FFParam-v2.0: A Comprehensive Tool for CHARMM Additive and Drude Polarizable Force-Field Parameter Optimization and Validation

Abstract

Developing production quality CHARMM force-field (FF) parameters is a very detailed process involving a variety of calculations many of which are specific for the molecule of interest. The first version of FFParam was developed as a standalone python package designed for optimization of electrostatic and bonded parameters of the CHARMM additive and polarizable Drude FFs using quantum mechanical (QM) target data. The new version of FFParam has multiple new capabilities for FF parameter optimization and validation, with emphasis on the ability to use condensed phase target data in the optimization. FFParam-v2 allows optimization of Lennard-Jones (LJ) parameters using potential energy scans of interactions between selected atoms in a molecule and noble gases, viz. He and Ne, and through condensed phase calculations from which experimental observables such as heats of vaporization and free energies of solvation may be obtained. This functionality serves as a gold-standard for both optimizing parameters and validating the performance of the final parameters. A new bonded parameter optimization algorithm has been introduced to account for simultaneously optimizing multiple molecules sharing parameters. FFParam-v2 also supports comparison of normal modes and the potential energy distribution of internal coordinates towards each normal mode obtained from QM and molecular mechanics calculations. Such comparison capability is vital to validate the balance amongst various bonded parameters that contribute to the complex normal modes of molecules. User interaction has been extended beyond the original graphical user interface (GUI), to include command line interface capabilities that allows for integration of FFParam in workflows thereby facilitating automation of parameter optimization. With these new functionalities, FFParam is a more comprehensive parameter optimization tool for both beginner and advanced users.

Graphical Abstract

Introduction

Molecular simulations using empirical force fields represent one of the most widely used approaches to study a range of complex biological and physical systems. To allow for accurate molecular simulations high quality force fields, such as those associated with AMBER^{1, 2} and CHARMM, ^{3, 4} are required. Achieving this accuracy requires systematic optimization procedures targeting a range of theoretical and experimental observables. Towards achieving this a number of parameter optimization engines, ^5–11 including FFParam¹² developed in our laboratory, have been presented and are available for use by the computational chemistry community.

The first version of FFParam¹² was specifically designed for optimizing electrostatic and bonded parameters within the CHARMM additive and Drude polarizable force fields (FF), ^{13, 14} leveraging quantum mechanical (QM) target data for the optimization. Featuring a graphical user interface (GUI) built with Qt libraries, FFParam-v1 ensures compatibility across different platforms. Through its intuitive GUI, FFParam-v1 facilitates the creation, extraction, and visualization of a multitude of QM derived target data and their molecular mechanical (MM) counterparts. Two QM engines, Gaussian^{15, 16} v03/v09 and Psi4, ¹⁷ and two MM engines, CHARMM¹⁸ and OpenMM, ¹⁹ are supported in FFParam-v1. Various results can be presented and analyzed through textual representation, graphical display, and molecular visualization functionalities designed using dedicated Qt widgets and pyOpenGL integration. The target data supported in FFParam-v1 includes dipole moments, molecular polarizability tensors, and water-model compound interactions for electrostatic parameters and potential energy scans (PES) for bonded parameter optimization. Algorithms such as Monte Carlo Simulated Annealing (MCSA)²⁰ and least square fitting (LSFitPar),²¹ specifically designed for the CHARMM and Drude parameter optimization protocols, available in FFParam-v1 can be used to minimize the difference between MM and target data for electrostatic and bonded terms. However, no capabilities for optimizing the van der Waals (vdW) associated terms were included. Thus, the first version of FFParam offers a comprehensive suite of features for optimizing CHARMM and Drude FF parameters provided that all atoms in the molecule have well-defined atom types and associated Lennard Jones (LJ) parameters. FFParam-v1 has been successfully applied in-house and by multiple research groups for parametrization of small molecules including molecular ions,²² drug-like molecules,^{23, 24} glycopeptides,²⁵ and adenosine receptor agonists.²⁶

ffTK⁵ is a FF optimization tool that harnesses the capabilities of the VMD program²⁷ for optimizing additive FF parameters within the realms of the CHARMM and AMBER FFs. Although developed independently, ffTK shares many features and protocols with FFParam-v1, as both are geared towards automating parameter optimization procedures that have been long-established. ffTK facilitates input file compatibility with Gaussian and, more recently, ORCA²⁸ for the calculation of QM target data, alongside utilizing NAMD as the MM engine. While ffTK remains a valuable tool for improving CHARMM/AMBER parameters, its scope is limited to additive FFs and it does not offer the capability for parameter validation through bulk properties calculations.

While both software packages have proven valuable to the MD community, there are notable features that need to be added to allow them to be capable of generating the full range of production-quality, generalized, and transferable FF parameters for CHARMM. The new version of FFParam has been completely restructured with multiple new capabilities not just for optimization of parameters but for parameter validation as well. Such capabilities facilitate the extension of the CHARMM and Drude FFs into unexplored chemical spaces enabling the assignment of new atom types and the optimization of corresponding LJ parameters. Most FFs, including AMBER and CHARMM, define atom types based on valency, chemical connectivities and ionization state of an atom as well as additional considerations and associate a fixed LJ parameter to the atom type. The fixed LJ parameters associated with atom types ensure their transferability across molecules. It has been argued that as vdW forces are primarily governed by inner shell electrons, the influence of the variations in the chemical environment on these forces is minimal, thereby reinforcing the case for the transferability of LJ parameters.^{29, 30} Therefore, for most of the atoms in a wide range of molecules, LJ parameters can directly be adopted from CGenFF,^31–33 which were primarily from the CHARMM36 additive biomolecular FF, in the case of CHARMM. Only for cases where desired experimental data cannot be reproduced satisfactorily or for molecules with novel atom types, will LJ parameter need to be optimized and validated. Over the last three decades, MacKerell and coworkers have used an optimization protocol for LJ parameters which utilizes QM-derived interaction potential energy scans (PES) between rare gas atoms (He, Ne) and model compounds along with reproduction of experimental thermodynamic properties.^34–37 Given the well-established dominance of the LJ term to heats of vaporization of polar-neutral organic molecules,³⁸ it becomes imperative to validate LJ parameters against thermodynamic properties. In addition, utilization of QM interaction PES allows for a better balance between the LJ parameters for the different atom types in a molecule thereby helping to overcome the parameter correlation problem.^{39, 40} Thus, the current version of FFParam is equipped to perform LJ parameter optimization using QM PES target data in conjunction with condensed phase properties such as pure solvent densities, heat of vaporization, isothermal compressibility, and dielectric constants and free energies of solvation in various liquids.

Methods

FFParam version 2.0 workflow

The parametrization workflow of the current version of FFParam builds on its first version. Scheme 1 highlights the newly added features in FFParam.v2 viz. extraction of vibrational modes and Hessian matrix from QM output, generating QM and MM input files for interaction energy calculation with water and noble gases, MCSA-based fitting of LJ and bonded parameters, and an entire module for condensed phase property calculations. The implementation and execution details are discussed in the following sections.

Scheme 1.

Flow Chart of the workflow of parameterization of FFParam v2. The text in solid boxes corresponds to the actions available in FFParam and dashed boxes denote to the data obtained upon execution of the corresponding action. Boxes with red outline denote newly added features in FFParam-v2.

Nonbond Parameter Optimization and Validation

FFParam.v1 included the capabilities to set up and perform QM and MM PES between model compounds and water. This allowed for optimization of the electrostatic parameters targeting the QM PES in conjunction with additional observables such as dipole moments and, in the case of the Drude FF, molecular polarizabilties. In FFParam.v2 the ability to perform optimization LJ parameters has been implemented. These additional capabilities, as described below, allow for comprehensive optimization and validation of the nonbond parameters in both the CHARMM and Drude FF.

The nonbond parameter optimization itself is typically initiated from assignment of initial atom types. This may be done using the CGenFF program³³ for CHARMM based on the published additive rules files and a modified set of rules developed in the MacKerell lab that assigns Drude FF atom types.⁴¹ Initial electrostatic parameters are also assigned with the CGenFF program^31–33 for CHARMM while deep neural network (DNN) models are used to generate initial values of the partial atomic charges, atomic polarizabilities, and Thole scale factors for the Drude FF.^{41, 42} Once the initial atom types have been assigned, QM PES between the model compounds and water or noble gases may then be analyzed along with dipole moments and molecular polarizabilities (with the Drude FF) as an initial test of the parameters. If experimental condensed phase data is available, the corresponding bulk simulations may be performed, and calculated data can be compared with experimental data. At this stage a decision may be made concerning the need for additional optimization of the nonbonded parameters based on reproduction of all the QM and experimental target data. If parameter optimization is required published protocols may be followed including the recently presented use of DNN to facilitate optimization of LJ parameters.⁴² That protocol was applied to the Drude FF but the approach is also suitable for the additive FF. As described in the following section, FFParam.v2 contains a full range of utilities for generation of and comparisons with the target data as well as tools to perform selected aspect the parameter fitting.

QM Nobel Gas-Model Compound Potential Energy Scans

Like the protocol devised for charge optimization in FFParam-v1 that employs interaction PES of specific atoms within the molecule with waters, FFParam-v2 offers the ability to calculate interaction PES between noble gases and model compounds as target data for LJ potential optimization. Absence of charge on noble gases eliminates charge-charge interactions and thus the PES is purely guided by vdW interactions with the CHARMM additive FF. With the Drude FF the presence of polarization typically leads to a dipole-induced dipole interaction of polar neutral model compounds with noble gases that contribute to the PES. The ability to perform noble gas-model compound PES has been implemented in FFParam by extending the input generator to utilize noble gases in addition to water molecules. Accordingly, the CreateQMInput > Water Interaction tab is renamed as CreateQMInput > Nonbond Interaction tab. Analogous to the donor-acceptor (.da) file used for water interactions, the noble gas interaction is guided by a “.vdw” file containing atoms of interest and reference atomic sites on the model compound for generating appropriate interaction position and orientation with He or Ne. The noble gas atom interaction orientations are designed to maximize the interaction with the chosen atom (e.g. that on which the LJ parameters are being optimized) while minimizing the interactions with other atoms on the model compound (Figure 1). The .vdw file is subsequently used for creating QM or MM model compound-noble gas input files for interaction PES calculations within a range of 1.5 to 7 Å. The QM calculation on these input files involves a scan in 0.05 Å increments along the direction of approach to find the minimum interaction energy of the model compound-noble gas complexes. The minimum interaction energies and corresponding distances are extracted in a text file. To perform the LJ parameter optimization, the concerned LJ parameters need to be added in the topology file of the model compound along with the rest of the parameters. Users can compare the minimum interaction energies and distances between QM and MM outcomes using the CompareMMvsQM tab. The difference between MM and QM minimum interaction energy and distance can be minimized by manually changing the LJ well depth (ε) and radius (R_min) parameters or using a Monte Carlo simulated annealing (MCSA) method designed for LJ parameter fitting.^{40, 42} The new MCSA method designed for LJ parameter considers the highly sensitive nature of ε and R_min and can be applied for simultaneously fitting multiple LJ parameters against the corresponding target data for multiple interaction orientations and model compounds.

Figure 1.

Example interaction orientations of He/Ne with a model compound generated by FFParam-v2.

Condensed Phase Simulations

Although various types of condensed phase simulations are routinely performed by many research groups involved in FF development, their setup, execution, and extraction of results may be time consuming. Moreover, setup of simulations using the Drude FF can be more challenging due to its higher sensitivity towards the initial simulation conditions. For example, if there are atoms in an initial simulation box that are close to each other, overpolarization can happen causing stability issues that cannot occur with an additive FF. This version of FFParam supports two MD simulation setup protocols for calculating condensed phase properties including heats of vaporization, densities, molecular volumes, isothermal compressibility, and dielectric constants of pure solvent and free energies of solvation in multiple solvents.

The molecule to be subjected to MD simulations for obtaining bulk properties need not be the same as the one used for rest of parameter optimization. Such compounds are typically simple molecules that include the atom type of interest while minimizing the number of other atom types and for which experimental data is available under relevant conditions from reliable source. For instance, when validating the LJ parameters of hydroxyl groups in carbohydrates model compounds such as ethanol or isopropanol would be utilized. It is also important to have highly optimized LJ parameters for other atom types in the model compound in order to elucidate the impact of the LJ parameters of the specific atom type on the bulk property. For operational simplicity, FFParam can replace the atom names in a pdb file of the molecule with the atom names in the topology file, provided that atom order is preserved, allowing the user to readily identify the atom types associated with the atoms in the model compound.

For setting up the simulation in CHARMM or OpenMM, FFParam only requires topology, parameter, and coordinate files of the concerned residue. FFParam now offers stepwise shell scripts for the entire process of bulk property simulation, starting from setup to data retrieval. This is particularly advantageous as MD simulations are typically run on HPC architectures. Although the MD simulation protocols are accessible through the FFParam-GUI, users may need to manually transfer job script files to an HPC environment, conduct the simulations, and subsequently synchronize the local directory prior to advancing to the analysis steps. This recurring transfer of files between local and HPC environments is avoidable, rendering the shell script architecture featured in FFParam particularly well-suited for such calculations. FFParam automates job submission on popular HPC job schedulers such as SLURM, SGE, and PBS. These scripts only require adjustments for executable paths and module names, allowing users to employ them with only minimal customization. Additionally, users have the option to substitute the locally modified job scheduler template file within a designated template directory for future use. While FFParam also supplies interactive shell scripts for running simulations on local machines, it’s worth noting that due to extended computational time, this may not be the most efficient choice.

In practice, for conducting condensed phase simulations, FFParam should be locally accessible on the machine. There’s no need for installation, but it’s crucial to set the PYTHONPATH environment variable to the top-level directory of FFParam. Once configured, the shell scripts mentioned below will accurately utilize various functions and scripts within FFParam necessary for completing the respective procedures.

FFParam Simulation Protocol for Heats of Vaporization or Sublimation

Heat of vaporization (ΔH_vap) is defined as the change in enthalpy upon conversion of one mole of liquid into gas at constant temperature. The same quantity is called heat of sublimation when one mole of a crystal converts into a gas at constant temperature. Heats of vaporization can be experimentally measured using calorimeter at the boiling point of the neat liquid or determined from the vapor pressure-temperature (P–T) plot using the Clausius-Clapeyron equation.⁴³ In several parameter optimization studies, MacKerell and coworkers have utilized MD protocols to calculate heats of vaporization.^{38, 43–46} Building in these FFParam offers intuitive shell scripts that greatly simplifies the complex MD protocol with minimum arguments and require little to no change in the base scripts.

The process for determining the heat of vaporization is structured into six straightforward steps (Figure 2). The initial and concluding stages involve creating the simulation box and extracting the final data, respectively. Second and third are independent simulations steps which can be executed using either CHARMM or OpenMM, with the flexibility to switch between them as needed. Output file names are designed to be interoperable between both MD engines and allow data extraction without any file format conversions.

Figure 2.

Structure of FFParam directory of simulation scripts for calculating heats of vaporization.

To set up pure solvent simulations the user needs to supply the FF type (either additive or Drude), residue name, topology and parameter files, coordinate file and experimentally known density value at the desired temperature and pressure. These files should be located in the parent directory. A simulation box containing 216 repeating units of the residue is generated by default. User does not need to provide desired box size, as it is derived from the provided density. After generating the simulation box, 500 ps of equilibration followed by 1 ns of production run can be performed using hvap_1_run_bulk.sh script. The switching function is used for non-bonded cutoff with CHARMM parameters ctonnb, ctofnb, cutnb, and cutim values of 10.0, 12.0, 16.0, 16.0, and 16.0, respectively, in conjunction with an isotropic long-range correction.⁴⁷ Electrostatic interactions are calculated using the Particle Mesh Ewald approach⁴⁸ with a real space cutoff of 12 Å. This treatment of nonbond interactions is used throughout all the condensed phase simulations described below unless noted. Since the run script is copied locally, especially in the case of CHARMM, users can change any default value according to the system under study. The gas phase simulation of a single molecule may seem a trivial task but can be a major source of error if gas phase energies are not converged. To achieve convergence, the last frame of the bulk phase trajectory is provided as input to hvap_2_run_gas.sh, and gas phase simulations of 1ns are performed utilizing each of the conformation in the bulk simulation box as the starting coordinates. The final E_intra(g) is calculated as an average of the potential energy over all the gas phase trajectories.

Once both bulk and gas phase simulations are performed, hvap_3_ext_bulk.sh and hvap_3_ext_gas.sh extract the energy, dipole, and volume from every frame in the trajectory file and save it into bulkreport.csv and gasreport.csv, respectively. The final script makes use of the .csv files and applies required equations to compute heat of vaporization,⁴³ density,³⁰ isothermal compressibility,⁴⁹ and dielectric constant⁵⁰ (See Supporting Information (SI) for required equations). See Table 1 and SI for required and additional arguments needed to execute each step. Additional scripts in the FFParam inventory allow for histogram analysis of rotatable bond dihedral angle and valence angle values sampled by molecules during bulk phase simulation.

Table 1.

Simulation scripts with required arguments and values in FFParam for generating the initial simulation box, running bulk phase and gas phase simulations, extracting the information from simulation trajectories, and obtaining final data related to the heat of vaporization. See Supporting Information (SI) for additional arguments and other details.

FFParamScript	Required Arguments	Input Values
hvap_0_setup.sh	Additive  Resi  Resistrfile  Resipdbfile  Density	<true/false> <resname> <strfile> <residue pdb file> <desired density>
hvap_1_run_bulk.sh	Additive  Resi  Resistrfile  Resibulkcorfile	<true/false> <resname> <strfile> <bulk crd/pdb file>
hvap_2_run_gas.sh	Additive  Resi  Resistrfile  Resibulkcorfile	<true/false> <resname> <strfile> <bulk crd/pdb file>
hvap_3_ext_bulk.sh	Additive  Resi  Resistrfile  Resibulkcorfile  resibulkdcdfile	<true/false> <resname> <strfile> <bulk crd/pdb file> <bulk prod dcd file>
hvap_4_ext_gas.sh	Additive  Resi  Resistrfile  Resicorfile	<true/false> <resname> <strfile> <any resi crd file in gas directory>
hvap_5_getresult.sh	Bulkreport  Monomerreport  Molweight	<bulkreport.csv> <monomerreport.csv> <molecular weight>

FFParam Simulation Protocol for Free Energy of Solvation

Solvation free energies are another very important property for determining the fitness of parameters in the context thermodynamic properties in a condensed phase. FFParam provides user-friendly CHARMM scripts that utilize Free energy Perturbation (FEP)/MD with explicit solvent molecules for determining absolute free energy of solvation of compounds. This FEP scheme was primarily designed by Roux and coworkers^{51, 52} and is frequently used within the FF developer community. The PERT module in CHARMM⁵³ is used in the script to partition the absolute solvation free energy in terms of its polar (i.e. electrostatic) and nonpolar components. The Weeks, Chandler, and Andersen (WCA) scheme^{54, 55} is utilized to separate the nonpolar component further into repulsive and attractive terms. The contributions to the free energy from electrostatics (Coulombic) and vdW dispersion (attractive) interactions are computed using a standard linear coupling approach. A 100 ps of MD simulation is typically performed for each interaction energy component using coupling parameters varying between 0.0 and 1.0, wherein 0 and 1 implies complete absence and presence of the specific interaction. For the attraction term, the coupling parameter ξ ranges from 0.0 to 1.0 with increments of 0.1. Similarly, the coupling parameter λ is used for the electrostatic free energy contribution, ranging from 0.0 to 1.0 in steps of 0.1.⁵¹ The free energy contribution stemming from the core repulsion is calculated using a staging parameter, s, varied as 0.0, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, and 1.0. For each specific value of s, simulations are run in the forward and backward directions. During all MD simulations, the center of mass of the solute is restrained in the center of simulation box using a harmonic potential with a force constant of 1.0 kcal Å⁻² mol⁻¹. MD simulations are performed with Langevin dynamics⁵⁶ with a friction constant of 5 ps⁻¹ at the user specified temperature (default = 298 K) applied on the non-H atoms of all of the solvent molecules. In the case of the Drude FF a friction constant of 5 ps⁻¹ and a temperature of 1 K are applied to the Drude particles. The integration time step of the dynamics is 2 fs for additive FF and 1 fs for Drude FF. All covalent bonds involving hydrogen atom are fixed with SHAKE constraints. Interaction energy trajectories obtained from each interaction energy component are subsequently analyzed using the weighted histogram analysis method (WHAM)⁵⁷ to obtain final data. Users are recommended to follow these simulation parameters for reproducibility of the results.

FFParam allows use of any solvent molecule for solvation free energy calculation provided that topology and parameters of solvent are supplied. For example, FEP calculations of ions in N-methylacetamide (NMA) and ethanol (EtOH) have been performed to facilitate the optimization of ion parameters for ion-protein complexes.⁵⁸ The procedure is explained here using water as the solvent. The fep_0_setup.sh script generates simulation box with user specified number of explicit water molecules (default=500). Depending on whether the model compound under study is defined by additive FF or Drude FF, either the TIP3P or SWM4 water model is used, respectively.⁵⁹ The box is generated using Packmol, an external package for generating initial configurations for MD simulations.^{60, 61} Users need to install Packmol separately from its github page (https://github.com/m3g/packmol) and specify the path while running the FFParam setup FEP simulation script. An alternative method is available specifically for water, wherein the model compound (solute) is placed in the center of pre-equilibrated water box containing 512 water molecules. Any water molecule within 1.8 Å of any atom of the solute is removed from the box. This results in variable number of waters in the simulation box, which is reported to the user. Before continuing with FEP calculation, the bulk simulation box is equilibrated for 1 ns using fep_1_run_eqpdlrc.sh script. The protocol includes a production run of 2 ns and continues to evaluate the LJ long range correction term in the solvation free energy as described by Baker et al.⁵² Once the production run is complete (indicated by presence of resi_box_prod.crd file), the user can directly continue with the stages of FEP calculation for bulk and gas phase using fep_2_run_bulk.sh and fep_3_run_gas.sh, respectively. Once all the simulations have been successfully completed, the directory containing trajectory files is analyzed using fep_4_run_wham.sh to obtain free energy components of the bulk and gas phases, which are output in bulk_freenergy.csv and gas_freenergy.csv. Finally, using the LJ long-range correction (lrc_energy.csv), fep_5_getresults.sh provides the absolute free energy of solvation. See Table 2 and SI for required and additional arguments needed to execute each step.

Table 2.

Simulation scripts in FFParam for executing various stages of free energy perturbation scheme for calculating free energy of solvation.

FFParamScript	Required Arguments	Input Values
fep_0_setup.sh	Additive  Resi  Resistrfile  Resipdbfile	<true/false> <resname> <strfile> <residue pdb file>
fep_1_run_bulk_eqpdlrc.sh	Additive  Resi  Resistrfile  Resibulkcorfile	<true/false> <resname> <strfile> <bulk crd/pdb file>
fep_2_run_bulk.sh	Additive  Resi  Resistrfile  Resibulkcorfile	<true/false> <resname> <strfile> <bulk crd file>
fep_3_run_gas.sh	Additive  Resi  Resistrfile  Resicorfile	<true/false> <resname> <strfile> <resi crd/pdb file>
fep_4_run_wham.sh	phase	<bulk/gas>
fep_5_getresult.sh	bulkGfile  gasGfile  resicharge	<bulkFreeEnergyComponent.csv> <monoFreeEnergyComponent.csv> <charge on residue>

Automated Fitting of Bonded Parameters Targeting Potential Energy Scans using MCSA

FFParam-v1 utilizes an external program LSFITPAR to automate the bonded parameter fitting.^{21, 32} LSFITPAR is a least squares fitting method to minimize the difference between MM data with QM target data. The approach allows for the application of harmonic restraints to existing bonded parameters to minimize their divergence from the initial values if needed. To fit a specific bonded parameter or collection of parameters, the MM PES is generated with all FF terms except the parameter related to the bonded term/s being fitted for which the force constants are set to zero. LSFITPAR optimizes the parameters by utilizing only the bonded potential function, rather than full energy function to maximize computational efficiency. As previously reported, LSFITPAR produces robust parameters, with minimal impact on well-behaved parameters.²¹ FFParam generates MM data with required restraints and also generates all required input parameters for executing LSFITPAR.

In certain scenarios a user may optimize parameters for a single dihedral while the adjacent bonded terms have not been adequately optimized. In these instances, the user may have to perform multiple iterations of the fitting procedure to account for all the relevant parameters. Employing the full energy function can serve as a potential solution to this challenge. In addition to the option of using LSFITPAR, a new MCSA fitting algorithm has been designed in the new version of FFParam for fitting bonded parameters. This algorithm also allows optimization of bonded parameters using QM PES from multiple molecules sharing that term. The algorithm leverages weighting schemes and other constraints also implemented in LSFITPAR. In each iteration, the MCSA algorithm utilizes user-specified MM engine CHARMM or OpenMM to obtain energy differences upon changing randomly selected terms in the bonded parameter allowing for minimization of that difference between the MM and QM target PES.

Comparison of Potential Energy Distributions of QM and MM derived Normal Modes

Analysis of bonded parameters, particularly the force constants, may be performed based on the vibrational spectra of a molecule based on the normal modes.⁶² Normal modes are associated with a vibrational frequency and the internal coordinates that contribute to that vibrational frequency. The distribution of internal coordinates contributing to each vibrational frequency is referred to as the potential energy distribution (PED). The MM PED from well-balanced bonded parameters should ideally match with QM PED indicating that the proper distortions of the molecule associated with the individual vibrations are present in the MM model. As the normal models typically include contributions from multiple internal coordinates their accurate treatment indicates that the various bonded parameters associated with each internal coordinate are properly balanced.

In practice, QM calculations are initially used to calculate the vibrational spectra from which the normal mode PED is extracted. As QM methods typically overestimate the vibrational frequencies they are typically scaled based on the QM model chemistry used for the calculation.⁶³ For example, vibrations may be scaled by a factor of 0.9434 in the case of MP2/6–31G(d) model chemistry QM spectra. Correlating the PED of QM and MM frequencies can be challenging due to the contribution of multiple local internal coordinates (ICs), which often differ between QM and MM spectra. In FFParam the QM and MM PED analysis can be performed using the MOLVIB functionality in CHARMM that utilizes ICs, complete and nonredundant sets of internal displacement coordinates describing vibrational modes, and a mapping of the ICs onto the normal modes (U Matrix). However, generating input for MOLVIB analysis can be challenging, especially in the case of the Drude topologies where the presence of Drude particles, which are treated as explicit particles, lead to different atom numbering and indices in MM versus QM. FFParam now generates MOLVIB input file for both additive and Drude FF topologies. It utilizes rules described by Pulay et al.⁶⁴ to define the normal models in terms of internal coordinates. Further, it allows execution of MOLVIB analysis in CHARMM and extracts QM and MM results in .csv file for comparison. Currently, there is no automated method for optimization of bonded parameters targeting QM vibrational spectra, though manual adjustments may be performed as well as comparing spectra for parameter validation. Ensuring an accurate representation of internal coordinates involved in lower frequency modes is particularly crucial as these are responsible for the largest structural distortions that occur in MD simulations.

Miscellaneous Operational Changes in FFParam v-2.0

The first version of FFParam is primarily operated through the GUI. Apart from shell scripts designed for performing MD simulations, regular actions of this version can now be operated using a command line interface, FFParam-CLI. Most of the action names in the GUI and CLI are the same simplifying their usage and enhancing interoperability between the GUI and CLI versions. In addition, FFParam-CLI provides some new capabilities that are a combination of multiple actions allowing high throughput application of FFParam-v2 as required for optimizing parameters for multiple molecules. Examples include CreateandRunQM and RunMMandAnalyze. As the names suggest, creating QM input file/s and running the QM calculation/s are combined together in the initial action, while running MM calculation and comparing with QM target data are combined into the later action. Both the GUI and CLI versions of the program can be installed together or separately. This allows installation of FFParam-CLI version on HPC architecture that does not support a GUI-version and related libraries. Additional details of FFParam-CLI version can be found in the User Manual hosted on the FFParam website. Another minor update in the new version of FFParam are modifications to take care of input and output format of more recent versions of both QM engines including Gaussian⁶⁵ v16 and Psi4 ≤ 1.9.¹⁷

Results and Discussion

Validation of a Model Compound using FFParam-v2

As a demonstration of new features in FFParam-v2 as well as to facilitate use of the CLI workflow for condensed phase calculations, we performed parameter validation of cyclopentanol for the additive and Drude FFs. The additive topology and parameters were generated using CGenFF v-2.3.0,³³ while the Drude topology and parameters were obtained using a version of the CGenFF program modified to Drude atom types and recently developed neural-network model for the electrostatic parameters.⁴¹ The topologies and parameters of both FFs can be found in section S1.6 of the SI. A detailed comparison of MM values with electrostatic QM target data, i.e. dipole moment, molecular polarizability, and water interaction energies can be found in Table S1, S2, S3 and S4 of SI. The structure was first optimized at MP2/6–31G* model chemistry prior to the calculation of target properties. For additive FF, the dipole moment was obtained at the same level of theory and basis-set for the optimized molecule and the water interactions were calculated by subtracting the monomer energies with optimized cyclopentanol-water complex energy at HF/6–31G* model chemistry. The obtained QM water interaction values were scaled by a factor of 1.16 for the reason reported previously.⁶⁶ The target dipole moment and molecular polarizability for Drude FF was obtained at MP2/cc-pVQZ model chemistry for cyclopentanol structure optimized at MP2/aug-cc-pVDZ. The obtained molecular polarizability tensor was scaled by a factor of 0.85.¹² For target water interaction values, the cyclopentanol-water complex was first optimized at MP2/aug-cc-pVDZ along the direction of approach of water and interaction energies were corrected for basis set superposition error (BSSE)⁶⁷ at MP2/cc-pVQZ model chemistry. The corresponding MM values were obtained using standard protocols discussed in the first version of FFParam.¹² Using the newly implemented scan feature in FFParam-v2, QM input for PES scan cyclopentanol-“Ne gas” complex targeting different atom types were generated and the energy values were computed using Psi4 at MP2/aug-cc-pVDZ. The corresponding additive and Drude FF energy values were generated using CHARMM script in FFParam. The comparison of QM and MM PES scans can be seen in Figure 3. The newly implemented bash script pipeline (ffpsimul) in FFParam-v2 was used to calculate the heat of vaporization and free energy of hydration of cyclopentanol. CHARMM was used as MM engine for these calculations with the results of both FFs compared to the experimental values in Table 3.^{46, 68} We note that no optimization of the parameters was performed. The detailed stepwise procedure is presented in sections S1.4, and S1.5 of the SI.

Figure 3.

Potential energy scans of the Ne-cyclopentanol model compound interactions with different atom types in cyclopentanol for the MP2/aug-cc-pVDZ, additive and Drude model chemistries.

Table 3.

Thermodynamic properties, density, molecular volume (Vm), heat of vaporization (ΔHvap) and free energy of hydration of cyclopentanol obtained using additive and Drude FF and compared against experimental values.

	Cyclopentanol
Pure solvent properties
	Expt	Additive	Drude
Density	0.942 g/mL	0.922 g/mL	0.983 g/mL
Molecular Volume	151.83 Å3	155.10 Å3	145.49 Å3
Heat of Vaporization	13.64 kcal/mol	8.42 kcal/mol	15.1 kcal/mol
Free Energy of Hydration	−5.49 kcal/mol	−6.12 kcal/mol	−6.83 kcal/mol

Conclusion

The new version of FFParam provides new optimization and validation tools and extension to a command line version. The ability to optimize LJ parameters using model compound-noble gas QM-derived PES in conjunction with a user-friendly module to obtain condensed phase properties are the most significant additions in FFParam v-2.0. In addition to LSFITPAR, user can choose a MCSA-based algorithm for optimization of bonded parameter. This new optimization algorithm also facilitates the optimization of parameters using QM PES along a dihedral shared by multiple molecules, thereby producing more transferable bonded parameters. Conducting optimization of a few bonded parameters in a molecule, while not changing others may create imbalanced vibrational modes. The ability of comparing QM and MM normal modes and the percent contribution of internal coordinates towards each normal mode will be instrumental in validating the balance among various bonded parameters. The extension of user interaction beyond the original GUI to include command line capabilities will allow for the integration of FFParam in workflows, thereby facilitating the high throughput parameter optimization. Accordingly, FFParam-v2.0 is a versatile and user-friendly tool that offers comprehensive optimization of CHARMM additive and Drude polarizable FF. The FFParam program, related tutorial and version updates may be obtained from SilcsBio LLC at https://ffparam.silcsbio.com/. The program is free to academic users.