Free Energy Calculation through Energy Reweighting from Molecular Mechanics to Quantum Mechanics
作者单位：Center for Laser and Computational BiophysicsState Key Laboratory of Precision Spectroscopy and Department of Physics and Institute of Theoretical and Computational ScienceEast China Normal University NYU-ECNU Center for Computational Chemistry at NYU Shanghai
会议名称：《中国化学会第30届学术年会-第十九分会：化学中的量子与经典动力学》
会议日期：2016年
学科分类：0809[工学-电子科学与技术（可授工学、理学学位）] 07[理学] 070205[理学-凝聚态物理] 08[工学] 0702[理学-物理学]
关 键 词：Bennett Acceptance Ratio thermodynamic perturbation variance biasing potential density functionals
摘 要：Calculations of the free energy difference between two states at quantum mechanical(QM) level directly are generally prohibitively expensive, because some intermediates states are usually required in order to increase the overlap in phase space between two adjacent states. Fortunately, free energy is a state function, of which the difference is path-independent. Therefore, in a more practical way the intermediate states can be described by molecular mechanics(MM). The free energy difference between two adjacent states can be estimated using the Bennett Acceptance Ratio(BAR), which has been shown to give the minimum variance with fixed number of samples. To further reduce the computational expense by refraining from sampling at QM level for the end states, Boresch proposed a method termed Non-Boltzmann Bennett’s acceptance ratio(NBB), which combines BAR and energy reweighting. However, we showed that the most efficient way to calculate the free energy difference between two QM states is BAR+TP, which gives the minimum variance of the results. In this scheme, the free energy differences between MM states are estimated using BAR, and at both ends a thermodynamic perturbation from MM to QM states are applied. In addition, the QM expense in this scheme is only half of that in NBB. We also show that defining the biasing potential as the difference of the solute-solvent interaction energy, instead of the total energy, can converge to the calculated solvation free energies much faster but possibly to different values. It has also been discovered in this study that BLYP yields better results than MP2 and some later functionals such as B3LYP, M06-2X, and ωB97X-D. This reweighting scheme can also be applied to protein-ligand binding free energy calculations and the corresponding work is in progress.