THE CONTRIBUTION TO THE ROTATIONAL CONSTANT OF $H_{2}$ AND HD DUE TO THE ELECTRONS IN THE $MOLECULE^{*}$

Abstract

“When the electrons are included in the complete Hamiltonian for a diatomic $molecule,^{1}$ a term $\pi_{xx}\pi_{x}P_{x}+\mu_{yy}P_{y}$ (1) occurs which is of some interest. The $\pi_{x}$ and $\pi_{y}$ are operators representing the components of internal angular momentum of the electrons, and $P_{x}$ and $P_{y}$ represent components of the total angular momentum. It follows that the term (1) represents a Coriolis type interaction between the rotational motion of the molecule and the internal motions of the electrons. A second order perturbation calculation has been carried out for $H_{2}$ and HD using the term in (1). The results are expressible in the form of a correction to the rotational constant. In the case of $H_{2}$ the calculations have been carried out using several of the existing approximations to the ground state wave function. Results indicate a close dependence of the magnitude of the correction on the form of the wave function. The numerical values of the correction factor are in fair agreement with those calculated from figures based on an irrotational flow $model.^{2}$”