Abstract
Historically, the non-orthogonality problem arose with the first attempts to pass from the qualitative quantum mechanical treatment of polyatomic molecules to more quantitative methods. Indeed, the very beginning of quantum chemistry was marked by the contradiction between considerations associating the strengths of the chemical bonds to the overlaps between atomic orbitals /1–4/ and treatments where the atomic orbitals were assumed to be orthogonal one to another /5/. The problem was at the same time a physical and a mathematical one, as will be illustrated below. Löwdin’s work (/6/ and references given later) played a decisive role in formulating correctly and analyzing this problem.
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References
J.C. Slater, Phys. Rev., 37, 481 (1931), 38, 325, 1109 (1932).
R.S. Mulliken, Phys. Rev., 41, 67 (1932).
L. Pauling, J. Amer. Chem. Soc., 53, 1367 (1931).
R.S. Mulliken, J. Amer. Chem. Soc., /2, 4493 (1950).
G.W. Wheland, J. Amer. Chem. Soc., 63, 2025 (1941);
B. H. Chirgwin and C.A. Coulson, Proc. Roy. Soc. (London), A201, 196 (1950).
P.O. Löwdin, Adv. in Quant. Chem., 5, 185 (1970).
Cf. M.J.S. Dewar, J. Amer. Chem. Soc. /4, 3341–3357 (1952).
Cf.e.g. Th. Förster, in “Modern Quantum Cemistry”, 0. Sinanoglu ed. New York, Acad. Press, 1965, vol III, p. 93.
G. Del Re, Adv. Quant. Chem., 8, 95 (1974).
C.A. Coulson, Revs. Mod. Phys., 32, 170 (1960).
G. Berthier, Tetrahedron, 19s. 2 1 (1963).
G. Klopman, B.O. Leary, Fortschr. Chem. Forsch., 15, 445 (1970).
J. Koutecky, Chem. Phys. Lett., 1, 249 (1967).
J. Hubbard, Proc. Roy. Soc. (London), A276, 238; A277, 237 (1964).
P.O. Löwdin, Arkiv Mat. Astron. Fysik, 35A, n. 9 (1947);
P.O. Löwdin, J. Chem. Phys. 18, 365 (1950).
T.B. Grimley, J. Phys. C: Solid St. Phys., 3, 1934 (1970).
B.C. Carlson and J.M. Keller, Phys. Rev., 105, 102 (1957).
G. Del Re, Theoret. Chim. Acta, 1, 188 (1963).
P.O. Löwdin, Adv. in Phys. 5, 1, (1956) See in particular pp. 40–56.
R. McWeeny, in Molecular Orbitals in Chemistry Physics and Biology (Eds. P.O. Löwdin, B. Pullman) New York Acad. Press (1969).
A. Veillard, G. Del Re, Theoret. Chim. Acta, 2, 55 (1964).
B.J. Duke, Theoret. Chim. Acta, 8, 87 (1967).
J.A. Chapman, D.P. Chong, Theoret. Chim. Acta, 10, 364 (1968).
P.O. Löwdin, J. Appl. Phys. (suppl.) 33, 251 (1962).
G. Del Re, Int. J. Quant. Chem., 1, 293 (1967).
H. Shull and P.O. Löwdin, J. Chem. Phys., 23, 1362, 1565 (1955).
A. Rastelli and G. Del Re, Int. J. Quant. Chem., 3, 543 (1969).
R.S. Mulliken, J. Amer. Chem. Soc., 88, 1849 (1966).
G. Del Re, Nuovo Cim. 13, 644 (1960).
K.Fukui, T. Youezawa, H. Shingu, J. Chem. Phys., 20, 722 (1952).
E. Goursat, Cours D’Analyses Mathématique Gauthiers-Villars, Paris 1949 (7ed.), col. 2 p. 65.
G. Del Re, Int. J. Quant. Chem., 7S, 193 (1973).
H. Kashivagi, F. Sasaki, Int. J. Quant. Chem., 7S, 515 (1973).
D.R. Hartree, Proc. Camb. Phys. Soc., 45, 230 (1949).
G. Berthier, Tetrahedron, 19, s. 2 1 (1963).
G. Del Re, in Localization and Delocalization in Quantum Chemistry (eds. 0. Chalvet et al) Reidel, Dordrecht, 1976, Vol. II, p. 149–170.
B. Lévy, unpublished.
W. Mayer, J. Chem. Phys., 58, 1017 (1973).
C. Edmiston and K. Ruedenberg, Rev. Mod. Phys., 35, 457 (1963).
I. Fisher-Hjalmars, J. Chem. Phys. 42, 1962 (1965).
S.F. Boys and J. Foster, Rev. Mod. Phys. 32, 305 (1960).
L.M. Fal, S. Wolfe and I.C. Csizmadia, J. Chem. Phys., 59, 4047 (1973).
J.P. Dahl, Acta Chem. Scand., 21, 1244 (1967).
J. Cizek, J. Mol. Phys., 6, 19 (1963).
A. Julg, Fortsch. Chem. Forsch. (1975) in press and references therein.
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Del Re, G. (1976). The Non-Orthogonality Problem and Orthogonalization Procedures. In: Calais, JL., Goscinski, O., Linderberg, J., Öhrn, Y. (eds) Quantum Science. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-1659-7_5
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DOI: https://doi.org/10.1007/978-1-4757-1659-7_5
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