Full dimensional Franck-Condon factors for the acetylene A^{~ 1}A_u—X^~1Σ⁺_g transition. I. Method for calculating polyatomic linear—bent vibrational intensity factors and evaluation of calculated intensities for the gerade vibrational modes in acetylene

Franck-Condon vibrational overlap integrals for the A^~1A_u—X^~1Σ⁺_g transition in acetylene have been calculated in full dimension in the harmonic normal mode basis. The calculation uses the method of generating functions first developed for polyatomic Franck-Condon factors by Sharp and Rosenstock [J. Chem. Phys. 41(11), 3453–3463 (1964)], and previously applied to acetylene by Watson [J. Mol. Spectrosc. 207(2), 276–284 (2001)] in a reduced-dimension calculation. Because the transition involves a large change in the equilibrium geometry of the electronic states, two different types of corrections to the coordinate transformation are considered to first order: corrections for axis-switching between the Cartesian molecular frames and corrections for the curvilinear nature of the normal modes at large amplitude. The angular factor in the wave function for the out-of-plane component of the trans bending mode, ν₄^″, is treated as a rotation, which results in an Eckart constraint on the polar coordinates of the bending modes. To simplify the calculation, the other degenerate bending mode, ν₅^″, is integrated in the Cartesian basis and later transformed to the constrained polar coordinate basis, restoring the conventional v and l quantum numbers. An updated A^~-state harmonic force field obtained recently in the R. W. Field research group is evaluated. The results for transitions involving the gerade vibrational modes are in qualitative agreement with experiment. Calculated results for transitions involving ungerade modes are presented in Paper II of this series [G. B. Park, J. H. Baraban, and R. W. Field, "Full dimensional Franck–Condon factors for the acetylene A^~1A_u—X^~1Σ⁺_g transition. II. Vibrational overlap factors for levels involving excitation in ungerade modes," J. Chem. Phys. 141, 134305 (2014)]