Density Matrices and Density Functionals pp 629-641 | Cite as
An Algorithm for Calculating Isoelectronic Changes in Energies, Densities, and One-Matrices
Abstract
A new algorithm is presented which enables the generation of approximate ground-state electron densities and approximate ground state energy differences of isoelectronic processes for interacting and non-interacting systems. This is accomplished starting exclusively from knowledge of the following: one isoelectronic ground state “seed” density ρA, the external potential vA which generates ρA, and the external potential vB for which the ground state energy EB and density ρB are sought. Use is made of a matching theorem in conjunction with trial one-matrices, the virial theorem, and a variation of a Legendre transform idea. Furthermore, knowledge of the exact energy EB enables the approximation of EB using either of two energy difference formulae which are approximations to the exact integrated Hellmann-Feynman energy difference.
Keywords
Ground State Energy Virial Theorem Legendre Transform Exact Energy Permutation ProblemPreview
Unable to display preview. Download preview PDF.
References
- 1.M. Levy, Phys. Rev. A 26, 1200 (1982).CrossRefGoogle Scholar
- 2.S. T. Epstein, A. C. Hurley, R. E. Wyatt, and R. G. Parr, J. Chem. Phys. 47, 1275 (1976).CrossRefGoogle Scholar
- 3.R. E. Stanton, J. Chem. Phys. 36, 1298 (1961).Google Scholar
- 4.M. Levy, J. Chem. Phys. 68, 5298 (1978).CrossRefGoogle Scholar
- 5.Although we are not dealing with the universal variational kinetic plus electron-electron repulsion functional here, neverthe less, we follow the spirit of the Legendre transform development in E. H. Lieb, Int. J. Quantum Chem. 24, 243 (1983) which, in part, can be looked upon as a generalization of the model poten¬tial section in J. K. Percus in Int. J. Quantum Chem. 13, 89 (1978).Google Scholar
- 6.J. E. Harriman in “Density Functional Theory”, Lecture Notes in Physics, Vol.187, edited by J. Keller and J. L. G£zquez, (Springer- Verlag, New York, 1983), pp. 37–88; Phys. Rev. A, 27, 632 (1983).Google Scholar
- 7.To perform calculations on interacting systems with this algorithm we begin with guessed one matrices rather than densities so that the problem of mapping y p does not arise. The reader should therefore substitute y for p when thinking of interacting systems.Google Scholar
- 8.P. Hohenberg and W. Kohn, Phys. Rev. 136, B864 (1964).CrossRefGoogle Scholar