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Ligand Field Theory
2.35 Ligand Field Theory R. J. DEETH University of Warwick, Coventry, UK 2.35.1 2.35.2 2.35.3 2.35.4 2.35.5 2.35.6
THE NATURE OF LFT LIGAND FIELD PARAMETERS ‘‘d–d ’’ ELECTRONIC TRANSITION INTENSITIES APPLICATIONS AND REFINEMENTS LFT IN THE FUTURE REFERENCES
439 439 441 441 441 442
Ligand field theory (LFT) was already a relatively mature subject when Comprehensive Coordination Chemistry (CCC, 1987) was published and virtually all of Figgis’ original Chapter 6 remains valid in terms of the mathematical techniques and the interpretation of the spectral and magnetic properties of high-symmetry, cubic systems. In 2000, Figgis, in collaboration with Hitchman,1 published the long-awaited updated edition of his classic text on LFT which covers the intervening developments in theory and applications especially with regard to the angular overlap model (AOM), the topic of the next section. However, the issue of the physical significance and transferability of ligand field parameters remains a contentious issue which was debated, sometimes hotly, during the late 1980s to early 1990s. Figgis was fairly skeptical and states in CCC (1987) that the ‘‘physical significance to be attached to the meaning of ligand field parameters is . . .very limited.’’ In contrast, the ‘‘Gerloch school’’ attempted to make a direct connection between the ligand field parameter values and the nature of the metal–ligand bonding.2–11 The physical basis for interpreting the significance of ligand field parameters was developed by Woolley12 whose starting point was the density functional theorem. His analysis leads to different expressions for the AOM e and e parameters, previously introduced by Scha¨ffer and Jørgenson13 in the context of the Wolfsberg–Helmholtz approximation, and to different interpretations of phenomena such as d–s mixing,4 phase-coupled ligators,8 bent bonding,9,10 and parameter transferability.6,14 These issues are discussed further in Chapter 2.36.
2.35.1
THE NATURE OF LFT
LFT is an example of effective operator theory and can be employed to construct multiplet states arising from d n (or f n) configurations. Hence, it is strictly only applicable to systems where the ground state and the lower energy excited states are dominated by d-(or f-) orbital contributions. LFT is thus most relevant for relatively ionic Werner-type transition metal (TM) complexes. Within this approximation, the mathematics for evaluating the multiplets and their relative energies is straightforward and all the necessary equations were well-established by the start of the 1960s. In a sense, therefore, LFT is an ‘‘exact’’ model and Figgis’ Chapter 6 in CCC (1987) remains a definitive account of the mechanics of how to carry out actual LFT calculations of the ‘‘d–d’’ (or ‘‘f–f ’’) spectroscopic and magnetic properties of TM complexes. The major advancements since CCC (1987) are in developing methods and computer codes (see Chapter 2.52) for extracting ligand field parameter values and what these mean in terms of metal–ligand bonding. 439
440 2.35.2
Ligand Field Theory LIGAND FIELD PARAMETERS
LFT is a parametric approach in which the symmetry of the complex is treated explicitly but the bonding is handled implicitly through the ligand field parameters. These parameters describe the three contributions to the overall Hamiltonian, H: the ligand field, HLF, interelectronic repulsion, HER and spin orbit coupling, HLS. The relative importance of each of these terms depends on the element’s position in the periodic table. First and second transition series: HLF > HER HLS Third transition series: HLF HER HLS Lanthanoids: HER > HLS > HLF Actinoids: HER HLS HLF Within the normal central field approximation, HER and HLS are spherically symmetric. Interelectronic repulsion in a complex is thus treated using the same electrostatic theory as for atomic spectroscopy. It is parameterized either within the original Condon–Shortley F0, F2, F4, scheme or the later Racah A, B, C scheme. Since LFT only gives energy differences, values for F0 (and A) cannot be determined. There is a simple mapping between the Condon–Shortley and Racah schemes and they will give identical energies if used in full-basis calculations. However, Racah noted that in free atoms or ions, the energy difference between the terms of maximum spin multiplicity required only one parameter, B. Hence, the Racah scheme is more popular for analyzing ‘‘d–d ’’ spectra since B is sufficient for calculating the spin-allowed transitions of a high-spin complex. Spin–orbit coupling is also based on atomic theory and requires only the one-electron spin–orbit coupling constant, . In addition, the calculation of magnetic moments includes Steven’s orbital reduction parameter, k. Figgis gives a comprehensive account in CCC (1987) of calculating magnetic properties and includes additional terms such as the Trees correction. The ligand field potential, VLF, defines the energies of the d-(or f-) orbitals and is the only part of a conventional LFT calculation which includes the symmetry of the complex. Hence, HLF is the only part of the Hamiltonian which can make general direct contact with ML bonding. HER and HLS may still be relevant but only in terms of the overall, averaged nature of the metal–ligand interaction. There are two important points to emphasize with regard to VLF. First, contributions to VLF are not computed from first principles. Instead, the potential is constructed parametrically and the parameter values are determined by fitting calculated properties to experiment. Secondly, there are two distinct ways in which VLF can be constructed–globally or via ligand superposition. The global approach is exemplified by the original crystal field theory (CFT). VLF is described as a linear combination of spherical harmonics which progressively lowers the symmetry from spherical to cubic and on to still lower symmetries. For high symmetries such as octahedral and tetrahedral (i.e., cubic), the global scheme is simple and elegant. The d-orbital splitting depends on a single parameter, . Since many complexes are (approximately) octahedral or tetrahedral, the global approach has been widely applied. However, as is well known, the eg–t2g splitting in octahedral symmetry is a competition between -and -bonding effects which the single global parameter cannot separate. Furthermore, as the symmetry is lowered, the number of global parameters increases and since they include both symmetry (i.e., angular) and bonding (i.e., radial) contributions, the connection between parameter values and the nature of individual ML interactions is difficult and sometimes impossible to extract. In other instances, the global scheme does not describe the bonding correctly. For example, in tetragonal symmetry, the global scheme has three parameters, Dq, Ds, and Dt. For tetragonal macrocyclic tetraaza NiII complexes with an NiN4X2 core, there are also three AOM parameters, e(N), e(X), and e(X) (vide infra) and hence the two parameters sets can be directly mapped onto each other. Values for Dq, Ds and Dt were derived by analyzing the d–d spectra and assignments were made based on the ‘‘reasonableness’’ of the ligand field parameter values and their variations. However, when the values are converted to their corresponding AOM values, Cl is predicted to be a -acceptor. Equally acceptable assignments of the d–d transition energies can be obtained with more reasonable AOM parameter values.15 As alluded to above, the superposition method, typified by the AOM, overcomes many of the problems of the global scheme and is discussed in detail in Chapter 2.52. VLF is constructed as a superposition of contributions from individual ML bonds which explicitly separates the angular and radial parts. The former is implicit in the geometry so that the AOM energy parameters focus
Ligand Field Theory
441
exclusively on the radial part. Furthermore, the individual M–L perturbations can be factored into local and components as monitored by the AOM e and e energy parameters. In octahedral symmetry, the – competition arises naturally since the d-orbital splitting is given by 3e–4e. Furthermore, by assuming two or more ligands are chemically equivalent, the number of AOM parameters can be kept manageable even for complexes with no symmetry which would, in principle, require a maximum of 14 independent global variables. Hence, by CCC (1987), the general consensus was that the best way to parameterize VLF was via a superposition method like the AOM. Chapter 2.52 provides more details and describes applications of the AOM.
2.35.3
‘‘d–d ’’ ELECTRONIC TRANSITION INTENSITIES
Perhaps the most significant theoretical advance in LFT arose out of the Gerloch group during the late 1980s culminating in a comprehensive review published in 1997.16 It concerned one of the most basic properties of the electronic spectrum which hitherto had not been readily calculable; namely the transition intensities. In the spirit of the ligand superposition model, Gerloch and co-workers developed a parametric approach for calculating ‘‘d–d ’’ transition intensities. In essence, the relative intensities of the ‘‘d–d ’’ electric dipole transitions are expressed in terms of local t intensity parameters which parallel the e energy parameters. The intensity parameters are further qualified in terms of their P and F contributions. That is, since the basic parity selection rule is l ¼ 1, only p or f contributions (i.e., l ¼ 1 or 3) are relevant for ‘‘d–d ’’ transitions. The method has been applied both to noncentrosymmetric (static) and centrosymmetric (dynamic) species, the latter requiring the additional development of normal coordinate analysis methods for handling the vibronic intensity mechanism. The review describes the application of the CLF intensity model to 43 chromophores. The ability to reproduce the observed intensity distributions, including those from experiments using linearly and circularly polarized light, is impressive. For example, the band areas for both the unpolarized absorption and CD spectra of Co(-isospartein)Cl2 are virtually perfect while in centrosymmetric complexes such as [PtCl4]2, [PtBr4]2, and [PdCl4]2 the vibronic analysis can also establish the relative importance of the possible contributing ungerade vibrational modes to the overall intensity. In these cases, the eu mode accounts for more than half of the total. Despite all the effort, however, the CLF spectral intensities model has not been widely adopted even though the latest version of the CAMMAG program (Chapter 2.54) provides the means to carry out the calculations. In the absence of a ‘‘champion’’ and in the light of the continuing rapid development of alternative, more widely applicable methods based on molecular orbital schemes, it seems likely that the promising CLF approach will languish.
2.35.4
APPLICATIONS AND REFINEMENTS
Even a cursory examination of the literature reveals that ligand field concepts are still widely employed to interpret and rationalize diverse experimental data on varied transition metal systems and the present volume contains myriad examples. Chapter 2.36 focuses specifically on the applications of the superposition models. However, the basic methods for carrying out LFT calculations have not altered significantly. Chapter 2.52 has overviews of available software packages. There have been some refinements of certain ligand field concepts. For example, the familiar ‘‘double hump’’ behavior of the ligand field stabilization energy has been reanalyzed by Johnson and Nelson who demonstrate the need to include contributions from d–d interelectron repulsion along with the conventional d-orbital splitting components.17–20 Also, there have been some attempts to reconcile the predictions of LFT with the results emerging from DFT. This theme is taken up again in Chapter 2.35.
2.35.5
LFT IN THE FUTURE
There is little doubt that as a pedagogic tool for introducing coordination chemistry, symmetry, and spectroscopy, LFT will remain a valuable part of the undergraduate syllabus. As such, many of the basic concepts derived from LFT will remain in service. However, the methodology of LFT
442
Ligand Field Theory
has been fully developed in that we cannot do better LFT calculations. Thus, given the fundamental limitations on the quantities which LFT can compute, it seems only a matter of time before more sophisticated methods, most likely based on DFT, will replace actual LFT calculations. One possible exception here is the development of empirical modeling schemes like the ligand field molecular mechanics (LFMM) method21 and the AOM extension of the General Utility Lattice Program (GULP) for simulating solid state systems.22 These models combine an AOM calculation of the ligand field stabilization energy with a conventional molecular mechanics/dynamics treatment to deliver a fast, empirical molecular modeling method capable of treating very large systems like metalloenzymes and oxide materials but in a way which captures the important electronic effects arising from incomplete d-shells (see Chapter 2.35). Perhaps the best example of the latter is the Jahn-Teller distortions of six-coordinate d 9 CuII 23,24 complexes and d 4 MnIII in LaMnO3 and Mn2O3.22 By targeting the modeling of large systems beyond the reach of quantum electronic structure methods like DFT, the LFMM method and extended GULP may continue to stimulate interest in LFT for some years to come.
2.35.6 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24.
REFERENCES
Figgis, B. N.; Hitchman, M. A. Ligand Field Theory and Its Applications 2000, Wiley: New York. Gerloch, M.; Woolley, R. G. J. Chem. Soc., Dalton Trans. 1981, 1714–1717. Gerloch, M.; Woolley, R. G. Prog. Inorg. Chem. 1983, 31, 371–446. Deeth, R. J.; Gerloch, M. Inorg. Chem. 1984, 23, 3846–3853. Deeth, R. J.; Gerloch, M. Inorg. Chem. 1984, 23, 3853–3861. Deeth, R. J.; Gerloch, M. Inorg. Chem. 1985, 24, 1754–1758. Deeth, R. J.; Gerloch, M. Inorg. Chem. 1985, 24, 4490–4493. Deeth, R. J.; Duer, M. J.; Gerloch, M. Inorg. Chem. 1987, 26, 2573–2578. Deeth, R. J.; Duer, M. J.; Gerloch, M. Inorg. Chem. 1987, 26, 2578–2582. Deeth, R. J.; Gerloch, M. Inorg. Chem. 1987, 26, 2582–2585. Bridgeman, A. J.; Gerloch, M. Prog. Inorg. Chem. 1997, 45, 179–281. Woolley, R. G. Mol. Phys. 1981, 42, 703–720. Schaeffer, C. E.; Jorgensen, C. K. Mol. Phys. 1965, 9, 401. Woolley, R. G. Chem. Phys. Lett. 1985, 118, 207–212. Deeth, R. J.; Kemp, C. M. J. Chem. Soc., Dalton Trans. 1992, 2013–2017. Bridgeman, A. J.; Gerloch, M. Coord. Chem. Rev. 1997, 165, 315–446. Johnson, D. A.; Nelson, P. G. J. Chem. Soc., Dalton Trans. 1995, 3483–3488. Johnson, D. A.; Nelson, P. G. Inorg. Chem. 1999, 38, 4949–4955. Johnson, D. A.; Nelson, P. G. Inorg. Chem. 1995, 34, 3253–3259. Johnson, D. A.; Nelson, P. G. Inorg. Chem. 1995, 34, 5666–5671. Deeth, R. J. Coord. Chem. Rev. 2001, 212, 11–34. Woodley, S. M.; Battle, P. D.; Catlow, C. R. A.; Gale, J. D. J. Phys. Chem. B 2001, 105, 6824–6830. Burton, V. J.; Deeth, R. J.; Kemp, C. M.; Gilbert, P. J. J. Am. Chem. Soc. 1995, 117, 8407–8415. Burton, V. J.; Deeth, R. J. J. Chem. Soc., Chem. Commun. 1995, 573–574.
# 2003, Elsevier Ltd. All Rights Reserved No part of this publication may be reproduced, stored in any retrieval system or transmitted in any form or by any means electronic, electrostatic, magnetic tape, mechanical, photocopying, recording or otherwise, without permission in writing from the publishers
Comprehensive Coordination Chemistry II ISBN (set): 0-08-0437486 Volume 2, (ISBN 0-08-0443249); pp 439–442
THE NATURE OF LFT LIGAND FIELD PARAMETERS ‘‘d–d ’’ ELECTRONIC TRANSITION INTENSITIES APPLICATIONS AND REFINEMENTS LFT IN THE FUTURE REFERENCES
439 439 441 441 441 442
Ligand field theory (LFT) was already a relatively mature subject when Comprehensive Coordination Chemistry (CCC, 1987) was published and virtually all of Figgis’ original Chapter 6 remains valid in terms of the mathematical techniques and the interpretation of the spectral and magnetic properties of high-symmetry, cubic systems. In 2000, Figgis, in collaboration with Hitchman,1 published the long-awaited updated edition of his classic text on LFT which covers the intervening developments in theory and applications especially with regard to the angular overlap model (AOM), the topic of the next section. However, the issue of the physical significance and transferability of ligand field parameters remains a contentious issue which was debated, sometimes hotly, during the late 1980s to early 1990s. Figgis was fairly skeptical and states in CCC (1987) that the ‘‘physical significance to be attached to the meaning of ligand field parameters is . . .very limited.’’ In contrast, the ‘‘Gerloch school’’ attempted to make a direct connection between the ligand field parameter values and the nature of the metal–ligand bonding.2–11 The physical basis for interpreting the significance of ligand field parameters was developed by Woolley12 whose starting point was the density functional theorem. His analysis leads to different expressions for the AOM e and e parameters, previously introduced by Scha¨ffer and Jørgenson13 in the context of the Wolfsberg–Helmholtz approximation, and to different interpretations of phenomena such as d–s mixing,4 phase-coupled ligators,8 bent bonding,9,10 and parameter transferability.6,14 These issues are discussed further in Chapter 2.36.
2.35.1
THE NATURE OF LFT
LFT is an example of effective operator theory and can be employed to construct multiplet states arising from d n (or f n) configurations. Hence, it is strictly only applicable to systems where the ground state and the lower energy excited states are dominated by d-(or f-) orbital contributions. LFT is thus most relevant for relatively ionic Werner-type transition metal (TM) complexes. Within this approximation, the mathematics for evaluating the multiplets and their relative energies is straightforward and all the necessary equations were well-established by the start of the 1960s. In a sense, therefore, LFT is an ‘‘exact’’ model and Figgis’ Chapter 6 in CCC (1987) remains a definitive account of the mechanics of how to carry out actual LFT calculations of the ‘‘d–d’’ (or ‘‘f–f ’’) spectroscopic and magnetic properties of TM complexes. The major advancements since CCC (1987) are in developing methods and computer codes (see Chapter 2.52) for extracting ligand field parameter values and what these mean in terms of metal–ligand bonding. 439
440 2.35.2
Ligand Field Theory LIGAND FIELD PARAMETERS
LFT is a parametric approach in which the symmetry of the complex is treated explicitly but the bonding is handled implicitly through the ligand field parameters. These parameters describe the three contributions to the overall Hamiltonian, H: the ligand field, HLF, interelectronic repulsion, HER and spin orbit coupling, HLS. The relative importance of each of these terms depends on the element’s position in the periodic table. First and second transition series: HLF > HER HLS Third transition series: HLF HER HLS Lanthanoids: HER > HLS > HLF Actinoids: HER HLS HLF Within the normal central field approximation, HER and HLS are spherically symmetric. Interelectronic repulsion in a complex is thus treated using the same electrostatic theory as for atomic spectroscopy. It is parameterized either within the original Condon–Shortley F0, F2, F4, scheme or the later Racah A, B, C scheme. Since LFT only gives energy differences, values for F0 (and A) cannot be determined. There is a simple mapping between the Condon–Shortley and Racah schemes and they will give identical energies if used in full-basis calculations. However, Racah noted that in free atoms or ions, the energy difference between the terms of maximum spin multiplicity required only one parameter, B. Hence, the Racah scheme is more popular for analyzing ‘‘d–d ’’ spectra since B is sufficient for calculating the spin-allowed transitions of a high-spin complex. Spin–orbit coupling is also based on atomic theory and requires only the one-electron spin–orbit coupling constant, . In addition, the calculation of magnetic moments includes Steven’s orbital reduction parameter, k. Figgis gives a comprehensive account in CCC (1987) of calculating magnetic properties and includes additional terms such as the Trees correction. The ligand field potential, VLF, defines the energies of the d-(or f-) orbitals and is the only part of a conventional LFT calculation which includes the symmetry of the complex. Hence, HLF is the only part of the Hamiltonian which can make general direct contact with ML bonding. HER and HLS may still be relevant but only in terms of the overall, averaged nature of the metal–ligand interaction. There are two important points to emphasize with regard to VLF. First, contributions to VLF are not computed from first principles. Instead, the potential is constructed parametrically and the parameter values are determined by fitting calculated properties to experiment. Secondly, there are two distinct ways in which VLF can be constructed–globally or via ligand superposition. The global approach is exemplified by the original crystal field theory (CFT). VLF is described as a linear combination of spherical harmonics which progressively lowers the symmetry from spherical to cubic and on to still lower symmetries. For high symmetries such as octahedral and tetrahedral (i.e., cubic), the global scheme is simple and elegant. The d-orbital splitting depends on a single parameter, . Since many complexes are (approximately) octahedral or tetrahedral, the global approach has been widely applied. However, as is well known, the eg–t2g splitting in octahedral symmetry is a competition between -and -bonding effects which the single global parameter cannot separate. Furthermore, as the symmetry is lowered, the number of global parameters increases and since they include both symmetry (i.e., angular) and bonding (i.e., radial) contributions, the connection between parameter values and the nature of individual ML interactions is difficult and sometimes impossible to extract. In other instances, the global scheme does not describe the bonding correctly. For example, in tetragonal symmetry, the global scheme has three parameters, Dq, Ds, and Dt. For tetragonal macrocyclic tetraaza NiII complexes with an NiN4X2 core, there are also three AOM parameters, e(N), e(X), and e(X) (vide infra) and hence the two parameters sets can be directly mapped onto each other. Values for Dq, Ds and Dt were derived by analyzing the d–d spectra and assignments were made based on the ‘‘reasonableness’’ of the ligand field parameter values and their variations. However, when the values are converted to their corresponding AOM values, Cl is predicted to be a -acceptor. Equally acceptable assignments of the d–d transition energies can be obtained with more reasonable AOM parameter values.15 As alluded to above, the superposition method, typified by the AOM, overcomes many of the problems of the global scheme and is discussed in detail in Chapter 2.52. VLF is constructed as a superposition of contributions from individual ML bonds which explicitly separates the angular and radial parts. The former is implicit in the geometry so that the AOM energy parameters focus
Ligand Field Theory
441
exclusively on the radial part. Furthermore, the individual M–L perturbations can be factored into local and components as monitored by the AOM e and e energy parameters. In octahedral symmetry, the – competition arises naturally since the d-orbital splitting is given by 3e–4e. Furthermore, by assuming two or more ligands are chemically equivalent, the number of AOM parameters can be kept manageable even for complexes with no symmetry which would, in principle, require a maximum of 14 independent global variables. Hence, by CCC (1987), the general consensus was that the best way to parameterize VLF was via a superposition method like the AOM. Chapter 2.52 provides more details and describes applications of the AOM.
2.35.3
‘‘d–d ’’ ELECTRONIC TRANSITION INTENSITIES
Perhaps the most significant theoretical advance in LFT arose out of the Gerloch group during the late 1980s culminating in a comprehensive review published in 1997.16 It concerned one of the most basic properties of the electronic spectrum which hitherto had not been readily calculable; namely the transition intensities. In the spirit of the ligand superposition model, Gerloch and co-workers developed a parametric approach for calculating ‘‘d–d ’’ transition intensities. In essence, the relative intensities of the ‘‘d–d ’’ electric dipole transitions are expressed in terms of local t intensity parameters which parallel the e energy parameters. The intensity parameters are further qualified in terms of their P and F contributions. That is, since the basic parity selection rule is l ¼ 1, only p or f contributions (i.e., l ¼ 1 or 3) are relevant for ‘‘d–d ’’ transitions. The method has been applied both to noncentrosymmetric (static) and centrosymmetric (dynamic) species, the latter requiring the additional development of normal coordinate analysis methods for handling the vibronic intensity mechanism. The review describes the application of the CLF intensity model to 43 chromophores. The ability to reproduce the observed intensity distributions, including those from experiments using linearly and circularly polarized light, is impressive. For example, the band areas for both the unpolarized absorption and CD spectra of Co(-isospartein)Cl2 are virtually perfect while in centrosymmetric complexes such as [PtCl4]2, [PtBr4]2, and [PdCl4]2 the vibronic analysis can also establish the relative importance of the possible contributing ungerade vibrational modes to the overall intensity. In these cases, the eu mode accounts for more than half of the total. Despite all the effort, however, the CLF spectral intensities model has not been widely adopted even though the latest version of the CAMMAG program (Chapter 2.54) provides the means to carry out the calculations. In the absence of a ‘‘champion’’ and in the light of the continuing rapid development of alternative, more widely applicable methods based on molecular orbital schemes, it seems likely that the promising CLF approach will languish.
2.35.4
APPLICATIONS AND REFINEMENTS
Even a cursory examination of the literature reveals that ligand field concepts are still widely employed to interpret and rationalize diverse experimental data on varied transition metal systems and the present volume contains myriad examples. Chapter 2.36 focuses specifically on the applications of the superposition models. However, the basic methods for carrying out LFT calculations have not altered significantly. Chapter 2.52 has overviews of available software packages. There have been some refinements of certain ligand field concepts. For example, the familiar ‘‘double hump’’ behavior of the ligand field stabilization energy has been reanalyzed by Johnson and Nelson who demonstrate the need to include contributions from d–d interelectron repulsion along with the conventional d-orbital splitting components.17–20 Also, there have been some attempts to reconcile the predictions of LFT with the results emerging from DFT. This theme is taken up again in Chapter 2.35.
2.35.5
LFT IN THE FUTURE
There is little doubt that as a pedagogic tool for introducing coordination chemistry, symmetry, and spectroscopy, LFT will remain a valuable part of the undergraduate syllabus. As such, many of the basic concepts derived from LFT will remain in service. However, the methodology of LFT
442
Ligand Field Theory
has been fully developed in that we cannot do better LFT calculations. Thus, given the fundamental limitations on the quantities which LFT can compute, it seems only a matter of time before more sophisticated methods, most likely based on DFT, will replace actual LFT calculations. One possible exception here is the development of empirical modeling schemes like the ligand field molecular mechanics (LFMM) method21 and the AOM extension of the General Utility Lattice Program (GULP) for simulating solid state systems.22 These models combine an AOM calculation of the ligand field stabilization energy with a conventional molecular mechanics/dynamics treatment to deliver a fast, empirical molecular modeling method capable of treating very large systems like metalloenzymes and oxide materials but in a way which captures the important electronic effects arising from incomplete d-shells (see Chapter 2.35). Perhaps the best example of the latter is the Jahn-Teller distortions of six-coordinate d 9 CuII 23,24 complexes and d 4 MnIII in LaMnO3 and Mn2O3.22 By targeting the modeling of large systems beyond the reach of quantum electronic structure methods like DFT, the LFMM method and extended GULP may continue to stimulate interest in LFT for some years to come.
2.35.6 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24.
REFERENCES
Figgis, B. N.; Hitchman, M. A. Ligand Field Theory and Its Applications 2000, Wiley: New York. Gerloch, M.; Woolley, R. G. J. Chem. Soc., Dalton Trans. 1981, 1714–1717. Gerloch, M.; Woolley, R. G. Prog. Inorg. Chem. 1983, 31, 371–446. Deeth, R. J.; Gerloch, M. Inorg. Chem. 1984, 23, 3846–3853. Deeth, R. J.; Gerloch, M. Inorg. Chem. 1984, 23, 3853–3861. Deeth, R. J.; Gerloch, M. Inorg. Chem. 1985, 24, 1754–1758. Deeth, R. J.; Gerloch, M. Inorg. Chem. 1985, 24, 4490–4493. Deeth, R. J.; Duer, M. J.; Gerloch, M. Inorg. Chem. 1987, 26, 2573–2578. Deeth, R. J.; Duer, M. J.; Gerloch, M. Inorg. Chem. 1987, 26, 2578–2582. Deeth, R. J.; Gerloch, M. Inorg. Chem. 1987, 26, 2582–2585. Bridgeman, A. J.; Gerloch, M. Prog. Inorg. Chem. 1997, 45, 179–281. Woolley, R. G. Mol. Phys. 1981, 42, 703–720. Schaeffer, C. E.; Jorgensen, C. K. Mol. Phys. 1965, 9, 401. Woolley, R. G. Chem. Phys. Lett. 1985, 118, 207–212. Deeth, R. J.; Kemp, C. M. J. Chem. Soc., Dalton Trans. 1992, 2013–2017. Bridgeman, A. J.; Gerloch, M. Coord. Chem. Rev. 1997, 165, 315–446. Johnson, D. A.; Nelson, P. G. J. Chem. Soc., Dalton Trans. 1995, 3483–3488. Johnson, D. A.; Nelson, P. G. Inorg. Chem. 1999, 38, 4949–4955. Johnson, D. A.; Nelson, P. G. Inorg. Chem. 1995, 34, 3253–3259. Johnson, D. A.; Nelson, P. G. Inorg. Chem. 1995, 34, 5666–5671. Deeth, R. J. Coord. Chem. Rev. 2001, 212, 11–34. Woodley, S. M.; Battle, P. D.; Catlow, C. R. A.; Gale, J. D. J. Phys. Chem. B 2001, 105, 6824–6830. Burton, V. J.; Deeth, R. J.; Kemp, C. M.; Gilbert, P. J. J. Am. Chem. Soc. 1995, 117, 8407–8415. Burton, V. J.; Deeth, R. J. J. Chem. Soc., Chem. Commun. 1995, 573–574.
# 2003, Elsevier Ltd. All Rights Reserved No part of this publication may be reproduced, stored in any retrieval system or transmitted in any form or by any means electronic, electrostatic, magnetic tape, mechanical, photocopying, recording or otherwise, without permission in writing from the publishers
Comprehensive Coordination Chemistry II ISBN (set): 0-08-0437486 Volume 2, (ISBN 0-08-0443249); pp 439–442