Time-dependent view spectroscopy

Zhang, J. and Imre, D.G. (1989). Spectroscopy and photodissociation dynamics of H2O Time-dependent view, J. Chem. Phys. 90, 1666-1676. 

L. The time-dependent view of spectroscopy (Heller, 1981). Suppose that at time t = 0 we make a Franck ondon transition to an upper electronic state. This takes the initial vibrational wave function up in energy and onto a different potential for the motion of the nuclei. This initial state is no longer stationary and it starts evolving in time. The first thing that will happen is tiiat the wave function will depart from the Franck-Condon region. What we want to know is how quickly it will do so. If the molecule is a diatomic, the initial state will periodically revive. But for a polyatomic, IVR will, over time, reduce tiie revival. Hence for a polyatomic we also want to know where the wave-packet goes to. This... 

Fig. la c. Illustration of the time dependent theory of emission spectroscopy for one-dimensional harmonic potential energy surfaces, a schematic view of the emission transition, b time dependence of the overlap < (f> t) >, e calculated emission spectrum... 

All of the analysis in this chapter will be carried out from the time-dependent theoretical point of view. This method of analysis gives results which are identical with those of the Franck-Condon analysis. However, thinking in the time domain offers a new point of view from which the unity between electronic and resonance Raman spectroscopy and the interpretation of the spectroscopic effects of multiple mode distortions can more readily be seen. Thus, before we discuss specific molecules, we will introduce the important aspects of time-dependent theory. 

In this book, NMR is viewed from the perspective of imaging. NMR spectroscopy, relaxometry, and transport measurements are considered to be useful for defining image contrast. Clearly, such an approach is likely to be foreign to an NMR spectroscopist, who may consider NMR imaging a modification of multi-dimensional NMR. These different perspectives can be related to each other by considering the time dependence of the Larmor frequency (1.1.7). 

To complete this chapter, we would like to mention that recent monographs have reviewed the use of in-situ spectroscopies for monitoring heterogeneously catalysed reaction under supercritical conditions, although very few studies in this field has been devoted to the study of the fluid-solid interface.182 The use of a multi-technique approach in order to maximise information under real, in-situ conditions has also been reviewed recently.183 The combined use of powerful spectroscopies with simultaneous on-line analysis of the catalytic activity of the sample will become more widespread in application allowing an interpretation of catalytic behaviour in terms of the physico-chemical properties of the solid. The next frontier in spectroscopic characterisation of metal catalysts will consist of time-dependent analysis of the gas/liquid-solid interface, particularly with a view to analyse short-lived intermediates during catalysed reactions and with the aim to determine the response of the catalyst surface and relate these responses to the physico-chemical properties of the solid. 

The time-dependent theory of spectroscopy bridges this gap. This approach has received less attention than the traditional time-independent view of spectroscopy, but since 1980, it has been very successfully applied to the field of coordination chemistry.The intrinsic time dependence of external perturbations, for example oscillating laser fields used in electronic spectroscopy, is also expKdtly treated by modern computational methods such as time-dependent density functional theory, a promising approach to the efficient calculation of electronic spectra and exdted-state structures not based on adjustable parameters, as described in Chapter 2.40. In contrast, the time-dependent theory of spectroscopy outlined in the following often relies on parameters obtained by adjusting a calculated spectrum to the experimental data. It provides a unified approach for several spectroscopic techniques and leads to intuitive physical pictures often qualitatively related to classical dynamics. The concepts at its core, time-dependent wave functions (wave packets) and autocorrelation functions, can be measured with femtosecond (fs) techniques, which often illustrate concepts very similar to those presented in the following for the analysis of steady-state spectra. The time-dependent approach therefore unifies spectroscopic... 

Molecular electronic absorption and emission spectroscopy, photodissociation, Raman spectroscopy, and vibrational overtone spectroscopy have been examined from a time-dependent perspective for their implications for potential energy surfaces and dynamics. A semiclassical point of view greatly aids intuitive understanding and computation of these various spectroscopies from limited local and regional knowledge of the potential surface. 

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