1. Variational calculations of fermion second-order reduced density matrices by semidefinite programming algorithm
- Author
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Nakata, Maho, Nakatsuji, Hiroshi, Ehara, Masahiro, FUKUDA, MITUHIRO, Fukuda, Mituhiro, Nakata, Kazuhide, and Fujisawa, Katsuki
- Subjects
Semidefinite programming ,Physics ,Matrix algebra ,Atoms in molecules ,Convergence (routing) ,General Physics and Astronomy ,Order (group theory) ,Reduced density matrix ,Fermion ,Physical and Theoretical Chemistry ,Algorithm ,Variable (mathematics) - Abstract
The ground-state fermion second-order reduced density matrix (2-RDM) is determined variationally using itself as a basic variable. As necessary conditions of the N-representability, we used the positive semidefiniteness conditions, P, Q, and G conditions that are described in terms of the 2-RDM. The variational calculations are performed by using recently developed semidefinite programming algorithm (SDPA). The calculated energies of various closed- and open-shell atoms and molecules are excellent, overshooting only slightly the full-CI energies. There was no case where convergence was not achieved. The calculated properties also reproduce well the full-CI results.
- Published
- 2001