Relativistic multi-configurational methods

Abstract

The Kramers restricted complete active space self-consistent field (KRCASSCF) and complete active space second-order perturbation theory (KRCASPT2) methods through the framework of the two-component spin-orbit relativistic effective core potential as relativistic multi-configurational methods have been developed. The first part of the thesis continues the development of KRCASSCF previously reported [Y.S. Kim and Y.S. Lee, J. Chem. Phys. 119, 12169 (2003)] and extends the theory by means of adding time-reversal symmetry into the relevant expressions so as to complete the course of theoretical development. We retained the usage of elementary spinor excitation operator for defining the spinor rotation operator and derived the gradient and Hessian in simpler forms than previously found. To eliminate redundant computation resulting from repeating sums in the derivatives, a suitable decomposition method is proposed, which also facilitates the implementation. The two-step near second-order approach is employed for convergence. The present implementation is applicable for both closed- and open-shell systems and is used to calculate the atoms of lower p-block. The results for 5p and 6p are in good agreement with the experiments, and those for 7p are comparable to multi-reference configuration interaction results, showing that KRCASSCF is a versatile tool for the relativistic electronic structure calculation of molecules containing moderate-weight through superheavy elements.In the second part of the thesis, we report a formulation and an implementation of KRCASPT2 based on the KRCASSCF reference function. The zeroth-order Hamiltonian is defined as a sum of nondiagonal one-electron operators with generalized two-component Fock matrix elements as scalar factors. The Kramers symmetry within the zeroth-order Hamiltonian is maintained via the use of a state-averaged density, allowing consistent treatments for degenerate states. The explicit expressions are derived for the m...