Cellular Ligand Field Research Articles

Ligand field theory, Pauli shields and ultra-covalency in organometallic chemistry.

This paper explores the ligand field picture applied to organometallic compounds. Given the dearth of experimental data, the high-level ab initio ligand field theory (aiLFT) method is deployed as a surrogate for experiment and the necessary d orbital sequences and relative energies are obtained computationally. These are fitted to local cellular ligand field (CLF) σ, π and δ bonding parameters. Results are reported for planar [Cu(CR3)4]-, (R = F, H), octahedral M(CO)6n (M = Fe, Mn, Cr, V, Ti; n = +2, +1, 0, -1, -2), and the sandwich compounds M(Cp)2 (Cp = cyclopentadienyl, M = Fe, Ni, V), [Ni(Cp)2]2+ and Cr(C6H6)2. With respect to the aiLFT framework, these organometallic systems behave just like coordination complexes and most maintain the integrity of their formal dn configurations. Both [Cu(CR3)4]- compounds are formulated as low-spin d8 CuIII species and have normal ligand fields consistent with their planar geometries. The metal carbonyls reveal a new way of counting valence electrons which only requires the CLF d orbital energy level diagram to rationalise the 18-electron rule as well as its many exceptions. The bonding in sandwich compounds shows a remarkable variation. In ferrocene, Cp- behaves as a strong field ligand, comparable to [CN]- in [Fe(CN)6]4-. Fe(Cp)2 is low spin as is Cr(C6H6)2. Cp- in Fe(Cp)2 is a weak σ donor, strong π donor and weak δ acceptor while benzene in Cr(C6H6)2 is also a weak σ and strong π donor but is a much better δ acceptor. In contrast, Cp- is weak field in high spin, 20-electron Ni(Cp)2 but 'ultra-covalent' in [Ni(Cp)2]2+. The formal IV oxidation state is too high for the ligand set and the integrity of the d6 configuration is lost. Similarly, [V(CO)6]- and [Ti(CO)6]2- are ultra-covalent except now the formal metal oxidation states are too negative. Both mechanisms relate to the breaching of the metal's 3s23p6 'Pauli shield' and these ultra-covalent systems lie outside the ab initio ligand field regime. However, within the ligand field regime, the bonding in 'coordination complexes' and 'organometallic compounds' has the same conceptual footing and the nature of the local σ, π and δ interactions can be extracted from analysing the ligand field d orbitals.

Ligand Field Theory for Linear ML2Complexes

AbstractPoint‐charge crystal field theory (CFT) for linear ML2systems guarantees dz2>dxz/dyz>dxy/dx2‐y2 (i. e. dσ>dπ>dδ). This is not what is found for CuCl2and other linear, divalent MX2complexes where dπ>dσ. This failure of CFT has also been attributed to its successor, ligand field theory (LFT). However, taking LFT to be parameterised CFT, any d orbital sequence is possible. The real test is whether the LFT parameters make chemical sense. A new cellular ligand field (CLF) analysis of CuCl2, including the equatorial toroidal void, which affects all the d orbitals, confirms eπ(Cl)>eσ(Cl). To account for this, the ‘distributed donation’ model is proposed linking σ and π bonding such that enhanced π donation is at the expense of reduced σ bonding and vice versa. This is the π‐donor analogue of the Dewar‐Chatt‐Duncanson model for π‐acceptor ligands. Ab initio LFT (AI LFT) calculations support a progressive π‐donation increase/σ donation decrease from Cu(II) to Sc(II) with eσfinally becoming negative. The model further predicts that adding equatorial ligands will force the π density back into the σ bond which is also confirmed by AI LFT calculations fortrans‐[CuCl2(NH3)4] where eσ(Cl)>eπ(Cl) even though the CuCl2unit is unchanged. The distributed donation model for linear σ‐only [MII(Lσ)2]nsystems (Lσ=NH3, H), where increasing π donation is not possible, implies that the M−L bonding in linear systems should be inherently weak.

Ligand Field Theory for Planar Complexes: First Principles Validation of the Critical Effects of Coordination Voids

Multi reference CASSCF/NEVPT2 wavefunction calculations on planar cis‐[MA2B2] complexes show that large dxz/dyz splittings are a feature of the symmetry of the ligand field and are not due to the Orgel effect or phase coupled ligation as previously proposed based on the MO version of the angular overlap model. Instead, the splitting can be attributed to the π components of the local ligand fields in the “void” regions above and below the molecular plane. The potential in these regions is lower than the d orbital barycentre leading to negative parameter values which is fully consistent with the cellular ligand field interpretation of ligand field theory. The wider implications of ligand field effects from coordination voids are considered.

Ligand field and density functional descriptions of the d-states and bonding in transition metal complexes

The d-orbital energy sequences for low symmetry transition metal complexes derived from Kohn-Sham density functional theory and ligand field theory are different due to each model's treatment of interelectron repulsion. The implications for providing a unified description of the underlying metal-ligand bonding are analysed and illustrated using conventional and time-dependent DFT. Previous detailed spectroscopic studies have established the d orbital sequence in planar coordination complexes containing pi-donor halide ligands as dx2-y2 >> dxy > dxz, dyz > dz2 while for a sigma-only system like [Pd(NH3)4]2+, ligand field approaches like the angular overlap model (AOM) or cellular ligand field (CLF) model predict dxz, dyz, and dxy, should be degenerate. However, the energies of the Kohn Sham (KS) 'd' orbitals of [PdCl4]2- and [Pd(NH3)4]2+ place dxy below the dxz/dyz pair. Direct use of the KS orbital eigenvalues in AOM or CLF analyses would imply both ligands are pi acceptors. This result is independent of the choice of functional or whether the calculation is carried out in vacuo or in a polarised continuum representing solvation by water. The origin of the difference between the KS and LFT d orbital sequences derives from their treatments of d-d interelectron repulsion. KS orbitals include interelectron repulsion contributions while LFT d orbitals do not. For a low-spin d8 complex, DFT gives less d-d interelectron repulsion in the xy plane leading to a lowering of dxy relative to dxy/dyz. This differential effect can be reversed qualitatively by progressively removing electron density from dz2 and placing it in dx2-y2. When about 0.6 electrons is rearranged, E(dxy) > E(dxz/dyz) for [PdCl4]2- and the dpi orbitals for [Pd(NH3)4]2+ are virtually degenerate. The wider ramifications of these interelectron repulsion effects are discussed for other symmetries. Excited d state energies for [PdCl4]2- are computed using both time dependent density functional theory (TDDFT) and determinant energies. The latter give the experimental sequence 1A2g < 1Eg < 1B1g while TDDFT gives 1Eg < 1A2g < 1B1g. Both give transition energies up to 30% lower than observed. A DFT analysis of the bonding energies in [PdCl4]2- indicates that the Pd-Cl pi bonding in the molecular plane is about 33% weaker than the out-of-plane pi interaction due to non-zero overlap between ligand orbitals. The normal LFT assumption of linear ligation may not always be valid.

A combined ligand field and density functional theory study of the structural and spectroscopic properties of [Cu(dien)2]2+

Issues regarding assignment of the ‘d–d’ spectrum of [Cu(dien)2]Br2·H2O have been resolved using density functional theory (DFT) calculations. The fully optimised structure of [Cu(dien)2]2+ is in good agreement with experiment with Cu–N distances within ≈0.02–0.06 Å. However, one axial contact is 0.22 Å longer than reported and the ground state Cu–N covalency is overestimated. This leads to computed EPR g values which are too low and to ‘d–d’ transition energies which are too high. However, the electronic structure can be tuned to the experimental g values by modifying the copper nuclear charge. The ‘d–d’ transition energies were computed from the optimised electronic state using Slater’s transition state approach. DFT agrees with cellular ligand field (CLF) calculations and demonstrates that amines are not π-bonding ligands and that electrostatic interactions are not required for the CLF model. Instead, the observed spectroscopic and structural data are successfully reinterpreted as arising from the superposition of two, slightly different complexes in a ratio of approximately 5.5∶1 and aligned at about 90° to one another. This significantly improves the agreement between the calculated and ‘observed’ structures. The implications for the interpretation of the ‘d–d’ spectra of other copper(II) amine complexes are discussed.

Molecular mechanics calculations on imine and mixed-ligand systems of CoIII, NiII and CuII

The force field for the cellular ligand field stabilisation energy/molecular mechanics (CLFSE/MM) method has been applied to 28 transition-metal complexes. Computed and experimental structures are compared for 12 ML x Cl 6- x species (M = Co III or Ni II ; L = amine donor; x = 6 or 4), 12 MA x B 6- x compounds (M = Ni II or Cu II ; A = imine, B = amine; x = 6, 4 or 3), one five-co-ordinate copper(II) imine–amine complex and three four-co-ordinate copper(II) imine and imine–amine molecules. For π-bonding ligands a stronger donor interaction is associated with a larger positive value of the CLF e π parameter but, due to the use of a crystal field type barycentre, the CLFSE actually goes up. The CLFSE thus has the wrong form for treating the π contributions to bond stretching and distance-dependent e π parameters are inappropriate. However, the desired bond lengths can be obtained by modifying the Morse function and e σ terms. The π contribution to the L–M–L angle bending operates in the correct sense but is small and can also be accommodated by altering the magnitude of e σ . For asymmetric π interactions (e πx ≠ e πy ) there is no effect on the M–L torsional potential for low-spin d6, high-spin d8 and d9 configurations where the π-symmetry d orbitals are completely filled. Hence, only the σ-bonding contributions to the CLFSE are retained. This approach still gives good agreement with experimental structures, even for formally π-bonding ligands, with average root-mean-square errors in M–L lengths and L–M–L angles of about 0.02 A and 3° for Co III , Ni II and four co-ordinate Cu II , excluding [Cu(bipy) 2 ] 2+ (bipy = 2,2′-bipyridyl), and about 0.05 A and 4° respectively for six-co-ordinate Cu II , excluding [Cu(terpy) 2 ] 2+ (terpy = 2,2′∶6′,2″ -terpyridyl). The subtle interplay between the axial Ni–Cl and equatorial Ni–N distances in trans-[NiN 4 Cl 2 ] macrocyclic species is reproduced for the first time by an MM-based approach. However, the model appears to give relatively poor agreement for [Cu(bipy) 2 (NH 3 )] 2+ , [Cu(terpy) 2 ] 2+ and [Cu(bipy) 2 ] 2+ . For the five-co-ordinate complex this is due to the intrinsic plasticity of five-co-ordinate copper(II) species. The energy difference between the limiting trigonal-bipyramidal and square-pyramidal geometries is only a few kcal mol -1 . For [Cu(terpy) 2 ] 2+ the limiting geometries of tetragonally elongated and compressed octahedra are also within a few kcal mol -1 although the present set of parameters overestimates the ligand contribution and predicts a compressed geometry. The calculated structure of [Cu(bipy) 2 ] 2+ is too flat but for four-co-ordinate species it is shown, using [CuCl 4 ] 2- as an example, that there are several ways to induce a tetrahedral distortion. The most satisfactory method is to include charges on Cu and the ligand donors whereupon the geometries of [CuCl 4 ] 2- and [Cu(bipy) 2 ] 2+ distort to the required flattened tetrahedral structures.

On the electronic structures and spectra of NiCl2 and CuCl2

The geometry and ground state of NiCl2 have been studied using local density-functional (LDF) calculations within the linear combination of Gaussian-type orbitals (LCGTO) framework. The molecule is found to be linear with a 3Σg– ground state in agreement with recent experimental results but contrary to previous theoretical studies. The calculated bond length and vibrational frequencies are in excellent agreement with experiment. A cellular ligand-field (CLF) analysis of the spectrum has been performed. The LDF and CLF calculations provide a consistent description of the bonding and suggest that the chloride ions are acting as good σ and π donors in this molecule with both roles enhanced compared to systems with higher co-ordination numbers. A proper account of the important interaction of the dσ orbital with the antibonding σg+ orbital is given using a cylindrically symmetric ‘void’ cell. A recent CLF analysis of CuCl2 is shown to be incorrect because of the treatment of the void interaction. A new study of the ligand-field spectrum of CuCl2 is presented, the results of which are consistent with the LDF and CLF studies on NiCl2 and with recent molecular orbital and LDF calculations on CuCl2.

The electronic structure of ‘linear’ nickel oxides

The geometries, ground states and low-lying excited states of the ‘linear’ nickel oxides NiO, [NiO2]2– and [NiO2]3– have been studied using local density-functional (LDF) calculations within the linear combination of Gaussian-type orbitals framework. The NiO molecule and the [NiO2]2– ion are predicted to have 3Σ– and 3Σg– ground states respectively. The calculated bond lengths and vibrational frequencies are in excellent agreement with experiment. Cellular ligand-field (CLF) analyses of the spectra and magnetic properties have also been performed. The LDF and CLF calculations provide a consistent description of the bonding and suggest that the oxide ions are acting as good σ and π donors in these molecules with both roles enhanced compared to systems with higher co-ordination numbers. The interaction between the dσ orbital and the antibonding σ orbital of predominantly nickel s-orbital character is important in understanding the electronic structure of these systems and its modelling in CLF analyses is described. The description of the bonding in NiO is consistent with that obtained from previous studies. The prediction of a 3Σg– ground state for the [NiO2]2– ion required a reassignment of the spectrum and led to a more satisfactory modelling of the magnetic moment than that given by earlier calculations. The ground state of the [NiO2]3– ion is predicted to be 2Σg+, consistent with its EPR spectrum. The bonding in this low-oxidation-state is weaker than in the nickel(II) oxides and involves considerable contributions from both nickel d and s orbitals.

Impact on ligand-field theory of the real ground state for CuCl2

The recent prediction by coupled pair functional Hartree–Fock calculations of a degenerate 2Πg ground term for linear CuCl2 has been confirmed by local density funtional (LDF) Slater-type orbital calculations. This has prompted a new cellular ligand field (CLF) analysis. Contrary to previous results on higher-co-ordinate chlorocuprates(II) and other complexes, the relative σ to π Cu–Cl bonding ratios for CuCl2, as predicted by the CLF eλ parameters on the one hand and by the LDF overlap populations on the other, do not agree. However, the CLF data do correlate with the computed LDF bonding energies but only when the whole d manifold (i.e. the 2Πg, 2Σg+ and 2Δg states) is taken into account. The interpretation and implications of these results within the ligand-field formalism are discussed.

D–d Spectral assignments in tetragonal nickel(II) complexes

Cellular ligand field (CLF) analyses have been made for seven tetragonal-octahedral nickel(II) complexes [NiCl2(tfeh)4][tfeh =(tetrafluoroethyl)hydrazine] and [NiX2([n]aneN4)](X = Cl– or NCS–; n= 14, 15 or 16 and [n]aneN4 represents an n-membered tetraaza macrocycle). Published assignments of the d–d spectra for all bar the [14]aneN4 complexes lead to a π-acceptor function for Cl– and NCS–. This result is chemically unreasonable for Cl– and previous studies indicate that NCS– is not a π acceptor towards NiII either. The d–d spectra have been reinterpreted within the CLF framework leading to a consistent set of assignments and ligand-field parameters. The latter monitor the interplay between axial and equatorial bonding consistent with Pauling's electroneutrality principle: i.e. as the strength of the equatorial donation decreases [eσ(N) gets smaller] the axial donors bind more strongly to compensate [eσ(X) and eπ(X) increase] such that the sum, Σ, of all the CLF parameters remains essentially constant for the same donor sets. For the macrocyclic complexes the significant increase in the axial bonding parameters need not necessarily be accompanied by a marked decrease in the Ni–X bond length. Steric interactions between H atoms on the macrocyclic ring and the axial donors appear to prevent a closer approach.

Energies, intensities, and circular dichroism of d-d transitions in trigonal-bipyramidal cobalt(II) and nickel(II) chromophores

The energies, electric-dipole absorbances, and rotary strengths of «d-d» transitions in a series of nominally trigonal-bipyramidal chromophores have been reproduced quantitatively within the cellular ligand-field (CLF) approach. The series comprise M(S-tan)X with M=Co(II) or Ni(II), X=NCS, Cl, Br, or I, and S-tan is the tripodal triamine Me 2 NCH 2 CH(Me)N(CH 2 CH 2 NMe 2 ) 2 . Separate analyses of the three spectral properties have established CLF energy parameters, eλ, and electric-dipole transition moment parameters, L tλ, that describe a consistent pattern of electron distribution throughout the series

Chirality and bonding in the first coordination shells of three CoN2Cl2 chromophores: quantitative reproduction of rotatory strengths

The «d−d» transition energies, absorption intensity distributions, and absolute rotatory strengths and their signs have been quantitatively reproduced for three approximately tetrahedral CoN 2 Cl 2 chromophores: dichloro[(−)-sparteine] cobalt(II), dichloro[(−)-α-isosparteine] cobalt(II), and dichloro[(+)-N,N,N',N'-tetramethyl-1,2-propylenediamine] cobalt(II). Reproduction of the signs and absolute magnitudes of the reported circular dichroism spectra has provided a very sensitive probe of the ligand field, represented here within the superpositional cellular ligand-field (CLF) model

ChemInform Abstract: Theoretical versus Experimental Charge and Spin‐Density Distributions in trans‐(Ni(NH3)4(NO2)2).

AbstractA comparison of data from three different theoretical models (ab initio UHF and DVXα MO calculations as well as cellular ligand field analysis (clf)) with experimental charge and spin‐density distributions, obtained from X‐ray and polarized neutron diffraction results, leads to a consistent picture of the electronic structure and M‐L bonding in the title complex.

Discrete variational X? calculations of the spectra of chlorocuprate(II) complexes: a detailed comparison with experiment and the cellular ligand field model

Discrete variational Xα self-consistent-charge (DVXα s.c.c.) calculations of the d–d and charge-transfer (c.t.) spectra of five chlorocuprate(II) complexes have been performed. The molecules studied are planar and distorted tetrahedral CuCl42–, square-pyramidal CuCl53–, and two tetragonal-octahedral CuCl64– species. Calculated orbital-energy differences using near-minimal basis sets optimised for each molecule are in excellent agreement with experiment for the d–d bands. Transition-state calculations for the c.t. absorptions predict higher energies than observed but the energy differences between successive bands are well reproduced also. Analysis of the DVXα s.c.c. charge distributions gives a description of the metal–ligand bonding closely parallel to cellular ligand field (c.l.f.) treatments. Further comparison of DVXα s.c.c. and c.l.f. data indicates that the former gives not only a good account of ‘d–s mixing’ in these systems but also quantitative confirmation of the empirical c.l.f. ‘sum rule.’ The present study suggests that the DVXα scheme provides independent validation of the underlying assumptions of the c.l.f. model in particular and ligand field theory in general.

Theoretical versus experimental charge and spin-density distributions in trans-[Ni(NH3)4(NO2)2

The experimental charge and spin-density distributions for [Ni(NH3)4(NO2)2] have been compared with theory at various levels. Ab initio unrestricted Hartree–Fock (UHF) and discrete variational Xα(DVXα) Hartree–Fock–Slater molecular orbital (m.o.) calculations are reported together with cellular ligand field (c.l.f.) results. The UHF and DVXα approaches yield closely similar descriptions of the charge and spin densities, and qualitatively reproduce the main features of both types of experimental data, namely the Ni–N covalence is strong, the NO2– ion is a better σ donor than the NH3 molecule, and the Ni–N π-bonding is small. Both theories indicate quite appreciable O(NO2) participation in the bonding and antibonding m.o.s involving nickel. C.l.f. calculations which include only the Ni–N interactions reproduce the experimental d–d spectra and the signs of the single-crystal paramagnetic anisotropies quite well, but assign a weaker σ-donor role to the nitrite ligand relative to NH3. An extension of the model to include explicit Ni–O interactions is more satisfactory and places the NO2– ion as the stronger σ donor consistent with the other theoretical and experimental data.

Ligand-field analysis of transition-metal complexes

Abstract The aim of this review is to give an account of recent theoretical work (‘Ligand-Field Analysis’) that has both led to clarification of the basic structure of ligand-field theory and has facilitated the acquisition of information about chemical bonding in paramagnetic transition-metal complexes that form insulating crystals. The review begins with a justification in modern terms for the classical crystal-field approach based on a well defined dn-configuration for the metal ion; the central idea is that the ground and low-lying electronic states are based on localized electron wavefunctions because the interelectron repulsion energy is so important in these systems. The ligand-field theory is developed in two stages; first, the group product wavefunction method is used to construct a physically important subspace of many-electron wavefunctions for a transition-metal complex. The full n-electron hamiltonian is then studied in this basis using Lowdin partitioning and the chain formalism of Haydock; a full theoretical characterization of the Ligand-Field hamiltonian, which refers explicitly to only the d-electrons, is given. The paper describes the parametrization of the ligand-field based on the Cellular Ligand Field (CLF) model which explicitly introduces the notion of the chemical functional group to ligand-field theory. The {e l k} -parameters associated with the local interactions of the metal ion and its individual ligands (l) are discussed, and the review includes some general remarks about these quantities for the ligand-fields of some typical transition-metal complexes. A short introduction to the modern electronic structure theory of materials is given as a postlude to the main review.