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Entropy from state probabilities: hydration entropy of cations.

ABSTRACT: Entropy is an important energetic quantity determining the progression of chemical processes. We propose a new approach to obtain hydration entropy directly from probability density functions in state space. We demonstrate the validity of our approach for a series of cations in aqueous solution. Extensive validation of simulation results was performed. Our approach does not make prior assumptions about the shape of the potential energy landscape and is capable of calculating accurate hydration entropy values. Sampling times in the low nanosecond range are sufficient for the investigated ionic systems. Although the presented strategy is at the moment limited to systems for which a scalar order parameter can be derived, this is not a principal limitation of the method. The strategy presented is applicable to any chemical system where sufficient sampling of conformational space is accessible, for example, by computer simulations.

SUBMITTER: Huber RG

PROVIDER: S-EPMC3668459 | biostudies-literature | 2013 May

REPOSITORIES: biostudies-literature

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Entropy from state probabilities: hydration entropy of cations.

Huber Roland G RG Fuchs Julian E JE von Grafenstein Susanne S Laner Monika M Wallnoefer Hannes G HG Abdelkader Nejma N Kroemer Romano T RT Liedl Klaus R KR

The journal of physical chemistry. B 20130520 21

Entropy is an important energetic quantity determining the progression of chemical processes. We propose a new approach to obtain hydration entropy directly from probability density functions in state space. We demonstrate the validity of our approach for a series of cations in aqueous solution. Extensive validation of simulation results was performed. Our approach does not make prior assumptions about the shape of the potential energy landscape and is capable of calculating accurate hydration e ...[more]

PMID: 23651109

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Project description:When constructing discrete (binned) distributions from samples of a data set, applications exist where it is desirable to assure that all bins of the sample distribution have nonzero probability. For example, if the sample distribution is part of a predictive model for which we require returning a response for the entire codomain, or if we use Kullback-Leibler divergence to measure the (dis-)agreement of the sample distribution and the original distribution of the variable, which, in the described case, is inconveniently infinite. Several sample-based distribution estimators exist which assure nonzero bin probability, such as adding one counter to each zero-probability bin of the sample histogram, adding a small probability to the sample pdf, smoothing methods such as Kernel-density smoothing, or Bayesian approaches based on the Dirichlet and Multinomial distribution. Here, we suggest and test an approach based on the Clopper-Pearson method, which makes use of the binominal distribution. Based on the sample distribution, confidence intervals for bin-occupation probability are calculated. The mean of each confidence interval is a strictly positive estimator of the true bin-occupation probability and is convergent with increasing sample size. For small samples, it converges towards a uniform distribution, i.e., the method effectively applies a maximum entropy approach. We apply this nonzero method and four alternative sample-based distribution estimators to a range of typical distributions (uniform, Dirac, normal, multimodal, and irregular) and measure the effect with Kullback-Leibler divergence. While the performance of each method strongly depends on the distribution type it is applied to, on average, and especially for small sample sizes, the nonzero, the simple "add one counter", and the Bayesian Dirichlet-multinomial model show very similar behavior and perform best. We conclude that, when estimating distributions without an a priori idea of their shape, applying one of these methods is favorable.

Dataset Information

Entropy from state probabilities: hydration entropy of cations.

Publications

Entropy from state probabilities: hydration entropy of cations.

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