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Triplet instability in doublet systems
1.R. J. Bartlett, J. Phys. Chem. 93, 1697 (1989), and references therein.
2.J. Gauss, in Encyclopedia of Computational Chemistry, edited by P. v. R. Schleyer, N. L. Allinger, T. Clark, J. Gasteiger, P. Kollmann, H. F. Schaefer, and P. R. Schreiner (Wiley, Chichester, 1998), p. 615.
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6.Quote attributed for T. H. Dunning.
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13.Excluded here are cases in which closed-shell systems (usually singlet biradicals) are treated with a spin-polarized UHF reference function.
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25.In multidimensional systems, the geometrical interpretation of what is meant by “beyond” is of course nontrivial. However, thinking of this in terms of a diatomics (or an isolated bond stretching coordinate) is sufficient here.
26.P. Pulay and T. P. Hamilton, J. Chem. Phys. 88, 4926 (1988).
27.When there is no triplet instability present, the UHF and RHF orbitals are the same. Then the occupied orbitals have UNO occupation numbers of two and the unoccupied orbitals have occupation number zero.
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29.P. Hassanzadeh and K. K. Irikura, Int. J. Quantum Chem. 19, 1315 (1998).
30.For CF, there is a minimum in the stability curve and corresponding rapid variation in the UNO occupations numbers at a distance roughly 0.25 Å beyond This is where the σ bond begins to rupture, but is sufficiently far from to have a negligible impact on calculated properties (see Sec. III).
31.I. M. Mills, in Molecular Spectroscopy: Modern Research, edited by K. N. Rao and C. W. Mathews (Academic, New York, 1972), p. 115.
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36.J. F. Stanton, J. Gauss, J. D. Watts, W. J. Lauderdale, and R. J. Bartlett, Int. J. Quantum Chem., Symp. 26, 879 (1992).
37.In addition to comparing them with results obtained by RKR inversion of experimental data, it is instructive to compare the constants (or, more precisely, the ratio between them) with the behavior expected from a Morse oscillator model
38.J. C. Saeh and J. F. Stanton, J. Chem. Phys. 111, 8265 (1999).
39.The word “almost” is used here, because the eigenvalue never reaches zero. In a case where there is a symmetry-breaking instability, the eigenvalue indeed reaches zero, and all derivatives of the energy will diverge at such a point for any calculation other than full CI. For PO, and any other case in which the two “competing” solutions mix at all distances, this will not occur and there is a limit on how poor the results can become.
40.NIST-JANAF Thermochemical Tables., edited by M. Chase, Jr. (NIST, Washington, DC., 1998).
41.K. Huber and G. Herzberg, Constants of Diatomic Molecules (Van Nostrand Reinhold, New York, 1979).
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