Abstract
AbstractThe matrix elements of various analytical functions f(X), X being the internuclear separation, are required for the description of transition probabilities and other molecular properties. These matrix elements can be conveniently estimated by assuming vibrational wave functions of two relatively dispalced linear harmonic oscillators of arbitrary frequencies to represent the vibrational levels of two electronic states of a molecule. Using this assumption, analytical expressions for the matrix elements of an arbitrary analytical function f(X) are obtained. Useful recursion relations among these matrix elements are derived and an elegant graphical representation of the recursion relations is obtained. These graphical representations are utilized to obtain new more general recursion relations among matrix elements of the arbitrary function f(X).
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