The Basis State Functions

We now turn to the vibrational wavefunctions appearing in the matrix element (7.70a). 

To evaluate the integral (7.70a), it is necessary to obtain expressions for the nuclear wavefunctions Xj and X/- The upper adiabatic state can often be described in the harmonic approximation as a product of three oscillator functions 

The normal coordinates qi and q2 for the symmetric stretching and bending vibrations are then linear combinations of the symmetry coordinates Si and S2 used above for calculating the electronic coupling factor gn and qj = C33S3 is the asymmetric stretching coordinate [70] 

The transformation coefficients of Equation 7.81 are determined by solving the usual secular equation in terms of the masses, force constants, and frequencies [267]. The numerical values of the coefficients cq for the ground state of the neutral molecule are [70] 

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