Ligand-field wavefunctions

If the point-charge ionic model places the empty 3d orbitals of a degenerate manifold an energy AEp above the 0-2p orbitals and AEj above liie 0-2s orbitals, the antibonding d-like states may be described in second-order perturbation theory to give the ligand-field wavefunctions... 

For Iran sition metals th c splittin g of th c d orbitals in a ligand field is most readily done using HHT. In all other sem i-ctn pirical meth -ods, the orbital energies depend on the electron occupation. HyperCh em s m oiccii lar orbital calcii latiori s give orbital cri ergy spacings that differ from simple crystal field theory prediction s. The total molecular wavcfunction is an antisymmetrized product of the occupied molecular orbitals. The virtual set of orbitals arc the residue of SCT calculations, in that they are deemed least suitable to describe the molecular wavefunction, ... 

Figure 13. Left ligand field energy-level diagram calculated for plastocyanin. Center contains energies and wavefunctions of the copper site. Energy levels determined after removing the rhombic distortions to give and C symmetries are shown in the left and right columns, respectively (from Ref. 11). Right electronic structural representation of the plastocyanin active site derived from ligand field calculations (from Ref. 11).

FIGURE 1.26 MO diagram for a high-spin d5 ion in a Td ligand field with sulfur ligands. Right-hand side gives the wavefunctions. 

The outline of the review is as follows in the next section (Sect. 2) we introduce the basic ideas of effective Hamiltonian theory based on the use of projection operators. The effective Hamiltonian (1-5) for the ligand field problem is constructed in several steps first by analogy with r-electron theory we use the group product function method of Lykos and Parr to define a set of n-electron wavefimctions which define a subspace of the full -particle Hilbert space in which we can give a detailed analysis of the Schrodinger equation for the full molecular Hamiltonian H (Sect. 3 and 4). This subspace consists of fully antisymmetrized product wavefimctions composed of a fixed ground state wavefunction, for the electrons in the molecule other than the electrons which are placed in states, constructed out of pure d-orbitals on the... 

The adequacy of the ligand field model can be questioned because the actual Mul liken charge on the iron is only 1.2 due to the dative bonds with the nitrogens. Also, the Cl calculations for the lowest states tended to find 20-30% Fe(III) character in the wavefunction. Nevertheless, this model does predict correctly that there should be a large manifold of states of ligand-field-split d character within 3 eV of the ground state. 

A Modern First-Principles View on Ligand Field Theory Through the Eyes of Correlated Multireference Wavefunctions... 

For open-shell systems with S > 1/2, the energy levels are far more complicated and, in general, must be represented as a linear combination of determinantal wavefunctions. The problem is well known in terms of the Ligand Field description of d-d spectra [26] and Lever [27] provides a discussion relevant to Charge Transfer (CT) spectra. Since HF and post-HF methods give proper determinantal wavefunctions, it is possible to construct the correct descriptions. 

All computations in this section have been performed using the ORCA program package [46], a DFT BP86 functional and a basis set of triple zeta quality (TZV(P)). In all MRCI computations the T gi, Tp, and T t tresholds were set to 10 , 10 " and 10 Eh, respectively which are the default values of the method. A CAS(n,5) has been chosen in all cases, unless otherwise specified. This choice is motivated, of course, by ligand field theory and provides a suitable model space over which the many-particle wavefunctions are expanded. 

Hamiltonian is not known and, as for the nonrelativistic case, further approximations have to be introduced in the wavefunction, it is tempting to derive approximate computational schemes which are still sufficiently accurate but more efficient. Here we will only summarize those approximate methods that have been used frequently to obtain information about the electronic structure of molecules with lanthanide atoms, i.e. relativistically corrected density-functional approach, pseudopotential method, intermediate neglect of differential overlap method, extended Huckel theory, and ligand field theory. 

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