Multistate Method to Efficiently Account for Tautomerism and Protonation in Alchemical Free-Energy Calculations.

The majority of drug-like molecules contain at least one ionizable group, and many common drug scaffolds are subject to tautomeric equilibria. Thus, these compounds are found in a mixture of protonation and/or tautomeric states at physiological pH. Intrinsically, standard classical molecular dynamics (MD) simulations cannot describe such equilibria between states, which negatively impacts the prediction of key molecular properties in silico. Following the formalism described by de Oliveira and co-workers (J. Chem. Theory Comput. 2019, 15, 424-435) to consider the influence of all states on the binding process based on alchemical free-energy calculations, we demonstrate in this work that the multistate method replica-exchange enveloping distribution sampling (RE-EDS) is well suited to describe molecules with multiple protonation and/or tautomeric states in a single simulation. We apply our methodology to a series of eight inhibitors of factor Xa with two protonation states and a series of eight inhibitors of glycogen synthase kinase 3ß (GSK3ß) with two tautomeric states. In particular, we show that given a sufficient phase-space overlap between the states, RE-EDS is computationally more efficient than standard pairwise free-energy methods.

Simulation of aqueous solutes using the adaptive solvent-scaling (AdSoS) scheme.

The Adaptive Solvent-Scaling (AdSoS) scheme [J. Chem. Phys. 155 (2021) 094107] is an adaptive-resolution approach for performing simulations of a solute embedded in a fine-grained (FG) solvent region surrounded by a coarse-grained (CG) solvent region, with a continuous FG ↔ CG switching of the solvent resolution across a buffer layer. Instead of relying on a distinct CG solvent model, AdSoS is based on CG models defined by a dimensional scaling of the FG solvent by a factor s, accompanied by the s-dependent modulation of its mass and interaction parameters. The latter changes are designed to achieve an isomorphism between the dynamics of the FG and CG models, and to preserve the dispersive and dielectric solvation properties of the solvent with respect to a solute at FG resolution. As a result, the AdSoS scheme minimizes the thermodynamic mismatch between different regions of the adaptive-resolution system. The present article generalizes the scheme initially introduced for a pure atomic liquid in slab geometry to more practically relevant situations involving (i) a molecular dipolar solvent (e.g., water); (ii) a radial geometry (i.e., spherical rather than planar layers); and (iii) the inclusion of a solute (e.g., water molecule, dipeptide, ion, or ion pair).

Influence of the Lennard-Jones Combination Rules on the Simulated Properties of Organic Liquids at Optimal Force-Field Parametrization.

We recently introduced the CombiFF scheme [Oliveira et al., J. Chem. Theory Comput. 2020, 16, 7525], an approach for the automated refinement of force-field parameters against experimental condensed-phase data for large compound families. Using this scheme, once the time-consuming task of target-data selection and curation has been performed, the force-field optimization itself is both straightforward and fast. As a result, CombiFF provides an ideal framework for evaluating the influence of functional-form decisions on the accuracy of a force field at an optimal level of parametrization. We already used this approach to assess the effect of using an all-atom representation compared to united-atom representations in the force field [Oliveira et al., J. Chem. Theory Comput. 2022, 18, 6757]. Here, CombiFF is applied to assess the effect of three Lennard-Jones combination rules, geometric-mean (GM), Lorentz-Berthelot (LB), or Waldman-Hagler (WH), on the simulated properties of organic liquids. The comparison is performed in terms of the experimental liquid density ρliq, vaporization enthalpy ΔHvap, surface-tension coefficient γ, static relative dielectric permittivity ϵ, and self-diffusion coefficient D. The calibrations of the three force-field variants are carried out independently against 2044 experimental values for ρliq, and ΔHvap concerning 1516 compounds. The resulting root-mean-square deviations from experiment are 30.0, 26.9, and 36.7 kg m-3 for ρliq and 2.8, 2.8, and 2.9 kJ mol-1 for ΔHvap, when applying the GM, LB, and WH combination rules, respectively. In terms of these (and the other) properties, the three combination rules perform comparatively well, with the GM and LB results being more similar to each other and slightly more accurate compared to experiment. In contrast, the use of distinct combination rules for the parameter calibration and property calculation leads to much larger errors.

Development of an open-source software for isomer enumeration.

This article documents enu, a freely-downloadable, open-source and stand-alone program written in C++ for the enumeration of the constitutional isomers and stereoisomers of a molecular formula. The program relies on graph theory to enumerate all the constitutional isomers of a given formula on the basis of their canonical adjacency matrix. The stereoisomers of a given constitutional isomer are enumerated as well, on the basis of the automorphism group of this matrix. The isomer list is then reported in the form of canonical SMILES strings within files in XML format. The specification of the molecule family of interest is very flexible and the code is optimized for computational efficiency. The algorithms and implementations underlying enu are described, and simple illustrative applications are presented. The enu code is freely available on GitHub at https://github.com/csms-ethz/CombiFF .

Force fields optimized against experimental data for large compound families using CombiFF: Validation considering non-target properties and polyfunctional compounds.

The CombiFF scheme is a workflow for the automated calibration of force-field parameters against condensed-phase experimental data considering simultaneously entire classes of organic molecules. The main steps of this scheme are: (i) selection of a molecule family; (ii) enumeration of all isomers; (iii) query for experimental data; (iv) automatic construction of the molecular topologies; (v) iterative refinement of the force-field parameters considering the entire family. In two recent articles, CombiFF was applied to the design of GROMOS-compatible united-atom force fields for the saturated acyclic haloalkanes and for saturated acyclic compounds involving eight common chemical functional groups of oxygen and nitrogen. This calibration and the subsequent initial validation involved two limitations: (i) the experimental data considered was restricted to values for the pure-liquid density ρliq and the vaporization enthalpy ΔHvap of the compounds; (ii) beyond monofunctional compounds, the training set only involved homo-polyhaloalkanes (possibly mixing halogen types) in the first study, and homo-polyfunctional compounds of the considered oxygen or nitrogen functional groups (no mixing of different group types) in the second one. The goal of this article is to further test the accuracy of CombiFF-generated force fields by extending the validation to: (i) nine additional properties that were not used as optimization targets (pure-liquid thermodynamic, dielectric and transport properties, as well as solvation properties); (ii) hetero-polyfunctional molecules that were not included in the calibration and initial validation sets. The results for the nine additional properties show good agreement with experiment, except for the shear viscosity and the dielectric permittivity. There, larger discrepancies are observed, likely due to the united-atom representation adopted for the aliphatic groups and to the implicit treatment of electronic polarization effects. The results for the hetero-polyfunctional molecules also show reasonable agreement with experiment in terms of the monitored properties.

Comparison of the United- and All-Atom Representations of (Halo)alkanes Based on Two Condensed-Phase Force Fields Optimized against the Same Experimental Data Set.

The level of accuracy that can be achieved by a force field is influenced by choices made in the interaction-function representation and in the relevant simulation parameters. These choices, referred to here as functional-form variants (FFVs), include for example the model resolution, the charge-derivation procedure, the van der Waals combination rules, the cutoff distance, and the treatment of the long-range interactions. Ideally, assessing the effect of a given FFV on the intrinsic accuracy of the force-field representation requires that only the specific FFV is changed and that this change is performed at an optimal level of parametrization, a requirement that may prove extremely challenging to achieve in practice. Here, we present a first attempt at such a comparison for one specific FFV, namely the choice of a united-atom (UA) versus an all-atom (AA) resolution in a force field for saturated acyclic (halo)alkanes. Two force-field versions (UA vs AA) are optimized in an automated way using the CombiFF approach against 961 experimental values for the pure-liquid densities ρliq and vaporization enthalpies ΔHvap of 591 compounds. For the AA force field, the torsional and third-neighbor Lennard-Jones parameters are also refined based on quantum-mechanical rotational-energy profiles. The comparison between the UA and AA resolutions is also extended to properties that have not been included as parameterization targets, namely the surface-tension coefficient γ, the isothermal compressibility κT, the isobaric thermal-expansion coefficient αP, the isobaric heat capacity cP, the static relative dielectric permittivity ϵ, the self-diffusion coefficient D, the shear viscosity η, the hydration free energy ΔGwat, and the free energy of solvation ΔGche in cyclohexane. For the target properties ρliq and ΔHvap, the UA and AA resolutions reach very similar levels of accuracy after optimization. For the nine other properties, the AA representation leads to more accurate results in terms of η; comparably accurate results in terms of γ, κT, αP, ϵ, D, and ΔGche; and less accurate results in terms of cP and ΔGwat. This work also represents a first step toward the calibration of a GROMOS-compatible force field at the AA resolution.

Leveraging the sampling efficiency of RE-EDS in OpenMM using a shifted reaction-field with an atom-based cutoff.

Replica-exchange enveloping distribution sampling (RE-EDS) is a pathway-independent multistate free-energy method currently implemented in the GROMOS software package for molecular dynamics (MD) simulations. It has a high intrinsic sampling efficiency as the interactions between the unperturbed particles have to be calculated only once for multiple end-states. As a result, RE-EDS is an attractive method for the calculation of relative solvation and binding free energies. An essential requirement for reaching this high efficiency is the separability of the nonbonded interactions into solute-solute, solute-environment, and environment-environment contributions. Such a partitioning is trivial when using a Coulomb term with a reaction-field (RF) correction to model the electrostatic interactions but not when using lattice-sum schemes. To avoid cutoff artifacts, the RF correction is typically used in combination with a charge-group-based cutoff, which is not supported by most small-molecule force fields as well as other MD engines. To address this issue, we investigate the combination of RE-EDS simulations with a recently introduced RF scheme including a shifting function that enables the rigorous calculation of RF electrostatics with atom-based cutoffs. The resulting approach is validated by calculating solvation free energies with the generalized AMBER force field in water and chloroform using both the GROMOS software package and a proof-of-concept implementation in OpenMM.

Replica-Exchange Enveloping Distribution Sampling Using Generalized AMBER Force-Field Topologies: Application to Relative Hydration Free-Energy Calculations for Large Sets of Molecules.

Free-energy differences between pairs of end-states can be estimated based on molecular dynamics (MD) simulations using standard pathway-dependent methods such as thermodynamic integration (TI), free-energy perturbation, or Bennett's acceptance ratio. Replica-exchange enveloping distribution sampling (RE-EDS), on the other hand, allows for the sampling of multiple end-states in a single simulation without the specification of any pathways. In this work, we use the RE-EDS method as implemented in GROMOS together with generalized AMBER force-field (GAFF) topologies, converted to a GROMOS-compatible format with a newly developed GROMOS++ program amber2gromos, to compute relative hydration free energies for a series of benzene derivatives. The results obtained with RE-EDS are compared to the experimental data as well as calculated values from the literature. In addition, the estimated free-energy differences in water and in vacuum are compared to values from TI calculations carried out with GROMACS. The hydration free energies obtained using RE-EDS for multiple molecules are found to be in good agreement with both the experimental data and the results calculated using other free-energy methods. While all considered free-energy methods delivered accurate results, the RE-EDS calculations required the least amount of total simulation time. This work serves as a validation for the use of GAFF topologies with the GROMOS simulation package and the RE-EDS approach. Furthermore, the performance of RE-EDS for a large set of 28 end-states is assessed with promising results.

The Role of Surface Chemistry in the Orientational Behavior of Water at an Interface.

Molecular dynamics studies have demonstrated that molecular water at an interface, with either a gas or a solid, displays anisotropic orientational behavior in contrast to its bulk counterpart. This effect has been recently implicated in the like-charge attraction problem for colloidal particles in solution. Here, negatively charged particles in solution display a long-ranged attraction where continuum electrostatic theory predicts monotonically repulsive interactions, particularly in solutions with monovalent salt ions at low ionic strength. Anisotropic orientational behavior of solvent molecules at an interface gives rise to an excess interfacial electrical potential which we suggest generates an additional solvation contribution to the total free energy that is traditionally overlooked in continuum descriptions of interparticle interactions in solution. In the present investigation we perform molecular dynamics simulation based calculations of the interfacial potential using realistic surface models representing various chemistries as well as different solvents. Similar to previous work that focused on simple model surfaces constructed by using oxygen atoms, we find that solvents at more realistic model surfaces exhibit substantial anisotropic orientational behavior. We explore the dependence of the interfacial solvation potential on surface properties such as surface group chemistry and group density at silica and carboxylated polystyrene interfaces. For water, we note surprisingly good agreement between results obtained for a simple O-atom wall and more complex surface models, suggesting a general qualitative consistency of the interfacial solvation effect for surfaces in contact with water. In contrast, for an aprotic solvent such as DMSO, surface chemistry appears to exert a stronger influence on the sign and magnitude of the interfacial solvation potential. The study carries broad implications for molecular-scale interactions and may find relevance in explaining a range of phenomena in soft-matter physics and cell biology.

RestraintMaker: a graph-based approach to select distance restraints in free-energy calculations with dual topology.

The calculation of relative binding free energies (RBFE) involves the choice of the end-state/system representation, of a sampling approach, and of a free-energy estimator. System representations are usually termed "single topology" or "dual topology". As the terminology is often used ambiguously in the literature, a systematic categorization of the system representations is proposed here. In the dual-topology approach, the molecules are simulated as separate molecules. Such an approach is relatively easy to automate for high-throughput RBFE calculations compared to the single-topology approach. Distance restraints are commonly applied to prevent the molecules from drifting apart, thereby improving the sampling efficiency. In this study, we introduce the program RestraintMaker, which relies on a greedy algorithm to find (locally) optimal distance restraints between pairs of atoms based on geometric measures. The algorithm is further extended for multi-state methods such as enveloping distribution sampling (EDS) or multi-site [Formula: see text]-dynamics. The performance of RestraintMaker is demonstrated for toy models and for the calculation of relative hydration free energies. The Python program can be used in script form or through an interactive GUI within PyMol. The selected distance restraints can be written out in GROMOS or GROMACS file formats. Additionally, the program provides a human-readable JSON format that can easily be parsed and processed further. The code of RestraintMaker is freely available on GitHub https://github.com/rinikerlab/restraintmaker.

Simultaneous parametrization of torsional and third-neighbor interaction terms in force-field development: The LLS-SC algorithm.

The calibration of torsional interaction terms by fitting relative gas-phase conformational energies against their quantum-mechanical values is a common procedure in force-field development. However, much less attention has been paid to the optimization of third-neighbor nonbonded interaction parameters, despite their strong coupling with the torsions. This article introduces an algorithm termed LLS-SC, aimed at simultaneously parametrizing torsional and third-neighbor interaction terms based on relative conformational energies. It relies on a self-consistent (SC) procedure where each iteration involves a linear least-squares (LLS) regression followed by a geometry optimization of the reference structures. As a proof-of-principle, this method is applied to obtain torsional and third-neighbor interaction parameters for aliphatic chains in the context of the GROMOS 53A6 united-atom force field. The optimized parameter set is compared to the original one, which has been fitted manually against thermodynamic properties for small linear alkanes. The LLS-SC implementation is freely available under http://github.com/mssm-labmmol/profiler.

Replica-Exchange Enveloping Distribution Sampling: Calculation of Relative Free Energies in GROMOS.

Molecular dynamics (MD) simulations have become an important tool to investigate biological systems. Free-energy calculations based on MD are playing an increasingly important role for computer-aided drug design and material discovery in recent years. Free-energy differences between pairs of end-states can be estimated using well-established methods such as thermodynamic integration (TI) or Bennett's acceptance ratio (BAR). An attractive alternative is the recently developed replica-exchange enveloping distribution sampling (RE-EDS) method, which enables estimating relative free-energy differences between multiple molecules from a single simulation. Here, we provide an introduction to the principles underlying RE-EDS and give an overview of the RE-EDS pipeline. In addition, we provide a description of the two complementary tools RestraintMaker and amber2gromos. We briefly discuss the findings of three recent applications of RE-EDS to calculate relative binding or hydration free energies. In all three studies, good agreement was found between the results obtained using RE-EDS and experimental values as well as values obtained using other free-energy methods.

Solvent-scaling as an alternative to coarse-graining in adaptive-resolution simulations: The adaptive solvent-scaling (AdSoS) scheme.

A new approach termed Adaptive Solvent-Scaling (AdSoS) is introduced for performing simulations of a solute embedded in a fine-grained (FG) solvent region itself surrounded by a coarse-grained (CG) solvent region, with a continuous FG ↔ CG switching of the solvent resolution across a buffer layer. Instead of relying on a distinct CG solvent model, the AdSoS scheme is based on CG models defined by a dimensional scaling of the FG solvent by a factor s, accompanied by an s-dependent modulation of the atomic masses and interaction parameters. The latter changes are designed to achieve an isomorphism between the dynamics of the FG and CG models, and to preserve the dispersive and dielectric solvation properties of the solvent with respect to a solute at FG resolution. This scaling approach offers a number of advantages compared to traditional coarse-graining: (i) the CG parameters are immediately related to those of the FG model (no need to parameterize a distinct CG model); (ii) nearly ideal mixing is expected for CG variants with similar s-values (ideal mixing holding in the limit of identical s-values); (iii) the solvent relaxation timescales should be preserved (no dynamical acceleration typical for coarse-graining); (iv) the graining level NG (number of FG molecules represented by one CG molecule) can be chosen arbitrarily (in particular, NG = s3 is not necessarily an integer); and (v) in an adaptive-resolution scheme, this level can be varied continuously as a function of the position (without requiring a bundling mechanism), and this variation occurs at a constant number of particles per molecule (no occurrence of fractional degrees of freedom in the buffer layer). By construction, the AdSoS scheme minimizes the thermodynamic mismatch between the different regions of the adaptive-resolution system, leading to a nearly homogeneous scaled solvent density s3ρ. Residual density artifacts in and at the surface of the boundary layer can easily be corrected by means of a grid-based biasing potential constructed in a preliminary pure-solvent simulation. This article introduces the AdSoS scheme and provides an initial application to pure atomic liquids (no solute) with Lennard-Jones plus Coulomb interactions in a slab geometry.

Efficient Alchemical Intermediate States in Free Energy Calculations Using λ-Enveloping Distribution Sampling.

Alchemical free energy calculations generally require intermediate states along a coupling parameter λ to establish sufficient phase space overlap for obtaining converged results. Such intermediate states can also be engineered to lower the energy barriers and, consequently, reduce the required sampling time. The recently introduced λ-enveloping distribution sampling (λ-EDS) scheme combines the properties of the minimum variance pathway and the EDS methods to improve sampling and allow for larger steps along the alchemical pathway compared to conventional approaches. This scheme also eliminates the need for soft-core potentials and retains the behavior of conventional λ-intermediate states as a limiting case. In this study, an automated procedure is developed to select the parameters of λ-EDS for optimal performance. The underlying theory is illustrated based on simulations of simple test systems (bond length changes in harmonic oscillators, mutations of dihedral angles, and charge creation in water), as well as on the calculation of the absolute hydration free energies of 12 small organic molecules.

Systematic optimization of a fragment-based force field against experimental pure-liquid properties considering large compound families: application to oxygen and nitrogen compounds.

The CombiFF approach is a workflow for the automated refinement of force-field parameters against experimental condensed-phase data, considering entire classes of organic molecules constructed using a fragment library via combinatorial isomer enumeration. One peculiarity of this approach is that it relies on an electronegativity-equalization scheme to account for induction effects within molecules, with values of the atomic hardness and electronegativity as electrostatic parameters, rather than the partial charges themselves. In a previous article [M. P. Oliveira, M. Andrey, S. R. Rieder, L. Kern, D. F. Hahn, S. Riniker, B. A. C. Horta and P. H. Hünenberger, J. Chem. Theory. Comput. 2020, 16, 7525], CombiFF was introduced and applied to calibrate a GROMOS-compatible united-atom force field for the saturated acyclic (halo-)alkane family. Here, this scheme is employed for the construction of a corresponding force field for saturated acyclic compounds encompassing eight common chemical functional groups involving oxygen and/or nitrogen atoms, namely: ether, aldehyde, ketone, ester, alcohol, carboxylic acid, amine, and amide. Monofunctional as well as homo-polyfunctional compounds are considered. A total of 1712 experimental liquid densities ρliq and vaporization enthalpies ΔHvap concerning 1175 molecules are used for the calibration (339 molecules) and validation (836 molecules) of the 102 non-bonded interaction parameters of the force field. Using initial parameter values based on the GROMOS 2016H66 parameter set, convergence is reached after five iterations. Given access to one processor per simulated system, this operation only requires a few days of wall-clock computing time. After optimization, the root-mean-square deviations from experiment are 29.9 (22.4) kg m-3 for ρliq and 4.1 (5.5) kJ mol-1 for ΔHvap for the calibration (validation) set. Thus, a very good level of agreement with experiment is achieved in terms of these two properties, although the errors are inhomogeneously distributed across the different chemical functional groups.

Evaluation of nine condensed-phase force fields of the GROMOS, CHARMM, OPLS, AMBER, and OpenFF families against experimental cross-solvation free energies.

Experimental solvation free energies are nowadays commonly included as target properties in the validation of condensed-phase force fields, sometimes even in their calibration. In a previous article [Kashefolgheta et al., J. Chem. Theory. Comput., 2020, 16, 7556-7580], we showed how the involved comparison between experimental and simulation results could be made more systematic by considering a full matrix of cross-solvation free energies . For a set of N molecules that are all in the liquid state under ambient conditions, such a matrix encompasses N×N entries for considering each of the N molecules either as solute (A) or as solvent (B). In the quoted study, a cross-solvation matrix of 25 × 25 experimental value was introduced, considering 25 small molecules representative for alkanes, chloroalkanes, ethers, ketones, esters, alcohols, amines, and amides. This experimental data was used to compare the relative accuracies of four popular condensed-phase force fields, namely GROMOS-2016H66, OPLS-AA, AMBER-GAFF, and CHARMM-CGenFF. In the present work, the comparison is extended to five additional force fields, namely GROMOS-54A7, GROMOS-ATB, OPLS-LBCC, AMBER-GAFF2, and OpenFF. Considering these nine force fields, the correlation coefficients between experimental values and simulation results range from 0.76 to 0.88, the root-mean-square errors (RMSEs) from 2.9 to 4.8 kJ mol-1, and average errors (AVEEs) from -1.5 to +1.0 kJ mol-1. In terms of RMSEs, GROMOS-2016H66 and OPLS-AA present the best accuracy (2.9 kJ mol-1), followed by OPLS-LBCC, AMBER-GAFF2, AMBER-GAFF, and OpenFF (3.3 to 3.6 kJ mol-1), and then by GROMOS-54A7, CHARM-CGenFF, and GROMOS-ATB (4.0 to 4.8 kJ mol-1). These differences are statistically significant but not very pronounced, and are distributed rather heterogeneously over the set of compounds within the different force fields.

On the Effect of the Various Assumptions and Approximations used in Molecular Simulations on the Properties of Bio-Molecular Systems: Overview and Perspective on Issues.

Computer simulations of molecular systems enable structure-energy-function relationships of molecular processes to be described at the sub-atomic, atomic, supra-atomic or supra-molecular level and plays an increasingly important role in chemistry, biology and physics. To interpret the results of such simulations appropriately, the degree of uncertainty and potential errors affecting the calculated properties must be considered. Uncertainty and errors arise from (1) assumptions underlying the molecular model, force field and simulation algorithms, (2) approximations implicit in the interatomic interaction function (force field), or when integrating the equations of motion, (3) the chosen values of the parameters that determine the accuracy of the approximations used, and (4) the nature of the system and the property of interest. In this overview, advantages and shortcomings of assumptions and approximations commonly used when simulating bio-molecular systems are considered. What the developers of bio-molecular force fields and simulation software can do to facilitate and broaden research involving bio-molecular simulations is also discussed.

Reaction-field electrostatics in molecular dynamics simulations: development of a conservative scheme compatible with an atomic cutoff.

In molecular dynamics (MD) simulations of condensed-phase systems, straight-cutoff truncation of the non-bonded interactions is well known to cause cutoff noise and serious artifacts in many simulated properties. These effects can be drastically reduced by applying the truncation based on distances between neutral charge groups (CG) rather than between individual atoms (AT). In addition, the mean effect of the omitted electrostatic interactions beyond the cutoff distance can be reintroduced using the reaction-field (RF) method, where the medium outside the cutoff sphere is approximated as a dielectric continuum of permittivity equal to that of the solvent. The RF scheme is generally applied with CG truncation. This is justified for low solvent permittivities, where the RF correction is small and an AT truncation would lead to severe issues, just as in the straight-cutoff case. However, it is less appropriate for solvents with high permittivities, where the RF correction acts as a physically motivated shifting function, and a CG truncation may in turn lead to artifacts and poorer energy conservation. In this study, we assess the impact of truncation artifacts considering the 57 organic liquids which were used in the calibration of the GROMOS-compatible 2016H66 force field. Combinations of shifting or switching schemes with RF-based electrostatic interactions as well as van der Waals (Lennard-Jones) interactions are then introduced to resolve the issues with AT truncation. These shifting and switching schemes have the following properties: (i) they bring the force but not the potential energy to zero at the cutoff; (ii) as a result, they lead to a modification of the interaction that is comparatively small; (iii) they permit to conduct rigorously conservative simulations; (iv) the energies can easily be corrected back to the unmodified form, either on the fly or in a post-processing step. The mathematical formalism of these schemes is presented in detail, and their validation is performed using the 57 organic liquids.

Systematic Optimization of a Fragment-Based Force Field against Experimental Pure-Liquid Properties Considering Large Compound Families: Application to Saturated Haloalkanes.

Direct optimization against experimental condensed-phase properties concerning small organic molecules still represents the most reliable way to calibrate the empirical parameters of a force field. However, compared to a corresponding calibration against quantum-mechanical (QM) calculations concerning isolated molecules, this approach is typically very tedious and time-consuming. The present article describes an integrated scheme for the automated refinement of force-field parameters against experimental condensed-phase data, considering entire classes of organic molecules constructed using a fragment library via combinatorial isomer enumeration. The main steps of the scheme, referred to as CombiFF, are as follows: (i) definition of a molecule family; (ii) combinatorial enumeration of all isomers; (iii) query for experimental data; (iv) automatic construction of the molecular topologies by fragment assembly; and (v) iterative refinement of the force-field parameters considering the entire family. As a first application, CombiFF is used here to design a GROMOS-compatible united-atom force field for the saturated acyclic haloalkane family. This force field relies on an electronegativity-equalization scheme for the atomic partial charges and involves no specific terms for σ-holes and halogen bonding. A total of 749 experimental liquid densities ρliq and vaporization enthalpies ΔHvap concerning 486 haloalkanes are considered for calibration and validation. The resulting root-mean-square deviations from experiment are 49.8 (27.6) kg·m-3 for ρliq and 2.7 (1.8) kJ·mol-1 for ΔHvap for the calibration (validation) set. The values are lower for the validation set which contains larger molecules (stronger influence of purely aliphatic interactions). The trends in the optimized parameters along the halogen series and across the compound family are in line with chemical intuition based on considerations related to size, polarizability, softness, electronegativity, induction, and hyperconjugation. This observation is particularly remarkable considering that the force-field calibration did not involve any QM calculation. Once the time-consuming task of target-data selection/curation has been performed, the optimization of a force field only takes a few days. As a result, CombiFF enables an easy assessment of the consequences of functional-form decisions on the accuracy of a force field at an optimal level of parametrization.

Evaluating Classical Force Fields against Experimental Cross-Solvation Free Energies.

Experimental solvation free energies are nowadays commonly included as target properties in the validation and sometimes even in the calibration of condensed-phase force fields. However, this is often done in a nonsystematic fashion, by considering available solvation free energies involving an arbitrary collection of solutes in a limited set of solvents (e.g., water, octanol, chloroform, cyclohexane, or hexane). Here, this approach is made more systematic by introducing the concept of cross-solvation free energies ΔsGA:B⊖ for a set of N molecules that are all in the liquid state under ambient conditions, namely the matrix of N2 entries for ΔsGA:B⊖ considering each of the N molecules either as a solute (A) or as a solvent (B). Relying on available experimental literature followed by careful data curation, a complete ΔsGA:B⊖ matrix of 625 entries is constructed for 25 molecules with one to seven carbon atoms representative for alkanes, chloroalkanes, ethers, ketones, esters, alcohols, amines, and amides. This matrix is then used to compare the relative accuracies of four popular condensed-phase force fields: GROMOS-2016H66, OPLS-AA, AMBER-GAFF, and CHARMM-CGenFF. In broad terms, and in spite of very different force-field functional-form choices and parametrization strategies, the four force fields are found to perform similarly well. Relative to the experimental values, the root-mean-square errors range between 2.9 and 4.0 kJ·mol-1 (lowest value of 2.9 for GROMOS and OPLS), and the average errors range between -0.8 and +1.0 kJ·mol-1 (lowest magnitude of 0.2 for AMBER and CHARMM). These differences are statistically significant but not very pronounced, especially considering the influence of outliers, some of which possibly caused by inaccurate experimental data.