Efficient global optimization of reactive force‐field parameters

Reactive force fields make low‐cost simulations of chemical reactions possible. However, optimizing them for a given chemical system is difficult and time‐consuming. We present a high‐performance implementation of global force‐field parameter optimization, which delivers parameter sets of the same quality with much less effort and in far less time than before, and also offers excellent parallel scaling. We demonstrate these features with example applications targeting the ReaxFF force field. © 2015 Wiley Periodicals, Inc.     

Paramfit: Automated optimization of force field parameters for molecular dynamics simulations

The generation of bond, angle, and torsion parameters for classical molecular dynamics force fields typically requires fitting parameters such that classical properties such as energies and gradients match precalculated quantum data for structures that scan the value of interest. We present a program, Paramfit, distributed as part of the AmberTools software package that automates and extends this fitting process, allowing for simplified parameter generation for applications ranging from single molecules to entire force fields. Paramfit implements a novel combination of a genetic and simplex algorithm to find the optimal set of parameters that replicate either quantum energy or force data. The program allows for the derivation of multiple parameters simultaneously using significantly fewer quantum calculations than previous methods, and can also fit parameters across multiple molecules with applications to force field development. Paramfit has been applied successfully to systems with a sparse number of structures, and has already proven crucial in the development of the Assisted Model Building with Energy Refinement Lipid14 force field. © 2014 Wiley Periodicals, Inc.     

Efficient parametrization of complex molecule–surface force fields

We present an efficient scheme for parametrizing complex molecule–surface force fields from ab initio data. The cost of producing a sufficient fitting library is mitigated using a 2D periodic embedded slab model made possible by the quantum mechanics/molecular mechanics scheme in CP2K. These results were then used in conjunction with genetic algorithm (GA) methods to optimize the large parameter sets needed to describe such systems. The derived potentials are able to well reproduce adsorption geometries and adsorption energies calculated using density functional theory. Finally, we discuss the challenges in creating a sufficient fitting library, determining whether or not the GA optimization has completed, and the transferability of such force fields to similar molecules. © 2015 Wiley Periodicals, Inc.     

MM3 parametrization of four‐ and five‐coordinated rhenium complexes by a genetic algorithm—Which factors influence the optimization performance?

Genetic algorithms (GA) were used to solve one of the multidimensional problems in computational chemistry, the optimization of force field parameters. The correlation between the composition of the GA, its parameters (p(c), p(m)) and the quality of the results were investigated. The composition was studied for all combinations of a Simple GA/Steady State GA with a Roulette Wheel/Tournament Selector using different values each for crossover (0.5, 0.7, 0.9) and mutation rates (0.01, 0.02, 0.05, 0.10, 0.20). The results show that the performance is strongly dependent on the GA scheme, where the Simple GA/Tournament Selector yields the best results. Two new MM3 parameters were introduced for rhenium compounds with coordination number four (204) and coordination number five (205), the formal oxidation states of rhenium ranging from +V to +VII. A manifold of parameters (Re-C, N, O, S) was obtained by using a diverse set of CSD structures. The advantage of the GA vs. UFF calculations is shown by comparison of several examples. The GA optimized parameters were able to reproduce the geometrical data of the X-ray structures.     

Parameterization of a reactive force field using a Monte Carlo algorithm

Parameterization of a molecular dynamics force field is essential in realistically modeling the physicochemical processes involved in a molecular system. This step is often challenging when the equations involved in describing the force field are complicated as well as when the parameters are mostly empirical. ReaxFF is one such reactive force field which uses hundreds of parameters to describe the interactions between atoms. The optimization of the parameters in ReaxFF is done such that the properties predicted by ReaxFF matches with a set of quantum chemical or experimental data. Usually, the optimization of the parameters is done by an inefficient single‐parameter parabolic‐search algorithm. In this study, we use a robust metropolis Monte‐Carlo algorithm with simulated annealing to search for the optimum parameters for the ReaxFF force field in a high‐dimensional parameter space. The optimization is done against a set of quantum chemical data for MgSO₄ hydrates. The optimized force field reproduced the chemical structures, the equations of state, and the water binding curves of MgSO₄ hydrates. The transferability test of the ReaxFF force field shows the extend of transferability for a particular molecular system. This study points out that the ReaxFF force field is not indefinitely transferable. © 2013 Wiley Periodicals, Inc.     

Scalable improvement of SPME multipolar electrostatics in anisotropic polarizable molecular mechanics using a general short‐range penetration correction up to quadrupoles

We propose a general coupling of the Smooth Particle Mesh Ewald SPME approach for distributed multipoles to a short‐range charge penetration correction modifying the charge‐charge, charge‐dipole and charge‐quadrupole energies. Such an approach significantly improves electrostatics when compared to ab initio values and has been calibrated on Symmetry‐Adapted Perturbation Theory reference data. Various neutral molecular dimers have been tested and results on the complexes of mono‐ and divalent cations with a water ligand are also provided. Transferability of the correction is adressed in the context of the implementation of the AMOEBA and SIBFA polarizable force fields in the TINKER‐HP software. As the choices of the multipolar distribution are discussed, conclusions are drawn for the future penetration‐corrected polarizable force fields highlighting the mandatory need of non‐spurious procedures for the obtention of well balanced and physically meaningful distributed moments. Finally, scalability and parallelism of the short‐range corrected SPME approach are addressed, demonstrating that the damping function is computationally affordable and accurate for molecular dynamics simulations of complex bio‐ or bioinorganic systems in periodic boundary conditions. © 2016 Wiley Periodicals, Inc.     

A partition function‐based weighting scheme in force field parameter development using ab initio calculation results in global configurational space

In force field parameter development using ab initio potential energy surfaces (PES) as target data, an important but often neglected matter is the lack of a weighting scheme with optimal discrimination power to fit the target data. Here, we developed a novel partition function‐based weighting scheme, which not only fits the target potential energies exponentially like the general Boltzmann weighting method, but also reduces the effect of fitting errors leading to overfitting. The van der Waals (vdW) parameters of benzene and propane were reparameterized by using the new weighting scheme to fit the high‐level ab initio PESs probed by a water molecule in global configurational space. The molecular simulation results indicate that the newly derived parameters are capable of reproducing experimental properties in a broader range of temperatures, which supports the partition function‐based weighting scheme. Our simulation results also suggest that structural properties are more sensitive to vdW parameters than partial atomic charge parameters in these systems although the electrostatic interactions are still important in energetic properties. As no prerequisite conditions are required, the partition function‐based weighting method may be applied in developing any types of force field parameters. © 2013 Wiley Periodicals, Inc.     

QuickFF: A program for a quick and easy derivation of force fields for metal‐organic frameworks from ab initio input

QuickFF is a software package to derive accurate force fields for isolated and complex molecular systems in a quick and easy manner. Apart from its general applicability, the program has been designed to generate force fields for metal‐organic frameworks in an automated fashion. The force field parameters for the covalent interaction are derived from ab initio data. The mathematical expression of the covalent energy is kept simple to ensure robustness and to avoid fitting deficiencies as much as possible. The user needs to produce an equilibrium structure and a Hessian matrix for one or more building units. Afterward, a force field is generated for the system using a three‐step method implemented in QuickFF. The first two steps of the methodology are designed to minimize correlations among the force field parameters. In the last step, the parameters are refined by imposing the force field parameters to reproduce the ab initio Hessian matrix in Cartesian coordinate space as accurate as possible. The method is applied on a set of 1000 organic molecules to show the easiness of the software protocol. To illustrate its application to metal‐organic frameworks (MOFs), QuickFF is used to determine force fields for MIL‐53(Al) and MOF‐5. For both materials, accurate force fields were already generated in literature but they requested a lot of manual interventions. QuickFF is a tool that can easily be used by anyone with a basic knowledge of performing ab initio calculations. As a result, accurate force fields are generated with minimal effort. © 2015 Wiley Periodicals, Inc.     

Estimating and modeling charge transfer from the SAPT induction energy

Recent studies using quantum mechanics energy decomposition methods, for example, SAPT and ALMO, have revealed that the charge transfer energy may play an important role in short ranged inter‐molecular interactions, and have a different distance dependence comparing with the polarization energy. However, the charge transfer energy component has been ignored in most current polarizable or non‐polarizable force fields. In this work, first, we proposed an empirical decomposition of SAPT induction energy into charge transfer and polarization energy that mimics the regularized SAPT method (ED‐SAPT). This empirical decomposition is free of the divergence issue, hence providing a good reference for force field development. Then, we further extended this concept in the context of AMOEBA polarizable force field, proposed a consistent approach to treat the charge transfer phenomenon. Current results show a promising application of this charge transfer model in future force field development. © 2017 Wiley Periodicals, Inc.     

Comparison of Force Fields on the Basis of Various Model Approaches—How To Design the Best Model for the [CnMIM][NTf2] Family of Ionic Liquids

In this contribution, we present two new united‐atom force fields (UA‐FFs) for 1‐alkyl‐3‐methylimidazolium bis(trifluoromethylsulfonyl)imide [C_nMIM][NTf₂] (n=1, 2, 4, 6, 8) ionic liquids (ILs). One is parametrized manually, and the other is developed with the gradient‐based optimization workflow (GROW). By doing so, we wanted to perform a hard test to determine how researchers could benefit from semiautomated optimization procedures. As with our already published all‐atom force field (AA‐FF) for [C_nMIM][NTf₂] (T. Köddermann, D. Paschek, R. Ludwig, ChemPhysChem­ 2007, 8, 2464 ), the new force fields were derived to fit experimental densities, self‐diffusion coefficients, and NMR rotational correlation times for the IL cation and for water molecules dissolved in [C₂MIM][NTf₂]. In the manual force field, the alkyl chains of the cation and the CF₃ groups of the anion were treated as united atoms. In the GROW force field, only the alkyl chains of the cation were united. All other parts of the structures of the ions remained unchanged to prevent any loss of physical information. Structural, dynamic, and thermodynamic properties such as viscosity, cation rotational correlation times, and heats of vaporization calculated with the new force fields were compared with values simulated with the previous AA‐FF and the experimental data. All simulated properties were in excellent agreement with the experimental values. Altogether, the UA‐FFs are slightly superior for speed‐up reasons. The UA‐FF speeds up the simulation by about 100 % and reduces the demanded disk space by about 78 %. More importantly, real time and efforts to generate force fields could be significantly reduced by utilizing GROW. The real time for the GROW parametrization in this work was 2 months. Manual parametrization, in contrast, may take up to 12 months, and this is, therefore, a significant increase in speed, though it is difficult to estimate the duration of manual parametrization.     

Accurate assessment of the strain energy in a protein-bound drug using QM/MM X-ray refinement and converged quantum chemistry

An ongoing question regarding the energetics of protein‐ligand binding has been; what is the strain energy that a ligand pays (if any) when binding to its protein target? The traditional method to estimate strain energy uses force fields to calculate the energy difference between the ligand bound conformation and its nearest local minimum/global minimum on the gas‐phase or aqueous phase potential energy surface. This makes the implicit assumption that the underlying force field as well as the reference crystal structure is accurate. Herein, we use ibuprofen as a test case and compare MMFF and ab initio QM methods to identify the local and global minimum conformations. Nine low energy conformations were identified with HF/6‐31G* geometry optimization in vacuo. We also obtained highly accurate relative energies for ibuprofen's conformational energy surface based on M06/aug‐cc‐pVXZ (X = D and T), MP2/aug‐cc‐pVXZ (X = D and T) and the MP2/CBS method (with and without solvent corrections). Moreover, we curate and re‐refine the ibuprofen‐protein complex (PDB 2BXG) using QM/MM X‐ray refinement approaches (HF/6‐31G* was the QM method and the MM model was the AMBER force field ff99sb), which were compared with the low energy conformers to calculate the strain energy. The result indicates that there was an 88% reduction in ibuprofen conformation strain using the QM/MM refined structure versus the original PDB ibuprofen conformations. Furthermore, our results indicate that, due to its inherent limitations in estimating electrostatic interactions, force fields are not suitable to gauge strain energy for charged drug molecules like ibuprofen. The present work offers a carefully validated conformational potential energy surface for a drug molecule as well as a reliable QM/MM re‐refined X‐ray structure that can be used to test current structure‐based drug design approaches. © 2011 Wiley Periodicals, Inc. J Comput Chem, 2011     

The quest for the best nonpolarizable water model from the adaptive force matching method

The recently introduced adaptive force matching (AFM) method is used to develop a significantly improved pair‐wise nonpolarizable potential for water. A rigid version of the potential is also presented to enable larger time steps for biological simulations. In this work, it is demonstrated that the AFM method can be used to systematically assess the importance of each functional term during the construction of a force field. For a water potential, it is established that a single off‐atom charge center (M) in the plane of water outperforms two out‐of‐plane charge sites for reproducing intermolecular forces. The four‐site pair‐wise nonpolarizable force field developed in this work rivals some of the most sophisticated polarizable models in terms of reproducing accurate ab initio forces. The force fields are parameterized to perform best in the temperature range from 0 to 40°C. Equilibrium and dynamical properties calculated with the flexible and rigid force fields are in good agreement with experimental results. For the flexible model, the agreement improves when path integral simulation is performed. These force fields provide high‐quality results at a very low computational cost and are thus well suited to atomistic scale biological simulations. The AFM method provides a mechanism for selecting important terms in force field expressions and is a very promising tool for producing accurate force fields in condensed phases. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2011     

Numerical interpretation of molecular surface field in dielectric modeling of solvation

Continuum solvent models, particularly those based on the Poisson‐Boltzmann equation (PBE), are widely used in the studies of biomolecular structures and functions. Existing PBE developments have been mainly focused on how to obtain more accurate and/or more efficient numerical potentials and energies. However to adopt the PBE models for molecular dynamics simulations, a difficulty is how to interpret dielectric boundary forces accurately and efficiently for robust dynamics simulations. This study documents the implementation and analysis of a range of standard fitting schemes, including both one‐sided and two‐sided methods with both first‐order and second‐order Taylor expansions, to calculate molecular surface electric fields to facilitate the numerical calculation of dielectric boundary forces. These efforts prompted us to develop an efficient approximated one‐dimensional method, which is to fit the surface field one dimension at a time, for biomolecular applications without much compromise in accuracy. We also developed a surface‐to‐atom force partition scheme given a level set representation of analytical molecular surfaces to facilitate their applications to molecular simulations. Testing of these fitting methods in the dielectric boundary force calculations shows that the second‐order methods, including the one‐dimensional method, consistently perform among the best in the molecular test cases. Finally, the timing analysis shows the approximated one‐dimensional method is far more efficient than standard second‐order methods in the PBE force calculations. © 2017 Wiley Periodicals, Inc.     

Force field dependence of phospholipid headgroup and acyl chain properties: Comparative molecular dynamics simulations of DMPC bilayers

The reliability of molecular simulations largely depends on the quality of the empirical force field parameters. Force fields used in lipid simulations continue to be improved to enhance the agreement with experiments for a number of different properties. In this work, we have carried out molecular dynamics simulations of neat DMPC bilayers using united‐atom Berger force field and three versions of all‐atom CHARMM force fields. Three different systems consisting of 48, 72, and 96 lipids were studied. Both particle mesh Ewald (PME) and spherical cut‐off schemes were used to evaluate the long‐range electrostatic interactions. In total, 21 simulations were carried out and analyzed to find out the dependence of lipid properties on force fields, system size, and schemes to calculate long‐range interactions. The acyl chain order parameters calculated from Berger and the recent versions of CHARMM simulations have shown generally good agreement with the experimental results. However, both sets of force fields deviate significantly from the experimentally observed P‐C dipolar coupling values for the carbon atoms that link the choline and glycerol groups with the phosphate groups. Significant differences are also observed in several headgroup parameters between CHARMM and Berger simulations. Our results demonstrate that when changes were introduced to improve CHARMM force field using PME scheme, all the headgroup parameters have not been reoptimized. The headgroup properties are likely to play a significant role in lipid–lipid, protein–lipid, and ligand–lipid interactions and hence headgroup parameters in phospholipids require refinement for both Berger and CHARMM force fields. © 2009 Wiley Periodicals, Inc.J Comput Chem, 2010     

Classical Reactive Molecular Dynamics Implementations: State of the Art

Reactive molecular dynamics (RMD) implementations equipped with force field approaches to simulate both the time evolution as well as chemical reactions of a broad class of materials are reviewed herein. We subdivide the RMD approaches developed during the last decade as well as older ones already reviewed in 1995 by Srivastava and Garrison and in 2000 by Brenner into two classes. The methods in the first RMD class rely on the use of a reaction cutoff distance and employ a sudden transition from the educts to the products. Due to their simplicity these methods are well suited to generate equilibrated atomistic or material‐specific coarse‐grained polymer structures. In connection with generic models they offer useful qualitative insight into polymerization reactions. The methods in the second RMD class are based on empirical reactive force fields and implement a smooth and continuous transition from the educts to the products. In this RMD class, the reactive potentials are based on many‐body or bond‐order force fields as well as on empirical standard force fields, such as CHARMM, AMBER or MM3 that are modified to become reactive. The aim with the more sophisticated implementations of the second RMD class is the investigation of the reaction kinetics and mechanisms as well as the evaluation of transition state geometries. Pure or hybrid ab initio, density functional, semi‐empirical, molecular mechanics, and Monte Carlo methods for which no time evolution of the chemical systems is achieved are excluded from the present review. So are molecular dynamics techniques coupled with quantum chemical methods for the treatment of the reactive regions, such as Car–Parinello molecular dynamics.     

Derivation of class II force fields: V. Quantum force field for amides,peptides, and related compounds

As the field of biomolecular structure advances, there is an ever-growing need for accurate modeling of molecular energy surfaces to simulate and predict the properties of these important systems. To address this need, a second generation amide force field for use in simulations of small organics as well as proteins and peptides has been derived. The critical question of what accuracy can be expected from calculations in general, and with this class II force field in particular, is addressed for structural, dynamic, and energetic properties. The force field is derived from a recent methodology we have developed that involves the systematic use of quantum mechanical observables. Systematic ab initio calculations were carried out for numerous configurations of 17 amide and related compounds. Relative energies and first and second derivatives of the energy of 638 structures of these compounds resulted in 140,970 ab initio quantum mechanical observables. The class II peptide quantum mechanical force field (QMFF), containing 732 force constants and reference values, was parameterized against these observables. A major objective of this work is to help establish the role of anharmonicity and coupling in improving the accuracy of molecular force fields, as these terms have not yet become an agreed upon standard in the ever more extensive simulations being used to probe biomolecular properties. This has been addressed by deriving a class I harmonic diagonal force field (HDFF), which was fit to the same energy surface as the QMFF, thus providing an opportunity to quantify the effects of these coupling and anharmonic contributions. Both force field representations are assessed in terms of their ability to fit the observables. They have also been tested by calculating the properties of 11 stationary states of these amide molecules. Optimized structures, vibrational frequencies, and conformational energies obtained from the quantum calculations and from both the QMFF and the HDFF are compared. Several strained and derivatized compounds including urea, formylformamide, and butyrolactam are included in these tests to assess the range of applicability (transferability) of the force fields. It was found that the class II coupled anharmonic force field reproduced the structures, energies, and vibrational frequencies significantly more faithfully than the class I harmonic diagonal force field. An important measure, rms energy deviation, was found to be 1.06 kcal/mol with the class II force field, and 2.30 kcal/mol with the harmonic diagonal force field. These deviations represent the error in relative configurational energy differences for strained and distorted structures calculated with the force fields compared with quantum mechanics. This provides a measure of the accuracy that might be expected in applications where strain may be important such as calculating the energy of a system as it approaches a (rotational) barrier, in ligand binding to a protein, or effects of introducing substituents into a molecule that may induce strain. Similar results were found for structural properties. Protein dynamics is becoming of ever-increasing interest, and, to simulate dynamic properties accurately, the dynamic behavior of model compounds needs to be well accounted for. To this end, the ability of the class I and class II force fields to reproduce the vibrational frequencies obtained from the quantum energy surface was assessed. An rms deviation of 43 cm⁻¹ was achieved with the coupled anharmonic force field, as compared to 105 cm⁻¹ with the harmonic diagonal force field. Thus, the analysis presented here of the class II force field for the amide functional group demonstrates that the incorporation of anharmonicity and coupling terms in the force field significantly improves the accuracy and transferability with regard to the simulation of structural, energetic, and dynamic properties of amides. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 430–458, 1998     

PEFF: A program for the development of empirical force fields

PEFF is a new computer program designed to assist in the development of empirical force fields used in molecular mechanics calculations. Its main features are: constrained and unconstrained energy minimization available with four different techniques, rigid group refinement, crystal lattice summations, calculation of normal modes, thermodynamic functions and crystallographic temperature factors, vibrational corrections of calculated crystal structures, and a multidimensional driver to scan the energy hypersurface. Used in force field optimization mode, the program employs a least-squares method to fit the force field parameters to a set of experimental data.