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Studies of the Statistical Exchange Approximation in First-Transition-Row Atoms and Ions: Mn+2 Ion

Timothy M. Wilson*, J. H. Wood, and J. C. Slater†

  • University of California, Los Alamos Scientific Laboratory, Los Alamos, New Mexico 87544

  • *Present address: Quantum Theoretical Research Group, Department of Physics, Oklahoma State University, Stillwater, Okla. 74074.
  • †University of Florida, Gainesville, Fla. and Massachusetts Institute of Technology, Cambridge, Mass. 02139.
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Phys. Rev. A 2, 620 – Published 1 September, 1970

DOI: https://doi.org/10.1103/PhysRevA.2.620

Abstract

A study of several statistical approximations to the Hartree-Fock (HF) one-electron effective exchange potential has been carried out through a series of restricted and spin-polarized Hartree-Fock-Slater (HFS) calculations on 3d-transition-row atoms and ions. The results of this study for the Mn+2 ion are reported in this paper and are compared with the corresponding HF results. Of the various approximations in which only the homogeneous part of the local exchange potential is kept, the simple Xα method is shown to give quite good results. This method amounts to multiplying the exchange potential −6[(34π)ρξ(r)]13, where ξ=±12, by a constant α which is usually determined by the requirement that the Xα orbitals correspond to a minimum in the HF energy. It is shown that the energy-dependent exchange schemes proposed earlier break down totally in the spin-polarized case. We examine the importance of including the inhomogeneous correction terms via the method recently proposed by Herman et al. and we discuss the possible importance of these terms in spin-polarized energy-band calculations. We conclude that the Xα method is both accurate and simple enough for practical use in carrying out energy-band calculations for magnetic solids.

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Phys. Rev. A 2, 620– Published 1 September, 1970
  • Received 15 January 1970

© 1970 American Physical Society

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