|relativistic electronic structure calculations for molecules and clusters|
The diagonalization of the effective Hamiltonian Heff yields the model-space parts of the target relativistic wavefunctions (|m>, |n>, ...). Provided that efficient `diagrammatic' algorithms are employed, no explicit approximation for the remainder (outer-space) parts of the wavefunctions is obtained. A convenient way to incorporate the contributions from these parts to transition property values consists in a perturbative calculation of transition density matrices.
The first-order approximation for the m - n transition spin-free density matrix mnR compatible with the use of the present approximation for Heff is given by
= <m | Esr
( < J |Esr
| K>HKJ'/ D(J',K)
J and J' are model-space determinant indices and the determinants |K> are out of the model space,Provided that the spin-orbit interactions outside of the model space are neglected, HJK = HScJK and the summation over K is similar with that required in non-relativistic or scalar-relativistic calculations.
The m -> n transition value of an one-electron property (Anm) is readily obtained as
Anm = tr (mnR A),
where A is the property matrix in the chosen spatial orbital basis.