Ligand field theory

Ligand field theory of d^3 transition metal ions in
cubic and quadrate fields is briefly summarized, along with
the features of the predicted spectra. Diffuse reflectance
spectra of a variety of quadrate chromium(III) complexes are
measured with special emphasis on uncovering the component
structures of the spin-forbidden transitions. Energy level
assignments are made for components of both spin-allowed
and spin-forbidden bands by fitting of the calculated and
observed energy levels. Electron correlation and ligand
field parameters are derived by the fitting procedure, and
the usefulness of the repulsion parameters Band C in bonding
considerations is discussed. Results reveal the need for certain
refinements of the present state of ligand field theory.
The need for improved experimental techniques to provide
more precise and abundant spectral data is evident. When
more data is available it will be possible to continue the extensions
of the theory of ligand fields to s ystems of lower symmetries.

Electronic-structure studies of Tetrakis(imidazole)sulphatocopper(II) - Cu(C3H4N2)4SO4 and Tetrakis(imidazole)diperchloratocopper(II) - Cu(C3H4N 2)4(ClO4)2 have been carried out by analysis of electronic spectra, magnetic properties and ESR spectra. Solution spectra of both systems in the visible and UV range as well as unpolarised single-crystal spectrum of Cu(Im)4SO4 in the visible have been recorded. Both ligand-field (LF) and charge-transfer (L --> M) bands have been identified and assigned, with the exception of the lowest energy LF band. The Angular Overlap Model has been used to calculate the LF band-maxima and compare with the observed band-maxima The ground-state energy-term for both Cu(Im)4SO4 and Cu(Im)4(ClO4)2 has been established with the use of ESR data to be 2B1g. Magnetic moment for the complexes have been obtained from precise magnetic susceptibility measurements with temperature variation and satisfactorily compared with the calculated values.

In the well-known weak field sequence of perturbations, which is called
the {L, S, J} representation, one considers the spin.-orbit perturbation
immediately after interelectronic repulsions. If fhe spin-orbit effect is
not large, as is the case for 3d^n systems, it is useful to obtain energy
levels in a representation, {L, S, X}, with a sequence of perturbations
in which the ligand field potential precedes the spin-orbit perturbation. For tetragonal ligand fields the {L,S,X} representation will give one
coupling scheme if the cubic orientation is not maintained. If we go
through cubic parentage, however, we have two additional coupling
schemes depending on whether the spin-orbit perturbation is applied
immediately after cubic or after cubic and axial potentials. We have
devised these three coupling schemes by deriving the wave functions
and energy matrices for the case of d^2 and d^8 electronic configurations. The purities of eigenfunctions for both the cubic and tetragonal cases have been obtained in the {L, S, X} and {L, S, J} representations. We find
that the eigenfunctions are considerably purer in the new {L, S, X} representations
even for large values of the spin-orbit constant.

The ligand field theory of complexes has been completely developed and the energy matrix elements for complexes in various geometries in different coupling schemes have been worked in considerable detail. However for many coupling schemes the computing of energy matrix elements is a tedious and laborious process. In the first part of my thesis we present a solution to the Weak-Field II problem using ladder operators and tensor operators. We used the Weak-Field II as an example to stress the complexity of computing energy matrix elements using ladder operators versus the simplicity of calculating matrix elements with tensor operators. Also the Weak-Field II was used as a model example hoping to be able to accomplish the same with the jj-II coupling scheme. In the last part of my thesis we present a derivation of simplifying expressions for the energy matrix elements for the d 2 complex in the jj-II coupling scheme. It is worth mentioning that the expressions derived can be applied to complexes other than octahedral and further they can be generalized for complexes with n-electrons in the valence shell. Finally, we present a thorough analysis of the electronic spectra of some Nickel(II) complexes.

We have studied the electronic spectra of tetragonal chromium (III) complexes namely trans-[Cr(NH3)4(CN)2]ClO4, trans-[Cr(en)2(CN)2]ClO4, and trans-[Cr(cyclam)(CN) 2]ClO4. These spectra have been analyzed by Gaussian analysis to locate the band maxima of the tetragonal components. The band maxima are then fitted with the tetragonal energy matrices of d3 configuration with full configuration interaction, neglecting spin-orbit interaction. The Dq, Dt, and Ds ligand field and the B and C electron correlation parameters have been extracted from the fitting procedure. The parameters have been analyzed to understand the bonding of these complexes. We have also uncovered the low intensity absorption doublet bands and a high intensity charge transfer band of trans-[Cr(en)2(CN)2]ClO4 which occur around 15,000cm-1 and 49,000cm-1, respectively.