Dataset Information

Bootstrap Embedding for Molecules.

ABSTRACT: Fragment embedding is one way to circumvent the high computational scaling of accurate electron correlation methods. The challenge of applying fragment embedding to molecular systems primarily lies in the strong entanglement and correlation that prevent accurate fragmentation across chemical bonds. Recently, Schmidt decomposition has been shown effective for embedding fragments that are strongly coupled to a bath in several model systems. In this work, we extend a recently developed quantum embedding scheme, bootstrap embedding (BE), to molecular systems. The resulting method utilizes the matching conditions naturally arising from using overlapping fragments to optimize the embedding. Numerical simulation suggests that the accuracy of the embedding improves rapidly with fragment size for small molecules, whereas larger fragments that include orbitals from different atoms may be needed for larger molecules. BE scales linearly with system size (apart from an integral transform) and hence can potentially be useful for large-scale calculations.

SUBMITTER: Ye HZ

PROVIDER: S-EPMC6727622 | biostudies-literature | 2019 Aug

REPOSITORIES: biostudies-literature

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Publications

Bootstrap Embedding for Molecules.

Ye Hong-Zhou HZ Ricke Nathan D ND Tran Henry K HK Van Voorhis Troy T

Journal of chemical theory and computation 20190805 8

Fragment embedding is one way to circumvent the high computational scaling of accurate electron correlation methods. The challenge of applying fragment embedding to molecular systems primarily lies in the strong entanglement and correlation that prevent accurate fragmentation across chemical bonds. Recently, Schmidt decomposition has been shown effective for embedding fragments that are strongly coupled to a bath in several model systems. In this work, we extend a recently developed quantum embe ...[more]

PMID: 31343878

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Project description:In many scientific studies, the underlying data-generating process is unknown and multiple statistical models are considered to describe it. For example, in a factorial experiment we might consider models involving just main effects, as well as those that include interactions. Model-averaging is a commonly-used statistical technique to allow for model uncertainty in parameter estimation. In the frequentist setting, the model-averaged estimate of a parameter is a weighted mean of the estimates from the individual models, with the weights typically being based on an information criterion, cross-validation, or bootstrapping. One approach to building a model-averaged confidence interval is to use a Wald interval, based on the model-averaged estimate and its standard error. This has been the default method in many application areas, particularly those in the life sciences. The MA-Wald interval, however, assumes that the studentized model-averaged estimate has a normal distribution, which can be far from true in practice due to the random, data-driven model weights. Recently, the model-averaged tail area Wald interval (MATA-Wald) has been proposed as an alternative to the MA-Wald interval, which only assumes that the studentized estimate from each model has a N(0, 1) or t-distribution, when that model is true. This alternative to the MA-Wald interval has been shown to have better coverage in simulation studies. However, when we have a response variable that is skewed, even these relaxed assumptions may not be valid, and use of these intervals might therefore result in poor coverage. We propose a new interval (MATA-SBoot) which uses a parametric bootstrap approach to estimate the distribution of the studentized estimate for each model, when that model is true. This method only requires that the studentized estimate from each model is approximately pivotal, an assumption that will often be true in practice, even for skewed data. We illustrate use of this new interval in the analysis of a three-factor marine global change experiment in which the response variable is assumed to have a lognormal distribution. We also perform a simulation study, based on the example, to compare the lower and upper error rates of this interval with those for existing methods. The results suggest that the MATA-SBoot interval can provide better error rates than existing intervals when we have skewed data, particularly for the upper error rate when the sample size is small.

Dataset Information

Bootstrap Embedding for Molecules.

Publications

Bootstrap Embedding for Molecules.

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