Abstract
We show that the importance sampling technique can effectively augment the range of problems where the nuclear ensemble approach can be applied. A sampling probability distribution function initially determines the collection of initial conditions for which calculations are performed, as usual. Then, results for a distinct target distribution are computed by introducing compensating importance sampling weights for each sampled point. This mapping between the two probability distributions can be performed whenever they are both explicitly constructed. Perhaps most notably, this procedure allows for the computation of temperature dependent observables. As a test case, we investigated the UV absorption spectra of phenol, which has been shown to have a marked temperature dependence. Application of the proposed technique to a range that covers 500 K provides results that converge to those obtained with conventional sampling. We further show that an overall improved rate of convergence is obtained when sampling is performed at intermediate temperatures. The comparison between calculated and the available measured cross sections is very satisfactory, as the main features of the spectra are correctly reproduced. As a second test case, one of Tully's classical models was revisited, and we show that the computation of dynamical observables also profits from the importance sampling technique. In summary, the strategy developed here can be employed to assess the role of temperature for any property calculated within the nuclear ensemble method, with the same computational cost as doing so for a single temperature.
Highlights
In photophysics and photochemistry, the nuclear ensemble approach consists in representing the molecular vibrational wave functions by a set of classical nuclear configurations
The importance sampling (IS) strategy was applied to compute the cross sections σ for the other two target temperatures. We compared both set of results by computing the normalized root mean square deviation (NRMSD): 1 nrms =
Since we are interested in describing the two first absorption bands of phenol, which are located in the 4−6.1 eV range, only points lying inside this interval entered in the calculation of the NRMSDs
Summary
The nuclear ensemble approach consists in representing the molecular vibrational wave functions by a set of classical nuclear configurations. For either static or dynamical simulations, one computes a given physical observable of interest for a set of independent phase space points These follow a certain probability distribution function (PDF), which can be constructed based on a quantum or classical description of the nuclei.[12] Once the calculations are done, the individual computed values are averaged, which is taken as the estimate for its real value. As a first test case for the proposed importance sampling strategy, we investigated the temperature dependence of the photoabsorption spectra of phenol, in the 4.0−6.1 eV interval This particular choice was motivated by the available experimental data[17] that covered a wide temperature range (296−773 K), showing a quite noticeable temperature effect. We notice a huge gap from theory regarding the role of temperature on UV-vis absorption cross sections While this first test case involves the calculation of a static property, the importance sampling strategy should be valid for dynamics simulations. A second goal is to describe the temperature dependent absorption spectra of phenol, by comparing it with the existing experimental data
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