Analytical dipole moment functions for diatomic molecules :

Abstract

We require the y-series expansion to satisfy the condition that the infinite sum of its coefficients M(, n) vanishes. Then, expressing M(, n) as some function of the index n and several parameters, we fit this function to a few known transition moments and obtain an infinite y-series representation with the correct asymptotic behavior for the CO dipole moment. We found three functional forms for M(, n) that produce infinite series reducible to closed forms. These new forms are adjusted further by a corrective term so that they obtain the correct general behavior at both large r and small r. The various CO dipole moment functions finally are used to predict hot-band transition moments.

The dipole moment of the ground electronic state (X('1)(SUMM)('+)) of CO as a function of the internuclear distance is determined using experimentally deduced rotationless vibrational transition moments. For this purpose, the dipole moment function is expanded in series of powers of the variables u, y, and z, where u=r-r(, e), y=1-exp(-au), and z=exp(au)-1, and exact Morse matrix elements of these quantities are used in computation. Using a standard factorization technique, we derive exact matrix elements of y, y('2), and y('3). For higher powers of y, we use matrix multiplication. The eigenfunctions of the perturbed Morse oscillator (PMO) are obtained by the method of matrix diagonalization. Morse and PMO cubic dipole moment functions in u, y and z are then determined for CO.