Sextic Centrifugal Distortion Terms Research Articles

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

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.

Infrared and microwave high-resolution spectrum of the ν 3 band of ozone

The vibration-rotation band ν 3 of ozone has been recorded with a high-resolution (0.012 cm −1) spectrometer, and microwave absorption spectra of ozone have been identified in the excited vibrational states (100) and (001). A strong Coriolis interaction has been observed. More than 1200 spectral lines have been identified in the ν 3 band, using a Watson-type Hamiltonian, including all the sextic centrifugal distortion terms. Band constants and an atlas listing line wavenumbers, intensities, and assignments are given, from 1007 to 1072 cm −1. It is shown that transitions with high values of the quantum numbers K −1 (≥11) contribute to significant absorption.

Simultaneous analysis of the ν2and ν4bands of methane

Vibration-rotation spectra of the ν2 and ν4 bands of CH4 have been analysed by a simultaneous diagonalization of the hamiltonian matrices for the v 2=1 and v 4=1 states coupled by the Bξ2,4 Coriolis interaction term. The effective hamiltonians used extend to sextic centrifugal distortion terms. The results are a significant improvement on any previous analysis; 438 assigned transitions up to J′=16 have been fitted with an overall standard deviation of 0·016 cm-1. The method used is compared with an alternative theoretical approach given by Berger.

High-resolution infrared spectrum of the ν1 + ν3 band of ozone

The ν 1 + ν 3 band of ozone (O 3) near 2110 cm −1 has been measured and analyzed using a Watson-type Hamiltonian including all seven sextic centrifugal distortion terms. Two weak perturbations have been found between K = n of ν 1 + ν 3 and K = n + 3 of 2 ν 3. Those perturbations locate the band center for 2 ν 3 at about 2058 cm −1. Aside from those perturbations the interactions of ν 1 + ν 3 with 2 ν 1 and 2 ν 3 have not been taken into account in the analysis. Effective band constants and an atlas listing line wavenumbers and assignments are given.