Abstract
The “permanent” method for nonorthogonal VB calculations is extensively developed, and the so-called “subgraph-driven” procedure is proposed. To achieve high efficiency, the summation of a huge number of permanents is treated as a whole system, and the intermediate quantities, the “contracted-cofactors” of various orders, are introduced for the systematic summation. These intermediate quantities can be characterized by pairing graphs of 2n elements (n = 1, 2, ... 1/2N − 2). Some test calculations for systems of up to 20 electrons are performed. The practice shows that this method is highly efficient, and the CPU time increases in a quite moderate way with the increasing number of electrons.
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References
For a recent review on VB theory, see the special issues of J. Mol. Struct. (Theochem) 229 (1991); 259 (1992); 260 (1992); 261 (1992).
M. Sironi, D.L. Cooper, J. Gerratt and M. Raimondi, J. Am. Chem. Soc. 112 (1990) 5054; M. Sironi, M. Raimondi, D.L. Cooper and J. Gerratt, J. Phys. Chem. 95 (1991) 10617.
M. Sironi, M. Raimondi, D.L. Cooper and J. Raimondi, Chem. Rev. 91 (1991) 929.
D.L. Cooper, J. Gerratt and M. Raimondi, Chem. Rev. 91 (1991) 929.
D.L. Cooper, J. Gerratt, M. Raimondi, M. Sironi and T. Thorsteinsson, Theor. Chim. Acta 85 (1993) 261.
J.H. Langenberg and P.J.A. Ruttink, Theor. Chim. Acta 85 (1993) 285.
C.A. Coulson and I. Fischer, Phil. Mag. 40 (1949) 306.
X. Li and J. Paldus, J. Mol. Struct. (Theochem) 229 (1991) 249.
C.A. Coulson,Valence (Oxford University Press, London, 1961).
L. Pauling,The Nature of the Chemical Bond (Cornell University Press, Ithaca, NY, 1960).
J. Verbeek and J.H. van Lenthe, J. Mol. Struct. (Theochem) 229 (1991) 115.
P. -O. Löwdin, Phys. Rev. 97 (1955) 1474.
J.H. van Lenthe and G.G. Balint-Kurti, Chem. Phys. Lett. 76 (1980) 138; J. Chem. Phys. 78 (1983)5699.
R. McWeeny, J. Mol. Struct. (Theochem) 168 (1988) 459; 229 (1991) 29; Int. J. Quant. Chem. (QCS) 24 (1990) 733.
Q. Zhang and X. Li, J. Mol. Struct. (Theochem) 198 (1989) 413; X. Li and Q. Zhang, Int. J. Quant. Chem. 36 (1989) 599.
[14]Q. Zhang and X. Li, J. Mol. Struct. (Theochem) 36 (1989) 599.
J. Li and W. Wu, Theor. Chim. Acta 89 (1994) 105.
J. Gerratt, Adv. At. Mol. Phys. 7 (1971) 41.
N.C. Pyper and J. Gerratt, Proc. Roy. Soc. Lond. A355 (1977) 407.
D.J. Klein and B.R. Junker, J. Chem. Phys. 54 (1971) 4294;
B.R. Junker and D.J. Klein, J. Chem. Phys. 55 (1971) 5532.
H. Minc,Permanents (Addison-Wesley, Reading, MA, 1978);
H.J. Ryser,Combinatorial Mathematics (Math. Ass. Am., NY, 1965);
W.B. Jurkat and H.J. Ryser, J. Algebra 3 (1966) 1;
A. Nijenhuis and H.S. Wilf,Combinatorial Algorithms (Academic Press, New York, 1975).
M. Raimondi and E. Gianinetti, J. Phys. Chem. 92 (1988) 899.
S. Rettrup, T. Thorsteinsson and C.R. Sarma, Int. J. Quant. Chem. 40 (1991) 709.
J. Verbeek, Nonorthogonal orbitals in ab initio many-electron wave functions, Ph.D. Thesis, Utrecht University (1990).
P. Pulay, J. Comp. Chem. 3 (1982) 556.
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On leave from Chemistry Department, Xiamen University, 361005 Xiamen, PR China.
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Li, J. New algorithm for nonorthogonal ab initio valence bond calculations II: Subgraph-driven method. J Math Chem 17, 295–321 (1995). https://doi.org/10.1007/BF01165751
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DOI: https://doi.org/10.1007/BF01165751