A Tour of the Foundations of
Computational Chemistry and Material Science
Lecture 1: ab initio Methods



Introduction

The problem is to determine the stationary state wave function tex2html_wrap_inline967 of an atom or ion, in the framework of special relativity and quantum mechanics, i.e. to find the solution of the eigenvalue problem;

equation17

where H is the Dirac Hamiltonian for an N-electron atom (or ion) less the rest energy. The state of an atom is specified by its energy E, as well as with values of the total angular momentum tex2html_wrap_inline969 with eigenvalues tex2html_wrap_inline971 and its projection on an arbitrary but fixed axis (say the Z axis) tex2html_wrap_inline973 with eigenvalues tex2html_wrap_inline975. The wave function must obey the Pauli-exclusion principle for fermions(electrons), i.e., be anti-symmetric with respect to an interchange of particles.



Author: Dr. Warren Perger and Ken Flurchick