Use of Hellmann—Feynman and Hypervirial Theorems to Obtain Anharmonic Vibration—Rotation Expectation Values and Their Application to Gas Diffraction

Abstract

A recursion relation for the moments of the probability function for a one‐dimensional anharmonic oscillator are derived by using a hypervirial relation. In addition it is shown that the first few moments of the probability function can be easily obtained by use of Hellmann—Feynman, virial, and Ehrenfest's theorems if the vibrational—rotational energy is known as a function of the anharmonic force constants. Expressions for the first four moments of a potential function containing cubic and quartic anharmonic terms are given by use of Dunham's expression for the vibrational energy. The application of anharmonic moments in gas electron diffraction is considered in detail.