THEORETICAL INVESTIGATION OF SPECTRAL AND MAGNETIC PROPERTIES OF BINUCLEAR CLUSTERS OF TRANSITION ELEMENTS
Abstract
Magnetic interaction in binuclear clusters constructed from two octahedral moieties is described by a model that couples local SCF MO's of each moiety using valence bond methodology. A non-relativistic hamiltonian matrix H is partitioned into H $\sb0$ which describes non-interacting moieties and H $\sb2$ which accounts for the exchange interaction. The formalism is tested by application to one-, two-, and three-bridged Cr$\sp{3+}$ and Mo$\sp{3+}$ systems. The method involves directly calculating as many as 680 energy levels arising from the interaction among 6 magnetic electrons (in local 0$\sb{\rm h}$ configurations t$\sp3$ or t$\sp2$e$\sp1$) outside a frozen core. Solution of the resulting pseudo-eigenvalue problem H D = S D E is accomplished by application of a newly developed algorithm which permits the diagonalization of large-sized matrices. All eigenvalues and vectors are obtained regardless of the vectors's degeneracy with the major restrication being implicit symmetry in the matrix to be diagonalized. Particular attention is paid to states arising from coupling among $\sp4$A$\sb{\rm 2g}$, $\sp2$E$\sb{\rm g}$, and $\sp4$T$\sb{\rm 2g}$. Except in 3-bridged cases, the ground state manifold of the binuclear cluster is readily fit to the Heisenberg-Dirac-Van Vleck (HDVV) model and values of the exchange parameter, J, are in good agreement with available data. Interpretation of interactions within excited manifolds is more difficult, since several fitting parameters characterizing both orbital and spin effects are required to characterize the net exchange interactions. These parameters express dependence on (a) the central transition metal ions (Cr$\sp{3+}$ vs. Mo$\sp{3+}$), (b) the number of bridging ligands (1, 2, or 3), and (c) overlap between MO's of the moieties. The effect of various approximations to the calculation of the overlap and kinetic energy matrices is studied by reporting calculated results.
Degree
Ph.D.
Subject Area
Chemistry
Off-Campus Purdue Users:
To access this dissertation, please log in to our
proxy server.