AB INITIO MO CALCULATIONS OF INFRARED INTENSITIES

Dipole Moment Derivative from the Energy Gradient.166 

The semiclassical theories described so far are aimed mostly at interpreting the experimentally determined vibrational absorption intensities of molecules in terms of quantities associated with the charge distribution and dynamics. Fewer attempts have been made for quantitative predictions of intensities based on transferable intensity parameters. Successful predictions are difficult to achieve because transferability properties are not so well expressed as in the case of force constants. This is determined by a number of factors (1) the high sensitivity of vibrational intensities associated with particular modes to changes in molecular environment (2) the physical limitations of the approximate point-charge models and (3) mathematical difficulties in applying non-approximate models such as polar tensors or bond polar parameters for larger molecules. 

All these problems in intensity predictions are, a priori, not present in quantum-mechanical calculations of intensities based on ab initio methods. The development of effective theoretical approaches for analytic evaluation of first, second and third derivatives of molecular properties, energy and dipole moment in particular, have made considerable impact on the computations of vibrational spectra by ab initio methods [166-169]. As we will see, however, in spite of die tremendous jHogress in theoretical developments and computational effectiveness, the accuracy of predictions based on even the most sophisticated wave functions is not fiilly satisfactory. At present, it is not possible to quote any particular percentage of deviations from experimental intensities for different levels of calculations because of considerable variations from molecule to molecule. 

There is a second important side of die application of ab initio MO calculations to the study of vibrational intensities. As for many odia physical and chemical phenomena, the quantum mechanical studies provide essential information about the fine mechanisms and factors determining the obsoved physical quantities, in our case the integrated absorption intensities of bands in the infrared spectra of molecules. As we have seen. 

This chapter is not aimed at describing the history of the application of semi empirical followed by ab initio molecular orbital methods in evaluating vibrational absorption intensities. There are a niunber of comprehensive review articles covering the early and later stages of these studies [21,52,53,168,169,173-176], We also do not intent to discuss details of the theoretical background of analytic derivative methods for calculations of intensities, also presented in excellent reviews [168,169,175], Our principal aim is to describe the current state-of-the-art in these calculations that are changing so frequently and so dramatically as a result of developments in computer technology, improved theoretical approaches or further perfectness in ab initio software. 

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