Spectral function statistical averages

A remark applies to the experimental values of deduced from experimental bandshapes. Since we deal with total (multimolecular) correlation functions, their moments might also contain contributions arising from the intercorrelations of different molecules - or multimolecular effects - since cross terms in the statistical averages do not necessarily vanish. On this account it is necessary to estimate the extent of high-frequency collective effects if any, whenever torques are to be computed from the spectral moments. 

An approach based on the sequential use of Monte Carlo simulation and Quantum Mechanics is suggested for the treatment of solvent effects with special attention to solvatochromic shifts. The basic idea is to treat the solute, the solvent and its interaction by quantum mechanics. This is a totally discrete model that avoids the use of a dielectric continuum. Statistical analysis is used to obtain uncorrelated structures. The radial distribution function is used to determine the solvation shells. Quantum mechanical calculations are then performed in supermolecular structures and the spectral shifts are obtained using ensemble average. Attention is also given to the case of specific hydrogen bond between the solute and solvent. 

The laser intensities required to exploit gaseous nonllnearltles in a short time period dictate employment of pulsed lasers. These are typically frequency-doubled neodymiumrYAG lasers at 532 nm which are ideally spectrally situated for CARS work from both a dye laser pumping and optical detection standpoint. These lasers operate at repetition rates in the 20-50 Hz range. The combustion medium cannot be followed in real time, but is statistically sampled by an ensemble of single shot measurements which form a probability distribution function (pdf). From the pdf, the parameter time average can be ascertained as well as the magnitude of the turbulent fluctuations. 

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