Relativistic Atomic Structure Calculations II: Computational Aspects of the Finite Basis Set Method

In the first of these lectures, we examined the basic theory of relativistic electronic structure calculations. The principal computational requirement in the determination of Dirac spinors within the Dirac—Hartree—Fock (DHF) approximation involves the solution of coupled first—order integro—differential equations. The traditional approach employs the finite—difference techniques introduced by Hartree in the calculation of non—relativistic self—consistent fields. The scheme is highly accurate and has been implemented by hand, on mechanical calculators and on electronic computers, for which many FORTRAN programs have been published. The first successful relativistic mean—field calculation using the finite—difference approximation, but which approximated the exchange potential, was performed by Williams in 1940. Today, a number of sophisticated programs are freely available as black—box atomic structure models which perform self—consistent field and multi—configurational calculations, but which are are not suited ideally to the calculation of relativistic many—body effects and which do not exhibit a computational structure which is compatible with the architecture of supercomputing machines.