Abstract
An alternative procedure is presented for the calculation of Hamiltonian matrix elements between non-orthogonal Slater determinants. Using the singular-value decomposition theorem a simple and general expression is derived for the cofactors needed in the Löwdin formula. The algorithm proposed has a cost in terms of CPU time proportional to N 4, N being the number of electrons, and does not present any problem of data storage.
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References
G. A. Gallup, R. L. Vance, J. R. Collins and J. Norbeck: Adv. Quantum Chem. 16, 229 (1982).
J. H. van Lenthe and G. G. Balint-Kurti: J. Chem. Phys. 78, 5699 (1983).
M. Raimondi, M. Simonetta and G. F. Tantardini: Comput. Phys. Rep. 2, 171 (1985).
D. L. Cooper, J. Gerratt and M. Raimondi: Adv. Chem. Phys. 69, 319 (1987).
R. McWeeny: Int. J. Quantum Chem. 34, 25 (1988).
F. Prosser and S. Hangstrom: Int. J. Quantum Chem. 2,89 (1968).
M. Raimondi, W. Champion and M. Karplus: Mol. Phys. 34,1483 (1977).
M. Raimondi and E. Gianinetti: J. Phys. Chem. 92,899 (1988).
S. Rettrupp, T. Thorsteinsson and C. R. Sarma: Int. J. Quantum Chem. 40, 709 (1991).
P. O. Löwdin: Phys. Rev. 97,1474 (1955).
J. W. Archbold: Algebra, Pitman, London, 338 (1961).
I. C. Hayes and A. J. Stone: Mol. Phys. 53,69 (1984).
V. Magnasco and G. Figari: Mol. Phys. 55,319 (1985).
J. Verbeek and J. H. van Lenthe: J. Mol. Struct. (Theochem) 75,115 (1991).
A. T. Amos and G. G. Hall: Proc. R. Soc. (London) A263, 483 (1961); see also, H. F. King, R. E. Stanton, H. Kim, R. E. Wyatt and R. G. Parr: J. Chem. Phys. 47, 1936 (1967).
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© 1997 Springer Science+Business Media Dordrecht
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Amovilli, C. (1997). On the Evaluation of the Matrix Elements Between Non-Orthogonal Slater Determinants. In: McWeeny, R., Maruani, J., Smeyers, Y.G., Wilson, S. (eds) Quantum Systems in Chemistry and Physics. Trends in Methods and Applications. Topics in Molecular Organization and Engineering, vol 16. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-4894-8_19
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DOI: https://doi.org/10.1007/978-94-011-4894-8_19
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-6052-3
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