Use of Hellmann—Feynman and Hypervirial Theorems to Obtain Anharmonic Vibration—Rotation Expectation Values and Their Application to Gas Diffraction
- 15 October 1966
- journal article
- research article
- Published by AIP Publishing in The Journal of Chemical Physics
- Vol. 45 (8), 2827-2831
- https://doi.org/10.1063/1.1728034
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.Keywords
This publication has 8 references indexed in Scilit:
- THE USE OF COMMUTATOR RELATIONSHIPS IN DETERMINING SCHRÖDINGER WAVE FUNCTIONSThe Quarterly Journal of Mathematics, 1965
- Higher-Order Stationary-Phase Approximations in Semiclassical ScatteringThe Journal of Chemical Physics, 1965
- Theory of the Effect of Temperature on the Electron Diffraction Patterns of Diatomic MoleculesThe Journal of Chemical Physics, 1963
- Calculation of Mean Atomic Positions in Vibrating Polyatomic MoleculesThe Journal of Chemical Physics, 1963
- Effects of Anharmonicity of Molecular Vibrations on the Diffraction of Electrons. II. Interpretation of Experimental Structural ParametersThe Journal of Chemical Physics, 1961
- Classical and Quantum Mechanical Hypervirial TheoremsThe Journal of Chemical Physics, 1960
- Effects of Anharmonicity of Vibration on the Diffraction of Electrons by Free MoleculesThe Journal of Chemical Physics, 1955
- The Energy Levels of a Rotating VibratorPhysical Review B, 1932