ROTATIONAL SPECTRA OF MOLECULES CONTAINING TWO INEQUIVALENT SYMMETRICAL INTERNAL ROTORS

Abstract

A computer program for predicting the rotational spectrum of a molecule containing two inequivalent symmetrical internal rotors has been written. This program includes both the kinetic and potential energy terms coupling the two tops. A plane (xz) of symmetry is assumed. The axis system is chosen in the molecule such that the coefficient of $P1^{P}X$ is zero (IAM), where the top with the lower barrier is called top 1. The Hamiltonian for the internal rotation of each top including terms of the form $C_{Iz}P_{l}K$ and $C_{2z}P_{2}K$ is set up in the free rotor basis and diagonalized. Matrices representing $P_{1}$, $P_{2}$, $(l_{1})_{K,K+1}$, $(l_{2})_{K,K+1}$, $(p_{2})_{K,K+1}$, $(1_{1})_{K,K+2}$, and $(1_{2})_{K,K+2}$ are set up and the basis set of each top truncated to the first five torsional states. The matrices $(25 \times 25)$ corresponding to the internal rotation problem of both tops including coupling are set up for each K. These are diagonalized. The overall rotation-torsional coupling matrices off diagonal in K are set up and transformed by the eigenvectors of the torsional problem. A Van Vleck transformation is then carried out to fold back the matrix elements connecting the ground torsional state and excited torsional states. The resulting $2J+1$ by $2J+1$ matrix for the ground torsional state is diagonalized to obtain the energy levels. The application of this program to the analysis of the spectrum of silyl methyl ether will be discussed. This work supported by a grant from the National Science Foundation.