?N["g\"B  TD?"0@NNN?N["g\"  H4Y ?"6@ NNN?NAF# 8Markov chain explores distribution of interest, with a preference of  downhill steps if the global minimum is to be found. } 2}: 0  HY ?"6@ NNN?N{R3V! z<The smallest value encountered by the Markov chain is noted.= 2=: *8 R"W$  !{RqW$   N ?"6@ NNN?NR"W$   T` Z ?"6@ NNN?NR"W$ TReduce T" : B  HZ ?"6@ NNN?Neh# NStart at current minimum. Markov chain is more confined to an area of interestO 2O: j  C 4Aprakash_patel"`}cg(  Z2<܍ ?"` 33___PPT10i.M2_<+D=' = @B +rIe%o o(miI   WEquation Equation.30,Microsoft Equation 3.0  Equation Equation.30,Microsoft Equation 3.0' $Photo Editor Photo MSPhotoEd.30@Microsoft Photo Editor 3.0 Photo/ 0DArialNew .0B 0DNew Century SchoolbookB 0 DTimes New RomanolbookB 0 B.:   @n?" dd@  @@`` : 2 ( oR$yX8p2uc-"$$tz:}ix@tGD+c-2$Z C^6.w5R$kL$>Jڳݱ7"$PZ6(<7 aGb$y)|{6b^JR$|L24'E]&+2$ ?MJ0-cQR$xdj?8pW~.2$(-rf/AZ6>$+Ʊ败 R$?UfsZ87[-3 b$Pf;)rDc5@;  0e0e     A@  A5% 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||s " 0e@        @ABC DEEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN E5%  N E5%  N F   5%    !"?N@ABC DEFFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab@=ʚ;d,;ʚ;g4!d!d B 0p$p4<4ddLpC 0- <4!d!dLhG 0<4BdBdLhG 080___PPT10 pp?  %re" [ o(miI   WEquation Equation.30,Microsoft Equation 3.0  Equation Equation.30,Microsoft Equation 3.0' $Photo Editor Photo MSPhotoEd.30@Microsoft Photo Editor 3.0 Photo/ 0DArialNew .0B 0DNew Century SchoolbookB 0 DTimes New RomanolbookB 0 B.:   @n?" dd@  @@`` : 2 ( oR$yX8p2uc-"$$tz:}ix@tGD+c-2$Z C^6.w5R$kL$>Jڳݱ7"$PZ6(<7 aGb$y)|{6b^JR$|L24'E]&+2$ ?MJ0-cQR$xdj?8pW~.2$(-rf/AZ6>$+Ʊ败 R$?UfsZ87[-3 b$Pf;)rDc5@;  0e0e     A@  A5% 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||s " 0e@        @ABC DEEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN E5%  N E5%  N F   5%    !"?N@ABC DEFFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab@=ʚ;d,;ʚ;g4dd B 0p$p4<4ddLpC 0- <4!d!dLhG 0<4BdBdLhG 080___PPT10 pp?  %   0L (  R  C *APicture1] hH 4 TA" MOE_Screenshot"`H>%4EH  B ?"6@ NNN?Ni$0CW, $ s *3"` 'zL  PAbstract 2 $:  & s *3"`&'z( dA bit of Ligand Field Theory 2$: g ' s *X3"` 47K  Iron(II) Hexammine [Fe(NH3)6]2+ 2'$/$'$/$'$/$$ : 'F Tbi  1 _ S  0t3"`Tby qFinding optimal parameters for spin-state changes in Iron(II) amine complexes in Ligand Field Molecular Mechanics r(2rP56:    6XZb  Prakash Patel1 , Rob Deeth2X(2 6 6 6 66: c + 6 XM bi  1MOAC Doctoral Training Centre, and the 2Inorganic Computational Chemistry Group, Department of Chemistry, ý.J(2 ' Y:  8 0P 4 The geometries and energies of six-coordinated amine complexes of Fe2+ at both spin states were explored using the DommiMOE program. Then the model parameters were refined using simulated annealing to give the correct geometries and predict the correct spin state of the metal, initially with [Fe(NH3)6]2+, then with three other amine complexes. The parameters found were applied to about 80 imine complexes, and after a slight modification, approximated the geometries reasonably well and most of the time predicted the correct spin state.xD    : B . # A"`'T  9 s *lX3"`'z T Introduction 2 $:  : <4CX ?"6@`NNN?Ng'.4 ,The importance of organometallic proteins in biochemistry has long been recognised, which the metal instrumental in many of these protein s catalytic or binding functions. At the moment there are very few methods that model transition metal-containing organometallic proteins effectively, either using quantum or classical mechanical methods. Here is outlined a very promising new Molecular Modelling approach to deal with transition metal complexes which can be used to model biological macromolecules.:  < s *OX3"`'z Molecular ModellingB 2 $, $:  ? B ?"6@ NNN?Nmi A B ?"6@ NNN?Nmi = <8TX ?"6@ NNN?N"'.4 VMolecular Modelling (MM) of Force-Field (FF) methods of finding molecular structures determine the relationship between the energy and structure by application of empirical rules based on classical mechanics. To find an optimal structure in MM, we optimise the total strain energy: D B <fX ?"6@ NNN?N'\4& \where the terms correspond to the deviation from the optimal bond lengths, bond angles, torsions, non-bonded interactions and electrostatic interactions from those given by the a particular forcefield. Modelling transition metals using conventional MM has always been difficult as they can have variable oxidation states, spin states and electronic effects, and can coordinate from 4 to 12 different ligands in a complex. Rob Deeth has addressed this problem by developing this Ligand Field Molecular Mechanics model of dealing with transition metal centres using an approach called Ligand Field Theory.]]:  D B ?"6@ NNN?NF$miF$j C S A ??"? &  T <tvX ?"6@ NNN?N}('am7 ' In a free transition metal ion, the preference of the d-electrons is to occupy each of the five d-orbitals, and when there are more than five d electrons, spin-pairing occurs. In an octahedrally-coordinated complex, the dxy, dyz and dxz orbitals become lower in energy than the dx2-y2 and dz2 orbitals and are filled first. Ligand Field Theory states that this is because the former orbitals repel the ligand electron densities less than the latter (the d-orbitals are mostly antibonding and repel ligand electron clouds). Depending on the ligands (the so-called ligand field strength), the d-electrons may desert the dx2-y2 and dz2 orbitals completely as the electron pairing becomes energetically more favourable than the electron repulsion of ligand bonding orbitals.    ,  M  >: V W C .Adorbitals2%m4+ \ < ?"6@ NNN?N.4 _ < ?"6@ NNN?N.4 b < ?"6@ NNN?N.4  < ?"6@ NNN?N.4  < ?"6@ NNN?N.4  < ?"6@ NNN?N.4F 2)p*2 3   +`)2v4N  S A 2)p*2-N  S fA 2)_-2n0  TA ?"6@ NNN?N2)L02 3 F `B*23   +K34  H8^X=J?"6@`NNN?N{(*023 @: Wt  BXX?"6@`NNN?N`*0{(3 :(2) High Ligand Field strength (e.g. CN-, phenantroline) J;(&.&+ : Wt  HX=J?"6@`NNN?N{(6-2*0 @: Wt  B*X?"6@`NNN?N`6-{(*0 7(1) Low Ligand Field strength (e.g. Cl-, I-, F-, H2O) 8'&.&.&.&.&: Wt  HX=J?"6@`NNN?N{(B*26- @,: WtA  BX?"6@`NNN?N`B*{(6- Free Fe2+ ion (high spin)> : WtB  Bo ?"0@NNN?N`B*2B*B  <1 ?"0@NNN?N`6-26-B  <1 ?"0@NNN?N`*02*0B  Bo ?"0@NNN?N`323B  Bo ?"0@NNN?N`B*`3B  <1 ?"0@NNN?N{(B*{(3B  Bo ?"0@NNN?N2B*23/F $   u> ?i   X$  + High Spin: h   hX4 *Low Spin: j  S A   ??"??%yB  _  HX ?"6@ NNN?NFB'L%G yDeeth has implemented LFMM into the Molecular Operating Environment (MOE), a popular MM dynamics program, to form DommiMOE, which uses the forcefield MMFF94 for non-transition metals. DommiMOE can optimise the geometry a complex for a given spin state, and so can give hypothetical structures of transition metal complexes for both spin states with the same set of parameters.zz  H|Y ?"6@ NNN?NP 4>_  @This is an octahedral high-spin complex where the Fe  N bond lengths were 2.20  (from X-ray crystallographic data). To obtain data on the a hypothetical low-spin structure, QM techniques were used, which predict that the Fe  N bond lengths to be around 2.00 . An estimate of 11 kcal/mol was also imposed on the energetic favourability of the high spin state to the low spin state. As with all MM-based methods, some model parameters have to be found which fit the required geometries and energies. Parameters modified included the Morse function parameters (Fe N bond length potential was modelled by a Morse function), octahedral-field splitting term, the ligand-ligand repulsion term and some electron-pairing energy terms. To measure the  fit of the parameters, a cost function was constructed such that the smaller its value, the better the parameters fit the data.mm0P  gt  c >A m Fe_hexammine"` 0_g  s *X3"`z4 K [Simulated Annealing 2$: "  BhY ?"6@ NNN?N7D\4N? rThe difference between low spin and high spin states is the metal-ligand bond lengths of low spin states are much smaller than those of high spin. For example, the Fe  N bond length in low spin and high spin amine complexes are about 2.00 and 2.20 respectively. This is because of the smaller repulsion of the ligands from the d-electron cloud at low spin. Deeth summarises this effect by the Ligand Field Stabilisation Energy (LFSE), and incorporated into the MM framework by adding to the MM equation:." : v  BY ?"6@ NNN?N4p287 r(1) is known as the high-spin state of Fe2+ as the total spin is greater than in (2), known as the low spin state.*s) H: j   S A  '??"?17` > '(  HL$Y ?"6@ NNN?N4gs rSimulated Annealing (SA) is a method of finding the maximum or minimum of a distribution (x) by using Markov Chain Monte Carlo (MCMC) to sample the parameter space, in this case the distribution needed to be minimised is the cost function A Markov chain (a  random walk ) is constructed whose limiting distribution is (x) - the target distribution. d`[""""""",Y  B ?"6@ NNN?N+$mi+$  HX ?"6@ NNN?N%4dg* `BIn simulated annealing, the target distribution (x) is changed to (x)1/T (T is known as the  temperature ), which has the same maxima and minima as (x) but is rather  steeper as T decreases from 1 to 0, and this makes the Markov chain less likely to escape local minima. If the temperature is carefully reduced, then (hopefully) at the end of the procedure the Markov chain will reside near the global minimum. 2"""""**""K""""",0c   s *HY3"`*47K1, WAmine Complexes 2$:   HXJY ?"6@ NNN?N5,4\2 66The simulated annealing procedure yielded some good parameters for the iron hexaammine complex, which were applied to three other amine complexes. From the bond lengths in their X-ray crystallographic structures, (1) and (2) were low spin complexes, while (3) was a high spin complex, which illustrates the sensitivity of the spin state of Fe2+ with nitrogen ligands. The parameters found for [Fe(NH3)6]2+ were found to reproduce the geometry of the complexes very well in their native spin states, and also the spin states of the complexes were correctly predicted.7""  S"*7"*"*"*"L   s *8cY3"`247KW4 WImine Complexes 2$: y  HdY ?"6@ NNN?N\44g; Can these parameters transfer to imine complexes? Unlike amine nitrogens, imine nitrogens are aromatic, and most Fe2+ imine complexes are low-spin. It was found that after some modification of the parameters, although the bond lengths were not very accurately reproduced, DommiMOE correctly predicted the spin state for most of the complexes (but not all). The most striking result was the predicted spin states of the low spin complex [Fe(1-10-phenantroline)3]2+ and the high spin [Fe(2-methyl-1-10-phenantroline)3]2+. Although the ligands in these complexes were very similar, DommiMOE correctly deduced their spin states, which correspond to a large change in geometry.i= t"*"f"*"*3"*"*",@  L  6?"6@ NNN?Nt!.:t!B  <?"0@NNN?N@DP@B  <?"0@NNN?NGDPGB  6?"0@NNN?N@DDGB  <?"0@NNN?N@PPGF dY<hE F  ;dYhD^   ByY?"6@ NNN?Nk`@DhE $[Fe(2-methyl-1-10-phenantroline)3]2+f% ememAe   BHY?"6@ NNN?NdY@Dk`E e(1-10-phenantroline)3]2+v%ememA   BdY?"6@ NNN?NdY< h@D >: Wtt   D# "A .?BUHKAQY<`7Dt   DF5 "A 5?CEPZOM`<|g7D  s *@Y3"`<47Kq> T Applications 2 $: n  s 8AG (\?Image1"`r;:NjWoC 3 H Y ?"6@ NNN?Nu>4YD B(The next step is to model Iron(II) porphyrins, which are planar complexes with the Fe2+ surrounded by four aromatic nitrogens (chemically similar to imine nitrogens). The most important example of an Iron(II) porphyrin is the O2 -binding site for haemoglobin, heme. Fe2+ in heme changes from high spin to low spin when it binds to an oxygen molecule, which changes the shape of the whole molecule. This change is important in the uptake and transport of oxygen. It would be very interesting to find out if DommiMOE can model this %U    "b G  $F: |~ 3   < 3  c"$) \g3N =  S X99?3  J >  # "`3  b ?  c 2A , .DETTOL3 b @  c 2A, .PAZXAP  b A  c 2AO f&PURYIK3  B  3 xY"` -  P1.$ :  C  3 Y"`m D-  P2.$ :  D  3 XY"`  - P3.$ : N8 4E7YaH N E47YaH 9  N?"6@`NNN?N4E7YaH 7  NtY?"6@`NNN?N81EQG The author would like to thank the MOAC Doctoral Centre staff and colleagues for their guidance and the Engineering and Physical Sciences Research Council Life Sciences Interface Programme for their generous support.:  5  HA moacc"`l51El8OH J  X3AdDownloads_Images_Logos_Version1Colour_EPSRC1RGBHI"`=Q^EX7Hj L C BA*the_warwick_uni_bluex 28 4SAv&  p4B%@ 7$D% m 4SAv&z   < A?sa"`7$D%B    `D??"0@NNN?Nr;sW? B  B  `D??"0@NNN?N; W? !B   `D??"0@NNN?N;@ !B  B  `D??"0@NNN?N9@V B    `D??"0@NNN?N:V <f!B ! B  `D??"0@NNN?N;xAB "   `D??"0@NNN?N;h@ !B #   `D??"0@NNN?N?!:@!B $  `D??"0@NNN?N?8! @!B %   `D??"0@NNN?N? !:@f!B &  `D??"0@NNN?NW?FxAB '   `D??"0@NNN?NxAF-BB ( B  `D??"0@NNN?NABB )   `D??"0@NNN?NAB) B * B  `D??"0@NNN?N?) -B B +  `D??"0@NNN?N>? B ,   `D??"0@NNN?N;f!T<I"B -  `D??"0@NNN?N;"T<I"B .  `D??"0@NNN?N; !<"B /  `D??"0@NNN?N; <9!B 0 B  `D??"0@NNN?N4: ; B h B TD?"0@NNN?N? !h@!B i TD?"0@NNN?NX?;@f!B j TD?"0@NNN?Nr;s=B l TD?"0@NNN?N = !="8 QGqT% p C^E~Rf% 7  B A sa"`QGqT% o  B ?"6@ NNN?NuL!LI" 8 Vp d%  CDWddf% R  D A sa2"`Vp d%B r TD?"0@NNN?N[!g\!B s TD?"0@NNN?N[f!g\!B t B TD?"0@NNN?N[f!g\"B u  TD?"0@NNN?N["g\I"B v TD?"0@NNN?N[9!g\I"B w TD?"0@NNN?N[ !\9!B x B TD?"0@NNN?N[ !\!B y  TD?"0@NNN?N[!]!B {  TD?"0@NNN?N]!w]!B | B TD?"0@NNN?N]!w]!B }  TD?"0@NNN?N]!w]!B ~ TD?"0@NNN?Ng\!w]!B  B TD?"0@NNN?N[!g\v"B   TD?"0@NNN?N[v"["B   TD?"0@NNN?N["g\"B  B TD?"0@NNN?N["g\"B  TD?"0@NNN?N["g\"  H4Y ?"6@ NNN?NAF# 8Markov chain explores distribution of interest, with a preference of  downhill steps if the global minimum is to be found. } 2}: 0  HY ?"6@ NNN?N{R3V! z<The smallest value encountered by the Markov chain is noted.= 2=: *8 R"W$  !{RqW$   N ?"6@ NNN?NR"W$   T` Z ?"6@ NNN?NR"W$ TReduce T" : B  HZ ?"6@ NNN?Neh# NStart at current minimum. Markov chain is more confined to an area of interestO 2O: j  C 4Aprakash_patel"`ag   Z2<܍ ?"` 33___PPT10i.M2_<+D=' = @B +rV͸e2|Z [ o(miI   WEquation Equation.30,Microsoft Equation 3.0  Equation Equation.30,Microsoft Equation 3.0' $Photo Editor Photo MSPhotoEd.30@Microsoft Photo Editor 3.0 Photo/ 0DArialNew .0B 0DNew Century SchoolbookB 0 DTimes New RomanolbookB 0 B.:   @n?" dd@  @@`` : 2 ( oR$yX8p2uc-"$$tz:}ix@tGD+c-2$Z C^6.w5R$kL$>Jڳݱ7"$PZ6(<7 aGb$y)|{6b^JR$|L24'E]&+2$ ?MJ0-cQR$xdj?8pW~.2$(-rf/AZ6>$+Ʊ败 R$?UfsZ87[-3 b$Pf;)rDc5@;  0e0e     A@  A5% 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||s " 0e@        @ABC DEEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN E5%  N E5%  N F   5%    !"?N@ABC DEFFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab@=ʚ;d,;ʚ;g4dd B 0p$p4<4ddLpC 0- <4!d!dLhG 0<4BdBdLhG 080___PPT10 pp?  %rZeZ/m [ o(miI   WEquation Equation.30,Microsoft Equation 3.0  Equation Equation.30,Microsoft Equation 3.0' $Photo Editor Photo MSPhotoEd.30@Microsoft Photo Editor 3.0 Photo/ 0DArialNew .0B 0DNew Century SchoolbookB 0 DTimes New RomanolbookB 0 B.:   @n?" dd@  @@`` : 2 ( oR$yX8p2uc-"$$tz:}ix@tGD+c-2$Z C^6.w5R$kL$>Jڳݱ7"$PZ6(<7 aGb$y)|{6b^JR$|L24'E]&+2$ ?MJ0-cQR$xdj?8pW~.2$(-rf/AZ6>$+Ʊ败 R$?UfsZ87[-3 b$Pf;)rDc5@;  0e0e     A@  A5% 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||s " 0e@        @ABC DEEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN E5%  N E5%  N F   5%    !"?N@ABC DEFFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab@=ʚ;d,;ʚ;g4dd B 0p$p4<4ddLpC 0- <4!d!dLhG 0<4BdBdLhG 080___PPT10 pp?  %rcme?m [ o(miI   WEquation Equation.30,Microsoft Equation 3.0  Equation Equation.30,Microsoft Equation 3.0' $Photo Editor Photo MSPhotoEd.30@Microsoft Photo Editor 3.0 Photo/ 0DArialNew .0B 0DNew Century SchoolbookB 0 DTimes New RomanolbookB 0 B.:   @n?" dd@  @@`` : 2 ( oR$yX8p2uc-"$$tz:}ix@tGD+c-2$Z C^6.w5R$kL$>Jڳݱ7"$PZ6(<7 aGb$y)|{6b^JR$|L24'E]&+2$ ?MJ0-cQR$xdj?8pW~.2$(-rf/AZ6>$+Ʊ败 R$?UfsZ87[-3 b$Pf;)rDc5@;  0e0e     A@  A5% 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||s " 0e@        @ABC DEEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN E5%  N E5%  N F   5%    !"?N@ABC DEFFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab@=ʚ;d,;ʚ;g42d2d B 0lp$p4<4ddLpC 0- <4!d!dLhG 0<4BdBdLhG 0      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|~80___PPT10 pp?  %re [ o(miI   WEquation Equation.30,Microsoft Equation 3.0  Equation Equation.30,Microsoft Equation 3.0' $Photo Editor Photo MSPhotoEd.30@Microsoft Photo Editor 3.0 Photo/ 0DArialNew .0B 0DNew Century SchoolbookB 0 DTimes New RomanolbookB 0 B.:   @n?" dd@  @@`` : 2 ( oR$yX8p2uc-"$$tz:}ix@tGD+c-2$Z C^6.w5R$kL$>Jڳݱ7"$PZ6(<7 aGb$y)|{6b^JR$|L24'E]&+2$ ?MJ0-cQR$xdj?8pW~.2$(-rf/AZ6>$+Ʊ败 R$?UfsZ87[-3 b$Pf;)rDc5@;  0e0e     A@  A5% 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||s " 0e@        @ABC DEEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN E5%  N E5%  N F   5%    !"?N@ABC DEFFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab@=ʚ;d,;ʚ;g4dddd B 0?\ p$p4<4ddLpC 0- <4!d!dLhG 0<4BdBdLhG 080___PPT10 pp?  % Ƞ  0L ğ(  R  C *APicture1] hH 4 TA" MOE_Screenshot"`H>%4EH  B ?"6@ NNN?Ni$0CW, $ s *3"` 'zL  PAbstract 2 $:  & s *3"`&'z( dA bit of Ligand Field Theory 2$: g ' s *X3"` 47K  Iron(II) Hexammine [Fe(NH3)6]2+ 2'$/$'$/$'$/$$ : 'F Tbi  1 _ S  0t3"`Tby qFinding optimal parameters for spin-state changes in Iron(II) amine complexes in Ligand Field Molecular Mechanics r(2rP56:    6XZb  Prakash Patel1 , Rob Deeth2X(2 6 6 6 66: c + 6 XM bi  1MOAC Doctoral Training Centre, and the 2Inorganic Computational Chemistry Group, Department of Chemistry, ý.J(2 ' Y:  8 0P 4 The geometries and energies of six-coordinated amine complexes of Fe2+ at both spin states were explored using the DommiMOE program. Then the model parameters were refined using simulated annealing to give the correct geometries and predict the correct spin state of the metal, initially with [Fe(NH3)6]2+, then with three other amine complexes. The parameters found were applied to about 80 imine complexes, and after a slight modification, approximated the geometries reasonably well and most of the time predicted the correct spin state.xD    : B . # A"`'T  9 s *lX3"`'z T Introduction 2 $:  : <4CX ?"6@`NNN?Ng'.4 ,The importance of organometallic proteins in biochemistry has long been recognised, which the metal instrumental in many of these protein s catalytic or binding functions. At the moment there are very few methods that model transition metal-containing organometallic proteins effectively, either using quantum or classical mechanical methods. Here is outlined a very promising new Molecular Modelling approach to deal with transition metal complexes which can be used to model biological macromolecules.:  < s *OX3"`'z Molecular ModellingB 2 $, $:  ? B ?"6@ NNN?Nmi A B ?"6@ NNN?Nmi = <8TX ?"6@ NNN?N"'.4 VMolecular Modelling (MM) of Force-Field (FF) methods of finding molecular structures determine the relationship between the energy and structure by application of empirical rules based on classical mechanics. To find an optimal structure in MM, we optimise the total strain energy: D B <fX ?"6@ NNN?N'\4& \where the terms correspond to the deviation from the optimal bond lengths, bond angles, torsions, non-bonded interactions and electrostatic interactions from those given by the a particular forcefield. Modelling transition metals using conventional MM has always been difficult as they can have variable oxidation states, spin states and electronic effects, and can coordinate from 4 to 12 different ligands in a complex. Rob Deeth has addressed this problem by developing this Ligand Field Molecular Mechanics model of dealing with transition metal centres using an approach called Ligand Field Theory.]]:  D B ?"6@ NNN?NF$miF$j C S A ??"? &  T <tvX ?"6@ NNN?N}('am7 ' In a free transition metal ion, the preference of the d-electrons is to occupy each of the five d-orbitals, and when there are more than five d electrons, spin-pairing occurs. In an octahedrally-coordinated complex, the dxy, dyz and dxz orbitals become lower in energy than the dx2-y2 and dz2 orbitals and are filled first. Ligand Field Theory states that this is because the former orbitals repel the ligand electron densities less than the latter (the d-orbitals are mostly antibonding and repel ligand electron clouds). Depending on the ligands (the so-called ligand field strength), the d-electrons may desert the dx2-y2 and dz2 orbitals completely as the electron pairing becomes energetically more favourable than the electron repulsion of ligand bonding orbitals.    ,  M  >: V W C .Adorbitals2%m4+ \ < ?"6@ NNN?N.4 _ < ?"6@ NNN?N.4 b < ?"6@ NNN?N.4  < ?"6@ NNN?N.4  < ?"6@ NNN?N.4  < ?"6@ NNN?N.4F 2)p*2 3   +`)2v4N  S A 2)p*2-N  S fA 2)_-2n0  TA ?"6@ NNN?N2)L02 3 F `B*23   +K34  H8^X=J?"6@`NNN?N{(*023 @: Wt  BXX?"6@`NNN?N`*0{(3 :(2) High Ligand Field strength (e.g. CN-, phenantroline) J;(&.&+ : Wt  HX=J?"6@`NNN?N{(6-2*0 @: Wt  B*X?"6@`NNN?N`6-{(*0 7(1) Low Ligand Field strength (e.g. Cl-, I-, F-, H2O) 8'&.&.&.&.&: Wt  HX=J?"6@`NNN?N{(B*26- @,: WtA  BX?"6@`NNN?N`B*{(6- Free Fe2+ ion (high spin)> : WtB  Bo ?"0@NNN?N`B*2B*B  <1 ?"0@NNN?N`6-26-B  <1 ?"0@NNN?N`*02*0B  Bo ?"0@NNN?N`323B  Bo ?"0@NNN?N`B*`3B  <1 ?"0@NNN?N{(B*{(3B  Bo ?"0@NNN?N2B*23/F $   u> ?i   X$  + High Spin: h   hX4 *Low Spin: j  S A   ??"??%yB  _  HX ?"6@ NNN?NFB'L%G yDeeth has implemented LFMM into the Molecular Operating Environment (MOE), a popular MM dynamics program, to form DommiMOE, which uses the forcefield MMFF94 for non-transition metals. DommiMOE can optimise the geometry a complex for a given spin state, and so can give hypothetical structures of transition metal complexes for both spin states with the same set of parameters.zz  H|Y ?"6@ NNN?NP 4>_  JThis is an octahedral high-spin complex where the Fe  N bond lengths were 2.20  (from X-ray crystallographic data). To obtain data on a hypothetical low-spin structure, QM techniques were used, which predict that the Fe  N bond lengths to be around 2.00 . An estimate of 11 kcal/mol was also imposed on the energetic favourability of the high spin state to the low spin state. As with all MM-based methods, some model parameters have to be found which fit the required geometries and energies. Parameters modified included the Morse function parameters (Fe N bond length potential was modelled by a Morse function), octahedral-field splitting term, the ligand-ligand repulsion term and some electron-pairing energy terms. To measure the  fit of the parameters, a cost function was constructed such that the smaller its value, the better the parameters fit the data.iiBP 3z gt  c >A m Fe_hexammine"` 0_g  s *X3"`z4 K [Simulated Annealing 2$: "  BhY ?"6@ NNN?N7D\4N? rThe difference between low spin and high spin states is the metal-ligand bond lengths of low spin states are much smaller than those of high spin. For example, the Fe  N bond length in low spin and high spin amine complexes are about 2.00 and 2.20 respectively. This is because of the smaller repulsion of the ligands from the d-electron cloud at low spin. Deeth summarises this effect by the Ligand Field Stabilisation Energy (LFSE), and incorporated into the MM framework by adding to the MM equation:." : v  BY ?"6@ NNN?N4p287 r(1) is known as the high-spin state of Fe2+ as the total spin is greater than in (2), known as the low spin state.*s) H: j   S A  '??"?17` > '(  HL$Y ?"6@ NNN?N4gs rSimulated Annealing (SA) is a method of finding the maximum or minimum of a distribution (x) by using Markov Chain Monte Carlo (MCMC) to sample the parameter space, in this case the distribution needed to be minimised is the cost function A Markov chain (a  random walk ) is constructed whose limiting distribution is (x) - the target distribution. d`[""""""",Y  B ?"6@ NNN?N+$mi+$  HX ?"6@ NNN?N%4dg* `BIn simulated annealing, the target distribution (x) is changed to (x)1/T (T is known as the  temperature ), which has the same maxima and minima as (x) but is rather  steeper as T decreases from 1 to 0, and this makes the Markov chain less likely to escape local minima. If the temperature is carefully reduced, then (hopefully) at the end of the procedure the Markov chain will reside near the global minimum. 2"""""**""K""""",0c   s *HY3"`*47K1, WAmine Complexes 2$:   HXJY ?"6@ NNN?N5,4\2 66The simulated annealing procedure yielded some good parameters for the iron hexaammine complex, which were applied to three other amine complexes. From the bond lengths in their X-ray crystallographic structures, (1) and (2) were low spin complexes, while (3) was a high spin complex, which illustrates the sensitivity of the spin state of Fe2+ with nitrogen ligands. The parameters found for [Fe(NH3)6]2+ were found to reproduce the geometry of the complexes very well in their native spin states, and also the spin states of the complexes were correctly predicted.7""  S"*7"*"*"*"L   s *8cY3"`247KW4 WImine Complexes 2$: y  HdY ?"6@ NNN?N\44g; Can these parameters transfer to imine complexes? Unlike amine nitrogens, imine nitrogens are aromatic, and most Fe2+ imine complexes are low-spin. It was found that after some modification of the parameters, although the bond lengths were not very accurately reproduced, DommiMOE correctly predicted the spin state for most of the complexes (but not all). The most striking result was the predicted spin states of the low spin complex [Fe(1-10-phenantroline)3]2+ and the high spin [Fe(2-methyl-1-10-phenantroline)3]2+. Although the ligands in these complexes were very similar, DommiMOE correctly deduced their spin states, which correspond to a large change in geometry.i= t"*"f"*"*3"*"*",@  L  6?"6@ NNN?Nt!.:t!B  <?"0@NNN?N@DP@B  <?"0@NNN?NGDPGB  6?"0@NNN?N@DDGB  <?"0@NNN?N@PPGF dY<hE F  ;dYhD^   ByY?"6@ NNN?Nk`@DhE $[Fe(2-methyl-1-10-phenantroline)3]2+f% ememAe   BHY?"6@ NNN?NdY@Dk`E e(1-10-phenantroline)3]2+v%ememA   BdY?"6@ NNN?NdY< h@D >: Wtt   D# "A .?BUHKAQY<`7Dt   DF5 "A 5?CEPZOM`<|g7D  s *@Y3"`<47Kq> T Applications 2 $: n  s 8AG (\?Image1"`r;:NjWoC 3 H Y ?"6@ NNN?Nu>4YD B(The next step is to model Iron(II) porphyrins, which are planar complexes with the Fe2+ surrounded by four aromatic nitrogens (chemically similar to imine nitrogens). The most important example of an Iron(II) porphyrin is the O2 -binding site for haemoglobin, heme. Fe2+ in heme changes from high spin to low spin when it binds to an oxygen molecule, which changes the shape of the whole molecule. This change is important in the uptake and transport of oxygen. It would be very interesting to find out if DommiMOE can model this %U    "b G  $F: |~ 3   < 3  c"$) \g3N =  S X99?3  J >  # "`3  b ?  c 2A , .DETTOL3 b @  c 2A, .PAZXAP  b A  c 2AO f&PURYIK3  B  3 xY"` -  P1.$ :  C  3 Y"`m D-  P2.$ :  D  3 XY"`  - P3.$ : N8 4E7YaH N E47YaH 9  N?"6@`NNN?N4E7YaH 7  NtY?"6@`NNN?N81EQG The author would like to thank the MOAC Doctoral Centre staff and colleagues for their guidance and the Engineering and Physical Sciences Research Council Life Sciences Interface Programme for their generous support.:  5  HA moacc"`l51El8OH J  X3AdDownloads_Images_Logos_Version1Colour_EPSRC1RGBHI"`=Q^EX7Hj L C BA*the_warwick_uni_bluex 28 4SAv&  p4B%@ 7$D% m 4SAv&z   < A?sa"`7$D%B    `D??"0@NNN?Nr;sW? B  B  `D??"0@NNN?N; W? !B   `D??"0@NNN?N;@ !B  B  `D??"0@NNN?N9@V B    `D??"0@NNN?N:V <f!B ! B  `D??"0@NNN?N;xAB "   `D??"0@NNN?N;h@ !B #   `D??"0@NNN?N?!:@!B $  `D??"0@NNN?N?8! @!B %   `D??"0@NNN?N? !:@f!B &  `D??"0@NNN?NW?FxAB '   `D??"0@NNN?NxAF-BB ( B  `D??"0@NNN?NABB )   `D??"0@NNN?NAB) B * B  `D??"0@NNN?N?) -B B +  `D??"0@NNN?N>? B ,   `D??"0@NNN?N;f!T<I"B -  `D??"0@NNN?N;"T<I"B .  `D??"0@NNN?N; !<"B /  `D??"0@NNN?N; <9!B 0 B  `D??"0@NNN?N4: ; B h B TD?"0@NNN?N? !h@!B i TD?"0@NNN?NX?;@f!B j TD?"0@NNN?Nr;s=B l TD?"0@NNN?N = !="8 QGqT% p C^E~Rf% 7  B A sa"`QGqT% o  B ?"6@ NNN?NuL!LI" 8 Vp d%  CDWddf% R  D A sa2"`Vp d%B r TD?"0@NNN?N[!g\!B s TD?"0@NNN?N[f!g\!B t B TD?"0@NNN?N[f!g\"B u  TD?"0@NNN?N["g\I"B v TD?"0@NNN?N[9!g\I"B w TD?"0@NNN?N[ !\9!B x B TD?"0@NNN?N[ !\!B y  TD?"0@NNN?N[!]!B {  TD?"0@NNN?N]!w]!B | B TD?"0@NNN?N]!w]!B }  TD?"0@NNN?N]!w]!B ~ TD?"0@NNN?Ng\!w]!B  B TD?"0@NNN?N[!g\v"B   TD?"0@NNN?N[v"["B   TD?"0@NNN?N["g\"B  B TD?"0@NNN?N["g\"B  TD?"0@NNN?N["g\"  H4Y ?"6@ NNN?NAF# 8Markov chain explores distribution of interest, with a preference of  downhill steps if the global minimum is to be found. } 2}: 0  HY ?"6@ NNN?N{R3V! z<The smallest value encountered by the Markov chain is noted.= 2=: *8 R"W$  !{RqW$   N ?"6@ NNN?NR"W$   T` Z ?"6@ NNN?NR"W$ TReduce T" : B  HZ ?"6@ NNN?Neh# NStart at current minimum. Markov chain is more confined to an area of interestO 2O: j  C 4Aprakash_patel"`ag   Z2<܍ ?"` 33___PPT10i.M2_<+D=' = @B +r0eF [ o(miI   WEquation Equation.30,Microsoft Equation 3.0  Equation Equation.30,Microsoft Equation 3.0' $Photo Editor Photo MSPhotoEd.30@Microsoft Photo Editor 3.0 Photo/ 0DArialNew .0B 0DNew Century SchoolbookB 0 DTimes New RomanolbookB 0 B.:   @n?" dd@  @@`` : 2 ( oR$yX8p2uc-"$$tz:}ix@tGD+c-2$Z C^6.w5R$kL$>Jڳݱ7"$PZ6(<7 aGb$y)|{6b^JR$|L24'E]&+2$ ?MJ0-cQR$xdj?8pW~.2$(-rf/AZ6>$+Ʊ败 R$?UfsZ87[-3 b$Pf;)rDc5@;  0e0e     A@  A5% 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||s " 0e@        @ABC DEEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN E5%  N E5%  N F   5%    !"?N@ABC DEFFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab@=ʚ;d,;ʚ;g4!d!d B 0 p$p4<4ddLpC 0- <4!d!dLhG 0<4BdBdLhG 080___PPT10 pp?  %    0L (  R  C *APicture1] hH 4 TA" MOE_Screenshot"`H>%4EH  B ?"6@ NNN?Ni$0CW, $ s *3"` 'zL  PAbstract 2 $:  & s *3"`&'z( dA bit of Ligand Field Theory 2$: g ' s *X3"` 47K  Iron(II) Hexammine [Fe(NH3)6]2+ 2'$/$'$/$'$/$$ : 'F Tbi  1 _ S  0t3"`Tby qFinding optimal parameters for spin-state changes in Iron(II) amine complexes in Ligand Field Molecular Mechanics r(2rP56:    6XZb  Prakash Patel1 , Rob Deeth2X(2 6 6 6 66: c + 6 XM bi  1MOAC Doctoral Training Centre, and the 2Inorganic Computational Chemistry Group, Department of Chemistry, ý.J(2 ' Y:  8 0P 4 The geometries and energies of six-coordinated amine complexes of Fe2+ at both spin states were explored using the DommiMOE program. Then the model parameters were refined using simulated annealing to give the correct geometries and predict the correct spin state of the metal, initially with [Fe(NH3)6]2+, then with three other amine complexes. The parameters found were applied to about 80 imine complexes, and after a slight modification, approximated the geometries reasonably well and most of the time predicted the correct spin state.xD    : B . # A"`'T  9 s *lX3"`'z T Introduction 2 $:  : <4CX ?"6@`NNN?Ng'.4 ,The importance of organometallic proteins in biochemistry has long been recognised, which the metal instrumental in many of these protein s catalytic or binding functions. At the moment there are very few methods that model transition metal-containing organometallic proteins effectively, either using quantum or classical mechanical methods. Here is outlined a very promising new Molecular Modelling approach to deal with transition metal complexes which can be used to model biological macromolecules.:  < s *OX3"`'z Molecular ModellingB 2 $, $:  ? B ?"6@ NNN?Nmi A B ?"6@ NNN?Nmi = <8TX ?"6@ NNN?N"'.4 VMolecular Modelling (MM) of Force-Field (FF) methods of finding molecular structures determine the relationship between the energy and structure by application of empirical rules based on classical mechanics. To find an optimal structure in MM, we optimise the total strain energy: D B <fX ?"6@ NNN?N'\4& \where the terms correspond to the deviation from the optimal bond lengths, bond angles, torsions, non-bonded interactions and electrostatic interactions from those given by the a particular forcefield. Modelling transition metals using conventional MM has always been difficult as they can have variable oxidation states, spin states and electronic effects, and can coordinate from 4 to 12 different ligands in a complex. Rob Deeth has addressed this problem by developing this Ligand Field Molecular Mechanics model of dealing with transition metal centres using an approach called Ligand Field Theory.]]:  D B ?"6@ NNN?NF$miF$j C S A ??"? &  T <tvX ?"6@ NNN?N}('am7 ' In a free transition metal ion, the preference of the d-electrons is to occupy each of the five d-orbitals, and when there are more than five d electrons, spin-pairing occurs. In an octahedrally-coordinated complex, the dxy, dyz and dxz orbitals become lower in energy than the dx2-y2 and dz2 orbitals and are filled first. Ligand Field Theory states that this is because the former orbitals repel the ligand electron densities less than the latter (the d-orbitals are mostly antibonding and repel ligand electron clouds). Depending on the ligands (the so-called ligand field strength), the d-electrons may desert the dx2-y2 and dz2 orbitals completely as the electron pairing becomes energetically more favourable than the electron repulsion of ligand bonding orbitals.    ,  M  >: V W C .Adorbitals2%m4+ \ < ?"6@ NNN?N.4 _ < ?"6@ NNN?N.4 b < ?"6@ NNN?N.4  < ?"6@ NNN?N.4  < ?"6@ NNN?N.4  < ?"6@ NNN?N.4F 2)p*2 3   +`)2v4N  S A 2)p*2-N  S fA 2)_-2n0  TA ?"6@ NNN?N2)L02 3 F `B*23   +K34  H8^X=J?"6@`NNN?N{(*023 @: Wt  BXX?"6@`NNN?N`*0{(3 :(2) High Ligand Field strength (e.g. CN-, phenantroline) J;(&.&+ : Wt  HX=J?"6@`NNN?N{(6-2*0 @: Wt  B*X?"6@`NNN?N`6-{(*0 7(1) Low Ligand Field strength (e.g. Cl-, I-, F-, H2O) 8'&.&.&.&.&: Wt  HX=J?"6@`NNN?N{(B*26- @,: WtA  BX?"6@`NNN?N`B*{(6- Free Fe2+ ion (high spin)> : WtB  Bo ?"0@NNN?N`B*2B*B  <1 ?"0@NNN?N`6-26-B  <1 ?"0@ NNN?N`*02*0B  Bo ?"0@NNN?N`323B  Bo ?"0@NNN?N`B*`3B  <1 ?"0@NNN?N{(B*{(3B  Bo ?"0@NNN?N2B*23/F $   u> ?i   X$  + High Spin: h   hX4 *Low Spin: j  S A   ??"??%yB  _  HX ?"6@ NNN?NFB'L%G yDeeth has implemented LFMM into the Molecular Operating Environment (MOE), a popular MM dynamics program, to form DommiMOE, which uses the forcefield MMFF94 for non-transition metals. DommiMOE can optimise the geometry a complex for a given spin state, and so can give hypothetical structures of transition metal complexes for both spin states with the same set of parameters.zz  H|Y ?"6@ NNN?NP 4>_  DThis is an octahedral high-spin complex where the Fe  N bond lengths were 2.20  (from X-ray crystallographic data). To obtain data on a hypothetical low-spin structure, QM techniques were used, which predict that the Fe  N bond lengths to be around 2.00 . Also, an estimate of 11 kcal/mol was set on the energetic favourability of the high spin state to the low spin state. As with all MM-based methods, some model parameters have to be found which fit the required geometries and energies. Parameters modified included the Morse function parameters (Fe N bond length potential was modelled by a Morse function), octahedral-field splitting term, the ligand-ligand repulsion term and some electron-pairing energy terms. To measure the  fit of the parameters, a cost function was constructed such that the smaller its value, the better the parameters fit the data.ffBP  Yt  c >A m Fe_hexammine"` 0_g  s *X3"`z4 K [Simulated Annealing 2$: "  BhY ?"6@ NNN?N7D\4N? rThe difference between low spin and high spin states is the metal-ligand bond lengths of low spin states are much smaller than those of high spin. For example, the Fe  N bond length in low spin and high spin amine complexes are about 2.00 and 2.20 respectively. This is because of the smaller repulsion of the ligands from the d-electron cloud at low spin. Deeth summarises this effect by the Ligand Field Stabilisation Energy (LFSE), and incorporated into the MM framework by adding to the MM equation:." : v  BY ?"6@ NNN?N4p287 r(1) is known as the high-spin state of Fe2+ as the total spin is greater than in (2), known as the low spin state.*s) H: j   S A  '??"?17` > '(  HL$Y ?"6@ NNN?N4gs rSimulated Annealing (SA) is a method of finding the maximum or minimum of a distribution (x) by using Markov Chain Monte Carlo (MCMC) to sample the parameter space, in this case the distribution needed to be minimised is the cost function A Markov chain (a  random walk ) is constructed whose limiting distribution is (x) - the target distribution. d`[""""""",Y  B ?"6@ NNN?N+$mi+$  HX ?"6@ NNN?N%4dg* `BIn simulated annealing, the target distribution (x) is changed to (x)1/T (T is known as the  temperature ), which has the same maxima and minima as (x) but is rather  steeper as T decreases from 1 to 0, and this makes the Markov chain less likely to escape local minima. If the temperature is carefully reduced, then (hopefully) at the end of the procedure the Markov chain will reside near the global minimum. 2"""""**""K""""",0c   s *HY3"`*47K1, WAmine Complexes 2$:   HXJY ?"6@ NNN?N5,4\2 66The simulated annealing procedure yielded some good parameters for the iron hexaammine complex, which were applied to three other amine complexes. From the bond lengths in their X-ray crystallographic structures, (1) and (2) were low spin complexes, while (3) was a high spin complex, which illustrates the sensitivity of the spin state of Fe2+ with nitrogen ligands. The parameters found for [Fe(NH3)6]2+ were found to reproduce the geometry of the complexes very well in their native spin states, and also the spin states of the complexes were correctly predicted.7""  S"*7"*"*"*"L   s *8cY3"`247KW4 WImine Complexes 2$: y  HdY ?"6@ NNN?N\44g; Can these parameters transfer to imine complexes? Unlike amine nitrogens, imine nitrogens are aromatic, and most Fe2+ imine complexes are low-spin. It was found that after some modification of the parameters, although the bond lengths were not very accurately reproduced, DommiMOE correctly predicted the spin state for most of the complexes (but not all). The most striking result was the predicted spin states of the low spin complex [Fe(1-10-phenantroline)3]2+ and the high spin [Fe(2-methyl-1-10-phenantroline)3]2+. Although the ligands in these complexes were very similar, DommiMOE correctly deduced their spin states, which correspond to a large change in geometry.i= t"*"f"*"*3"*"*",@  L  6?"6@ NNN?Nt!.:t!B  <?"0@NNN?N@DP@B  <?"0@NNN?NGDPGB  6?"0@NNN?N@DDGB  <?"0@NNN?N@PPGF dY<hE F  ;dYhD^   ByY?"6@ NNN?Nk`@DhE $[Fe(2-methyl-1-10-phenantroline)3]2+f% ememAe   BHY?"6@ NNN?NdY@Dk`E e(1-10-phenantroline)3]2+v%ememA   BdY?"6@ NNN?NdY< h@D >: Wtt   D# "A .?BUHKAQY<`7Dt   DF5 "A 5?CEPZOM`<|g7D  s *@Y3"`<47Kq> T Applications 2 $: n  s 8AG (\?Image1"`r;:NjWoC 3 H Y ?"6@ NNN?Nu>4YD B(The next step is to model Iron(II) porphyrins, which are planar complexes with the Fe2+ surrounded by four aromatic nitrogens (chemically similar to imine nitrogens). The most important example of an Iron(II) porphyrin is the O2 -binding site for haemoglobin, heme. Fe2+ in heme changes from high spin to low spin when it binds to an oxygen molecule, which changes the shape of the whole molecule. This change is important in the uptake and transport of oxygen. It would be very interesting to find out if DommiMOE can model this %U    "b G  $F: |~ 3   < 3  c"$) \g3N =  S X99?3  J >  # "`3  b ?  c 2A , .DETTOL3 b @  c 2A, .PAZXAP  b A  c 2AO f&PURYIK3  B  3 xY"` -  P1.$ :  C  3 Y"`m D-  P2.$ :  D  3 XY"`  - P3.$ : N8 4E7YaH N E47YaH 9  N?"6@`NNN?N4E7YaH 7  NtY?"6@`NNN?N81EQG The author would like to thank the MOAC Doctoral Centre staff and colleagues for their guidance and the Engineering and Physical Sciences Research Council Life Sciences Interface Programme for their generous support.:  5  HA moacc"`l51El8OH J  X3AdDownloads_Images_Logos_Version1Colour_EPSRC1RGBHI"`=Q^EX7Hj L C BA*the_warwick_uni_bluex 28 4SAv&  p4B%@ 7$D% m 4SAv&z   < A?sa"`7$D%B    `D??"0@NNN?Nr;sW? B  B  `D??"0@NNN?N; W? !B   `D??"0@NNN?N;@ !B  B  `D??"0@NNN?N9@V B    `D??"0@NNN?N:V <f!B ! B  `D??"0@NNN?N;xAB "   `D??"0@NNN?N;h@ !B #   `D??"0@NNN?N?!:@!B $  `D??"0@NNN?N?8! @!B %   `D??"0@NNN?N? !:@f!B &  `D??"0@NNN?NW?FxAB '   `D??"0@NNN?NxAF-BB ( B  `D??"0@NNN?NABB )   `D??"0@NNN?NAB) B * B  `D??"0@NNN?N?) -B B +  `D??"0@NNN?N>? B ,   `D??"0@NNN?N;f!T<I"B -  `D??"0@NNN?N;"T<I"B .  `D??"0@NNN?N; !<"B /  `D??"0@NNN?N; <9!B 0 B  `D??"0@NNN?N4: ; B h B TD?"0@NNN?N? !h@!B i TD?"0@NNN?NX?;@f!B j TD?"0@NNN?Nr;s=B l TD?"0@NNN?N = !="8 QGqT% p C^E~Rf% 7  B A sa"`QGqT% o  B ?"6@ NNN?NuL!LI" 8 Vp d%  CDWddf% R  D A sa2"`Vp d%B r TD?"0@NNN?N[!g\!B s TD?"0@NNN?N[f!g\!B t B TD?"0@NNN?N[f!g\"B u  TD?"0@NNN?N["g\I"B v TD?"0@NNN?N[9!g\I"B w TD?"0@NNN?N[ !\9!B x B TD?"0@NNN?N[ !\!B y  TD?"0@NNN?N[!]!B {  TD?"0@NNN?N]!w]!B | B TD?"0@NNN?N]!w]!B }  TD?"0@NNN?N]!w]!B ~ TD?"0@NNN?Ng\!w]!B  B TD?"0@NNN?N[!g\v"B   TD?"0@NNN?N[v"["B   TD?"0@NNN?N["g\"B  B TD?"0@NNN?N["g\"B  TD?"0@NNN?N["g\"  H4Y ?"6@ NNN?NAF# 8Markov chain explores distribution of interest, with a preference of  downhill steps if the global minimum is to be found. } 2}: 0  HY ?"6@ NNN?N{R3V! z<The smallest value encountered by the Markov chain is noted.= 2=: *8 R"W$  !{RqW$   N ?"6@ NNN?NR"W$   T` Z ?"6@ NNN?NR"W$ TReduce T" : B  HZ ?"6@ NNN?Neh# NStart at current minimum. Markov chain is more confined to an area of interestO 2O: j  C 4Aprakash_patel"`ag   Z2<܍ ?"` 33___PPT10i.M2_<+D=' = @B +r%GYeGO [ o(miI   WEquation Equation.30,Microsoft Equation 3.0  Equation Equation.30,Microsoft Equation 3.0' $Photo Editor Photo MSPhotoEd.30@Microsoft Photo Editor 3.0 Photo/ 0DArialNew .0B 0DNew Century SchoolbookB 0 DTimes New RomanolbookB 0 B.:   @n?" dd@  @@`` : 2 ( oR$yX8p2uc-"$$tz:}ix@tGD+c-2$Z C^6.w5R$kL$>Jڳݱ7"$PZ6(<7 aGb$y)|{6b^JR$|L24'E]&+2$ ?MJ0-cQR$xdj?8pW~.2$(-rf/AZ6>$+Ʊ败 R$?UfsZ87[-3 b$Pf;)rDc5@;  0e0e     A@  A5% 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||s " 0e@        @ABC DEEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN E5%  N E5%  N F   5%    !"?N@ABC DEFFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab@=ʚ;d,;ʚ;g4!d!d B 0 p$p4<4ddLpC 0- <4!d!dLhG 0<4BdBdLhG 080___PPT10 pp?  % Ԡ̠  0L П(  R  C *APicture1] hH 4 TA" MOE_Screenshot"`H>%4EH  B ?"6@ NNN?Ni$0CW, $ s *3"` 'zL  PAbstract 2 $:  & s *3"`&'z( dA bit of Ligand Field Theory 2$: g ' s *X3"` 47K  Iron(II) Hexammine [Fe(NH3)6]2+ 2'$/$'$/$'$/$$ : 'F Tbi  1 _ S  0t3"`Tby qFinding optimal parameters for spin-state changes in Iron(II) amine complexes in Ligand Field Molecular Mechanics r(2rP56:    6XZb  Prakash Patel1 , Rob Deeth2X(2 6 6 6 66: c + 6 XM bi  1MOAC Doctoral Training Centre, and the 2Inorganic Computational Chemistry Group, Department of Chemistry, ý.J(2 ' Y:  8 0P 4 The geometries and energies of six-coordinated amine complexes of Fe2+ at both spin states were explored using the DommiMOE program. Then the model parameters were refined using simulated annealing to give the correct geometries and predict the correct spin state of the metal, initially with [Fe(NH3)6]2+, then with three other amine complexes. The parameters found were applied to about 80 imine complexes, and after a slight modification, approximated the geometries reasonably well and most of the time predicted the correct spin state.xD    : B . # A"`'T  9 s *lX3"`'z T Introduction 2 $:  : <4CX ?"6@`NNN?Ng'.4 ,The importance of organometallic proteins in biochemistry has long been recognised, which the metal instrumental in many of these protein s catalytic or binding functions. At the moment there are very few methods that model transition metal-containing organometallic proteins effectively, either using quantum or classical mechanical methods. Here is outlined a very promising new Molecular Modelling approach to deal with transition metal complexes which can be used to model biological macromolecules.:  < s *OX3"`'z Molecular ModellingB 2 $, $:  ? B ?"6@ NNN?Nmi A B ?"6@ NNN?Nmi = <8TX ?"6@ NNN?N"'.4 VMolecular Modelling (MM) of Force-Field (FF) methods of finding molecular structures determine the relationship between the energy and structure by application of empirical rules based on classical mechanics. To find an optimal structure in MM, we optimise the total strain energy: D B <fX ?"6@ NNN?N'\4& \where the terms correspond to the deviation from the optimal bond lengths, bond angles, torsions, non-bonded interactions and electrostatic interactions from those given by the a particular forcefield. Modelling transition metals using conventional MM has always been difficult as they can have variable oxidation states, spin states and electronic effects, and can coordinate from 4 to 12 different ligands in a complex. Rob Deeth has addressed this problem by developing this Ligand Field Molecular Mechanics model of dealing with transition metal centres using an approach called Ligand Field Theory.]]:  D B ?"6@ NNN?NF$miF$j C S A ??"? &  T <tvX ?"6@ NNN?N}('am7 ' In a free transition metal ion, the preference of the d-electrons is to occupy each of the five d-orbitals, and when there are more than five d electrons, spin-pairing occurs. In an octahedrally-coordinated complex, the dxy, dyz and dxz orbitals become lower in energy than the dx2-y2 and dz2 orbitals and are filled first. Ligand Field Theory states that this is because the former orbitals repel the ligand electron densities less than the latter (the d-orbitals are mostly antibonding and repel ligand electron clouds). Depending on the ligands (the so-called ligand field strength), the d-electrons may desert the dx2-y2 and dz2 orbitals completely as the electron pairing becomes energetically more favourable than the electron repulsion of ligand bonding orbitals.    ,  M  >: V W C .Adorbitals2%m4+ \ < ?"6@ NNN?N.4 _ < ?"6@ NNN?N.4 b < ?"6@ NNN?N.4  < ?"6@ NNN?N.4  < ?"6@ NNN?N.4  < ?"6@ NNN?N.4F 2)p*2 3   +`)2v4N  S A 2)p*2-N  S fA 2)_-2n0  TA ?"6@ NNN?N2)L02 3 F `B*23   +K34  H8^X=J?"6@`NNN?N{(*023 @: Wt  BXX?"6@`NNN?N`*0{(3 :(2) High Ligand Field strength (e.g. CN-, phenantroline) J;(&.&+ : Wt  HX=J?"6@`NNN?N{(6-2*0 @: Wt  B*X?"6@`NNN?N`6-{(*0 7(1) Low Ligand Field strength (e.g. Cl-, I-, F-, H2O) 8'&.&.&.&.&: Wt  HX=J?"6@`NNN?N{(B*26- @,: WtA  BX?"6@`NNN?N`B*{(6- Free Fe2+ ion (high spin)> : WtB  Bo ?"0@NNN?N`B*2B*B  <1 ?"0@NNN?N`6-26-B  <1 ?"0@NNN?N`*02*0B  Bo ?"0@NNN?N`323B  Bo ?"0@NNN?N`B*`3B  <1 ?"0@NNN?N{(B*{(3B  Bo ?"0@NNN?N2B*23/F $   u> ?i   X$  + High Spin: h   hX4 *Low Spin: j  S A   ??"??%yB  _  HX ?"6@ NNN?NFB'L%G yDeeth has implemented LFMM into the Molecular Operating Environment (MOE), a popular MM dynamics program, to form DommiMOE, which uses the forcefield MMFF94 for non-transition metals. DommiMOE can optimise the geometry a complex for a given spin state, and so can give hypothetical structures of transition metal complexes for both spin states with the same set of parameters.zz  H|Y ?"6@ NNN?NP 4>_  2This is an octahedral high-spin complex where the Fe  N bond lengths were 2.20  (from X-ray crystallographic data). To obtain data on a hypothetical low-spin structure, QM techniques were used, which predict that the Fe  N bond lengths to be around 2.00 . Also, an estimate of 11 kcal/mol was set on the energetic favourability of the high spin state to the low spin state. As with all MM-based methods, some model parameters have to be found which fit the required geometries and energies. Parameters modified included the Morse function parameters (Fe N bond length potential was modelled by a Morse function), octahedral-field splitting term, the ligand-ligand repulsion term and some electron-pairing energy terms. To measure the  fit of the parameters, a cost function was constructed such that the smaller its value, the better the parameters fit the data.ff0P  dt  c >A m Fe_hexammine"` 0_g  s *X3"`z4 K [Simulated Annealing 2$: F  BhY ?"6@ NNN?N7D\4N? The difference between low spin and high spin states is the metal-ligand bond lengths of low spin states are much smaller than those of high spin. For example, the Fe  N bond length in low spin and high spin amine complexes are about 2.00 and 2.20 respectively. This is because of the smaller repulsion of the ligands from the d-electron cloud at low spin than at high spin. Deeth summarises this effect by the Ligand Field Stabilisation Energy (LFSE), and incorporated into the MM framework by adding to the MM equation:." : v  BY ?"6@ NNN?N4p287 r(1) is known as the high-spin state of Fe2+ as the total spin is greater than in (2), known as the low spin state.*s) H: j   S A  '??"?17` > '(  HL$Y ?"6@ NNN?N4gs rSimulated Annealing (SA) is a method of finding the maximum or minimum of a distribution (x) by using Markov Chain Monte Carlo (MCMC) to sample the parameter space, in this case the distribution needed to be minimised is the cost function A Markov chain (a  random walk ) is constructed whose limiting distribution is (x) - the target distribution. d`[""""""",Y  B ?"6@ NNN?N+$mi+$  HX ?"6@ NNN?N%4dg* `BIn simulated annealing, the target distribution (x) is changed to (x)1/T (T is known as the  temperature ), which has the same maxima and minima as (x) but is rather  steeper as T decreases from 1 to 0, and this makes the Markov chain less likely to escape local minima. If the temperature is carefully reduced, then (hopefully) at the end of the procedure the Markov chain will reside near the global minimum. 2"""""**""K""""",0c   s *HY3"`*47K1, WAmine Complexes 2$:   HXJY ?"6@ NNN?N5,4\2 66The simulated annealing procedure yielded some good parameters for the iron hexaammine complex, which were applied to three other amine complexes. From the bond lengths in their X-ray crystallographic structures, (1) and (2) were low spin complexes, while (3) was a high spin complex, which illustrates the sensitivity of the spin state of Fe2+ with nitrogen ligands. The parameters found for [Fe(NH3)6]2+ were found to reproduce the geometry of the complexes very well in their native spin states, and also the spin states of the complexes were correctly predicted.7""  S"*7"*"*"*"L   s *8cY3"`247KW4 WImine Complexes 2$: y  HdY ?"6@ NNN?N\44g; Can these parameters transfer to imine complexes? Unlike amine nitrogens, imine nitrogens are aromatic, and most Fe2+ imine complexes are low-spin. It was found that after some modification of the parameters, although the bond lengths were not very accurately reproduced, DommiMOE correctly predicted the spin state for most of the complexes (but not all). The most striking result was the predicted spin states of the low spin complex [Fe(1-10-phenantroline)3]2+ and the high spin [Fe(2-methyl-1-10-phenantroline)3]2+. Although the ligands in these complexes were very similar, DommiMOE correctly deduced their spin states, which correspond to a large change in geometry.i= t"*"f"*"*3"*"*",@  L  6?"6@ NNN?Nt!.:t!B  <?"0@NNN?N@DP@B  <?"0@NNN?NGDPGB  6?"0@NNN?N@DDGB  <?"0@NNN?N@PPGF dY<hE F  ;dYhD^   ByY?"6@ NNN?Nk`@DhE $[Fe(2-methyl-1-10-phenantroline)3]2+f% ememAe   BHY?"6@ NNN?NdY@Dk`E e(1-10-phenantroline)3]2+v%ememA   BdY?"6@ NNN?NdY< h@D >: Wtt   D# "A .?BUHKAQY<`7Dt   DF5 "A 5?CEPZOM`<|g7D  s *@Y3"`<47Kq> T Applications 2 $: n  s 8AG (\?Image1"`r;:NjWoC 3 H Y ?"6@ NNN?Nu>4YD B(The next step is to model Iron(II) porphyrins, which are planar complexes with the Fe2+ surrounded by four aromatic nitrogens (chemically similar to imine nitrogens). The most important example of an Iron(II) porphyrin is the O2 -binding site for haemoglobin, heme. Fe2+ in heme changes from high spin to low spin when it binds to an oxygen molecule, which changes the shape of the whole molecule. This change is important in the uptake and transport of oxygen. It would be very interesting to find out if DommiMOE can model this %U    "b G  $F: |~ 3   < 3  c"$) \g3N =  S X99?3  J >  # "`3  b ?  c 2A , .DETTOL3 b @  c 2A, .PAZXAP  b A  c 2AO f&PURYIK3  B  3 xY"` -  P1.$ :  C  3 Y"`m D-  P2.$ :  D  3 XY"`  - P3.$ : N8 4E7YaH N E47YaH 9  N?"6@`NNN?N4E7YaH 7  NtY?"6@`NNN?N81EQG The author would like to t                          ! " # $ % & ' ( ) * + , - . / 0 1 2 3 4 5 6 7 8 9 : ; < = > ? @ A B C D E F G H I J K L M N O P Q R S T U V W X Y Z [ \ ] ^ _ ` a b c d e f g h i j k l m n o p q r s t u v w x y z { | } ~  hank the MOAC Doctoral Centre staff and colleagues for their guidance and the Engineering and Physical Sciences Research Council Life Sciences Interface Programme for their generous support.:  5  HA moacc"`l51El8OH J  X3AdDownloads_Images_Logos_Version1Colour_EPSRC1RGBHI"`=Q^EX7Hj L C BA*the_warwick_uni_bluex 28 4SAv&  p4B%@ 7$D% m 4SAv&z   < A?sa"`7$D%B    `D??"0@NNN?Nr;sW? B  B  `D??"0@NNN?N; W? !B   `D??"0@NNN?N;@ !B  B  `D??"0@NNN?N9@V B    `D??"0@NNN?N:V <f!B ! B  `D??"0@NNN?N;xAB "   `D??"0@NNN?N;h@ !B #   `D??"0@NNN?N?!:@!B $  `D??"0@NNN?N?8! @!B %   `D??"0@NNN?N? !:@f!B &  `D??"0@NNN?NW?FxAB '   `D??"0@NNN?NxAF-BB ( B  `D??"0@NNN?NABB )   `D??"0@NNN?NAB) B * B  `D??"0@NNN?N?) -B B +  `D??"0@NNN?N>? B ,   `D??"0@NNN?N;f!T<I"B -  `D??"0@NNN?N;"T<I"B .  `D??"0@NNN?N; !<"B /  `D??"0@NNN?N; <9!B 0 B  `D??"0@NNN?N4: ; B h B TD?"0@NNN?N? !h@!B i TD?"0@NNN?NX?;@f!B j TD?"0@NNN?Nr;s=B l TD?"0@NNN?N = !="8 QGqT% p C^E~Rf% 7  B A sa"`QGqT% o  B ?"6@ NNN?NuL!LI" 8 Vp d%  CDWddf% R  D A sa2"`Vp d%B r TD?"0@NNN?N[!g\!B s TD?"0@NNN?N[f!g\!B t B TD?"0@NNN?N[f!g\"B u  TD?"0@NNN?N["g\I"B v TD?"0@NNN?N[9!g\I"B w TD?"0@NNN?N[ !\9!B x B TD?"0@NNN?N[ !\!B y  TD?"0@NNN?N[!]!B {  TD?"0@NNN?N]!w]!B | B TD?"0@NNN?N]!w]!B }  TD?"0@NNN?N]!w]!B ~ TD?"0@NNN?Ng\!w]!B  B TD?"0@NNN?N[!g\v"B   TD?"0@NNN?N[v"["B   TD?"0@NNN?N["g\"B  B TD?"0@NNN?N["g\"B  TD?"0@NNN?N["g\"  H4Y ?"6@ NNN?NAF# 8Markov chain explores distribution of interest, with a preference of  downhill steps if the global minimum is to be found. } 2}: 0  HY ?"6@ NNN?N{R3V! z<The smallest value encountered by the Markov chain is noted.= 2=: *8 R"W$  !{RqW$   N ?"6@ NNN?NR"W$   T` Z ?"6@ NNN?NR"W$ TReduce T" : B  HZ ?"6@ NNN?Neh# NStart at current minimum. Markov chain is more confined to an area of interestO 2O: j  C 4Aprakash_patel"`ag   Z2<܍ ?"` 33___PPT10i.M2_<+D=' = @B +regǯ [ o(miI   WEquation Equation.30,Microsoft Equation 3.0  Equation Equation.30,Microsoft Equation 3.0' $Photo Editor Photo MSPhotoEd.30@Microsoft Photo Editor 3.0 Photo/ 0DArialNew .0B 0DNew Century SchoolbookB 0 DTimes New RomanolbookB 0 B.:   @n?" dd@  @@`` : 2 ( oR$yX8p2uc-"$$tz:}ix@tGD+c-2$Z C^6.w5R$kL$>Jڳݱ7"$PZ6(<7 aGb$y)|{6b^JR$|L24'E]&+2$ ?MJ0-cQR$xdj?8pW~.2$(-rf/AZ6>$+Ʊ败 R$?UfsZ87[-3 b$Pf;)rDc5@;  0e0e     A@  A5% 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||s " 0e@        @ABC DEEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN E5%  N E5%  N F   5%    !"?N@ABC DEFFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab@=ʚ;d,;ʚ;g4!d!d B 0 p$p4<4ddLpC 0- <4!d!dLhG 0<4BdBdLhG 080___PPT10 pp?  %re߯z [ o(miI   ZEquation Equation.30,Microsoft Equation 3.0  Equation Equation.30,Microsoft Equation 3.0' $Photo Editor Photo MSPhotoEd.30@Microsoft Photo Editor 3.0 Photo/ 0DArialNew q_0B 0"DNew Century SchoolbookB 0 DTimes New RomanolbookB 0 B.:   @n?" dd@  @@`` : 2 ( oR$yX8p2uc-"$$tz:}ix@tGD+c-2$Z C^6.w5R$kL$>Jڳݱ7"$PZ6(<7 aGb$y)|{6b^JR$|L24'E]&+2$ ?MJ0-cQR$xdj?8pW~.2$(-rf/AZ6>$+Ʊ败 R$?UfsZ87[-3 b$Pf;)rDc5@;  0e0e     A@  A5% 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||s " 0e@        @ABC DEEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN E5%  N E5%  N F   5%    !"?N@ABC DEFFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab@=ʚ;d,;ʚ;g4dd B 0fp$p4<4ddLpC 0hq_ <4!d!dLhG 0<4BdBdLhG 080___PPT10 pp?  %[ rj  0L n(  R  C *APicture1] hH 4 TA" MOE_Screenshot"`H>%4EH  B ?"6@ NNN?Ni$0CW, $ s *= 3"` 'zL  PAbstract 2 $:  & H? ?3?"6?@`NNN?N&'z( dA bit of Ligand Field Theory 2$:  ' HH ?3?"6?@`NNN?N 47K  Iron(II) Hexammine [Fe(NH3)6]2+ 2'$/$'$/$'$/$$ : 'F Tbi  1 _ S  0^ 3"`Tby qFinding optimal parameters for spin-state changes in Iron(II) amine complexes in Ligand Field Molecular Mechanics r(2rP56:    6` Zb  Prakash Patel1 , Rob Deeth2X(2 6 6 6 66: c + 68w M bi  1MOAC Doctoral Training Centre, and the 2Inorganic Computational Chemistry Group, Department of Chemistry, ý.J(2 ' Y:  8 0Ċ P 4 The geometries and energies of six-coordinated amine complexes of Fe2+ at both spin states were explored using the DommiMOE program. Then the model parameters were refined using simulated annealing to give the correct geometries and predict the correct spin state of the metal, initially with [Fe(NH3)6]2+, then with three other amine complexes. The parameters found were applied to about 80 imine complexes, and after a slight modification, approximated the geometries reasonably well and most of the time predicted the correct spin state.xD    : B . # A"`'T   9 H,f ?3?"6?@`NNN?N'z T Introduction 2 $:  : <8  ?"6@`NNN?Ng'.4 ,The importance of organometallic proteins in biochemistry has long been recognised, which the metal instrumental in many of these protein s catalytic or binding functions. At the moment there are very few methods that model transition metal-containing organometallic proteins effectively, either using quantum or classical mechanical methods. Here is outlined a very promising new Molecular Modelling approach to deal with transition metal complexes which can be used to model biological macromolecules.:  < H ?3?"6?@`NNN?N'z [Molecular Modelling 2$:  ? B ?"6@ NNN?Nmi A B ?"6@ NNN?Nmi = <  ?"6@ NNN?N"'.4 VMolecular Modelling (MM) of Force-Field (FF) methods of finding molecular structures determine the relationship between the energy and structure by application of empirical rules based on classical mechanics. To find an optimal structure in MM, we optimise the total strain energy: D B <  ?"6@ NNN?N'\4& \where the terms correspond to the deviation from the optimal bond lengths, bond angles, torsions, non-bonded interactions and electrostatic interactions from those given by the a particular forcefield. Modelling transition metals using conventional MM has always been difficult as they can have variable oxidation states, spin states and electronic effects, and can coordinate from 4 to 12 different ligands in a complex. Rob Deeth has addressed this problem by developing this Ligand Field Molecular Mechanics model of dealing with transition metal centres using an approach called Ligand Field Theory.]]:  D B ?"6@ NNN?NF$miF$j C S A ??"? &  T <ʊ  ?"6@ NNN?N}('am7 ' In a free transition metal ion, the preference of the d-electrons is to occupy each of the five d-orbitals, and when there are more than five d electrons, spin-pairing occurs. In an octahedrally-coordinated complex, the dxy, dyz and dxz orbitals become lower in energy than the dx2-y2 and dz2 orbitals and are filled first. Ligand Field Theory states that this is because the former orbitals repel the ligand electron densities less than the latter (the d-orbitals are mostly antibonding and repel ligand electron clouds). Depending on the ligands (the so-called ligand field strength), the d-electrons may desert the dx2-y2 and dz2 orbitals completely as the electron pairing becomes energetically more favourable than the electron repulsion of ligand bonding orbitals.    ,  M  >: V W C .Adorbitals2%m4+ \ < ?"6@ NNN?N.4 _ < ?"6@ NNN?N.4 b < ?"6@ NNN?N.4  < ?"6@ NNN?N.4  < ?"6@ NNN?N.4  < ?"6@ NNN?N.4F 2)p*2 3   +`)2v4N  S A 2)p*2-N  S fA 2)_-2n0  TA ?"6@ NNN?N2)L02 3 F `B*23   +K34  H֊ =J?"6@`NNN?N{(*023 @: Wt  B ?"6@`NNN?N`*0{(3 :(2) High Ligand Field strength (e.g. CN-, phenantroline) J;(&.&+ : Wt  H =J?"6@`NNN?N{(6-2*0 @: Wt  B ?"6@`NNN?N`6-{(*0 7(1) Low Ligand Field strength (e.g. Cl-, I-, F-, H2O) 8'&.&.&.&.&: Wt  H~ =J?"6@`NNN?N{(B*26- @,: WtA  Bx ?"6@`NNN?N`B*{(6- Free Fe2+ ion (high spin)> : WtB  Bo ?"0@NNN?N`B*2B*B  <1 ?"0@NNN?N`6-26-B  <1 ?"0@NNN?N`*02*0B  Bo ?"0@NNN?N`323B  Bo ?"0@NNN?N`B*`3B  <1 ?"0@NNN?N{(B*{(3B  Bo ?"0@NNN?N2B*23/F $   u> ?i   - $  + High Spin: h   6 4 *Low Spin: j  S A   ??"??%yB  _  H(?  ?"6@ NNN?NFB'L%G yDeeth has implemented LFMM into the Molecular Operating Environment (MOE), a popular MM dynamics program, to form DommiMOE, which uses the forcefield MMFF94 for non-transition metals. DommiMOE can optimise the geometry a complex for a given spin state, and so can give hypothetical structures of transition metal complexes for both spin states with the same set of parameters.zz  H\H  ?"6@ NNN?NP 4>_  2This is an octahedral high-spin complex where the Fe  N bond lengths were 2.20  (from X-ray crystallographic data). To obtain data on a hypothetical low-spin structure, QM techniques were used, which predict that the Fe  N bond lengths to be around 2.00 . Also, an estimate of 11 kcal/mol was set on the energetic favourability of the high spin state to the low spin state. As with all MM-based methods, some model parameters have to be found which fit the required geometries and energies. Parameters modified included the Morse function parameters (Fe N bond length potential was modelled by a Morse function), octahedral-field splitting term, the ligand-ligand repulsion term and some electron-pairing energy terms. To measure the  fit of the parameters, a cost function was constructed such that the smaller its value, the better the parameters fit the data.ff0P  dt  c >A m Fe_hexammine"` 0_g%  H_ ?3?"6?@`NNN?Nz4 K oSimulated Annealing2 2 $ '$: F  Bd  ?"6@ NNN?N7D\4N? The difference between low spin and high spin states is the metal-ligand bond lengths of low spin states are much smaller than those of high spin. For example, the Fe  N bond length in low spin and high spin amine complexes are about 2.00 and 2.20 respectively. This is because of the smaller repulsion of the ligands from the d-electron cloud at low spin than at high spin. Deeth summarises this effect by the Ligand Field Stabilisation Energy (LFSE), and incorporated into the MM framework by adding to the MM equation:." : v  Bl  ?"6@ NNN?N4p287 r(1) is known as the high-spin state of Fe2+ as the total spin is greater than in (2), known as the low spin state.*s) H: j   S A  '??"?17` > '(  Hpw  ?"6@ NNN?N4gs rSimulated Annealing (SA) is a method of finding the maximum or minimum of a distribution (x) by using Markov Chain Monte Carlo (MCMC) to sample the parameter space, in this case the distribution needed to be minimised is the cost function A Markov chain (a  random walk ) is constructed whose limiting distribution is (x) - the target distribution. d`[""""""",Y  B ?"6@ NNN?N+$mi+$  Hl  ?"6@ NNN?N%4dg* `BIn simulated annealing, the target distribution (x) is changed to (x)1/T (T is known as the  temperature ), which has the same maxima and minima as (x) but is rather  steeper as T decreases from 1 to 0, and this makes the Markov chain less likely to escape local minima. If the temperature is carefully reduced, then (hopefully) at the end of the procedure the Markov chain will reside near the global minimum. 2"""""**""K""""",0c   s * 3"`*47K1, kAmine Complexes2 2$ '$:   H  ?"6@ NNN?N5,4\2 66The simulated annealing procedure yielded some good parameters for the iron hexaammine complex, which were applied to three other amine complexes. From the bond lengths in their X-ray crystallographic structures, (1) and (2) were low spin complexes, while (3) was a high spin complex, which illustrates the sensitivity of the spin state of Fe2+ with nitrogen ligands. The parameters found for [Fe(NH3)6]2+ were found to reproduce the geometry of the complexes very well in their native spin states, and also the spin states of the complexes were correctly predicted.7""  S"*7"*"*"*"L   s *쵋 3"`247KW4 kImine Complexes2 2$ '$: y  H  ?"6@ NNN?N\44g; Can these parameters transfer to imine complexes? Unlike amine nitrogens, imine nitrogens are aromatic, and most Fe2+ imine complexes are low-spin. It was found that after some modification of the parameters, although the bond lengths were not very accurately reproduced, DommiMOE correctly predicted the spin state for most of the complexes (but not all). The most striking result was the predicted spin states of the low spin complex [Fe(1-10-phenantroline)3]2+ and the high spin [Fe(2-methyl-1-10-phenantroline)3]2+. Although the ligands in these complexes were very similar, DommiMOE correctly deduced their spin states, which correspond to a large change in geometry.i= t"*"f"*"*3"*"*",@  L  6?"6@ NNN?Nt!.:t!B  <?"0@NNN?N@DP@B  <?"0@NNN?NGDPGB  6?"0@NNN?N@DDGB  <?"0@NNN?N@PPGF dY<hE F  ;dYhD^   B̋ ?"6@ NNN?Nk`@DhE $[Fe(2-methyl-1-10-phenantroline)3]2+f% ememAe   BӋ ?"6@ NNN?NdY@Dk`E e(1-10-phenantroline)3]2+v%ememA   B8 ?"6@ NNN?NdY< h@D >: Wtt   D# "A .?BUHKAQY<`7Dt   DF5 "A 5?CEPZOM`<|g7D  s * 3"`<47Kq> T Applications 2 $: n  s 8AG (\?Image1"`r;:NjWoC 3 H  ?"6@ NNN?Nu>4YD B(The next step is to model Iron(II) porphyrins, which are planar complexes with the Fe2+ surrounded by four aromatic nitrogens (chemically similar to imine nitrogens). The most important example of an Iron(II) porphyrin is the O2 -binding site for haemoglobin, heme. Fe2+ in heme changes from high spin to low spin when it binds to an oxygen molecule, which changes the shape of the whole molecule. This change is important in the uptake and transport of oxygen. It would be very interesting to find out if DommiMOE can model this %U    "b G  $F: |~ 3   < 3  c"$) \g3N =  S X99?3  J >  # "`3  b ?  c 2A , .DETTOL3 b @  c 2A, .PAZXAP  b A  c 2AO f&PURYIK3  B  3 p "` -  P1.$ :  C  3  "`m D-  P2.$ :  D  3 P "`  - P3.$ : N8 4E7YaH N E47YaH 9  N?"6@`NNN?N4E7YaH 7  N`) ?"6@`NNN?N81EQG The author would like to thank the MOAC Doctoral Centre staff and colleagues for their guidance and the Engineering and Physical Sciences Research Council Life Sciences Interface Programme for their generous support.:  5  HA moacc"`l51El8OH J  X3AdDownloads_Images_Logos_Version1Colour_EPSRC1RGBHI"`=Q^EX7Hj L C BA*the_warwick_uni_bluex 28 4SAv&  p4B%@ 7$D% m 4SAv&z   < A?sa"`7$D%B    `D??"0@NNN?Nr;sW? B  B  `D??"0@NNN?N; W? !B   `D??"0@NNN?N;@ !B  B  `D??"0@NNN?N9@V B    `D??"0@NNN?N:V <f!B ! B  `D??"0@NNN?N;xAB "   `D??"0@NNN?N;h@ !B #   `D??"0@NNN?N?!:@!B $  `D??"0@NNN?N?8! @!B %   `D??"0@NNN?N? !:@f!B &  `D??"0@NNN?NW?FxAB '   `D??"0@NNN?NxAF-BB ( B  `D??"0@NNN?NABB )   `D??"0@NNN?NAB) B * B  `D??"0@NNN?N?) -B B +  `D??"0@NNN?N>? B ,   `D??"0@NNN?N;f!T<I"B -  `D??"0@NNN?N;"T<I"B .  `D??"0@NNN?N; !<"B /  `D??"0@NNN?N; <9!B 0 B  `D??"0@NNN?N4: ; B h B TD?"0@NNN?N? !h@!B i TD?"0@NNN?NX?;@f!B j TD?"0@NNN?Nr;s=B l TD?"0@NNN?N = !="8 QGqT% p C^E~Rf% 7  B A sa"`QGqT% o  B ?"6@ NNN?NuL!LI" 8 Vp d%  CDWddf% R  D A sa2"`Vp d%B r TD?"0@NNN?N[!g\!B s TD?"0@NNN?N[f!g\!B t B TD?"0@NNN?N[f!g\"B u  TD?"0@NNN?N["g\I"B v TD?"0@NNN?N[9!g\I"B w TD?"0@NNN?N[ !\9!B x B TD?"0@NNN?N[ !\!B y  TD?"0@NNN?N[!]!B {  TD?"0@NNN?N]!w]!B | B TD?"0@NNN?N]!w]!B }  TD?"0@NNN?N]!w]!B ~ TD?"0@NNN?Ng\!w]!B  B TD?"0@NNN?N[!g\v"B   TD?"0@NNN?N[v"["B   TD?"0@NNN?N["g\"B  B TD?"0@NNN?N["g\"B  TD?"0@NNN?N["g\"  H|I  ?"6@ NNN?NAF# 8Markov chain explores distribution of interest, with a preference of  downhill steps if the global minimum is to be found. } 2}: 0  H R  ?"6@ NNN?N{R3V! z<The smallest value encountered by the Markov chain is noted.= 2=: *8 R"W$  !{RqW$   N ?"6@ NNN?NR"W$   TP]  ?"6@ NNN?NR"W$ TReduce T" : B  Hg  ?"6@ NNN?Neh# NStart at current minimum. Markov chain is more confined to an area of interestO 2O: j  C 4Aprakash_patel"`ag   Z2<܍ ?"` 33___PPT10i.M2_<+D=' = @B +r%ex o(miI   ZEquation Equation.30,Microsoft Equation 3.0  Equation Equation.30,Microsoft Equation 3.0' $Photo Editor Photo MSPhotoEd.30@Microsoft Photo Editor 3.0 Photo/ 0DArialNew q_0B 0"DNew Century SchoolbookB 0 DTimes New RomanolbookB 0 B.:   @n?" dd@  @@`` : 2 ( oR$yX8p2uc-"$$tz:}ix@tGD+c-2$Z C^6.w5R$kL$>Jڳݱ7"$PZ6(<7 aGb$y)|{6b^JR$|L24'E]&+2$ ?MJ0-cQR$xdj?8pW~.2$(-rf/AZ6>$+Ʊ败 R$?UfsZ87[-3 b$Pf;)rDc5@;  0e0e     A@  A5% 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||s " 0e@        @ABC DEEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN E5%  N E5%  N F   5%    !"?N@ABC DEFFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab@=ʚ;d,;ʚ;g42d2d B 0p$p4<4ddLpC 0hq_ <4!d!dLhG 0<4BdBdLhG 080___PPT10 pp?  %rxex; o(miI   ZEqu 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||s " 0e@  ation Equation.30,Microsoft Equation 3.0  Equation Equation.30,Microsoft Equation 3.0' $Photo Editor Photo MSPhotoEd.30@Microsoft Photo Editor 3.0 Photo/ 0DArialNew q_0B 0"DNew Century SchoolbookB 0 DTimes New RomanolbookB 0 B.:   @n?" dd@  @@`` : 2 ( oR$yX8p2uc-"$$tz:}ix@tGD+c-2$Z C^6.w5R$kL$>Jڳݱ7"$PZ6(<7 aGb$y)|{6b^JR$|L24'E]&+2$ ?MJ0-cQR$xdj?8pW~.2$(-rf/AZ6>$+Ʊ败 R$?UfsZ87[-3 b$Pf;)rDc5@;  0e0e     A@  A5% 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||s " 0e@        @ABC DEEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN E5%  N E5%  N F   5%    !"?N@ABC DEFFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab@=ʚ;d,;ʚ;g42d2d B 0bp$p4<4ddLpC 0hq_ <4!d!dLhG 0<4BdBdLhG 080___PPT10 pp?  %[ rj  0L n(  R  C *APicture1] hH 4 TA" MOE_Screenshot"`H>%4EH  B ?"6@ NNN?Ni$0CW, $ s *= 3"` 'zL  PAbstract 2 $:  & H? ?3?"6?@`NNN?N&'z( dA bit of Ligand Field Theory 2$:  ' HH ?3?"6?@`NNN?N 47K  Iron(II) Hexammine [Fe(NH3)6]2+ 2'$/$'$/$'$/$$ : 'F Tbi  1 _ S  0^ 3"`Tby qFinding optimal parameters for spin-state changes in Iron(II) amine complexes in Ligand Field Molecular Mechanics r(2rP56:    6` Zb  Prakash Patel1 , Rob Deeth2X(2 6 6 6 66: c + 68w M bi  1MOAC Doctoral Training Centre, and the 2Inorganic Computational Chemistry Group, Department of Chemistry, ý.J(2 ' Y:  8 0Ċ P 4 The geometries and energies of six-coordinated amine complexes of Fe2+ at both spin states were explored using the DommiMOE program. Then the model parameters were refined using simulated annealing to give the correct geometries and predict the correct spin state of the metal, initially with [Fe(NH3)6]2+, then with three other amine complexes. The parameters found were applied to about 80 imine complexes, and after a slight modification, approximated the geometries reasonably well and most of the time predicted the correct spin state.xD    : B . # A"`'T   9 H,f ?3?"6?@`NNN?N'z T Introduction 2 $:  : <8  ?"6@`NNN?Ng'.4 ,The importance of organometallic proteins in biochemistry has long been recognised, which the metal instrumental in many of these protein s catalytic or binding functions. At the moment there are very few methods that model transition metal-containing organometallic proteins effectively, either using quantum or classical mechanical methods. Here is outlined a very promising new Molecular Modelling approach to deal with transition metal complexes which can be used to model biological macromolecules.:  < H ?3?"6?@`NNN?N]'z [Molecular Modelling 2$:  ? B ?"6@ NNN?Nmi A B ?"6@ NNN?Nmi = <  ?"6@ NNN?N"'.4 VMolecular Modelling (MM) of Force-Field (FF) methods of finding molecular structures determine the relationship between the energy and structure by application of empirical rules based on classical mechanics. To find an optimal structure in MM, we optimise the total strain energy: D B <  ?"6@ NNN?N'\4& \where the terms correspond to the deviation from the optimal bond lengths, bond angles, torsions, non-bonded interactions and electrostatic interactions from those given by the a particular forcefield. Modelling transition metals using conventional MM has always been difficult as they can have variable oxidation states, spin states and electronic effects, and can coordinate from 4 to 12 different ligands in a complex. Rob Deeth has addressed this problem by developing this Ligand Field Molecular Mechanics model of dealing with transition metal centres using an approach called Ligand Field Theory.]]:  D B ?"6@ NNN?NF$miF$j C S A ??"? &  T <ʊ  ?"6@ NNN?N}('am7 ' In a free transition metal ion, the preference of the d-electrons is to occupy each of the five d-orbitals, and when there are more than five d electrons, spin-pairing occurs. In an octahedrally-coordinated complex, the dxy, dyz and dxz orbitals become lower in energy than the dx2-y2 and dz2 orbitals and are filled first. Ligand Field Theory states that this is because the former orbitals repel the ligand electron densities less than the latter (the d-orbitals are mostly antibonding and repel ligand electron clouds). Depending on the ligands (the so-called ligand field strength), the d-electrons may desert the dx2-y2 and dz2 orbitals completely as the electron pairing becomes energetically more favourable than the electron repulsion of ligand bonding orbitals.    ,  M  >: V W C .Adorbitals2%m4+ \ < ?"6@ NNN?N.4 _ < ?"6@ NNN?N.4 b < ?"6@ NNN?N.4  < ?"6@ NNN?N.4  < ?"6@ NNN?N.4  < ?"6@ NNN?N.4F 2)p*2 3   +`)2v4N  S A 2)p*2-N  S fA 2)_-2n0  TA ?"6@ NNN?N2)L02 3 F `B*23   +K34  H֊ =J?"6@`NNN?N{(*023 @: Wt  B ?"6@`NNN?N`*0{(3 :(2) High Ligand Field strength (e.g. CN-, phenantroline) J;(&.&+ : Wt  H =J?"6@`NNN?N{(6-2*0 @: Wt  B ?"6@`NNN?N`6-{(*0 7(1) Low Ligand Field strength (e.g. Cl-, I-, F-, H2O) 8'&.&.&.&.&: Wt  H~ =J?"6@`NNN?N{(B*26- @,: WtA  Bx ?"6@`NNN?N`B*{(6- Free Fe2+ ion (high spin)> : WtB  Bo ?"0@NNN?N`B*2B*B  <1 ?"0@NNN?N`6-26-B  <1 ?"0@NNN?N`*02*0B  Bo ?"0@NNN?N`323B  Bo ?"0@NNN?N`B*`3B  <1 ?"0@NNN?N{(B*{(3B  Bo ?"0@NNN?N2B*23/F $   u> ?i   - $  + High Spin: h   6 4 *Low Spin: j  S A   ??"??%yB  _  H(?  ?"6@ NNN?NFB'L%G yDeeth has implemented LFMM into the Molecular Operating Environment (MOE), a popular MM dynamics program, to form DommiMOE, which uses the forcefield MMFF94 for non-transition metals. DommiMOE can optimise the geometry a complex for a given spin state, and so can give hypothetical structures of transition metal complexes for both spin states with the same set of parameters.zz  H\H  ?"6@ NNN?NP 4>_  2This is an octahedral high-spin complex where the Fe  N bond lengths were 2.20  (from X-ray crystallographic data). To obtain data on a hypothetical low-spin structure, QM techniques were used, which predict that the Fe  N bond lengths to be around 2.00 . Also, an estimate of 11 kcal/mol was set on the energetic favourability of the high spin state to the low spin state. As with all MM-based methods, some model parameters have to be found which fit the required geometries and energies. Parameters modified included the Morse function parameters (Fe N bond length potential was modelled by a Morse function), octahedral-field splitting term, the ligand-ligand repulsion term and some electron-pairing energy terms. To measure the  fit of the parameters, a cost function was constructed such that the smaller its value, the better the parameters fit the data.ff0P  dt  c >A m Fe_hexammine"` 0_g%  H_ ?3?"6?@`NNN?Nz4 K oSimulated Annealing2 2 $ '$: F  Bd  ?"6@ NNN?N7D\4N? The difference between low spin and high spin states is the metal-ligand bond lengths of low spin states are much smaller than those of high spin. For example, the Fe  N bond length in low spin and high spin amine complexes are about 2.00 and 2.20 respectively. This is because of the smaller repulsion of the ligands from the d-electron cloud at low spin than at high spin. Deeth summarises this effect by the Ligand Field Stabilisation Energy (LFSE), and incorporated into the MM framework by adding to the MM equation:." : v  Bl  ?"6@ NNN?N4p287 r(1) is known as the high-spin state of Fe2+ as the total spin is greater than in (2), known as the low spin state.*s) H: j   S A  '??"?17` > '(  Hpw  ?"6@ NNN?N4gs rSimulated Annealing (SA) is a method of finding the maximum or minimum of a distribution (x) by using Markov Chain Monte Carlo (MCMC) to sample the parameter space, in this case the distribution needed to be minimised is the cost function A Markov chain (a  random walk ) is constructed whose limiting distribution is (x) - the target distribution. d`[""""""",Y  B ?"6@ NNN?N+$mi+$  Hl  ?"6@ NNN?N%4dg* `BIn simulated annealing, the target distribution (x) is changed to (x)1/T (T is known as the  temperature ), which has the same maxima and minima as (x) but is rather  steeper as T decreases from 1 to 0, and this makes the Markov chain less likely to escape local minima. If the temperature is carefully reduced, then (hopefully) at the end of the procedure the Markov chain will reside near the global minimum. 2"""""**""K""""",0c   s * 3"`*47K1, kAmine Complexes2 2$ '$:   H  ?"6@ NNN?N5,4\2 66The simulated annealing procedure yielded some good parameters for the iron hexaammine complex, which were applied to three other amine complexes. From the bond lengths in their X-ray crystallographic structures, (1) and (2) were low spin complexes, while (3) was a high spin complex, which illustrates the sensitivity of the spin state of Fe2+ with nitrogen ligands. The parameters found for [Fe(NH3)6]2+ were found to reproduce the geometry of the complexes very well in their native spin states, and also the spin states of the complexes were correctly predicted.7""  S"*7"*"*"*"L   s *쵋 3"`247KW4 kImine Complexes2 2$ '$: y  H  ?"6@ NNN?N\44g; Can these parameters transfer to imine complexes? Unlike amine nitrogens, imine nitrogens are aromatic, and most Fe2+ imine complexes are low-spin. It was found that after some modification of the parameters, although the bond lengths were not very accurately reproduced, DommiMOE correctly predicted the spin state for most of the complexes (but not all). The most striking result was the predicted spin states of the low spin complex [Fe(1-10-phenantroline)3]2+ and the high spin [Fe(2-methyl-1-10-phenantroline)3]2+. Although the ligands in these complexes were very similar, DommiMOE correctly deduced their spin states, which correspond to a large change in geometry.i= t"*"f"*"*3"*"*",@  L  6?"6@ NNN?Nt!.:t!B  <?"0@NNN?N@DP@B  <?"0@NNN?NGDPGB  6?"0@NNN?N@DDGB  <?"0@NNN?N@PPGF dY<hE F  ;dYhD^   B̋ ?"6@ NNN?Nk`@DhE $[Fe(2-methyl-1-10-phenantroline)3]2+f% ememAe   BӋ ?"6@ NNN?NdY@Dk`E e(1-10-phenantroline)3]2+v%ememA   B8 ?"6@ NNN?NdY< h@D >: Wtt   D# "A .?BUHKAQY<`7Dt   DF5 "A 5?CEPZOM`<|g7D  s * 3"`<47Kq> T Applications 2 $: n  s 8AG (\?Image1"`r;:NjWoC 3 H  ?"6@ NNN?Nu>4YD B(The next step is to model Iron(II) porphyrins, which are planar complexes with the Fe2+ surrounded by four aromatic nitrogens (chemically similar to imine nitrogens). The most important example of an Iron(II) porphyrin is the O2 -binding site for haemoglobin, heme. Fe2+ in heme changes from high spin to low spin when it binds to an oxygen molecule, which changes the shape of the whole molecule. This change is important in the uptake and transport of oxygen. It would be very interesting to find out if DommiMOE can model this %U    "b G  $F: |~ 3   < 3  c"$) \g3N =  S X99?3  J >  # "`3  b ?  c 2A , .DETTOL3 b @  c 2A, .PAZXAP  b A  c 2AO f&PURYIK3  B  3 p "` -  P1.$ :  C  3  "`m D-  P2.$ :  D  3 P "`  - P3.$ : N8 4E7YaH N E47YaH 9  N?"6@`NNN?N4E7YaH 7  N`) ?"6@`NNN?N81EQG The author would like to thank the MOAC Doctoral Centre staff and colleagues for their guidance and the Engineering and Physical Sciences Research Council Life Sciences Interface Programme for their generous support.:  5  HA moacc"`l51El8OH J  X3AdDownloads_Images_Logos_Version1Colour_EPSRC1RGBHI"`=Q^EX7Hj L C BA*the_warwick_uni_bluex 28 4SAv&  p4B%@ 7$D% m 4SAv&z   < A?sa"`7$D%B    `D??"0@NNN?Nr;sW? B  B  `D??"0@NNN?N; W? !B   `D??"0@NNN?N;@ !B  B  `D??"0@NNN?N9@V B    `D??"0@NNN?N:V <f!B ! B  `D??"0@NNN?N;xAB "   `D??"0@NNN?N;h@ !B #   `D??"0@NNN?N?!:@!B $  `D??"0@NNN?N?8! @!B %   `D??"0@NNN?N? !:@f!B &  `D??"0@NNN?NW?FxAB '   `D??"0@NNN?NxAF-BB ( B  `D??"0@NNN?NABB )   `D??"0@NNN?NAB) B * B  `D??"0@NNN?N?) -B B +  `D??"0@NNN?N>? B ,   `D??"0@NNN?N;f!T<I"B -  `D??"0@NNN?N;"T<I"B .  `D??"0@NNN?N; !<"B /  `D??"0@NNN?N; <9!B 0 B  `D??"0@NNN?N4: ; B h B TD?"0@NNN?N? !h@!B i TD?"0@NNN?NX?;@f!B j TD?"0@NNN?Nr;s=B l TD?"0@NNN?N = !="8 QGqT% p C^E~Rf% 7  B A sa"`QGqT% o  B ?"6@ NNN?NuL!LI" 8 Vp d%  CDWddf% R  D A sa2"`Vp d%B r TD?"0@NNN?N[!g\!B s TD?"0@NNN?N[f!g\!B t B TD?"0@NNN?N[f!g\"B u  TD?"0@NNN?N["g\I"B v TD?"0@NNN?N[9!g\I"B w TD?"0@NNN?N[ !\9!B x B TD?"0@NNN?N[ !\!B y  TD?"0@NNN?N[!]!B {  TD?"0@NNN?N]!w]!B | B TD?"0@NNN?N]!w]!B }  TD?"0@NNN?N]!w]!B ~ TD?"0@NNN?Ng\!w]!B  B TD?"0@NNN?N[!g\v"B   TD?"0@NNN?N[v"["B   TD?"0@NNN?N["g\"B  B TD?"0@NNN?N["g\"B  TD?"0@NNN?N["g\"  H|I  ?"6@ NNN?NAF# 8Markov chain explores distribution of interest, with a preference of  downhill steps if the global minimum is to be found. } 2}: 0  H R  ?"6@ NNN?N{R3V! z<The smallest value encountered by the Markov chain is noted.= 2=: *8 R"W$  !{RqW$   N ?"6@ NNN?NR"W$   TP]  ?"6@ NNN?NR"W$ TReduce T" : B  Hg  ?"6@ NNN?Neh# NStart at current minimum. Markov chain is more confined to an area of interestO 2O: j  C 4Aprakash_patel"`ag   Z2<܍ ?"` 33___PPT10i.M2_<+D=' = @B +roeKIA o(miI   _Equation Equation.30,Microsoft Equation 3.0  Equation Equation.30,Microsoft Equation 3.0_ $Photo Editor Photo MSPhotoEd.30@Microsoft Photo Editor 3.0 Photo/ 0DArialNew .0B 0DNew Century SchoolbookB 0 DTimes New RomanolbookB 0 B.:   @n?" dd@  @@`` : 2 ( oR$yX8p2uc-"$$tz:}ix@tGD+c-2$Z C^6.w5R$kL$>Jڳݱ7"$PZ6(<7 aGb$y)|{6b^JR$|L24'E]&+2$ ?MJ0-cQR$xdj?8pW~.2$(-rf/AZ6>$+Ʊ败 R$?UfsZ87[-3 b$Pf;)rDc5@;  0e0e     A@  A5% 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||s " 0e@        @ABC DEEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN E5%  N E5%  N F   5%    !"?N@ABC DEFFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab@=ʚ;d,;ʚ;g42d2d B 0bH p$p4<4ddLpC 0- <4!d!dLhG 0<4BdBdLhG 080___PPT10 pp?  %[ rj  0L n(  R  C *APicture1] hH 4 TA" MOE_Screenshot"`H>%4EH  B ?"6@ NNN?Ni$0CW, $ s *83"` 'zL  PAbstract 2 $:  & H?3?"6?@`NNN?N&'z( dA bit of Ligand Field Theory 2$:  ' H_?3?"6?@`NNN?N 47K  Iron(II) Hexammine [Fe(NH3)6]2+ 2'$/$'$/$'$/$$ : 'F Tbi  1 _ S  0$3"`Tby qFinding optimal parameters for spin-state changes in Iron(II) amine complexes in Ligand Field Molecular Mechanics r(2rP56:    6_Zb  Prakash Patel1 , Rob Deeth2X(2 6 6 6 66: c + 6 _M bi  1MOAC Doctoral Training Centre, and the 2Inorganic Computational Chemistry Group, Department of Chemistry, ý.J(2 ' Y:  8 08_P 4 The geometries and energies of six-coordinated amine complexes of Fe2+ at both spin states were explored using the DommiMOE program. Then the model parameters were refined using simulated annealing to give the correct geometries and predict the correct spin state of the metal, initially with [Fe(NH3)6]2+, then with three other amine complexes. The parameters found were applied to about 80 imine complexes, and after a slight modification, approximated the geometries reasonably well and most of the time predicted the correct spin state.xD    : B . # A"`'T   9 H._?3?"6?@`NNN?N'z T Introduction 2 $:  : < D_ ?"6@`NNN?Ng'.4 ,The importance of organometallic proteins in biochemistry has long been recognised, which the metal instrumental in many of these protein s catalytic or binding functions. At the moment there are very few methods that model transition metal-containing organometallic proteins effectively, either using quantum or classical mechanical methods. Here is outlined a very promising new Molecular Modelling approach to deal with transition metal complexes which can be used to model biological macromolecules.:  < HQ_?3?"6?@`NNN?N]'z [Molecular Modelling 2$:  ? B ?"6@ NNN?Nmi A B ?"6@ NNN?Nmi = <Z_ ?"6@ NNN?N"'.4 VMolecular Modelling (MM) of Force-Field (FF) methods of finding molecular structures determine the relationship between the energy and structure by application of empirical rules based on classical mechanics. To find an optimal structure in MM, we optimise the total strain energy: D B <lf_ ?"6@ NNN?N'\4& \where the terms correspond to the deviation from the optimal bond lengths, bond angles, torsions, non-bonded interactions and electrostatic interactions from those given by the a particular forcefield. Modelling transition metals using conventional MM has always been difficult as they can have variable oxidation states, spin states and electronic effects, and can coordinate from 4 to 12 different ligands in a complex. Rob Deeth has addressed this problem by developing this Ligand Field Molecular Mechanics model of dealing with transition metal centres using an approach called Ligand Field Theory.]]:  D B ?"6@ NNN?NF$miF$j C S A ??"? &  T <u_ ?"6@ NNN?N}('am7 ' In a free transition metal ion, the preference of the d-electrons is to occupy each of the five d-orbitals, and when there are more than five d electrons, spin-pairing occurs. In an octahedrally-coordinated complex, the dxy, dyz and dxz orbitals become lower in energy than the dx2-y2 and dz2 orbitals and are filled first. Ligand Field Theory states that this is because the former orbitals repel the ligand electron densities less than the latter (the d-orbitals are mostly antibonding and repel ligand electron clouds). Depending on the ligands (the so-called ligand field strength), the d-electrons may desert the dx2-y2 and dz2 orbitals completely as the electron pairing becomes energetically more favourable than the electron repulsion of ligand bonding orbitals.    ,  M  >: V W C .Adorbitals2%m4+ \ < ?"6@ NNN?N.4 _ < ?"6@ NNN?N.4 b < ?"6@ NNN?N.4  < ?"6@ NNN?N.4  < ?"6@ NNN?N.4  < ?"6@ NNN?N.4F 2)p*2 3   +`)2v4N  S A 2)p*2-N  S fA 2)_-2n0  TA ?"6@ NNN?N2)L02 3 F `B*23   +K34  Hl_=J?"6@`NNN?N{(*023 @: Wt  B _?"6@`NNN?N`*0{(3 :(2) High Ligand Field strength (e.g. CN-, phenantroline) J;(&.&+ : Wt  H_=J?"6@`NNN?N{(6-2*0 @: Wt  B _?"6@`NNN?N`6-{(*0 7(1) Low Ligand Field strength (e.g. Cl-, I-, F-, H2O) 8'&.&.&.&.&: Wt  H`_=J?"6@`NNN?N{(B*26- @,: WtA  BL_?"6@`NNN?N`B*{(6- Free Fe2+ ion (high spin)> : WtB  Bo ?      @ABC DEEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN E5%"0@NNN?N`B*2B*B  <1 ?"0@NNN?N`6-26-B  <1 ?"0@NNN?N`*02*0B  Bo ?"0@NNN?N`323B  Bo ?"0@NNN?N`B*`3B  <1 ?"0@NNN?N{(B*{(3B  Bo ?"0@NNN?N2B*23/F $   u> ?i   _$  + High Spin: h   _4 *Low Spin: j  S A   ??"??%yB  _  H0_ ?"6@ NNN?NFB'L%G yDeeth has implemented LFMM into the Molecular Operating Environment (MOE), a popular MM dynamics program, to form DommiMOE, which uses the forcefield MMFF94 for non-transition metals. DommiMOE can optimise the geometry a complex for a given spin state, and so can give hypothetical structures of transition metal complexes for both spin states with the same set of parameters.zz  Hl` ?"6@ NNN?NP 4>_  2This is an octahedral high-spin complex where the Fe  N bond lengths were 2.20  (from X-ray crystallographic data). To obtain data on a hypothetical low-spin structure, QM techniques were used, which predict that the Fe  N bond lengths to be around 2.00 . Also, an estimate of 11 kcal/mol was set on the energetic favourability of the high spin state to the low spin state. As with all MM-based methods, some model parameters have to be found which fit the required geometries and energies. Parameters modified included the Morse function parameters (Fe N bond length potential was modelled by a Morse function), octahedral-field splitting term, the ligand-ligand repulsion term and some electron-pairing energy terms. To measure the  fit of the parameters, a cost function was constructed such that the smaller its value, the better the parameters fit the data.ff0P  dt  c >A m Fe_hexammine"` 0_g%  H_?3?"6?@`NNN?Nz4 K oSimulated Annealing2 2 $ '$: F  BT` ?"6@ NNN?N7D\4N? The difference between low spin and high spin states is the metal-ligand bond lengths of low spin states are much smaller than those of high spin. For example, the Fe  N bond length in low spin and high spin amine complexes are about 2.00 and 2.20 respectively. This is because of the smaller repulsion of the ligands from the d-electron cloud at low spin than at high spin. Deeth summarises this effect by the Ligand Field Stabilisation Energy (LFSE), and incorporated into the MM framework by adding to the MM equation:." : v  B!` ?"6@ NNN?N4p287 r(1) is known as the high-spin state of Fe2+ as the total spin is greater than in (2), known as the low spin state.*s) H: j   S A  _??"?17` > _(  H_ ?"6@ NNN?N4gs rSimulated Annealing (SA) is a method of finding the maximum or minimum of a distribution (x) by using Markov Chain Monte Carlo (MCMC) to sample the parameter space, in this case the distribution needed to be minimised is the cost function A Markov chain (a  random walk ) is constructed whose limiting distribution is (x) - the target distribution. d`[""""""",Y  B ?"6@ NNN?N+$mi+$  H|0` ?"6@ NNN?N%4dg* `BIn simulated annealing, the target distribution (x) is changed to (x)1/T (T is known as the  temperature ), which has the same maxima and minima as (x) but is rather  steeper as T decreases from 1 to 0, and this makes the Markov chain less likely to escape local minima. If the temperature is carefully reduced, then (hopefully) at the end of the procedure the Markov chain will reside near the global minimum. 2"""""**""K""""",0c   s *L`3"`*47K1, kAmine Complexes2 2$ '$:   HN` ?"6@ NNN?N5,4\2 66The simulated annealing procedure yielded some good parameters for the iron hexaammine complex, which were applied to three other amine complexes. From the bond lengths in their X-ray crystallographic structures, (1) and (2) were low spin complexes, while (3) was a high spin complex, which illustrates the sensitivity of the spin state of Fe2+ with nitrogen ligands. The parameters found for [Fe(NH3)6]2+ were found to reproduce the geometry of the complexes very well in their native spin states, and also the spin states of the complexes were correctly predicted.7""  S"*7"*"*"*"L   s *T+`3"`247KW4 kImine Complexes2 2$ '$: y  H i` ?"6@ NNN?N\44g; Can these parameters transfer to imine complexes? Unlike amine nitrogens, imine nitrogens are aromatic, and most Fe2+ imine complexes are low-spin. It was found that after some modification of the parameters, although the bond lengths were not very accurately reproduced, DommiMOE correctly predicted the spin state for most of the complexes (but not all). The most striking result was the predicted spin states of the low spin complex [Fe(1-10-phenantroline)3]2+ and the high spin [Fe(2-methyl-1-10-phenantroline)3]2+. Although the ligands in these complexes were very similar, DommiMOE correctly deduced their spin states, which correspond to a large change in geometry.i= t"*"f"*"*3"*"*",@  L  6?"6@ NNN?Nt!.:t!B  <?"0@NNN?N@DP@B  <?"0@NNN?NGDPGB  6?"0@NNN?N@DDGB  <?"0@NNN?N@PPGF dY<hE F  ;dYhD^   B(}`?"6@ NNN?Nk`@DhE $[Fe(2-methyl-1-10-phenantroline)3]2+f% ememAe   B`?"6@ NNN?NdY@Dk`E e(1-10-phenantroline)3]2+v%ememA   B`?"6@ NNN?NdY< h@D >: Wtt   D# "A .?BUHKAQY<`7Dt   DF5 "A 5?CEPZOM`<|g7D  s *`3"`<47Kq> T Applications 2 $: n  s 8AG (\?Image1"`r;:NjWoC 3 Ht` ?"6@ NNN?Nu>4YD B(The next step is to model Iron(II) porphyrins, which are planar complexes with the Fe2+ surrounded by four aromatic nitrogens (chemically similar to imine nitrogens). The most important example of an Iron(II) porphyrin is the O2 -binding site for haemoglobin, heme. Fe2+ in heme changes from high spin to low spin when it binds to an oxygen molecule, which changes the shape of the whole molecule. This change is important in the uptake and transport of oxygen. It would be very interesting to find out if DommiMOE can model this %U    "b G  $F: |~ 3   < 3  c"$) \g3N =  S X99?3  J >  # "`3  b ?  c 2A , .DETTOL3 b @  c 2A, .PAZXAP  b A  c 2AO f&PURYIK3  B  3 H`"` -  P1.$ :  C  3 <`"`m D-  P2.$ :  D  3 `"`  - P3.$ : N8 4E7YaH N E47YaH 9  N?"6@`NNN?N4E7YaH 7  N `?"6@`NNN?N81EQG The author would like to thank the MOAC Doctoral Centre staff and colleagues for their guidance and the Engineering and Physical Sciences Research Council Life Sciences Interface Programme for their generous support.:  5  HA moacc"`l51El8OH J  X3AdDownloads_Images_Logos_Version1Colour_EPSRC1RGBHI"`=Q^EX7Hj L C BA*the_warwick_uni_bluex 28 4SAv&  p4B%@ 7$D% m 4SAv&z   < A?sa"`7$D%B    `D??"0@NNN?Nr;sW? B  B  `D??"0@NNN?N; W? !B   `D??"0@NNN?N;@ !B  B  `D??"0@NNN?N9@V B    `D??"0@NNN?N:V <f!B ! B  `D??"0@NNN?N;xAB "   `D??"0@NNN?N;h@ !B #   `D??"0@NNN?N?!:@!B $  `D??"0@NNN?N?8! @!B %   `D??"0@NNN?N? !:@f!B &  `D??"0@NNN?NW?FxAB '   `D??"0@NNN?NxAF-BB ( B  `D??"0@NNN?NABB )   `D??"0@NNN?NAB) B * B  `D??"0@NNN?N?) -B B +  `D??"0@NNN?N>? B ,   `D??"0@NNN?N;f!T<I"B -  `D??"0@NNN?N;"T<I"B .  `D??"0@NNN?N; !<"B /  `D??"0@NNN?N; <9!B 0 B  `D??"0@NNN?N4: ; B h B TD?"0@NNN?N? !h@!B i TD?"0@NNN?NX?;@f!B j TD?"0@NNN?Nr;s=B l TD?"0@NNN?N = !="8 QGqT% p C^E~Rf% 7  B A sa"`QGqT% o  B ?"6@ NNN?NuL!LI" 8 Vp d%  CDWddf% R  D A sa2"`Vp d%B r TD?"0@NNN?N[!g\!B s TD?"0@NNN?N[f!g\!B t B TD?"0@NNN?N[f!g\"B u  TD?"0@NNN?N["g\I"B v TD?"0@NNN?N[9!g\I"B w TD?"0@NNN?N[ !\9!B x B TD?"0@NNN?N[ !\!B y  TD?"0@NNN?N[!]!B {  TD?"0@NNN?N]!w]!B | B TD?"0@NNN?N]!w]!B }  TD?"0@NNN?N]!w]!B ~ TD?"0@NNN?Ng\!w]!B  B TD?"0@NNN?N[!g\v"B   TD?"0@NNN?N[v"["B   TD?"0@NNN?N["g\"B  B TD?"0@NNN?N["g\"B  TD?"0@NNN?N["g\"  H\` ?"6@ NNN?NAF# 8Markov chain explores distribution of interest, with a preference of  downhill steps if the global minimum is to be found. } 2}: 0  Ha ?"6@ NNN?N{R3V! z<The smallest value encountered by the Markov chain is noted.= 2=: *8 R"W$  !{RqW$   N ?"6@ NNN?NR"W$   T` ?"6@ NNN?NR"W$ TReduce T" : B  Ha ?"6@ NNN?Neh# NStart at current minimum. 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Then the model parameters were refined using simulated annealing to give the correct geometries and predict the correct spin state of the metal, initially with [Fe(NH3)6]2+, then with three other amine complexes. The parameters found were applied to about 80 imine complexes, and after a slight modification, approximated the geometries reasonably well and most of the time predicted the correct spin state.xD    : B . # A"`'T   9 H._?3?"6?@`NNN?N'z T Introduction 2 $:  : < D_ ?"6@`NNN?Ng'.4 ,The importance of organometallic proteins in biochemistry has long been recognised, which the metal instrumental in many of these protein s catalytic or binding functions. At the moment there are very few methods that model transition metal-containing organometallic proteins effectively, either using quantum or classical mechanical methods. Here is outlined a very promising new Molecular Modelling approach to deal with transition metal complexes which can be used to model biological macromolecules.:  < HQ_?3?"6?@`NNN?N]'z [Molecular Modelling 2$:  ? B ?"6@ NNN?Nmi A B ?"6@ NNN?Nmi = <Z_ ?"6@ NNN?N"'.4 VMolecular Modelling (MM) of Force-Field (FF) methods of finding molecular structures determine the relationship between the energy and structure by application of empirical rules based on classical mechanics. To find an optimal structure in MM, we optimise the total strain energy: D B <lf_ ?"6@ NNN?N'\4& \where the terms correspond to the deviation from the optimal bond lengths, bond angles, torsions, non-bonded interactions and electrostatic interactions from those given by the a particular forcefield. Modelling transition metals using conventional MM has always been difficult as they can have variable oxidation states, spin states and electronic effects, and can coordinate from 4 to 12 different ligands in a complex. Rob Deeth has addressed this problem by developing this Ligand Field Molecular Mechanics model of dealing with transition metal centres using an approach called Ligand Field Theory.]]:  D B ?"6@ NNN?NF$miF$j C S A ??"? &  T <u_ ?"6@ NNN?N}('am7 ' In a free transition metal ion, the preference of the d-electrons is to occupy each of the five d-orbitals, and when there are more than five d electrons, spin-pairing occurs. In an octahedrally-coordinated complex, the dxy, dyz and dxz orbitals become lower in energy than the dx2-y2 and dz2 orbitals and are filled first. Ligand Field Theory states that this is because the former orbitals repel the ligand electron densities less than the latter (the d-orbitals are mostly antibonding and repel ligand electron clouds). Depending on the ligands (the so-called ligand field strength), the d-electrons may desert the dx2-y2 and dz2 orbitals completely as the electron pairing becomes energetically more favourable than the electron repulsion of ligand bonding orbitals.    ,  M  >: V W C .Adorbitals2%m4+ \ < ?"6@ NNN?N.4 _ < ?"6@ NNN?N.4 b < ?"6@ NNN?N.4  < ?"6@ NNN?N.4  < ?"6@ NNN?N.4  < ?"6@ NNN?N.4F 2)p*2 3   +`)2v4N  S A 2)p*2-N  S fA 2)_-2n0  TA ?"6@ NNN?N2)L02 3 F `B*23   +K34  Hl_=J?"6@`NNN?N{(*023 @: Wt  B _?"6@`NNN?N`*0{(3 :(2) High Ligand Field strength (e.g. CN-, phenantroline) J;(&.&+ : Wt  H_=J?"6@`NNN?N{(6-2*0 @: Wt  B _?"6@`NNN?N`6-{(*0 7(1) Low Ligand Field strength (e.g. Cl-, I-, F-, H2O) 8'&.&.&.&.&: Wt  H`_=J?"6@`NNN?N{(B*26- @,: WtA  BL_?"6@`NNN?N`B*{(6- Free Fe2+ ion (high spin)> : WtB  Bo ?"0@NNN?N`B*2B*B  <1 ?"0@NNN?N`6-26-B  <1 ?"0@NNN?N`*02*0B  Bo ?"0@NNN?N`323B  Bo ?"0@NNN?N`B*`3B  <1 ?"0@NNN?N{(B*{(3B  Bo ?"0@NNN?N2B*23/F $   u> ?i   _$  + High Spin: h   _4 *Low Spin: j  S A   ??"??%yB  _  H0_ ?"6@ NNN?NFB'L%G yDeeth has implemented LFMM into the Molecular Operating Environment (MOE), a popular MM dynamics program, to form DommiMOE, which uses the forcefield MMFF94 for non-transition metals. DommiMOE can optimise the geometry a complex for a given spin state, and so can give hypothetical structures of transition metal complexes for both spin states with the same set of parameters.zz  Hl` ?"6@ NNN?NP 4>_  2This is an octahedral high-spin complex where the Fe  N bond lengths were 2.20  (from X-ray crystallographic data). To obtain data on a hypothetical low-spin structure, QM techniques were used, which predict that the Fe  N bond lengths to be around 2.00 . Also, an estimate of 11 kcal/mol was set on the energetic favourability of the high spin state to the low spin state. As with all MM-based methods, some model parameters have to be found which fit the required geometries and energies. Parameters modified included the Morse function parameters (Fe N bond length potential was modelled by a Morse function), octahedral-field splitting term, the ligand-ligand repulsion term and some electron-pairing energy terms. To measure the  fit of the parameters, a cost function was constructed such that the smaller its value, the better the parameters fit the data.ff0P  dt  c >A m Fe_hexammine"` 0_g%  H_?3?"6?@`NNN?Nz4 K oSimulated Annealing2 2 $ '$: F  BT` ?"6@ NNN?N7D\4N? The difference between low spin and high spin states is the metal-ligand bond lengths of low spin states are much smaller than those of high spin. For example, the Fe  N bond length in low spin and high spin amine complexes are about 2.00 and 2.20 respectively. This is because of the smaller repulsion of the ligands from the d-electron cloud at low spin than at high spin. Deeth summarises this effect by the Ligand Field Stabilisation Energy (LFSE), and incorporated into the MM framework by adding to the MM equation:." : v  B!` ?"6@ NNN?N4p287 r(1) is known as the high-spin state of Fe2+ as the total spin is greater than in (2), known as the low spin state.*s) H: j   S A  _??"?17` > _(  H_ ?"6@ NNN?N4gs rSimulated Annealing (SA) is a method of finding the maximum or minimum of a distribution (x) by using Markov Chain Monte Carlo (MCMC) to sample the parameter space, in this case the distribution needed to be minimised is the cost function A Markov chain (a  random walk ) is constructed whose limiting distribution is (x) - the target distribution. d`[""""""",Y  B ?"6@ NNN?N+$mi+$  H|0` ?"6@ NNN?N%4dg* `BIn simulated annealing, the target distribution (x) is changed to (x)1/T (T is known as the  temperature ), which has the same maxima and minima as (x) but is rather  ste  N E5%  N F   5%    !"?N@eper as T decreases from 1 to 0, and this makes the Markov chain less likely to escape local minima. If the temperature is carefully reduced, then (hopefully) at the end of the procedure the Markov chain will reside near the global minimum. 2"""""**""K""""",0c   s *L`3"`*47K1, kAmine Complexes2 2$ '$:   HN` ?"6@ NNN?N5,4\2 66The simulated annealing procedure yielded some good parameters for the iron hexaammine complex, which were applied to three other amine complexes. From the bond lengths in their X-ray crystallographic structures, (1) and (2) were low spin complexes, while (3) was a high spin complex, which illustrates the sensitivity of the spin state of Fe2+ with nitrogen ligands. The parameters found for [Fe(NH3)6]2+ were found to reproduce the geometry of the complexes very well in their native spin states, and also the spin states of the complexes were correctly predicted.7""  S"*7"*"*"*"L   s *T+`3"`247KW4 kImine Complexes2 2$ '$: y  H i` ?"6@ NNN?N\44g; Can these parameters transfer to imine complexes? Unlike amine nitrogens, imine nitrogens are aromatic, and most Fe2+ imine complexes are low-spin. It was found that after some modification of the parameters, although the bond lengths were not very accurately reproduced, DommiMOE correctly predicted the spin state for most of the complexes (but not all). The most striking result was the predicted spin states of the low spin complex [Fe(1-10-phenantroline)3]2+ and the high spin [Fe(2-methyl-1-10-phenantroline)3]2+. Although the ligands in these complexes were very similar, DommiMOE correctly deduced their spin states, which correspond to a large change in geometry.i= t"*"f"*"*3"*"*",@  L  6?"6@ NNN?Nt!.:t!B  <?"0@NNN?N@DP@B  <?"0@NNN?NGDPGB  6?"0@NNN?N@DDGB  <?"0@NNN?N@PPGF dY<hE F  ;dYhD^   B(}`?"6@ NNN?Nk`@DhE $[Fe(2-methyl-1-10-phenantroline)3]2+f% ememAe   B`?"6@ NNN?NdY@Dk`E e(1-10-phenantroline)3]2+v%ememA   B`?"6@ NNN?NdY< h@D >: Wtt   D# "A .?BUHKAQY<`7Dt   DF5 "A 5?CEPZOM`<|g7D  s *`3"`<47Kq> T Applications 2 $: n  s 8AG (\?Image1"`r;:NjWoC 3 Ht` ?"6@ NNN?Nu>4YD B(The next step is to model Iron(II) porphyrins, which are planar complexes with the Fe2+ surrounded by four aromatic nitrogens (chemically similar to imine nitrogens). The most important example of an Iron(II) porphyrin is the O2 -binding site for haemoglobin, heme. Fe2+ in heme changes from high spin to low spin when it binds to an oxygen molecule, which changes the shape of the whole molecule. This change is important in the uptake and transport of oxygen. It would be very interesting to find out if DommiMOE can model this %U    "b G  $F: |~ 3   < 3  c"$) \g3N =  S X99?3  J >  # "`3  b ?  c 2A , .DETTOL3 b @  c 2A, .PAZXAP  b A  c 2AO f&PURYIK3  B  3 H`"` -  P1.$ :  C  3 <`"`m D-  P2.$ :  D  3 `"`  - P3.$ : N8 4E7YaH N E47YaH 9  N?"6@`NNN?N4E7YaH 7  N `?"6@`NNN?N81EQG The author would like to thank the MOAC Doctoral Centre staff and colleagues for their guidance and the Engineering and Physical Sciences Research Council Life Sciences Interface Programme for their generous support.:  5  HA moacc"`l51El8OH J  X3AdDownloads_Images_Logos_Version1Colour_EPSRC1RGBHI"`=Q^EX7Hj L C BA*the_warwick_uni_bluex 28 4SAv&  p4B%@ 7$D% m 4SAv&z   < A?sa"`7$D%B    `D??"0@NNN?Nr;sW? B  B  `D??"0@NNN?N; W? !B   `D??"0@NNN?N;@ !B  B  `D??"0@NNN?N9@V B    `D??"0@NNN?N:V <f!B ! 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" # $ % & ' ( ) * + , - . / 0 1 2 3 4 5 6 7 8 9 : ; < = > ? @ A B C D E F G H I J K L M N O P Q R S T U V W X Y Z [ \ ] ^ _ ` a b c d e f g h i j k l m n o p q r s t u v w x z { | } ~  y +2$ ?MJ0-cQR$xdj?8pW~.2$(-rf/AZ6>$+Ʊ败 R$?UfsZ87[-3 b$Pf;)rDc5@;  0e0e     A@  A5% 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||s " 0e@  ABC DEFFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab@=ʚ;d,;ʚ;g4-d-dv 0pLp$p4<4dd` 0,hd <4!d!d 0,<4BdBd 0,80___PPT10 pp?  %  0L (  R  C *APicture1] hH 4 TA" MOE_Screenshot"`H>%4EH  B ?"6@ NNN?Ni$0CW, $ s *3"` 'zL  PAbstract 2 $:  & H?3?"6?@`NNN?N&'z( dA bit of Ligand Field Theory 2$:  ' H(?3?"6?@`NNN?N 47K  Iron(II) Hexammine [Fe(NH3)6]2+ 2'$/$'$/$'$/$$ : 'F Tbi  1 _ S  0H3"`Tby qFinding optimal parameters for spin-state changes in Iron(II) amine complexes in Ligand Field Molecular Mechanics r(2rP56:    6Zb  Prakash Patel1 , Rob Deeth2X(2 6 6 6 66: c + 64-M bi  1MOAC Doctoral Training Centre, and the 2Inorganic Computational Chemistry Group, Department of Chemistry, ý.J(2 ' Y:  8 041P 4 The geometries and energies of six-coordinated amine complexes of Fe2+ at both spin states were explored using the DommiMOE program. Then the model parameters were refined using simulated annealing to give the correct geometries and predict the correct spin state of the metal, initially with [Fe(NH3)6]2+, then with three other amine complexes. The parameters found were applied to about 80 imine complexes, and after a slight modification, approximated the geometries reasonably well and most of the time predicted the correct spin state.xD    : B . # A"`'T   9 HH?3?"6?@`NNN?N'z T Introduction 2 $:  : <4J ?"6@`NNN?Ng'.4 The importance of metalloproteins in biochemistry has long been recognised. Metal centres are instrumental in many catalytic and binding functions. Computer modelling can help probe their properties but few methods exist that model transition metal-containing proteins effectively, either using quantum or classical mechanical methods. Here is outlined a very promising new molecular modelling approach to deal with transition metal complexes which can be used to model biological macromolecules. 6 #j  h: 3 < HN?3?"6?@`NNN?N]'z }Molecular Mechanics 2$ :  ? B ?"6@ NNN?Nmi A B ?"6@ NNN?Nmio = <g ?"6@ NNN?N"'.4 Molecular Mechanics (MM), or Force-Field (FF) methods, of finding molecular structures determine the relationship between the energy and structure by application of empirical rules based on classical mechanics. To find an optimal structure in MM, we optimise the total potential energyb  :  B <: V W C .Adorbitals2%m4+ \ < ?"6@ NNN?N.4 _ < ?"6@ NNN?N.4 b < ?"6@ NNN?N.4  < ?"6@ NNN?N.4  < ?"6@ NNN?N.4  < ?"6@ NNN?N.4F 2)p*2 3   +`)2v4N  S A 2)p*2-N  S fA 2)_-2n0  TA ?"6@ NNN?N2)L02 3 F `B*23   +K34  H=J?"6@`NNN?N{(*023 R : Wt  BH}?"6@`NNN?N`*0{(3 :(2) High Ligand Field strength (e.g. CN-, phenantroline) J;(&.&+ : Wt  H=J?"6@`NNN?N{(6-2*0 R : Wt  B?"6@`NNN?N`6-{(*0 7(1) Low Ligand Field strength (e.g. Cl-, I-, F-, H2O) 8'&.&.&.&.&: Wt  H=J?"6@`NNN?N{(B*26- R, : WtA  B?"6@`NNN?N`B*{(6- Free Fe2+ ion (high spin)> : WtB  Bo ?"0@NNN?N`B*2B*B  <1 ?"0@NNN?N`6-26-B  <1 ?"0@NNN?N`*02*0B  Bo ?"0@NNN?N`323B  Bo ?"0@NNN?N`B*`3B  <1 ?"0@NNN?N{(B*{(3B  Bo ?"0@NNN?N2B*23/F $   u> ?i   T$  + High Spin: h   4 *Low Spin: \  S A   ???%yB    H ?"6@ NNN?NFB'L%G rDeeth has implemented LFMM into the Molecular Operating Environment (MOE), a popular modelling program, to form DommiMOE, which uses the MMFF94 FF for non-transition metals. DommiMOE can optimise the geometry of a complex for a given spin state, and so can give hypothetical structures of transition metal complexes for both spin states with the same set of parameters.ssPU ' <   H( ?"6@ NNN?NP 4>_  jThis is an octahedral high-spin complex where the Fe  N bond lengths are 2.20  (from X-ray crystallographic data). To obtain data on a hypothetical low-spin structure, QM techniques were used, which predict that the Fe  N bond lengths are around 2.00 . Also, an estimate of 11 kcal/mol was set on the energetic favourability of the high spin state over the low spin state. As with all MM-based methods, some model parameters have to be found which fit the required geometries and energies. Parameters modified included the Morse function parameters (Fe N bond length potential was modelled by a Morse function), octahedral-field splitting term, the ligand-ligand repulsion term and some electron-pairing energy terms. To measure the  fit of the parameters, a cost function was constructed such that the smaller its value, the better the parameters fit the data.eejF   bt  c >A m Fe_hexammine"` 0_g%  H?3?"6?@`NNN?Nz4 K oSimulated Annealing2 2 $ '$: Z  B ?"6@ NNN?N7D\4N? The difference between low spin and high spin states is the metal-ligand bond lengths of low spin states are much smaller than those of high spin. For example, the Fe  N bond length in low spin and high spin amine complexes are about 2.00 and 2.20 respectively. This is because of the smaller repulsion of the ligands from the d-electron cloud at low spin than at high spin. Deeth summarised this effect by the Ligand Field Stabilisation Energy (LFSE), and incorporated into the MM framework by adding to the MM equation:."0  : v  Bd ?"6@ NNN?N4p287 r(1) is known as the high-spin state of Fe2+ as the total spin is greater than in (2), known as the low spin state.*s) H: \   S A  _??17` > _<  H ?"6@ NNN?N4gs Simulated Annealing (SA) is a method of finding the maximum or minimum of a distribution (x) by using Markov Chain Monte Carlo (MCMC) to sample the parameter space, in this case the distribution needed to be minimised is the cost function. A Markov chain (a  random walk ) is constructed whose limiting distribution is (x) - the target distribution. da[""""""">Y P  B ?"6@ NNN?N+$mi+$  H ?"6@ NNN?N%4dg* `BIn simulated annealing, the target distribution (x) is changed to (x)1/T (T is known as the  temperature ), which has the same maxima and minima as (x) but is rather  steeper as T decreases from 1 to 0, and this makes the Markov chain less likely to escape local minima. If the temperature is carefully reduced, then (hopefully) at the end of the procedure the Markov chain will reside near the global minimum. 2"""""**""K""""",0c   s *l53"`*47K1, kAmine Complexes2 2$ '$:   H8 ?"6@ NNN?N5,4\2 66The simulated annealing procedure yielded some good parameters for the iron hexaammine complex, which were applied to three other amine complexes. From the bond lengths in their X-ray crystallographic structures, (1) and (2) were low spin complexes, while (3) was a high spin complex, which illustrates the sensitivity of the spin state of Fe2+ with nitrogen ligands. The parameters found for [Fe(NH3)6]2+ were found to reproduce the geometry of the complexes very well in their native spin states, and also the spin states of the complexes were correctly predicted.7""  S"*7"*"*"*"L   s *O3"`247KW4 kImine Complexes2 2$ '$:   HP ?"6@ NNN?N\44g; 8Can these parameters transfer to imine complexes? Unlike amine nitrogens, imine nitrogens are unsaturated, and most Fe2+ imine complexes are low-spin. After further refinement of the parameters to account for p bonding, DommiMOE correctly predicted the spin state for most of the complexes, although the geometries require more analysis. The most striking result was the predicted spin states of the low spin complex [Fe(1-10-phenantroline)3]2+ and the high spin [Fe(2-methyl-1-10-phenantroline)3]2+. Although the ligands in these complexes were very similar, DommiMOE correctly deduced their spin states, which correspond to a large change in geometry.V= w"*Z"c"f"*"*3"*"*"@   .k!@  6?"6@ NNN?Nt!.:t!B  <?"0@NNN?N@DP@B  <?"0@NNN?NGDPGB  6?"0@N      @ABC DEEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN E5%NN?N@DDGB  <?"0@NNN?N@PPG)F dY<hE F  ;dYhD^   Bc?"6@ NNN?Nk`@DhE $[Fe(2-methyl-1-10-phenantroline)3]2+f% ememAe   Bj?"6@ NNN?NdY@Dk`E e(1-10-phenantroline)3]2+v%ememA   BXp?"6@ NNN?NdY< h@D P : Wtt   D# "A .?BUHKAQY<`7Dt   DF5 "A 5?CEPZOM`<|g7D  s *Dx3"`<47Kq> T Applications 2 $: n  s 8AG (\?Image1"`r;:NjWoC 3 H ?"6@ NNN?Nu>4YD RThe next step is to model iron porphyrins. The porphyrin is a symmetric planar ligand which binds the metal via four aromatic nitrogens (chemically similar to imine nitrogens). An important example of an iron porphyrin is the O2 -binding site for haemoglobin. Fe2+ in heme changes from high spin to low spin when it binds to an oxygen molecule, which changes the shape of the whole molecule. This change is important in the uptake and transport of oxygen. It would be very interesting to find out if DommiMOE can model this %Z " "(  '  : |~ 3   < 3  c"$) \g3N =  S X99?3  J >  # "`3  b ?  c 2A , .DETTOL3 b @  c 2A, .PAZXAP  b A  c 2AO f&PURYIK3  B  3 "` -  P1.$ :  C  3 "`m D-  P2.$ :  D  3 "`  - P3.$ : F 4EfaH   E4faH 9  N?"6@`NNN?N4EfaH% 7  Nd?"6@`NNN?N>:1EK\G aThe author would like to thank Rob Deeth and the MOAC Doctoral Centre staff and colleagues for their help and guidance and the Engineering and Physical Sciences Research Council Life Sciences Interface Programme for their generous support.,5z:  5  HA moacc"`51E9OH J  X3AdDownloads_Images_Logos_Version1Colour_EPSRC1RGBHI"`]`Ed9Hj L C BA*the_warwick_uni_bluex 28 4SAv&  p4B%@ 7$D% m 4SAv&z   < A?sa"`7$D%B    `D??"0@NNN?Nr;sW? B  B  `D??"0@NNN?N; W? !B   `D??"0@NNN?N;@ !B  B  `D??"0@NNN?N9@V B    `D??"0@NNN?N:V <f!B ! B  `D??"0@NNN?N;xAB "   `D??"0@NNN?N;h@ !B #   `D??"0@NNN?N?!:@!B $  `D??"0@NNN?N?8! @!B %   `D??"0@NNN?N? !:@f!B &  `D??"0@NNN?NW?FxAB '   `D??"0@NNN?NxAF-BB ( B  `D??"0@NNN?NABB )   `D??"0@NNN?NAB) B * B  `D??"0@NNN?N?) -B B +  `D??"0@NNN?N>? B ,   `D??"0@NNN?N;f!T<I"B -  `D??"0@NNN?N;"T<I"B .  `D??"0@NNN?N; !<"B /  `D??"0@NNN?N; <9!B 0 B  `D??"0@NNN?N4: ; B h B TD?"0@NNN?N? !h@!B i TD?"0@NNN?NX?;@f!B j TD?"0@NNN?Nr;s=B l TD?"0@NNN?N = !="8 QGqT% p C^E~Rf% 7  B A sa"`QGqT% o  B ?"6@ NNN?NuL!LI" 8 Vp d%  CDWddf% R  D A sa2"`Vp d%B r TD?"0@NNN?N[!g\!B s TD?"0@NNN?N[f!g\!B t B TD?"0@NNN?N[f!g\"B u  TD?"0@NNN?N["g\I"B v TD?"0@NNN?N[9!g\I"B w TD?"0@NNN?N[ !\9!B x B TD?"0@NNN?N[ !\!B y  TD?"0@NNN?N[!]!B {  TD?"0@NNN?N]!w]!B | B TD?"0@NNN?N]!w]!B }  TD?"0@NNN?N]!w]!B ~ TD?"0@NNN?Ng\!w]!B  B TD?"0@NNN?N[!g\v"B   TD?"0@NNN?N[v"["B   TD?"0@NNN?N["g\"B  B TD?"0@NNN?N["g\"B  TD?"0@NNN?N["g\"  H ?"6@ NNN?NAF# 6Markov chain explores distribution of interest, with a preference of  downhill steps if the global minimum is to be found. } 2}: 0  H ?"6@ NNN?N{R3V! z<The smallest value encountered by the Markov chain is noted.= 2=: *8 R"W$  !{RqW$   N ?"6@ NNN?NR"W$   T ?"6@ NNN?NR"W$ TReduce T" : B  H ?"6@ NNN?Neh# NStart at current minimum. Markov chain is more confined to an area of interestO 2O: j  C 4Aprakash_patel"`ag   Z2<܍ ?"` 33___PPT10i.M2_<+D=' = @B +rE  !  !  A(miI3I   eEquation Equation.30,Microsoft Equation 3.0  Equation Equation.30,Microsoft Equation 3.0_ * |                           ! ( ) + , - . / 0 1 2 3 4 5 6 7 8 9 : ; < = > ? @ A B C D E F G H I J K L M N O P Q R S T U V W X Y Z [ \ ] ^ _ ` a b c d e f g h i j k l m n o p q r s t u v w x y z { } ~   '    N E5%  N F   5%    !"?N@ABC DEFFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab@=ʚ;d,;ʚ;g4-d-d :A 0p$p4<4ddL$ 0ԧ? <4!d!dL # 0<4BdBdL # 080___PPT10 pp?  %r9 m  (miI3I   eEquation Equation.30,Microsof¼trKmoyܼݼܼ¼ܼݼ¼ݻݼݼt Equation 3.0  Equation Equation.30,Microsoft Equation 3.0_ $Photo Editor Photo MSPhotoEd.30@Microsoft Photo Editor 3.0 Photo/ 00DArialew ?0:A 0DNew Century Schoolbook:A 0 DTimes New Romanolbook:A 00DSymbolew Romanolbook:A 0  B.:   @n?" dd@  @@`` : 2 (oR$yX8p2uc-"$$tz:}ix@tGD+c-2$Z C^6.w5R$kL$>Jڳݱ7"$PZ6(<7 aGb$y)|{6b^JR$|L24'E]&+2$ ?MJ0-cQR$xdj?8pW~.2$(-rf/AZ6>$+Ʊ败 R$?UfsZ87[-3 b$Pf;)rDc5@;  0e0e     A@  A5% 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||s " 0e@        @ABC DEEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN E5%  N E5%  N F   5%    !"?N@ABC DEFFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab@=ʚ;d,;ʚ;g4-d-d :A 0 p$p4<4ddL$ 0ԧ? <4!d!dL # 0<4BdBdL # 080___PPT10 pp?  %{  0L (  R  C *APicture1] hH 4 TA" MOE_Screenshot"`H>%4EH  B ?"6@ NNN?Ni$0CW, $ s *P?3"` 'zL  PAbstract 2 $:  & HlR??3?"6?@`NNN?N&'z( dA bit of Ligand Field Theory 2$:  ' H|[??3?"6?@`NNN?N 47K  Iron(II) Hexammine [Fe(NH3)6]2+ 2'$/$'$/$'$/$$ : 'F Tbi  1 _ S  0r?3"`Tby qFinding optimal parameters for spin-state changes in Iron(II) amine complexes in Ligand Field Molecular Mechanics r(2rP56:    6s?Zb  Prakash Patel1 , Rob Deeth2X(2 6 6 6 66: c + 6?M bi  1MOAC Doctoral Training Centre, and the 2Inorganic Computational Chemistry Group, Department of Chemistry, ý.J(2 ' Y:  8 0$?P 4 The geometries and energies of six-coordinated amine complexes of Fe2+ at both spin states were explored using the DommiMOE program. Then the model parameters were refined using simulated annealing to give the correct geometries and predict the correct spin state of the metal, initially with [Fe(NH3)6]2+, then with three other amine complexes. The parameters found were applied to about 80 imine complexes, and after a slight modification, approximated the geometries reasonably well and most of the time predicted the correct spin state.xD    : B . # A"`'T   9 Hy??3?"6?@`NNN?N'z T Introduction 2 $:  : <Hq  ?"6@`NNN?Ng'.4 PThe importance of metalloproteins in biochemistry has long been recognised. Metal centres are instrumental in many catalytic and binding functions. Computer modelling can help probe their properties but few methods exist that model transition metal-containing proteins effectively, either using quantum or classical mechanical methods. Here is outlined a very promising new molecular modelling approach to deal with transition metal complexes which can be used to model biological macromolecules.:  < H|i?3?"6?@`NNN?N]'z [Molecular Mechanics 2$:  ? B ?"6@ NNN?Nmi A B ?"6@ NNN?Nmi = <i ?"6@ NNN?N"'.4 [Molecular Mechanics (MM), or Force-Field (FF) methods, of finding molecular structures determine the relationship between the energy and structure by application of empirical rules based on classical mechanics. To find an optimal structure in MM, we optimise the total potential energy: D B <4i ?"6@ NNN?N'\4& \where the terms correspond to the deviation from the reference bond lengths, bond angles, torsions, non-bonded interactions and electrostatic interactions from those given by the a particular force field. Modelling transition metals using conventional MM has always been difficult as they can have variable oxidation states, spin states and electronic effects, and can coordinate from 4 to 12 different ligands in a complex. This has been addressed in ý by developing the Ligand Field Molecular Mechanics model of dealing with transition metal centres using an approach called Ligand Field Theory.]]:  D B ?"6@ NNN?NF$miF$\ C S A ?? &  T <: V W C .Adorbitals2%m4+ \ < ?"6@ NNN?N.4 _ < ?"6@ NNN?N.4 b < ?"6@ NNN?N.4  < ?"6@ NNN?N.4  < ?"6@ NNN?N.4  < ?"6@ NNN?N.4F 2)p*2 3   +`)2v4N  S A 2)p*2-N  S fA 2)_-2n0  TA ?"6@ NNN?N2)L02 3 F `B*23   +K34  H : WtB  Bo ?"0@NNN?N`B*2B*B  <1 ?"0@NNN?N`6-26-B  <1 ?"0@NNN?N`*02*0B  Bo ?"0@NNN?N`323B  Bo ?"0@NNN?N`B*`3B  <1 ?"0@NNN?N{(B*{(3B  Bo ?"0@NNN?N2B*23/F $   u> ?i   xI$  + High Spin: h   $I4 *Low Spin: \  S A   ???%yB  X  HrI ?"6@ NNN?NFB'L%G rDeeth has implemented LFMM into the Molecular Operating Environment (MOE), a popular modelling program, to form DommiMOE, which uses the MMFF94 FF for non-transition metals. DommiMOE can optimise the geometry of a complex for a given spin state, and so can give hypothetical structures of transition metal complexes for both spin states with the same set of parameters.ss  H? ?"6@ NNN?NP 4>_  0This is an octahedral high-spin complex where the Fe  N bond lengths are 2.20  (from X-ray crystallographic data). To obtain data on a hypothetical low-spin structure, QM techniques were used, which predict that the Fe  N bond lengths are around 2.00 . Also, an estimate of 11 kcal/mol was set on the energetic favourability of the high spin state over the low spin state. As with all MM-based methods, some model parameters have to be found which fit the required geometries and energies. Parameters modified included the Morse function parameters (Fe N bond length potential was modelled by a Morse function), octahedral-field splitting term, the ligand-ligand repulsion term and some electron-pairing energy terms. To measure the  fit of the parameters, a cost function was constructed such that the smaller its value, the better the parameters fit the data.ee0O  ft  c >A m Fe_hexammine"` 0_g%  HX?3?"6?@`NNN?Nz4 K oSimulated Annealing2 2 $ '$: F  BT ?"6@ NNN?N7D\4N? The difference between low spin and high spin states is the metal-ligand bond lengths of low spin states are much smaller than those of high spin. For example, the Fe  N bond length in low spin and high spin amine complexes are about 2.00 and 2.20 respectively. This is because of the smaller repulsion of the ligands from the d-electron cloud at low spin than at high spin. Deeth summarised this effect by the Ligand Field Stabilisation Energy (LFSE), and incorporated into the MM framework by adding to the MM equation:." : v  B ?"6@ NNN?N4p287 r(1) is known as the high-spin state of Fe2+ as the total spin is greater than in (2), known as the low spin state.*s) H: \   S A  _??17` > _*  HF ?"6@ NNN?N4gs tSimulated Annealing (SA) is a method of finding the maximum or minimum of a distribution (x) by using Markov Chain Monte Carlo (MCMC) to sample the parameter space, in this case the distribution needed to be minimised is the cost function. A Markov chain (a  random walk ) is constructed whose limiting distribution is (x) - the target distribution. da[""""""",Y  B ?"6@ NNN?N+$mi+$  H F ?"6@ NNN?N%4dg* `BIn simulated annealing, the target distribution (x) is changed to (x)1/T (T is known as the  temperature ), which has the same maxima and minima as (x) but is rather  steeper as T decreases from 1 to 0, and this makes the Markov chain less likely to escape local minima. If the temperature is carefully reduced, then (hopefully) at the end of the procedure the Markov chain will reside near the global minimum. 2"""""**""K""""",0c   s * F3"`*47K1, kAmine Complexes2 2$ '$:   H$+F ?"6@ NNN?N5,4\2 66The simulated annealing procedure yielded some good parameters for the iron hexaammine complex, which were applied to three other amine complexes. From the bond lengths in their X-ray crystallographic structures, (1) and (2) were low spin complexes, while (3) was a high spin complex, which illustrates the sensitivity of the spin state of Fe2+ with nitrogen ligands. The parameters found for [Fe(NH3)6]2+ were found to reproduce the geometry of the complexes very well in their native spin states, and also the spin states of the complexes were correctly predicted.7""  S"*7"*"*"*"L   s *CF3"`247KW4 kImine Complexes2 2$ '$:   H@    6?"6@ NNN?Nt!.:t!B  <?"0@NNN?N@DP@B  <?"0@NNN?NGDPGB  6?"0@NNN?N@DDGB  <?"0@NNN?N@PPGF dY<hE F  ;dYhD^   B@^F?"6@ NNN?Nk`@DhE $[Fe(2-methyl-1-10-phenantroline)3]2+f% ememAe   BeF?"6@ NNN?NdY@Dk`E e(1-10-phenantroline)3]2+v%ememA   B(tF?"6@ NNN?NdY< h@D >: Wtt   D# "A .?BUHKAQY<`7Dt   DF5 "A 5?CEPZOM`<|g7D  s *(~F3"`<47Kq> T Applications 2 $: n  s 8AG (\?Image1"`r;:NjWoC 3 HF ?"6@ NNN?Nu>4YD The next step is to model iron porphyrins. The porphyrin is a symmetric planar ligand which binds the metal via four aromatic nitrogens (chemically similar to imine nitrogens). An important example of an iron porphyrin is the O2 -binding site for haemoglobin. Fe2+ in heme changes from high spin to low spin when it binds to an oxygen molecule, which changes the shape of the whole molecule. This change is important in the uptake and transport of oxygen. It would be very interesting to find out if DommiMOE can model this %Z " "P  F  a: |~ 3   < 3  c"$) \g3N =  S X99?3  J >  # "`3  b ?  c 2A , .DETTOL3 b @  c 2A, .PAZXAP  b A  c 2AO f&PURYIK3  B  3 $F"` -  P1.$ :  C  3  F"`m D-  P2.$ :  D  3 F"`  - P3.$ : F 4EfaH   E4faH 9  N?"6@`NNN?N4EfaH 7  NF?"6@`NNN?N;1E$]G OThe author would like to thank Rob Deeth and the MOAC Doctoral Centre staff and colleagues for their help and guidance and the Engineering and Physical Sciences Research Council Life Sciences Interface Programme for their generous support.#:  5  HA moacc"`61E9OH J  X3AdDownloads_Images_Logos_Version1Colour_EPSRC1RGBHI"`]^Ee7Hj L C BA*the_warwick_uni_bluex 28 4SAv&  p4B%@ 7$D% m 4SAv&z   < A?sa"`7$D%B    `D??"0@NNN?Nr;sW? B  B  `D??"0@NNN?N; W? !B   `D??"0@NNN?N;@ !B  B  `D??"0@NNN?N9@V B    `D??"0@NNN?N:V <f!B ! B  `D??"0@NNN?N;xAB "   `D??"0@NNN?N;h@ !B #   `D??"0@NNN?N?!:@!B $  `D??"0@NNN?N?8! @!B %   `D??"0@NNN?N? !:@f!B &  `D??"0@NNN?NW?FxAB '   `D??"0@NNN?NxAF-BB ( B  `D??"0@NNN?NABB )   `D??"0@NNN?NAB) B * B  `D??"0@NNN?N?) -B B +  `D??"0@NNN?N>? B ,   `D??"0@NNN?N;f!T<I"B -  `D??"0@NNN?N;"T<I"B .  `D??"0@NNN?N; !<"B /  `D??"0@NNN?N; <9!B 0 B  `D??"0@NNN?N4: ; B h B TD?"0@NNN?N? !h@!B i TD?"0@NNN?NX?;@f!B j TD?"0@NNN?Nr;s=B l TD?"0@NNN?N = !="8 QGqT% p C^E~Rf% 7  B A sa"`QGqT% o  B ?"6@ NNN?NuL!LI" 8 Vp d%  CDWddf% R  D A sa2"`Vp d%B r TD?"0@NNN?N[!g\!B s TD?"0@NNN?N[f!g\!B t B TD?"0@NNN?N[f!g\"B u  TD?"0@NNN?N["g\I"B v TD?"0@NNN?N[9!g\I"B w TDesign TemplateEmbedded OLE Servers Slide Titles Titles_ㅠ uowuowpaahRobsonD?"0@NNN?N[ !\9!B x B TD?"0@NNN?N[ !\!B y  TD?"0@NNN?N[!]!B {  TD?"0@NNN?N]!w]!B | B TD?"0@NNN?N]!w]!B }  TD?"0@NNN?N]!w]!B ~ TD?"0@NNN?Ng\!w]!B  B TD?"0@NNN?N[!g\v"B   TD?"0@NNN?N[v"["B   TD?"0@NNN?N["g\"B  B TD?"0@NNN?N["g\"B  TD?"0@NNN?N["g\"  HxF ?"6@ NNN?NAF# 6Markov chain explores distribution of interest, with a preference of  downhill steps if the global minimum is to be found. } 2}: 0  HF ?"6@ NNN?N{R3V! z<The smallest value encountered by the Markov chain is noted.= 2=: *8 R"W$  !{RqW$   N ?"6@ NNN?NR"W$   ThF ?"6@ NNN?NR"W$ TReduce T" : B  HF ?"6@ NNN?Neh# NStart at current minimum. Markov chain is more confined to an area of interestO 2O: j  C 4Aprakash_patel"`ag   Z2<܍ ?"` 33___PPT10i.M2_<+D=' = @B +r0  m v  (miI3I   eEquation Equation.30,Microsoft Equation 3.0  Equation Equation.30,Microsoft Equation 3.0_ $Photo Editor Photo MSPhotoEd.30@Microsoft Photo Editor 3.0 Photo/ 00DArialew ?0:A 0DNew Century Schoolbook:A 0 DTimes New Romanolbook:A 00DSymbolew Romanolbook:A 0  B.:   @n?" dd@  @@`` : 2 (oR$yX8p2uc-"$$tz:}ix@tGD+c-2$Z C^6.w5R$kL$>Jڳݱ7"$PZ6(<7 aGb$y)|{6b^JR$|L24'E]&+2$ ?MJ0-cQR$xdj?8pW~.2$(-rf/AZ6>$+Ʊ败 R$?UfsZ87[-3 b$Pf;)rDc5@;  0e0e     A@  A5% 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||s " 0e@        @ABC DEEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN E5%  N E5%  N F   5%    !"?N@ABC DEFFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab@=ʚ;d,;ʚ;g4-d-d :A 0 p$p4<4ddL$ 0ԧ? <4!d!dL # 0<4BdBdL # 080___PPT10 pp?  %r m u