Spin-Orbit Interaction with Nonlinear Wave Functions

摘要

The computation of the spin-orbit interaction is discussed for electronic wave functions expressed in the new nonlinear expansion form.This form is based on spin eigenfunctions using the graphical unitary group approach(GUGA).The nodes of a Shavitt graph in GUGA are connected by arcs,and a Configuration State Function(CSF)is represented as a walk along arcs from the vacuum node to a head node.The wave function is a linear combination of product functions each of which is a linear combination of all CSFs,wherein each CSF coefficient is a product of nonlinear arc factors.When the spin-orbit interaction is included the Shavitt graph is a union of single-headed Shavitt graphs each with the same total number of electrons and orbitals.Thus spin-orbit Shavitt graphs are multiheaded.For full-CI multiheaded Shavitt graphs,analytic expressions are presented for the number of walks,the number of nodes,the number of arcs,and the number of node pairs in the associated auxiliary pair graph.