Molecular orbital anharmonic estimates for the infrared spectrum of CO2

The vibrational spectrum of CO2 up to second overtones has been calculated at four different ab initio levels using second order perturbation theory equations in a simplified manner, in which just a few cross-terms suitable for numerical estimation are considered in the Taylor series representing the potential energy and dipole moment functions. The series coefficients are obtained through polynomial regression of estimated single point energy and dipole values for a few distorted geometries along each normal coordinate. The effect of Fermi resonance on near-degenerate energy levels was also taken into account through the usual first order perturbation equations. MP2/6-31G(extended) frequency estimates have a root mean square error of just 32.14 cm(-1). This accuracy is achieved partly due to the underestimation of the harmonic frequencies, which compensates for the neglect of the cross-term chi(ij) anharmonic constants. The chi(ii) constants which depend on cubic and quartic energy coefficients are reasonably well estimated at all ab initio levels. The energy coefficient beta(sbb) responsible for the magnitude of the Fermi resonance is estimated with a maximum error of just 13%. Despite the inclusion of anharmonicities, errors for band intensities are still much larger than for the frequencies. Both electrical and mechanical anharmonicities may be equally important to the band intensity.