Approximations in Relativistic Density Functional Theory

Prior to the wholesale adoption of DFT by quantum chemists, a variety of approximations were used to implement DFT methods in relativistic and nonrelativistic programs. A large portion of the literature on relativistic effects from DFT calculations is due to these programs, most of which are still in use today. In this appendix, we briefly describe some of these approximations. 

A different approach was developed by Baerends, Ellis, and Ros (1973). In addition to adopting the Slater potential for the exchange, their approach had two distinct features. The first was an efficient numerical integration procedure, the discrete variational method (DVM), which permitted the use of any type of basis function for expansion, not only Slater-type orbitals or Gaussian-type orbitals, but also numerical atomic orbitals. The second feature was an evaluation of the Coulomb potential from 

Relativistic corrections have also been included in DFT calculations using perturbation theory, first by Herman and Skillman (1963) and later by Snijders and Baerends (Snijders 1979, Snijders and Baerends 1977, 1978). Following a non-relativistic Hartree-Fock-Slater calculation, first-order perturbation theory was used to calculate the relativistic corrections from the Breit-Pauli terms of 0(c ). Herman and Skillman applied this approach to first order only for the energies. 

In the approach by Snijders and Baerends, the spinors from the nonrelativistic equation satisfy the equation 

The mass-velocity corrections to the orbital energy and the orbital are calculated from 

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