A nonadditive methanol force field: bulk liquid and liquid-vapor interfacial properties via molecular dynamics simulations using a fluctuating charge model

We study the bulk and interfacial properties of methanol via molecular dynamics simulations using a CHARMM (Chemistry at HARvard Molecular Mechanics) fluctuating charge force field. We discuss the parametrization of the electrostatic model as part of the ongoing CHARMM development for polarizable protein force fields. The bulk liquid properties are in agreement with available experimental data and competitive with existing fixed-charge and polarizable force fields. The liquid density and vaporization enthalpy are determined to be 0.809 g/cm3 and 8.9 kcal/mol compared to the experimental values of 0.787 g/cm3 and 8.94 kcal/mol, respectively. The liquid structure as indicated by radial distribution functions is in keeping with the most recent neutron diffraction results; the force field shows a slightly more ordered liquid, necessarily arising from the enhanced condensed phase electrostatics (as evidenced by an induced liquid phase dipole moment of 0.7 D), although the average coordination with two neighboring molecules is consistent with the experimental diffraction study as well as with recent density functional molecular dynamics calculations. The predicted surface tension of 19.66+/-1.03 dyn/cm is slightly lower than the experimental value of 22.6 dyn/cm, but still competitive with classical force fields. The interface demonstrates the preferential molecular orientation of molecules as observed via nonlinear optical spectroscopic methods. Finally, via canonical molecular dynamics simulations, we assess the model's ability to reproduce the vapor-liquid equilibrium from 298 to 423 K, the simulation data then used to obtain estimates of the model's critical temperature and density. The model predicts a critical temperature of 470.1 K and critical density of 0.312 g/cm3 compared to the experimental values of 512.65 K and 0.279 g/cm3, respectively. The model underestimates the critical temperature by 8% and overestimates the critical density by 10%, and in this sense is roughly equivalent to the underlying fixed-charge CHARMM22 force field.     

Thermodynamic and structural properties of methanol-water solutions using nonadditive interaction models

We study bulk structural and thermodynamic properties of methanol-water solutions via molecular dynamics simulations using novel interaction potentials based on the charge equilibration (fluctuating charge) formalism to explicitly account for molecular polarization at the atomic level. The study uses the TIP4P-FQ potential for water-water interactions, and the CHARMM-based (Chemistry at HARvard Molecular Mechanics) fluctuating charge potential for methanol-methanol and methanol-water interactions. In terms of bulk solution properties, we discuss liquid densities, enthalpies of mixing, dielectric constants, self-diffusion constants, as well as structural properties related to local hydrogen bonding structure as manifested in radial distribution functions and cluster analysis. We further explore the electronic response of water and methanol in the differing local environments established by the interaction of each species predominantly with molecules of the other species. The current force field for the alcohol-water interaction performs reasonably well for most properties, with the greatest deviation from experiment observed for the excess mixing enthalpies, which are predicted to be too favorable. This is qualitatively consistent with the overestimation of the methanol-water gas-phase interaction energy for the lowest-energy conformer (methanol as proton donor). Hydration free energies for methanol in TIP4P-FQ water are predicted to be -5.6 +/- 0.2 kcal/mol, in respectable agreement with the experimental value of -5.1 kcal/mol. With respect to solution microstructure, the present cluster analysis suggests that the microscale environment for concentrations where select thermodynamic quantities reach extremal values is described by a bipercolating network structure.     

A polarizable force field for water using an artificial neural network

A force field for liquid water including polarization effects has been constructed using an artificial neural network (ANN). It is essential to include a many-body polarization effect explicitly into a potential energy function in order to treat liquid water which is dense and highly polar. The new potential energy function is a combination of empirical and nonempirical potentials. The TIP4P model was used for the empirical part of the potential. For the nonempirical part, an ANN with a back-propagation of error algorithm (BPNN) was introduced to reproduce the complicated many-body interaction energy surface from ab initio quantum mechanical calculations. BPNN, described in terms of a matrix, provides enough flexibility to describe the complex potential energy surface (PES). The structural and thermodynamic properties, calculated by isobaric-isothermal (constant-NPT) Monte Carlo simulations with the new polarizable force field for water, are compatible with experimental results. Thus, the simulation establishes the validity of using our estimated PES with a polarization effect for accurate predictions of liquid state properties. Applications of this approach are simple and systematic so that it can easily be applied to the development of other force fields besides the water-water system.     

Implementation of extended Lagrangian dynamics in GROMACS for polarizable simulations using the classical Drude oscillator model

Explicit treatment of electronic polarization in empirical force fields used for molecular dynamics simulations represents an important advancement in simulation methodology. A straightforward means of treating electronic polarization in these simulations is the inclusion of Drude oscillators, which are auxiliary, charge‐carrying particles bonded to the cores of atoms in the system. The additional degrees of freedom make these simulations more computationally expensive relative to simulations using traditional fixed‐charge (additive) force fields. Thus, efficient tools are needed for conducting these simulations. Here, we present the implementation of highly scalable algorithms in the GROMACS simulation package that allow for the simulation of polarizable systems using extended Lagrangian dynamics with a dual Nosé–Hoover thermostat as well as simulations using a full self‐consistent field treatment of polarization. The performance of systems of varying size is evaluated, showing that the present code parallelizes efficiently and is the fastest implementation of the extended Lagrangian methods currently available for simulations using the Drude polarizable force field.     

Effect of flexibility on surface tension and coexisting densities of water

Molecular dynamics simulations of pure water at the liquid-vapor interface are performed using direct simulation of interfaces in a liquid slab geometry. The effect of intramolecular flexibility on coexisting densities and surface tension is analyzed. The dipole moment profile across the liquid-vapor interface shows different values for the liquid and vapor phases. The flexible model is a polarizable model. This effect is minor for liquid densities and is large for surface tension. The liquid densities increase from 2% at 300 K to 9% at 550 K when the force field is changed from a fully rigid simple point charge extended (SPCE) model to that of a fully flexible model with the same intermolecular interaction parameters. The increases in surface tension at both temperatures are around 11% and 36%, respectively. The calculated properties of the flexible models are closer to the experimental data than those of the rigid SPCE. The effect of the maximum number of reciprocal vectors (h(z) (max)) and the surface area on the calculated properties at 300 K is also analyzed. The coexiting densities are not sensitive to those variables. The surface tension fluctuates with h(z) (max) with an amplitude larger than 10 mN m(-1). The effect of using small interfacial areas is slightly larger than the error in the simulations.     

Incorporation of a QM/MM buffer zone in the variational double self-consistent field method

The explicit polarization (X-Pol) potential is an electronic-structure-based polarization force field, designed for molecular dynamics simulations and modeling of biopolymers. In this approach, molecular polarization and charge transfer effects are explicitly treated by a combined quantum mechanical and molecular mechanical (QM/MM) scheme, and the wave function of the entire system is variationally optimized by a double self-consistent field (DSCF) method. In the present article, we introduce a QM buffer zone for a smooth transition from a QM region to an MM region. Instead of using the Mulliken charge approximation for all QM/MM interactions, the Coulombic interactions between the adjacent fragments are determined directly by electronic structure theory. The present method is designed to accelerate the speed of convergence of the total energy and charge density of the system.     

A force field for guanidinium-based ionic liquids that utilizes the electron charge distribution of the actual liquid: a molecular simulation study

We propose a new all-atom force field for guanidinium-based ionic liquids (GILs) which is based on the charge distribution in the actual liquid. It comprises all cations that can be built by attaching alkyl chains of variable length to an acyclic or cyclic guanidinium compound and that are paired with nitrate or perchlorate anions. We based the parametrization of the force field on liquid-phase charge distributions to improve the prediction of energetic and dynamic properties of GILs. The impact of electron charge transfer and polarization on various properties of GILs is systematically assessed. A significant average electron charge transfer between -0.12 and -0.06 e from anions to the central guanidinium group of the cations and a strong polarization of acyclic cations are observed by applying a combined quantum mechanical/molecular mechanical (QM/MM) approach. Molecular dynamics simulations of GILs are performed, utilizing the proposed force field. Derived structures approach the accuracy of QM/MM structures, and a previously reported crystal structure remains stable throughout the simulations. Mass densities are reproduced with a deviation of only 1.4% from experimental data. The calculated melting point of a GIL crystal deviates only 8% from the measured value. Self-diffusion coefficients of various GILs are reported, and a comparison with a diffusion coefficient derived from experimental data indicates that the values are within a reasonable range. We observe that the melting point of a GIL crystal was lowered up to 60 K and that diffusion coefficients are substantially increased by a factor of up to 3.5 upon consideration of charge transfer and polarization. The results demonstrate that liquid-phase partial charges are capable of improving the quality of ionic liquid force fields substantially and that their utilization led to a model that can be applied to predict structural, energetic, and dynamic properties of GILs.     

Molecular dynamics simulations of aqueous ions at the liquid–vapor interface accelerated using graphics processors

Molecular dynamics (MD) simulations are a vital tool in chemical research, as they are able to provide an atomistic view of chemical systems and processes that is not obtainable through experiment. However, large‐scale MD simulations require access to multicore clusters or supercomputers that are not always available to all researchers. Recently, scientists have returned to exploring the power of graphics processing units (GPUs) for various applications, such as MD, enabled by the recent advances in hardware and integrated programming interfaces such as NVIDIA's CUDA platform. One area of particular interest within the context of chemical applications is that of aqueous interfaces, the salt solutions of which have found application as model systems for studying atmospheric process as well as physical behaviors such as the Hoffmeister effect. Here, we present results of GPU‐accelerated simulations of the liquid–vapor interface of aqueous sodium iodide solutions. Analysis of various properties, such as density and surface tension, demonstrates that our model is consistent with previous studies of similar systems. In particular, we find that the current combination of water and ion force fields coupled with the ability to simulate surfaces of differing area enabled by GPU hardware is able to reproduce the experimental trend of increasing salt solution surface tension relative to pure water. In terms of performance, our GPU implementation performs equivalent to CHARMM running on 21 CPUs. Finally, we address possible issues with the accuracy of MD simulaions caused by nonstandard single‐precision arithmetic implemented on current GPUs. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2011     

Recent applications and developments of charge equilibration force fields for modeling dynamical charges in classical molecular dynamics simulations

With the continuing advances in computational hardware and novel force fields constructed using quantum mechanics, the outlook for non-additive force fields is promising. Our work in the past several years has demonstrated the utility of polarizable force fields, in our hands those based on the charge equilibration formalism, for a broad range of physical and biophysical systems. We have constructed and applied polarizable force fields for small molecules, proteins, lipids, and lipid bilayers and recently have begun work on carbohydrate force fields. The latter area has been relatively untouched by force field developers with particular focus on polarizable, non-additive interaction potential models. In this review of our recent work, we discuss the formalism we have adopted for implementing the charge equilibration method for phase-dependent polarizable force fields, lipid molecules, and small-molecule carbohydrates. We discuss the methodology, related issues, and briefly discuss results from recent applications of such force fields.     

Combining the polarizable Drude force field with a continuum electrostatic Poisson–Boltzmann implicit solvation model

In this work, we have combined the polarizable force field based on the classical Drude oscillator with a continuum Poisson–Boltzmann/solvent‐accessible surface area (PB/SASA) model. In practice, the positions of the Drude particles experiencing the solvent reaction field arising from the fixed charges and induced polarization of the solute must be optimized in a self‐consistent manner. Here, we parameterized the model to reproduce experimental solvation free energies of a set of small molecules. The model reproduces well‐experimental solvation free energies of 70 molecules, yielding a root mean square difference of 0.8 kcal/mol versus 2.5 kcal/mol for the CHARMM36 additive force field. The polarization work associated with the solute transfer from the gas‐phase to the polar solvent, a term neglected in the framework of additive force fields, was found to make a large contribution to the total solvation free energy, comparable to the polar solute–solvent solvation contribution. The Drude PB/SASA also reproduces well the electronic polarization from the explicit solvent simulations of a small protein, BPTI. Model validation was based on comparisons with the experimental relative binding free energies of 371 single alanine mutations. With the Drude PB/SASA model the root mean square deviation between the predicted and experimental relative binding free energies is 3.35 kcal/mol, lower than 5.11 kcal/mol computed with the CHARMM36 additive force field. Overall, the results indicate that the main limitation of the Drude PB/SASA model is the inability of the SASA term to accurately capture non‐polar solvation effects. © 2018 Wiley Periodicals, Inc.     

Molecular dynamics simulations of methane hydrate using polarizable force fields

Molecular dynamics simulations of methane hydrate have been carried out using the polarizable AMOEBA and COS/G2 force fields. Properties calculated include the temperature dependence of the lattice constant, the OC and OO radial distribution functions, and the vibrational spectra. Both the AMOEBA and COS/G2 force fields are found to successfully account for the available experimental data, with overall somewhat better agreement with experiment being found for the AMOEBA model. Comparison is made with previous results obtained using TIP4P and SPC/E effective two-body force fields and the polarizable TIP4P-FQ force field, which allows for in-plane polarization only. Significant differences are found between the properties calculated using the TIP4P-FQ model and those obtained using the other models, indicating an inadequacy of restricting explicit polarization to in-plane only.     

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.     

Simulation of phase separation in alcohol/water mixtures using two-body force field and standard molecular dynamics

Standard molecular dynamics simulations have been carried out on pure alcohols and alcohol/water mixtures. A simple atom-atom force field consisting of Lennard-Jones potentials plus coulombic terms over atomic point charges, but without explicit polarization terms, has been specifically fitted to reproduce several experimental properties of the pure alcohols, and has been used for mixtures by developing combination rules with the TIP3P water model. Densities, enthalpies of vaporization, radial distribution functions, self-diffusion coefficients, and rotational correlation functions of the pure alcohols are well reproduced and compare favorably with those from more sophisticated force fields. Some key aspects of the phase behaviour are correctly reproduced by the molecular dynamics simulation, showing a distinct demixing process for the n-butanol/water mixture as opposed to the stability of the t-butanol/water mixtures. The results demonstrate the ability of a molecular dynamics simulation, even in its standard form and with easily accessible time ranges, but with a carefully optimized force field, to simulate and, to a certain extent, predict the properties of binary mixtures.     

Conformational simulations of aqueous solvated alpha-conotoxin GI and its single disulfide analogues using a polarizable force field model

The solution conformation of alpha-conotoxin GI and its two single disulfide analogues are simulated using a polarizable force field in combination with the molecular fragmentation quantum chemical calculation. The polarizability is explicitly described by allowing the partial charges and fragment dipole moments to be variables, with values coming from the linear-scaling energy-based molecular fragmentation calculations at the B3LYP/6-31G(d) level. In comparison with the full quantum chemical calculations, the fragmentation approaches can yield precise ground-state energies, dipole moments, and static polarizabilities for peptides. The B3LYP/6-31G(d) charges and fragment-centered dipole moments are introduced in calculations of electrostatic terms in both AmberFF03 and OPLS force fields. Our test calculations on the gas-phase glucagon (PDB code: 1gcn) and solvated alpha-conotoxin GI (PDB code: 1not) demonstrate that the present polarization model is capable of describing the structural properties (such as the relative conformational energies, intramolecular hydrogen bonds, and disulfide bonds) with accuracy comparable to some other polarizable force fields (ABEEM/MM and OPLS-PFF) and the quantum mechanics/molecular mechanics (QM/MM) hybrid model. The employment of fragment-centered dipole moments in calculations of dipole-dipole interactions can save computational time in comparison with those polarization models using atom-centered dipole moments without much loss of accuracy. The molecular dynamics simulations using the polarizable force field demonstrate that two single disulfide GI analogues are more flexible and less structured than the native alpha-conotoxin GI, in agreement with NMR experiments. The polarization effect is important in simulations of the folding/unfolding process of solvated proteins.     

Molecular modeling and dynamics studies with explicit inclusion of electronic polarizability: theory and applications

A current emphasis in empirical force fields is on the development of potential functions that explicitly treat electronic polarizability. In the present article, the commonly used methodologies for modeling electronic polarization are presented along with an overview of selected application studies. Models presented include induced point-dipoles, classical Drude oscillators, and fluctuating charge methods. The theoretical background of each method is followed by an introduction to extended Lagrangian integrators required for computationally tractable molecular dynamics simulations using polarizable force fields. The remainder of the review focuses on application studies using these methods. Emphasis is placed on water models, for which numerous examples exist, with a more thorough discussion presented on the recently published models associated with the Drude-based CHARMM and the AMOEBA force fields. The utility of polarizable models for the study of ion solvation is then presented followed by an overview of studies of small molecules (e.g., CCl₄, alkanes, etc.) and macromolecule (proteins, nucleic acids and lipid bilayers) application studies. The review is written with the goal of providing a general overview of the current status of the field and to facilitate future application and developments.     

A polarizable ellipsoidal force field for halogen bonds

The anisotropic effects and short‐range quantum effects are essential characters in the formation of halogen bonds. Since there are an array of applications of halogen bonds and much difficulty in modeling them in classical force fields, the current research reports solely the polarizable ellipsoidal force field (PEff) for halogen bonds. The anisotropic charge distribution was represented with the combination of a negative charged sphere and a positively charged ellipsoid. The polarization energy was incorporated by the induced dipole model. The resulting force field is “physically motivated,” which includes separate, explicit terms to account for the electrostatic, repulsion/dispersion, and polarization interaction. Furthermore, it is largely compatible with existing, standard simulation packages. The fitted parameters are transferable and compatible with the general AMBER force field. This PEff model could correctly reproduces the potential energy surface of halogen bonds at MP2 level. Finally, the prediction of the halogen bond properties of human Cathepsin L (hcatL) has been found to be in excellent qualitative agreement with the cocrystal structures. © 2013 Wiley Periodicals, Inc.     

Co-ion and ion competition effects: ion distributions close to a hydrophobic solid surface in mixed electrolyte solutions

We consider within a modified Poisson-Boltzmann theory an electrolyte, with different mixtures of NaCl and NaI, near uncharged and charged solid hydrophobic surfaces. The parametrized potentials of mean force acting on Na+, Cl-, and I- near an uncharged self-assembled monolayer were deduced from molecular simulations with polarizable force fields. We study what happens when the surface presents negative charges. At moderately charged surfaces, we observe strong co-ion adsorption and clear specific ion effects at biological concentrations. At high surface charge densities, the co-ions are pushed away from the interface. We predict that Cl- ions can also be excluded from the surface by increasing the concentration of NaI. This ion competition effect (I- versus Cl-) may be relevant for ion-specific partitioning in multiphase systems where polarizable ions accumulate in phases with large surface areas.     

Comparison of selected polarizable and nonpolarizable water models in molecular dynamics simulations of ice I(h)

We present a molecular dynamics simulation study in which we determined the melting point of ice I(h) for the polarizable SWM4-NDP water model (Lamoureux et al., Chem. Phys. Lett., 2006, 418, 245-249) and compared the performance of several popular water force fields, both polarizable and nonpolarizable, in terms of melting temperature, stability and orientational structuring of ice. The simulations yield the melting temperature of SWM4-NDP ice as low as T(m) = 185 ± 10 K, despite the quadrupole moment of a SWM4-NDP water molecule being close to the experimental gas phase value. The results thus show that the dependence of T(m) on the molecular quadrupole, observed for the three- and four-site water models, is generally lost if polarization is explicitly included. The study also shows that adding polarizability to a planar three-charge water model increases orientational disorder in hexagonal ice. In addition, analysis of the tetrahedral order in bulk ice reveals a correlation between the pre-existing degree of orientational disorder in ice simulated using different polarizable and nonpolarizable models and the melting temperature of the models. Our findings thus suggest some new considerations regarding the role of polarization forces in a crystalline solid that may guide future development of reliable polarizable water models for ice.     

Preparation of solvent-free, pore-spanning lipid bilayers: modeling the low tension of plasma membranes

Plasma membrane tension, produced by the underlying cytoskeleton, governs many dynamic processes such as fusion, blebbing, exo- and endocytosis, cell migration, and adhesion. Here, a new protocol is introduced to model this intricate and often overlooked aspect of the plasma membrane. Lipid bilayers spanning pores of 600 nm radius were prepared by adsorption and spreading of giant unilamellar vesicles (GUVs) on moderately hydrophilic porous substrates prepared by gold-coating and subsequent self-assembly of a mercaptoethanol monolayer. Rupture of GUVs formed tens of micrometer sized pore-spanning membrane patches displaying low tension of σ ≤ 3.5 mN m(-1) and lateral diffusion constants of about 8 μm(2) s(-1). Site-specific force indentation experiments were performed to determine membrane tension as a function of lipid composition: for pure DOPC bilayers, a tension of 1.018 ± 0.014 mN m(-1) was measured, which was increased by the addition of cholesterol to 3.50 ± 0.15 mN m(-1). Compared to DOPC, POPC bilayers displayed a larger tension of 2.00 ± 0.09 mN m(-1). Addition and subsequent partitioning of 2-propanol was shown to significantly reduce the membrane tension as a function of its concentration.