A key step during indirect alchemical free energy simulations using quantum mechanical/molecular mechanical (QM/MM) hybrid potential energy functions is the calculation of the free energy difference Δ A low→high between the low level (e.g., pure MM) and the high level of theory (QM/MM). A reliable approach uses nonequilibrium work (NEW) switching simulations in combination with Jarzynski’s equation; however, it is computationally expensive. In this study, we investigate whether it is more efficient to use more shorter switches or fewer but longer switches. We compare results obtained with various protocols to reference free energy differences calculated with Crooks’ equation. The central finding is that fewer longer switches give better converged results. As few as 200 sufficiently long switches lead to Δ A low→high values in good agreement with the reference results. This optimized protocol reduces the computational cost by a factor of 40 compared to earlier work. We also describe two tools/ways of analyzing the raw data to detect sources of poor convergence. Specifically, we find it helpful to analyze the raw data (work values from the NEW switching simulations) in a quasi-time series-like manner. Principal component analysis helps to detect cases where one or more conformational degrees of freedom are different at the low and high level of theory.

Non-equilibrium work switching simulations and Jarzynski’s equation are a reliable method for computing free energy differences, ΔAlow→high, between two levels of theory, such as a pure molecular mechanical (MM) and a quantum mechanical/molecular mechanical (QM/MM) description of a system of interest. Despite the inherent parallelism, the computational cost of this approach can quickly become very high. This is particularly true for systems where the core region, the part of the system to be described at different levels of theory, is embedded in an environment such as explicit solvent water. We find that even for relatively simple solute–water systems, switching lengths of at least 5 ps are necessary to compute ΔAlow→high reliably. In this study, we investigate two approaches towards an affordable protocol, with an emphasis on keeping the switching length well below 5 ps. Inserting a hybrid charge intermediate state with modified partial charges, which resembles the charge distribution of the desired high level, makes it possible to obtain reliable calculations with 2 ps switches. Attempts using step-wise linear switching paths, on the other hand, did not lead to improvement, i.e., a faster convergence for all systems. To understand these findings, we analyzed the solutes’ properties as a function of the partial charges used and the number of water molecules in direct contact with the solute, and studied the time needed for water molecules to reorient themselves upon a change in the solute’s charge distribution.

Nonequilibrium work switching simulations and Jarzynski’s equation are a reliable method to compute free energy differences, ΔAlow→high, between two levels of theory, such as a pure molecular mechanical (MM) and a quantum mechanical/molecular mechanical (QM/MM) description of a system of interest. Despite the inherent parallelism, the computational cost of this approach can quickly get very high. This is particularly true for systems where the core region, the part of the system to be described at different levels of theory, is embedded in an environment, such as explicit solvent water. We find that even for relatively simple solute–water systems, switching lengths of at least 5 ps are necessary to compute ΔAlow→high reliably. In this study, we investigate two approaches towards an affordable protocol, with emphasis on keeping the switching length well below 5 ps. Inserting a hybrid charge intermediate state with modified partial charges which resembles the charge distribution of the desired high level makes it possible to obtain reliable calculations with 2 ps switches. Attempts using step-wise linear switching paths, on the other hand, did not lead to improvement, i.e., faster convergence for all systems. To understand these findings, we analyzed the solutes’ properties as a function of partial charges used, the number of waters in direct contact with the solute, and studied the time needed for water molecules to reorient themselves upon a change in the solute’s charge distribution.

To achieve chemical accuracy in free energy calculations, it is necessary to accurately describe the system's potential energy surface and efficiently sample configurations from its Boltzmann distribution. While neural network potentials (NNPs) have shown significantly higher accuracy than classical molecular mechanics (MM) force fields, they have limited range of applicability and are significantly slower than MM potentials, often by orders of magnitude. To address this challenge, Rufa et al suggested a two-stage approach that uses a fast and established MM alchemical energy protocol, followed by reweighting the results using NNPs, known as endstate correction or indirect free energy calculation. In this study, we systematically investigate the accuracy, robustness, and efficiency of free energy calculations between a MM reference and a neural network target potential (ANI-2x) using free energy perturbation (FEP) and non-equilibrium (NEQ) switching simulation in vacuum. We investigate the influence of longer switching lengths and the impact of slow degrees of freedom on outliers in the work distribution. We compare the results to multistage equilibrium free energy calculations (MFES) for an established dataset. Our results demonstrate that free energy calculations between NNPs and MM potentials should not be performed using FEP but require NEQ switching simulations to obtain accurate free energy estimates. NEQ switching simulations between MM and NNPs are highly efficient, robust, and trivial to implement.