New vibrational force-field expansion of coupled linear benders: application to the X state of acetylene

A new vibrational force-field Hamiltonian is constructed for the coupled linear bend vibrations of C2H2 (X1Σg+) represented by circular boson operators. A total of 14 expansion coefficients and the two harmonic frequencies in the force-field Hamiltonian are determined from a least-squares fit to the experimental vibrational term values, i.e., 59 term values in the previous literatures and 23 new term values derived from the present high-resolution dispersed fluorescence measurements. The derived Hamiltonian reproduces well the experimental vibrational term values up to 8000 cm−1 with a standard deviation σ of 0.35 cm−1.