Open AccessReaction Path-Force Matching in Collective Variables: Determining Ab Initio QM/MM Free Energy Profiles by Fitting Mean Force
Author(s) -
Bryant Kim,
Ryan Snyder,
Mulpuri Nagaraju,
Yan Zhou,
Pedro Ojeda-May,
Seth Keeton,
Mellisa Hege,
Yihan Shao,
Jingzhi Pu
Publication year - 2021
Publication title -
journal of chemical theory and computation
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.001
H-Index - 185
eISSN - 1549-9626
pISSN - 1549-9618
DOI - 10.1021/acs.jctc.1c00245
Subject(s) - potential of mean force , energy profile , ab initio , potential energy , free energy perturbation , hamiltonian (control theory) , energy (signal processing) , umbrella sampling , path (computing) , mean free path , chemistry , statistical physics , molecular dynamics , physics , computational chemistry , classical mechanics , computer science , quantum mechanics , mathematics , mathematical optimization , scattering , programming language
First-principles determination of free energy profiles for condensed-phase chemical reactions is hampered by the daunting costs associated with configurational sampling on ab initio quantum mechanical/molecular mechanical (AI/MM) potential energy surfaces. Here, we report a new method that enables efficient AI/MM free energy simulations through mean force fitting. In this method, a free energy path in collective variables (CVs) is first determined on an efficient reactive aiding potential. Based on the configurations sampled along the free energy path, correcting forces to reproduce the AI/MM forces on the CVs are determined through force matching. The AI/MM free energy profile is then predicted from simulations on the aiding potential in conjunction with the correcting forces. Such cycles of correction-prediction are repeated until convergence is established. As the instantaneous forces on the CVs sampled in equilibrium ensembles along the free energy path are fitted, this procedure faithfully restores the target free energy profile by reproducing the free energy mean forces. Due to its close connection with the reaction path-force matching (RP-FM) framework recently introduced by us, we designate the new method as RP-FM in collective variables (RP-FM-CV). We demonstrate the effectiveness of this method on a type-II solution-phase SN 2 reaction, NH 3 + CH 3 Cl (the Menshutkin reaction), simulated with an explicit water solvent. To obtain the AI/MM free energy profiles, we employed the semiempirical AM1/MM Hamiltonian as the base level for determining the string minimum free energy pathway, along which the free energy mean forces are fitted to various target AI/MM levels using the Hartree-Fock (HF) theory, density functional theory (DFT), and the second-order Møller-Plesset perturbation (MP2) theory as the AI method. The forces on the bond-breaking and bond-forming CVs at both the base and target levels are obtained by force transformation from Cartesian to redundant internal coordinates under the Wilson B -matrix formalism, where the linearized FM is facilitated by the use of spline functions. For the Menshutkin reaction tested, our FM treatment greatly reduces the deviations on the CV forces, originally in the range of 12-33 to ∼2 kcal/mol/Å. Comparisons with the experimental and benchmark AI/MM results, tests of the new method under a variety of simulation protocols, and analyses of the solute-solvent radial distribution functions suggest that RP-FM-CV can be used as an efficient, accurate, and robust method for simulating solution-phase chemical reactions.