Many-electron theory: Density functional approach generalized to treat spin eigenfunctions and relation to spinless low-order density matrices
✍ Scribed by N. H. March
- Publisher
- John Wiley and Sons
- Year
- 1999
- Tongue
- English
- Weight
- 285 KB
- Volume
- 74
- Category
- Article
- ISSN
- 0020-7608
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✦ Synopsis
Many-electron theory is treated here with much attention focused on the synthesis of the density functional and density matrix theory. This synthesis shows that the exchange᎐correlation potential, normally obtained as the functional derivative with respect to the electron density of an assumed approximate exchange᎐correlation energy, can be written exactly in terms of the ''near-diagonal'' behavior of the fully interacting first-order density matrix and the diagonal of the second-order density matrix, thereby bypassing the functional derivative. Also involved, since the exchange᎐correlation potential is an ''artifact'' of reducing the many-electron Schrodinger equation to one-body Slater᎐Kohn᎐Sham equations, are the one-body orbitals derived from these latter equations, not just the density thereby obtained. This situation has then motivated a discussion of what constraints are placed on the low-order density matrices of atoms and molecules, described by an assumed spin-independent Hamiltonian, by the requirement that these matrices are constructed from an N-electron wave function which is an eigenfunction of the spin operators S 2 and S . Some briefer discussion is added on the z optimally convergent determinantal expansion of such an N-electron wave function, the relation between Brueckner and Lowdin natural orbitals being commented on as a by-product.
In this latter context, it is noted that the exchange-only potential of density functional theory can be represented as a sum of two line integrals, each of which is path-dependent, the sum being, of course, path-independent. But in addition to knowledge of Slater᎐Kohn᎐Sham orbitals appearing as in the Harbola᎐Sahni exchange-Ž . only potential which is one of the path-dependent terms , there is a kinetic correction.