The ν7 vibrational states of C 3O 2: A least-squares fit of the rigid-bender model to the v7ν7l7 energies and rotational constants

Abstract

The rigid-bender model is used to treat the large-amplitude, low-frequency, bending vibration ν 7 of C 3O 2. Different parameterizations of the bending potential function are considered, and a simple two-term power series is found to give the best fit. With this parameterization, using a least-squares fit to energies and B values, the ν 7 potential function is determined for the ground state as well as for the states in which ν 2, ν 3, ν 4, ν 6, 2 ν 6, ν 1 + ν 3, ν 1 + ν 4, ν 2 + ν 3, and 2 ν 2 + ν 4 are excited. The excitation of other vibrations has in some cases a drastic effect on the ν 7 potential. In the ground state the potential has a 29 cm −1 barrier at the linear position, in ν 1 + ν 3 the barrier increases to 79 cm −1, while in 2 ν 2 + ν 4 the barrier vanishes. An equilibrium potential is determined by correcting the ground state potential for the effects of zero-point motion of the normal vibrations ν 1, …, ν 6. This potential has a 35.6-cm −1 barrier with a minimum at α = 11.14°, where 2α is the angular deviation from linearity. The model accurately predicts the quartic and sextic centrifugal distortion terms for the low-lying v 7 ν 7 l 7 states. Second-order l-type coupling is included in the calculations of the quartic terms. The effects of this coupling, which are most pronounced for the ν 7 ≥ 2 states, adequately explain the negative D term recently reported for the ν 2 + 4 ν 7 0 state.