Contact transformational and quantum chemical calculations of the integrated intensities of fundamental, first and second overtone, binary combination and difference infrared absorption bands of the water molecule

Abstract

Double contact transformation theory, considering both mechanical and electrical anharmonicity effects up to the same (2nd) order in perturbation (inclusion of quartic terms in the energy expansion and cubic terms in the dipole moment function) is used to calculate the integrated intensities of fundamentals and of first and second overtones and binary combination and difference bands in H 2O. It is shown that the simplicity and the symmetry of the H 2O molecule reduces the general, sometimes rather complicated expressions, both for the transition moments and the intensities, to the simpler working equations actually used. In the numerical calculations, use was made of large basis ab initio calculated energy and dipole moment function expansion coefficients. The intensities of 15 bands have been calculated, for which in 13 cases an experimental value is available. The order of magnitude of the experimental values and the observed sequence is in most cases correctly reproduced, not only within one group of bands but also throughout the whole series. In nine cases the ratio between the theoretical and experimental transition moments is smaller than 1.4. For the fundamental transitions the influence of the inclusion of anharmonicity is small: only for the low intensity ν 1 mode does the effect become important and amounts to 15% of the value obtained in the double harmonic approximation. The transition moments for the first overtone are analysed in detail in order to estimate the relative importance of mechanical and electrical anharmonicity: in the stretching modes mechanical anharmonicity dominates whereas in the bending mode the largest contribution arises from the electrical one. The calculations for the second overtones show that the 3ν 3 band whose intensity has been quoted as “medium” should by far be the most intense mainly due to an effect of mechanical anharmonicity. The purely anharmonic bands with the highest intensity are the binary combination bands ν 1 + ν 3 and ν 2 + ν 3. The origin of their relatively large intensity is shown to be different: whereas in the ν 1 + ν 3 case it is the mechanical anharmonicity which gives the largest contribution, in the ν 2 + ν 3 case the electrical anharmonicity dominates. In the case of the difference bands, the relative order of magnitude of ν 1−ν 2 and ν 3−ν 1 is reproduced, the lower intensity of ν 3−ν 1 being essentially due to the statistical factor appearing in the final formula for the integrated intensity. The intensity of the ν 3−ν 2 band however is not correctly reproduced and at present no explanation can be offered for this discrepancy. The temperature effect on all the calculated intensities is examined in detail. Up to 500 K all bands, except the difference bands, are hardly affected (less than 1%) indicating that the statistical factor in the intensity formulae may be taken equal to 1 in the cases considered up to this temperature.