Electric Circuit Models for the Vibration Spectrum of Polyatomic Molecules

Abstract

Electrical circuits are developed to determine the normal frequencies and normal modes of vibration of polyatomic molecules having arbitrary configurations. The networks for each molecule are set up without equations from physical considerations alone and may be solved by an a.c. network analyzer, by numerical methods, or by digital (punch card, etc.) calculating machines. The networks also allow the establishment of the resultant secular equations of the molecule by simple inspection. The potential function considered is either a general quadratic form of the displacements, or it may correspond to the customary ``valence-force'' system employing stretching, bending, and twisting of the valence bonds and valence angles. A companion paper contains network analyzer tests on the CO2, OCS, and ethyl alcohol molecules by the ``valence-force'' model. Both the normal frequencies and normal modes of vibration check satisfactorily with known results within the accuracy of the instruments.