scholarly journals Efficient computation of free energy of crystal phases due to external potentials by error-biased Bennett acceptance ratio method

2010 ◽  
Vol 132 (8) ◽  
pp. 084101 ◽  
Author(s):  
Pankaj A. Apte
Keyword(s):  
Free Energy ◽  
Ratio Method ◽  
Efficient Computation ◽  
Acceptance Ratio ◽  
Bennett Acceptance Ratio ◽  
Crystal Phases

scholarly journals Efficient Computation of Free Energy Surfaces of Diels–Alder Reactions in Explicit Solvent at Ab Initio QM/MM Level

Molecules ◽  
2018 ◽  
Vol 23 (10) ◽  
pp. 2487 ◽  
Author(s):  
Pengfei Li ◽  
Fengjiao Liu ◽  
Xiangyu Jia ◽  
Yihan Shao ◽  
Wenxin Hu ◽  
...  
Keyword(s):  
Free Energy ◽  
Ab Initio ◽  
Umbrella Sampling ◽  
Diels Alder ◽  
Efficient Computation ◽  
Acceptance Ratio ◽  
Step Procedure ◽  
Explicit Solvent ◽  
Energy Surfaces ◽  
Semi Empirical

For Diels–Alder (DA) reactions in solution, an accurate and converged free energy (FE) surface at ab initio (ai) quantum mechanical/molecular mechanical (QM/MM) level is imperative for the understanding of reaction mechanism. However, this computation is still far too expensive. In a previous work, we proposed a new method termed MBAR+wTP, with which the computation of the ai FE profile can be accelerated by several orders of magnitude via a three-step procedure: (I) an umbrella sampling (US) using a semi-empirical (SE) QM/MM Hamiltonian is performed; (II) the FE profile is generated using the Multistate Bennett Acceptance Ratio (MBAR) analysis; and (III) a weighted Thermodynamic Perturbation (wTP) from the SE Hamiltonian to the ai Hamiltonian is performed to obtain the ai QM/MM FE profile using weight factors from the MBAR analysis. In this work, this method is extended to the calculations of two-dimensional FE surfaces of two Diels–Alder reactions of cyclopentadiene with either acrylonitrile or 1-4-naphthoquinone at ai QM/MM level. The accurate activation free energies at the ai QM/MM level, which are much closer to the experimental measurements than those calculated by other methods, indicate that this MBAR+wTP method can be applied in the studies of complex reactions in condensed phase with much-enhanced efficiency.

scholarly journals Multiensemble Markov models of molecular thermodynamics and kinetics

2016 ◽  
Vol 113 (23) ◽  
pp. E3221-E3230 ◽  
Author(s):  
Hao Wu ◽  
Fabian Paul ◽  
Christoph Wehmeyer ◽  
Frank Noé
Keyword(s):  
Detailed Balance ◽  
Rare Event ◽  
Umbrella Sampling ◽  
High Dimensional ◽  
Acceptance Ratio ◽  
Markov State ◽  
Markov State Models ◽  
Bennett Acceptance Ratio ◽  
Special Cases ◽  
State Models

We introduce the general transition-based reweighting analysis method (TRAM), a statistically optimal approach to integrate both unbiased and biased molecular dynamics simulations, such as umbrella sampling or replica exchange. TRAM estimates a multiensemble Markov model (MEMM) with full thermodynamic and kinetic information at all ensembles. The approach combines the benefits of Markov state models—clustering of high-dimensional spaces and modeling of complex many-state systems—with those of the multistate Bennett acceptance ratio of exploiting biased or high-temperature ensembles to accelerate rare-event sampling. TRAM does not depend on any rate model in addition to the widely used Markov state model approximation, but uses only fundamental relations such as detailed balance and binless reweighting of configurations between ensembles. Previous methods, including the multistate Bennett acceptance ratio, discrete TRAM, and Markov state models are special cases and can be derived from the TRAM equations. TRAM is demonstrated by efficiently computing MEMMs in cases where other estimators break down, including the full thermodynamics and rare-event kinetics from high-dimensional simulation data of an all-atom protein–ligand binding model.

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