TY - JOUR

T1 - Use of Interaction Energies in QM/MM Free Energy Simulations

AU - Hudson, Phillip S.

AU - Woodcock, H. Lee

AU - Boresch, Stefan

N1 - Publisher Copyright:
© 2019 American Chemical Society.

PY - 2019/8

Y1 - 2019/8

N2 - The use of the most accurate (i.e., QM or QM/MM) levels of theory for free energy simulations (FES) is typically not possible. Primarily, this is because the computational cost associated with the extensive configurational sampling needed for converging FES is prohibitive. To ensure the feasibility of QM-based FES, the "indirect" approach is generally taken, necessitating a free energy calculation between the MM and QM/MM potential energy surfaces. Ideally, this step is performed with standard free energy perturbation (Zwanzig's equation) as it only requires simulations be carried out at the low level of theory; however, work from several groups over the past few years has conclusively shown that Zwanzig's equation is ill-suited to this task. As such, many approximations have arisen to mitigate difficulties with Zwanzig's equation. One particularly popular notion is that the convergence of Zwanzig's equation can be improved by using interaction energy differences instead of total energy differences. Although problematic numerical fluctuations (a major problem when using Zwanzig's equation) are indeed reduced, our results and analysis demonstrate that this "interaction energy approximation" (IEA) is theoretically incorrect, and the implicit approximation invoked is spurious at best. Herein, we demonstrate this via solvation free energy calculations using IEA from two different low levels of theory to the same target high level. Results from this proof-of-concept consistently yield the wrong results, deviating by ∼1.5 kcal/mol from the rigorously obtained value.

AB - The use of the most accurate (i.e., QM or QM/MM) levels of theory for free energy simulations (FES) is typically not possible. Primarily, this is because the computational cost associated with the extensive configurational sampling needed for converging FES is prohibitive. To ensure the feasibility of QM-based FES, the "indirect" approach is generally taken, necessitating a free energy calculation between the MM and QM/MM potential energy surfaces. Ideally, this step is performed with standard free energy perturbation (Zwanzig's equation) as it only requires simulations be carried out at the low level of theory; however, work from several groups over the past few years has conclusively shown that Zwanzig's equation is ill-suited to this task. As such, many approximations have arisen to mitigate difficulties with Zwanzig's equation. One particularly popular notion is that the convergence of Zwanzig's equation can be improved by using interaction energy differences instead of total energy differences. Although problematic numerical fluctuations (a major problem when using Zwanzig's equation) are indeed reduced, our results and analysis demonstrate that this "interaction energy approximation" (IEA) is theoretically incorrect, and the implicit approximation invoked is spurious at best. Herein, we demonstrate this via solvation free energy calculations using IEA from two different low levels of theory to the same target high level. Results from this proof-of-concept consistently yield the wrong results, deviating by ∼1.5 kcal/mol from the rigorously obtained value.

KW - HYDRATION FREE-ENERGIES

KW - GENERAL FORCE-FIELD

KW - QUANTUM-MECHANICAL CALCULATIONS

KW - NONEQUILIBRIUM WORK METHODS

KW - BINDING FREE-ENERGIES

KW - SOLVATION FREE-ENERGY

KW - MOLECULAR-DYNAMICS

KW - PERTURBATION CALCULATIONS

KW - CHEMICAL-PROCESSES

KW - COMPLEX MATERIALS

UR - http://www.scopus.com/inward/record.url?scp=85071134780&partnerID=8YFLogxK

U2 - 10.1021/acs.jctc.9b00084

DO - 10.1021/acs.jctc.9b00084

M3 - Article

VL - 15

SP - 4632

EP - 4645

JO - Journal of Chemical Theory and Computation

JF - Journal of Chemical Theory and Computation

SN - 1549-9618

IS - 8

ER -