### Abstract

Following the previously proposed equilibrate-state sampling based adaptive sampling regime Optimum Bennett Acceptance Ratio (OBAR), we introduce its nonequilibrium extension, the Optimum Crooks' Equation (OCE) in the current work. The efficiency of the NonEquilibrium Work (NEW) stratification is improved by adaptively manipulating the significance of each nonequilibrium realization followed by importance sampling. As is exhibited in the equilibrium case, the nonequilibrium extension outperforms the simple equal time rule used in nonequilibrium stratification in the sense of minimizing the total variance of the free energy estimate. The speedup of this non-equal time rule is more than 1-fold. The Time Derivative of total Variance (TDV) proposed for the OBAR criterion is extended to determine the importance of each nonequilibrium transformation, which is linearly dependent on the variance. The TDV in the nonequilibrium case gives a totally different importance rank from the standard errors of the free energy differences and OBAR TDV due to the duration of nonequilibrium pulling being added into the OCE equation. The performance of the OCE workflow is demonstrated in the solvation of several small molecules with a series of lambda increments and relaxation times between successive perturbations. To the best of our knowledge, such a nonequilibrium adaptive sampling regime in alchemical transformation is unprecedented.

Original language | English (US) |
---|---|

Pages (from-to) | 2009-2021 |

Number of pages | 13 |

Journal | Physical Chemistry Chemical Physics |

Volume | 20 |

Issue number | 3 |

DOIs | |

State | Published - Jan 1 2018 |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)
- Physical and Theoretical Chemistry

### Cite this

*Physical Chemistry Chemical Physics*,

*20*(3), 2009-2021. https://doi.org/10.1039/c7cp07573a

**BAR-based optimum adaptive sampling regime for variance minimization in alchemical transformation : The nonequilibrium stratification.** / Wang, Xiaohui; Tu, Xingzhao; Zhang, John; Sun, Zhaoxi.

Research output: Contribution to journal › Article

*Physical Chemistry Chemical Physics*, vol. 20, no. 3, pp. 2009-2021. https://doi.org/10.1039/c7cp07573a

}

TY - JOUR

T1 - BAR-based optimum adaptive sampling regime for variance minimization in alchemical transformation

T2 - The nonequilibrium stratification

AU - Wang, Xiaohui

AU - Tu, Xingzhao

AU - Zhang, John

AU - Sun, Zhaoxi

PY - 2018/1/1

Y1 - 2018/1/1

N2 - Following the previously proposed equilibrate-state sampling based adaptive sampling regime Optimum Bennett Acceptance Ratio (OBAR), we introduce its nonequilibrium extension, the Optimum Crooks' Equation (OCE) in the current work. The efficiency of the NonEquilibrium Work (NEW) stratification is improved by adaptively manipulating the significance of each nonequilibrium realization followed by importance sampling. As is exhibited in the equilibrium case, the nonequilibrium extension outperforms the simple equal time rule used in nonequilibrium stratification in the sense of minimizing the total variance of the free energy estimate. The speedup of this non-equal time rule is more than 1-fold. The Time Derivative of total Variance (TDV) proposed for the OBAR criterion is extended to determine the importance of each nonequilibrium transformation, which is linearly dependent on the variance. The TDV in the nonequilibrium case gives a totally different importance rank from the standard errors of the free energy differences and OBAR TDV due to the duration of nonequilibrium pulling being added into the OCE equation. The performance of the OCE workflow is demonstrated in the solvation of several small molecules with a series of lambda increments and relaxation times between successive perturbations. To the best of our knowledge, such a nonequilibrium adaptive sampling regime in alchemical transformation is unprecedented.

AB - Following the previously proposed equilibrate-state sampling based adaptive sampling regime Optimum Bennett Acceptance Ratio (OBAR), we introduce its nonequilibrium extension, the Optimum Crooks' Equation (OCE) in the current work. The efficiency of the NonEquilibrium Work (NEW) stratification is improved by adaptively manipulating the significance of each nonequilibrium realization followed by importance sampling. As is exhibited in the equilibrium case, the nonequilibrium extension outperforms the simple equal time rule used in nonequilibrium stratification in the sense of minimizing the total variance of the free energy estimate. The speedup of this non-equal time rule is more than 1-fold. The Time Derivative of total Variance (TDV) proposed for the OBAR criterion is extended to determine the importance of each nonequilibrium transformation, which is linearly dependent on the variance. The TDV in the nonequilibrium case gives a totally different importance rank from the standard errors of the free energy differences and OBAR TDV due to the duration of nonequilibrium pulling being added into the OCE equation. The performance of the OCE workflow is demonstrated in the solvation of several small molecules with a series of lambda increments and relaxation times between successive perturbations. To the best of our knowledge, such a nonequilibrium adaptive sampling regime in alchemical transformation is unprecedented.

UR - http://www.scopus.com/inward/record.url?scp=85040965601&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85040965601&partnerID=8YFLogxK

U2 - 10.1039/c7cp07573a

DO - 10.1039/c7cp07573a

M3 - Article

VL - 20

SP - 2009

EP - 2021

JO - Physical Chemistry Chemical Physics

JF - Physical Chemistry Chemical Physics

SN - 1463-9076

IS - 3

ER -