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The Hellmann—Feynman-theorem expression for the z component of the force on a single nucleus is differentiated successively to obtain expressions which are related to the harmonic and anharmonic potential constants in a molecule. The method used to simplify the differentiations is also used to derive two expressions for the field-gradient part of the nuclear-quadrupole coupling constant; the two expressions involve only convergent integrals. The virial-theorem expression for diatomic molecules is differentiated to obtain equations for the cubic and quartic potential constants and for the Dunham constants a1 and a2. Application of the equations to quantum-chemical calculation of the potential constants is discussed.
R. H. Schwendeman (Sat,) studied this question.