Anharmonic spectroscopy, dynamic

Brennan CJ. Femtosecond wavevector overtone spectroscopy of anharmonic lattice dynamics in ferroelectric crystals. Cambridge, MA Massachusetts Institute of Technology, 1997. 

Many Good Reasons to Prefer Dynamical Anharmonic Spectroscopy. 106... 

In this chapter, our goal is to present theoretical methods applied to gas phase vibrational spectroscopy. This is reviewed in Sect. 3 where we present harmonic and anharmonic spectra calculations, with special emphasis on dynamical approaches to anharmonic spectroscopy. In particular, we present the many reasons and advantages of dynamical anharmonic theoretical spectroscopy over harmonic/ anharmonic non-dynamical methods in Sect. 3.1. Illustrations taken from our work on dynamical theoretical spectroscopy are then presented in Sects. 4-6 in relation to action spectroscopy experiments. All examples presented here are conducted either in relation to finite temperature IR-MPD and IR-PD experiments, or to cold IR-MPD experiments. Beyond the conformational dynamics provided by the finite temperature trajectories, the chosen examples illustrate how the dynamical spectra manage to capture vibrational anharmonicities of different origins, of different strengths, in various domains of the vibrations from 100 to 4,000 cm and on various molecular systems. Other comprehensive reviews on theoretical anharmonic spectroscopy can be found in [7-9]. 

The approach to the evaluation of vibrational spectra described above is based on classical simulations for which quantum corrections are possible. The incorporation of quantum effects directly in simulations of large molecular systems is one of the most challenging areas in theoretical chemistry today. The development of quantum simulation methods is particularly important in the area of molecular spectroscopy for which quantum effects can be important and where the goal is to use simulations to help understand the structural and dynamical origins of changes in spectral lineshapes with environmental variables such as the temperature. The direct evaluation of quantum time- correlation functions for anharmonic systems is extremely difficult. Our initial approach to the evaluation of finite temperature anharmonic effects on vibrational lineshapes is derived from the fact that the moments of the vibrational lineshape spectrum can be expressed as functions of expectation values of positional and momentum operators. These expectation values can be evaluated using extremely efficient quantum Monte-Carlo techniques. The main points are summarized below. 

The electronic absorption spectra of complex molecules at elevated temperatures in condensed matter are generally very broad and virtually featureless. In contrast, vibrational spectra of complex molecules, even in room-temperature liquids, can display sharp, well-defined peaks, many of which can be assigned to specific vibrational modes. The inverse of the line width sets a time scale for the dynamics associated with a transition. The relatively narrow line widths associated with many vibrational transitions make it possible to use pulse durations with correspondingly narrow bandwidths to extract information. For a vibration with sufficiently large anharmonicity or a sufficiently narrow absorption line, the system behaves as a two-level transition coupled to its environment. In this respect, time domain vibrational spectroscopy of internal molecular modes is more akin to NMR than to electronic spectroscopy. The potential has already been demonstrated, as described in some of the chapters in this book, to perform pulse sequences that are, in many respects, analogous to those used in NMR. Commercial equipment is available that can produce the necessary infrared (IR) pulses for such experiments, and the equipment is rapidly becoming less expensive, more compact, and more reliable. It is possible, even likely, that coherent IR pulse-sequence vibrational spectrometers will... 

We now show that the algebraic realization of the one-dimensional Morse potential can be adopted as a starting point for recovering this same problem in a conventional wave-mechanics formulation. This will be useful for several reasons (1) The connection between algebraic and conventional coordinate spaces is a rigorous one, which can be depicted explicitly, however, only in very simple cases, such as in the present one-dimensional situation (2) for traditional spectroscopy it can be useful to know that boson operators have a well-defined differential operator counterpart, which will be appreciated particularly in the study of transition operators and related quantities and (3) the one-dimensional Morse potential is not the unique outcome of the dynamical symmetry based on U(2). As already mentioned, the Poschl-Teller potential, being isospectral with the Morse potential in the bound-state portion of the spectrum, can be also described in an algebraic fashion. This is particularly apparent after a detailed study of the differential version of these two anharmonic potential models. Here we limit ourselves to a brief description. A more complete analysis can be found elsewhere [25]. As a... 

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