Theorem of Differentiation of the Energy of a Multiatomic System with Respect to Atomic Coordinates (Part I)
DOI:
https://doi.org/10.15407/ujpe59.07.0719Keywords:
energy of multiatomic system, Gell-Mann–Feynman theoremAbstract
The theorem asserting that the arbitrary-order derivative of the average energy of a solid with respect to atomic coordinates equals the average value of the corresponding derivative of the potential energy operator with respect to atomic coordinates has been proved. This theorem is a generalization of the well-known Gell-Mann–Feynman theorem, which was proved only for the first derivative of the average energy with respect to atomic coordinates. A necessity in
such a generalization is associated with the calculation of force constants in solids, which are the derivatives of the average energy with respect to atomic coordinates, and, maybe, other physical quantities.
References
I.A. Marushko, Phys. Status Solidi B 106, 707 (1981).
https://doi.org/10.1002/pssb.2221060237
C.C.J. Roothaan, Rev. Mod. Phys. 23, 69 (1951).
https://doi.org/10.1103/RevModPhys.23.69
R.P. Feynman, Phys. Rev. 56, 340 (1939).
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