Relationship Between the Zero Point Energy of a Polyatomic Molecule and its Molecular Structure

Abstract

Criteria are established for the definition of the mean characteristic eigenvalue, λ0, of a system of coupled harmonic oscillators. The first criterion is that λ0 lead to a convergent series for the zero point energy of the systems; the second criterion is that λ0 be obtained directly from the matrix elements of the equations of motion, without solution for the individual eigenvalues. Two general types of λ0's are found and their properties are discussed. Detailed application is made to the zero point energy differences of the isotopic methanes, ethylenes and benzenes.