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A Monte Carlo Resampling approach for the calculation of hybrid classical and quantum free energies

A Monte Carlo Resampling approach for the calculation of hybrid classical and quantum free energies
A Monte Carlo Resampling approach for the calculation of hybrid classical and quantum free energies
Hybrid free energy methods allow estimation of free energy differences at the quantum mechanics (QM) level with high efficiency by performing sampling at the classical mechanics (MM) level. Various approaches to allow the calculation of QM corrections to classical free energies have been proposed. The single step free energy perturbation approach starts with a classically generated ensemble, a subset of structures of which are post-processed to obtain QM energies for use with the Zwanzig equation. This gives an estimate of the free energy difference associated with the change from an MM to a QM Hamiltonian. Owing to the poor numerical properties of the Zwanzig equation however, recent developments have produced alternative methods which aim to provide access to the properties of the true QM ensemble. Here we propose an approach based on the resampling of MM structural ensembles and application of a Monte Carlo acceptance test which in principle, can generate the exact QM ensemble or intermediate ensembles between the MM and QM states. We carry out a detailed comparison against the Zwanzig equation and recently proposed non-Boltzmann methods. As a test system we use a set of small molecule hydration free energies for which hybrid free energy calculations are performed at the semi-empirical Density Functional Tight Binding level. Equivalent ensembles at this level of theory have also been generated allowing the reverse QM to MM perturbations to be performed along with a detailed analysis of the results. Additionally, a previously published nucleotide base pair data set simulated at the QM level using ab initio molecular dynamics is also considered. We provide a strong rationale for the use of the Monte Carlo Resampling and non-Boltzmann approaches by showing that configuration space overlaps can be estimated which provide useful diagnostic information regarding the accuracy of these hybrid approaches.
1549-9618
1-10
Cave-Ayland, Christopher
0fac5a8c-02ac-4b42-857f-4b0288c9b125
Skylaris, Chris
8f593d13-3ace-4558-ba08-04e48211af61
Essex, Jonathan
1f409cfe-6ba4-42e2-a0ab-a931826314b5
Cave-Ayland, Christopher
0fac5a8c-02ac-4b42-857f-4b0288c9b125
Skylaris, Chris
8f593d13-3ace-4558-ba08-04e48211af61
Essex, Jonathan
1f409cfe-6ba4-42e2-a0ab-a931826314b5

Cave-Ayland, Christopher, Skylaris, Chris and Essex, Jonathan (2016) A Monte Carlo Resampling approach for the calculation of hybrid classical and quantum free energies. Journal of Chemical Theory and Computation, 1-10. (doi:10.1021/acs.jctc.6b00506).

Record type: Article

Abstract

Hybrid free energy methods allow estimation of free energy differences at the quantum mechanics (QM) level with high efficiency by performing sampling at the classical mechanics (MM) level. Various approaches to allow the calculation of QM corrections to classical free energies have been proposed. The single step free energy perturbation approach starts with a classically generated ensemble, a subset of structures of which are post-processed to obtain QM energies for use with the Zwanzig equation. This gives an estimate of the free energy difference associated with the change from an MM to a QM Hamiltonian. Owing to the poor numerical properties of the Zwanzig equation however, recent developments have produced alternative methods which aim to provide access to the properties of the true QM ensemble. Here we propose an approach based on the resampling of MM structural ensembles and application of a Monte Carlo acceptance test which in principle, can generate the exact QM ensemble or intermediate ensembles between the MM and QM states. We carry out a detailed comparison against the Zwanzig equation and recently proposed non-Boltzmann methods. As a test system we use a set of small molecule hydration free energies for which hybrid free energy calculations are performed at the semi-empirical Density Functional Tight Binding level. Equivalent ensembles at this level of theory have also been generated allowing the reverse QM to MM perturbations to be performed along with a detailed analysis of the results. Additionally, a previously published nucleotide base pair data set simulated at the QM level using ab initio molecular dynamics is also considered. We provide a strong rationale for the use of the Monte Carlo Resampling and non-Boltzmann approaches by showing that configuration space overlaps can be estimated which provide useful diagnostic information regarding the accuracy of these hybrid approaches.

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Accepted/In Press date: 28 December 2016
e-pub ahead of print date: 28 December 2016
Organisations: Faculty of Natural and Environmental Sciences, Computational Systems Chemistry

Identifiers

Local EPrints ID: 405232
URI: https://eprints.soton.ac.uk/id/eprint/405232
ISSN: 1549-9618
PURE UUID: 35f69810-bf82-408a-8032-4cb0dca04b4a
ORCID for Christopher Cave-Ayland: ORCID iD orcid.org/0000-0003-0942-8030
ORCID for Chris Skylaris: ORCID iD orcid.org/0000-0003-0258-3433
ORCID for Jonathan Essex: ORCID iD orcid.org/0000-0003-2639-2746

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Date deposited: 31 Jan 2017 14:19
Last modified: 31 Jul 2019 05:05

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