Classical Molecular Mechanics Force Fields Research Articles

On hidden anisotropy of formally charged fragments.

The proper and precise reproduction of the molecular electrostatic potential (MEP) is crucial to describe correctly electrostatic interactions in molecular modeling. Most of the classical molecular mechanics force fields for biomolecules and drug-like molecules use the atom-centered point charges to describe MEP. However, it has been systematically pointed out in literature that such an approximation is not always enough, and some groups, like amino group or heavy halogens, require the use of anisotropic model for better description of their MEP. At the same time, the formally charged groups have not been as extensively and systematically studied as their neutral counterparts. In this report, we demonstrate that the anisotropic models for formally charged groups do bring improvements in the reference MEP reproduction, that are comparable in magnitude to those for neutral groups.

Molecular force fields with gradient-domain machine learning (GDML): Comparison and synergies with classical force fields.

Modern machine learning force fields (ML-FF) are able to yield energy and force predictions at the accuracy of high-level ab initio methods, but at a much lower computational cost. On the other hand, classical molecular mechanics force fields (MM-FF) employ fixed functional forms and tend to be less accurate, but considerably faster and transferable between molecules of the same class. In this work, we investigate how both approaches can complement each other. We contrast the ability of ML-FF for reconstructing dynamic and thermodynamic observables to MM-FFs in order to gain a qualitative understanding of the differences between the two approaches. This analysis enables us to modify the generalized AMBER force field by reparametrizing short-range and bonded interactions with more expressive terms to make them more accurate, without sacrificing the key properties that make MM-FFs so successful.

Quantum Mechanical Modeling of the Interactions between Noble Metal (Ag and Au) Nanoclusters and Water with the Effective Fragment Potential Method.

Explicit solvent interactions can significantly alter the physical and chemical properties of noble metal (e.g., gold and silver) nanoclusters. In order to compute these solvent interactions at a reasonable computational cost, a quantum mechanical (QM)/molecular mechanics (MM) approach, where the metal nanocluster is treated with full QM and the water molecules are treated with a MM force field, can be used. However, classical MM force fields were typically parameterized using molecules containing main group elements as the reference. The accuracy of noble metal–solvent interactions obtained with these force fields therefore remains unpredictable. The effective fragment potential (EFP) force field, designed to model explicitly solvated systems, represents an attractive method to simulate solvated noble metal nanoclusters because it is derived from first principles and contains few or no fitted parameters, depending on implementation. At the density functional theory-optimized geometries, good correlation is obtained between the nanocluster–water interaction energies computed with EFP and those computed with the reference coupled cluster singles, doubles, and perturbative triples method. It is shown that the EFP method gives qualitatively accurate interaction energies at medium–large intermolecular distances for various molecular configurations. In order to achieve higher quantitative accuracy, the first solvation shell should be treated with full QM, if possible. EFP is therefore a promising method for the QM modeling of explicitly solvated silver and gold nanoclusters.

Computation of Hydration Free Energies Using the Multiple Environment Single System Quantum Mechanical/Molecular Mechanical Method.

A recently developed MESS-E-QM/MM method (multiple-environment single-system quantum mechanical molecular/mechanical calculations with a Roothaan-step extrapolation) is applied to the computation of hydration free energies for the blind SAMPL4 test set and for 12 small molecules. First, free energy simulations are performed with a classical molecular mechanics force field using fixed-geometry solute molecules and explicit TIP3P solvent, and then the non-Boltzmann-Bennett method is employed to compute the QM/MM correction (QM/MM-NBB) to the molecular mechanical hydration free energies. For the SAMPL4 set, MESS-E-QM/MM-NBB corrections to the hydration free energy can be obtained 2 or 3 orders of magnitude faster than fully converged QM/MM-NBB corrections, and, on average, the hydration free energies predicted with MESS-E-QM/MM-NBB fall within 0.10-0.20 kcal/mol of full-converged QM/MM-NBB results. Out of five density functionals (BLYP, B3LYP, PBE0, M06-2X, and ωB97X-D), the BLYP functional is found to be most compatible with the TIP3P solvent model and yields the most accurate hydration free energies against experimental values for solute molecules included in this study.

Direct minimization: Alternative to the traditional [formula omitted] norm to derive partial atomic charges

Partial charges play an important role in simulating and understanding molecular properties. The derivation of an accurate charge model for monopolar atoms is a significant part of the parameterization of today’s classical molecular mechanics force fields used in molecular dynamics simulations (MD). Hence, interest in the accurate prediction of partial charges from ab initio methods exists for a long time. Several methods have been developed, either based on population analysis that partitions the electron density into atomic populations, or on the assignment of partial atomic charges to reproduce a precalculated electrostatic potential (ESP method). In the latter approach, the charges are represented by parameters that are optimized by minimizing a loss function. ESP charge fitting, which is addressed in our work, is in most cases performed by minimization of a least squares or L2 like loss functions. To our knowledge, no attempt was made to use different metrics such as least absolute deviations L1 and to study their influence on the derived charges. The possibility of using different metrics to derive atomic charges is explored in this paper as a further extension of the ESP method. A direct iterative steepest descent minimization approach is employed in order to treat loss functions based on norms such as L1. The implemented algorithm allows for dealing with chemical equivalency and total charge constraints while permitting using different loss functions. We compare the results from the L1 norm to the values obtained from the standard L2 norm and the L4 norm for the 20 standard amino acids.We suggest that close to the solution the L1 norm expresses the impact of the electrostatic potential on the partial atomic charges to be obtained more accurately.

General Model for Treating Short-Range Electrostatic Penetration in a Molecular Mechanics Force Field.

Classical molecular mechanics force fields typically model interatomic electrostatic interactions with point charges or multipole expansions, which can fail for atoms in close contact due to the lack of a description of penetration effects between their electron clouds. These short-range penetration effects can be significant and are essential for accurate modeling of intermolecular interactions. In this work we report parametrization of an empirical charge–charge function previously reported (PiquemalJ.-P.; J. Phys. Chem. A2003, 107, 1035326313624) to correct for the missing penetration term in standard molecular mechanics force fields. For this purpose, we have developed a database (S101×7) of 101 unique molecular dimers, each at 7 different intermolecular distances. Electrostatic, induction/polarization, repulsion, and dispersion energies, as well as the total interaction energy for each complex in the database are calculated using the SAPT2+ method (ParkerT. M.; J. Chem. Phys.2014, 140, 09410624606352). This empirical penetration model significantly improves agreement between point multipole and quantum mechanical electrostatic energies across the set of dimers and distances, while using only a limited set of parameters for each chemical element. Given the simplicity and effectiveness of the model, we expect the electrostatic penetration correction will become a standard component of future molecular mechanics force fields.

Electrostatic Interactions in Aminoglycoside-RNA Complexes

Electrostatic interactions often play key roles in the recognition of small molecules by nucleic acids. An example is aminoglycoside antibiotics, which by binding to ribosomal RNA (rRNA) affect bacterial protein synthesis. These antibiotics remain one of the few valid treatments against hospital-acquired infections by Gram-negative bacteria. It is necessary to understand the amplitude of electrostatic interactions between aminoglycosides and their rRNA targets to introduce aminoglycoside modifications that would enhance their binding or to design new scaffolds. Here, we calculated the electrostatic energy of interactions and its per-ring contributions between aminoglycosides and their primary rRNA binding site. We applied either the methodology based on the exact potential multipole moment (EPMM) or classical molecular mechanics force field single-point partial charges with Coulomb formula. For EPMM, we first reconstructed the aspherical electron density of 12 aminoglycoside-RNA complexes from the atomic parameters deposited in the University at Buffalo Databank. The University at Buffalo Databank concept assumes transferability of electron density between atoms in chemically equivalent vicinities and allows reconstruction of the electron densities from experimental structural data. From the electron density, we then calculated the electrostatic energy of interaction using EPMM. Finally, we compared the two approaches. The calculated electrostatic interaction energies between various aminoglycosides and their binding sites correlate with experimentally obtained binding free energies. Based on the calculated energetic contributions of water molecules mediating the interactions between the antibiotic and rRNA, we suggest possible modifications that could enhance aminoglycoside binding affinity.

MoD-QM/MM Structural Refinement Method: Characterization of Hydrogen Bonding in the Oxytricha nova G-Quadruplex.

A generalization of the Moving-Domain Quantum Mechanics/Molecular Mechanics (MoD-QM/MM) hybrid method [Gascon, J. A.; Leung, S. S. F.; Batista, E. R.; Batista, V. S. J. Chem. Theory Comput. 2006, 2, 175-186] is introduced to provide a self-consistent computational protocol for structural refinement of extended systems. The method partitions the system into molecular domains that are iteratively optimized as quantum mechanical (QM) layers embedded in their surrounding molecular environment to obtain an ab initio quality description of the geometry and the molecular electrostatic potential of the extended system composed of those constituent fragments. The resulting methodology is benchmarked as applied to model systems that allow for full QM optimization as well as through refinement of the hydrogen bonding geometry in Oxytricha nova guanine quadruplex for which several studies have been reported, including the X-ray structure and NMR data. Calculations of (1)H NMR chemical shifts based on the gauge independent atomic orbital (GIAO) method and direct comparisons with experiments show that solvated MoD-QM/MM structures, sampled from explicit solvent molecular dynamics simulations, allow for NMR simulations in much improved agreement with experimental data than models based on the X-ray structure or those optimized using classical molecular mechanics force fields.

Benchmark Torsional Potentials of Building Blocks for Conjugated Materials: Bifuran, Bithiophene, and Biselenophene.

The utility of π-conjugated oligomers and polymers continues to grow, and oligofurans, oligothiophenes, and oligoselenophenes have shown great promise in the context of organic electronic materials. Vital to the performance of these materials is the maintenance of planarity along the conjugated backbone. Consequently, there has been a great deal of work modeling the torsional behavior of these prototypical components of conjugated organic materials both in the gas and condensed phases. Such simulations generally rely on classical molecular mechanics force fields or density functional theory (DFT) potentials. Unfortunately, there is a lack of benchmark quality, converged ab initio torsional potentials for bifuran, bithiophene, and biselenophene against which these lower level theoretical methods can be calibrated. To remedy this absence, we present highly accurate torsional potentials for these three molecules based on focal point analyses. These potentials will enable the benchmarking and parametrization of DFT functionals and classical molecular mechanics force fields. Here, we provide an initial assessment of the performance of common DFT functional and basis set combinations, to identify methods that provide robust descriptions of the torsional behavior of these prototypical building blocks for conjugated systems.

A Computational and Experimental Study of the Heat Transfer Properties of Nine Different Ionic Liquids

New experimental thermal conductivity, density, viscosity, glass transition temperature, and heat capacity values were measured for nine ionic liquids (ILs): [emim][TFA], [emim][OTf], [emim][DEP], [emim][MeSO3], [emim][SCN], [hmim][Tf2N], [bDMApy][Tf2N], [hDMApy][Tf2N], and [hmDMApy][Tf2N]. Classical molecular mechanics force fields were developed and used to calculate thermodynamic and transport properties for these ILs using molecular dynamics. Two versions of each force field were developed: one with integer charges of ± 1 and one with all charges scaled by 0.8. The force fields with total charges of ± 0.8 generally gave better agreement with experimental results. Very good agreement was obtained for density and heat capacity. Simulated values for thermal conductivity slightly overpredicted experimental results but captured trends between different ILs very well. Experimental Prandtl numbers were determined as a function of temperature and can exceed 10 000 at low temperature. Prandtl numbers on the or...

Free Energies of Binding from Large-Scale First-Principles Quantum Mechanical Calculations: Application to Ligand Hydration Energies

Schemes of increasing sophistication for obtaining free energies of binding have been developed over the years, where configurational sampling is used to include the all-important entropic contributions to the free energies. However, the quality of the results will also depend on the accuracy with which the intermolecular interactions are computed at each molecular configuration. In this context, the energy change associated with the rearrangement of electrons (electronic polarization and charge transfer) upon binding is a very important effect. Classical molecular mechanics force fields do not take this effect into account explicitly, and polarizable force fields and semiempirical quantum or hybrid quantum-classical (QM/MM) calculations are increasingly employed (at higher computational cost) to compute intermolecular interactions in free-energy schemes. In this work, we investigate the use of large-scale quantum mechanical calculations from first-principles as a way of fully taking into account electronic effects in free-energy calculations. We employ a one-step free-energy perturbation (FEP) scheme from a molecular mechanical (MM) potential to a quantum mechanical (QM) potential as a correction to thermodynamic integration calculations within the MM potential. We use this approach to calculate relative free energies of hydration of small aromatic molecules. Our quantum calculations are performed on multiple configurations from classical molecular dynamics simulations. The quantum energy of each configuration is obtained from density functional theory calculations with a near-complete psinc basis set on over 600 atoms using the ONETEP program.

Simulation of mesogenic diruthenium tetracarboxylates: Development of a force field for coordination polymers of the MMX type

A classical molecular mechanics force field, able to simulate coordination polymers (CP) based on ruthenium carboxylates (Ru2 (O2CReq )4 Lax) (eq = equatorial group containing aliphatic chains, Lax = axial ligand), has been developed. New parameters extracted from experimental data and quantum calculations on short aliphatic chains model systems were included in the generalized AMBER force field. The proposed parametrization was evaluated using model systems with known structure, containing either short or long aliphatic chains; experimental results were reproduced satisfactorily. This modified force field, although in a preliminary stage, could then be applied to long chain liquid crystalline compounds. The resulting atomistic simulations allowed assessing the relative influence of the factors determining the CP conformation, determinant for the physical properties of these materials.

Quantitative Assessment of Force Fields on Both Low-Energy Conformational Basins and Transition-State Regions of the (ϕ-ψ) Space.

The free energy surfaces (FESs) of alanine dipeptide are studied to illustrate a new strategy to assess the performance of classical molecular mechanics force field on the full range of the (ϕ-ψ) conformational space. The FES is obtained from metadynamics simulations with five commonly used force fields and from ab initio density functional theory calculations in both gas phase and aqueous solution. The FESs obtained at the B3LYP/6-311+G(2d,p)//B3LYP/6-31G(d,p) level of theory are validated by comparison with previously reported MP2 and LMP2 results as well as with experimentally obtained probability distribution between the C5-β (or β-PPII) and αR states. A quantitative assessment is made for each force field in three conformational basins, LeRI (C5-β-C7eq), LeRII (β2-αR), and LeRIII(αL-C7ax-αD) as well as three transition-state regions linking the above conformational basins. The performance of each force field is evaluated in terms of the average free energy of each region in comparison with that of the ab initio results. We quantify how well a force field FES matches the ab initio FES through the calculation of the standard deviation of a free energy difference map between the two FESs. The results indicate that the performance varies largely from region to region or from force field to force field. Although not one force field is able to outperform all others in all conformational areas, the OPLSAA/L force field gives the best performance overall, followed by OPLSAA and AMBER03. For the three top performers, the average free energies differ from the corresponding ab initio values from within the error range (<0.4 kcal/mol) to ∼1.5 kcal/mol for the low-energy regions and up to ∼2.0 kcal/mol for the transition-state regions. The strategy presented and the results obtained here should be useful for improving the parametrization of force fields targeting both accuracy in the energies of conformers and the transition-state barriers.

Direct Simulation of Electron Transfer Reactions in DNA Radical Cations

The electron transfer properties of DNA radical cations are important in DNA damage and repair processes. Fast long-range charge transfer has been demonstrated experimentally, but the subtle influences that experimental conditions as well as DNA sequences and geometries have on the details of electron transfer parameters are still poorly understood. In this work, we employ an atomistic QM/MM approach, based on a one-electron tight binding Hamiltonian and a classical molecular mechanics forcefield, to conduct nanosecond length MD simulations of electron holes in DNA oligomers. Multiple spontaneous electron transfer events were observed in 100 ns simulations with neighboring adenine or guanine bases. Marcus parameters of charge transfer could be extracted directly from the simulations. The reorganization energy lambda for hopping between neighboring bases was found to be ca. 25 kcal/mol and charge transfer rates of 4.1 x 10(9) s(-1) for AA hopping and 1.3 x 10(9) s(-1) for GG hopping were obtained.

Motifs in nucleic acids: molecular mechanics restraints for base pairing and base stacking.

In building and refining nucleic acid structures, it is often desirable to enforce particular base pairing and/or base stacking interactions. Energy-based modeling programs with classical molecular mechanics force fields do not lend themselves to the easy imposition of penalty terms corresponding to such restraints, because the requirement that two bases lie in or near the same plane (pairing) or that they lie in parallel planes (stacking) cannot be easily expressed in terms of traditional interactions involving two atoms (bonds), three atoms (angles), or four atoms (torsions). Here we derive expressions that define a collection of pseudobonds and pseudoangles through which molecular mechanics restraints for base pairing and stacking can be imposed. We have implemented these restraints into the JUMNA package for modeling DNA and RNA structures. JUMNA scripts can specify base pairing with a variety of standard geometries (Watson-Crick, Hoogsteen, wobble, etc.), or with user-defined geometries; they can also specify stacking arrangements. We have also implemented "soft-core" functions to modify van der Waals and electrostatic interactions to avoid steric conflicts in particularly difficult refinements where two backbones need to pass through one another. Test cases are presented to show the utility of the method. The restraints could be adapted for implementation in other molecular mechanics packages.

A transferable polarizable electrostatic force field for molecular mechanics based on the chemical potential equalization principle

A polarizable electrostatic potential model for classical molecular mechanics is presented. Based on the chemical potential equalization (CPE) principle, the model is developed starting from the original formulation of Mortier, Ghosh, and Shankar [J. Am. Chem. Soc. 108, 4315 (1986)]. Following York and Yang [J. Chem. Phys. 104, 159 (1996)] we present an SP-basis CPE parametrization to describe realistically any sort of molecular system. By fitting ab initio electronic properties, such as dipole moment, polarizability and global molecular hardness of a restricted set of organic molecules, we derive atomic parameters to be applied to a more vast target set of compounds. We show, indeed, that the atomic CPE parameters calculated for the learning set of molecules give reliable values for several electronic properties of various compounds not included in the learning set. The multipole moments obtained by using the proposed CPE parametrization are compared to the results of a fixed charge parametrization like that used by a popular classical molecular mechanics force field, such as AMBER. We show that the fixed charge parametrization can well reproduce only the multipole moments of the molecular conformation or the isomer used for the fit, while being inaccurate when different molecular conformations or isomers are considered. On the contrary, the CPE model realistically reproduces the charge reorganization due to nuclear structural changes of the molecule, such as isomerization or conformational transition. The CPE model has been also tested on various molecular complexes to investigate the polarization response in the case of realistic molecule–molecule interactions. The main result of the paper is the demonstration that the construction of a general polarizable electrostatic force field for classical molecular mechanics is now a viable way.