Monte Carlo methods spectral effects

We incorporate disorder into the calculation by ensemble-averaging the set of coupling-weighted spectral overlaps for many aggregates using a Monte Carlo method [38]. In this way the effect of disorder on both electronic couplings and spectral overlap is properly accounted for by ensemble averaging 8,aMSa( )-... 

How can the spectral fine structure effects of a perturbation be allowed for in calculations One approach is to avoid using the group formulation. It is possible to apply the continuous energy formulation with Monte Carlo methods 32, 33). They are, however, not practical for routine application. 

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. 

A systematic comparison of experimentally obtained spectral data with modeling results based on Monte Carlo simulations can pinpoint and show ways to correct for all these effects and eventually bring the measurement accuracy in line with the accuracy of the physical parameters characterizing the X-ray - sample interaction processes. Ultimately, the quality of results that can be reached with this method depends on the accuracy of available physical parameters, mainly the cross sections for X-ray interactions that are, in the most favorable circumstances, 5% for K radiation of elements between Z= 20 and 50,10 - 15% for L radiation between Z= 50 and 80 (Elam et al. 2002 Somogyi et al. 2000). 

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