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Adiabatic second-order energy derivatives in quantum mechanics

Published online by Cambridge University Press:  24 October 2008

W. Byers Brown  and
H. C. Longuet Higgins
W. Byers Brown
Affiliation:
Department of Chemistry, University of Manchester
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Abstract

The general equation for the adiabatic second-order derivative of the energy En of an eigenstate with respect to parameters λ and λ′ occurring in the Hamiltonian ℋ is

The applications of this equation to molecules (λ, λ′ = nuclear position coordinates) and to enclosed assemblies of interacting particles (λ = λ′ = volume) are discussed, and the classical analogue of the equation for a micro-canonical ensemble is derived.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 54 , Issue 2 , April 1958 , pp. 251 - 257
Copyright
Copyright © Cambridge Philosophical Society 1958

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References

REFERENCES

(1)Brown, W. B.Molecular Phys. 1 (1958), to appear.Google Scholar
(2)Brown, W. B.J. Chem. Phys. 28 (1958), to appear.Google Scholar
(3)Feynman, R. P.Phys. Rev. 56 (1939), 340.CrossRefGoogle Scholar
(4)Frost, A. A. and Lykos, P. G.J. Chem. Phys. 25 (1956), 1299.CrossRefGoogle Scholar
(5)Gibbs, J. W.Elementary principles in statistical mechanics (1902), chapter 14. Reprinted in Collected Works, 2 (Yale, 1948).Google Scholar
(6)Kramers, H. A.Proc. K. Akad. Wet. Amst. 30 (1927), 145.Google Scholar
(7)Longuet-Higgins, H. C.Proc. Roy. Soc. A, 235 (1956), 537.Google Scholar
(8)Longuet-Higgins, H. C. and Brown, D. A.J. Inorg. Nucl. Chem. 1 (1955), 60 and 352.CrossRefGoogle Scholar
(9)Platt, J. R.J. Chem. Phys. 18 (1950), 932.CrossRefGoogle Scholar
(10)Schiff, L. I.Quantum, mechanics (New York, 1955), chapter 7.Google Scholar
(11)Slater, J. C.J. Chem. Phys. 1 (1933), 687.CrossRefGoogle Scholar