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Accounting for translational invariance in analyzing contributions of perturbation theory to force-constant tensors of molecules

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Abstract

It has been shown that there are an infinite number of modes of representation of force constants in the form of a sum of the contributions of first-order and second-order perturbation theory, depending on the selection of the admixture of translation of the nuclear skeleton as a whole to the displacement of the nuclei. In particular, any force constant can be reprsented in the form of a specially constructed second-order relaxation term (or first-order with zero contribution); a representation has been found in which the first-order contributions for the displacements of all nuclei in the molecule are identical; rules of the sums for the relaxation terms have been derived, relating the changes in the Gel-Mann-Feynman forces on the nuclei in the molecule with displacements of various nuclei. For the electronic ground state of the molecule, the optimal representation of the force constants has been found, in which the minimum in the first-order contribution is combined with the minimum in the absolute magnitude of the second-order relaxation contribution. It has been proven that in the case of an unperturbed electronic state, the first-order contribution to any diagonal force constant is positive.

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Literature cited

  1. L. Salem, “Theoretical interpretation of force constants,” J. Chem. Phys., 38, No. 5, 1227–1236 (1963).

    Google Scholar 

  2. A. B. Anderson, N. C. Handy, and R. G. Parr, “Relationships between vibrational force constants and quadrupole coupling constants for molecules and solids,” J. Phys. Chem., 50, No. 8, 3634–3635 (1969).

    Google Scholar 

  3. M. Mokarram and J. L. Ragle, “On the relationship between deuteron quadrupole coupling constants and force constants in diatomic hydrides,” J. Chem. Phys., 59, No. 5, 2770–2776 (1973).

    Google Scholar 

  4. I. B. Bersuker, “The origin of dynamic instability of molecular systems,” Teor. Éksp. Khim., 16, No. 3, 291–299 (1980).

    Google Scholar 

  5. I. B. Bersuker, N. N. Gorinchoi, and V. Z. Polinger, “On the origin of dynamic instability of molecular system,” Theor. Chim. Acta, 66, No. 3/4, 161–172 (1984).

    Google Scholar 

  6. T. K. Rebane, “On the contribution of first-order perturbation theory to curvature of the adiabatic potential surface of a molecule,” Teor. Éksp. Khim., 20, No. 5, 660–669 (1984).

    Google Scholar 

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Authors and Affiliations

  1. Leningrad University, USSR

    T. K. Rebane

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  1. T. K. Rebane
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Translated from Teoreticheskaya i Éksperimental'naya Khimiya, Vol. 21, No. 3, pp. 280–287, May–June, 1985.

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Rebane, T.K. Accounting for translational invariance in analyzing contributions of perturbation theory to force-constant tensors of molecules. Theor Exp Chem 21, 268–275 (1985). https://doi.org/10.1007/BF00523986

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  • DOI: https://doi.org/10.1007/BF00523986

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