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 -representability, we used the positive semidefiniteness conditions, and 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.
REFERENCES
1.
K.
Husimi
, Proc. Phys. Math. Soc. Jpn.
22
, 264
(1940
).2.
P.-O.
Löwdin
, Phys. Rev.
99
, 1474
(1955
).3.
H. Nakatsuji, in Many-Electron Densities and Reduced Density Matrices, edited by J. Cioslowski (Kluwer Academic, New York, 2000).
4.
5.
6.
7.
8.
M.
Ehara
, M.
Nakata
, H.
Kou
, K.
Yasuda
, and H.
Nakatsuji
, Chem. Phys. Lett.
305
, 483
(1999
).9.
M.
Nakata
, M.
Ehara
, K.
Yasuda
, and H.
Nakatsuji
, J. Chem. Phys.
112
, 8772
(2000
).10.
11.
12.
C.
Garrod
and M. A.
Fusco
, Int. J. Quantum Chem.
x
, 495
(1976
).13.
14.
15.
K. Fujisawa, M. Kojima, K. Nakata, SDPA (SemiDefinite Programming Algorithm) User’s Manual Version 5.00, August 1999, ftp://ftp.is.titech.ac.jp/pub/OpRes/software/SDPA/5.00/.
16.
R. M. Erdahl and C. Garrod, in Proceedings of the Conference on Density Matrices, Kingston, June 1974, edited by A. J. Coleman and R. M. Erdahl.
17.
18.
Yu. Nesterov and A. S. Nemirovskii, Interior Point Polynomial Method in Convex Programming: Theory and Applications (SIAM, Philadelphia, 1993).
19.
M. Kojima, Semidefinite Programming and Interior-Point Methods, http://www.is.titech.ac.jp/̃kojima/wabun.html, 1996 (in Japanese).
20.
21.
T. H. Dunning, Jr. and P. J. Hay, in Method of Electronic Structure Theory, edited by H. F. Schaefer III (Plenum, New York, 1977), Vol. 2; Actually, basis sets are taken from EMSL Gaussian Basis Set Order Form, http://www.emsl.pnl.gov:2080/forms/basisform.html.
22.
23.
K. P. Huber and G. Herzberg, Molecular Spectra and Molecular Structure IV, Electronic Constants of Diatomic Molecules (Van Nostrand Reinhold, New York, 1979).
24.
J. H. Callomon, E. Horita, K. Kuchitsu, W. J. Lafferty, A. G. Maki, and C.S. Pote, Landolt–Börnstein (Springer-Verlag, Berlin, 1976).
25.
This content is only available via PDF.
© 2001 American Institute of Physics.
2001
American Institute of Physics
You do not currently have access to this content.