Simulation of liquid imidazole using a high-rank quantum topological electrostatic potential

Rigid body molecular dynamics simulations were carried out on pure liquid imidazole at four different temperatures and at 1 atm. Imidazole, which is important both in life science and materials science, is one of the simplest molecules to possess both a lone pair and a π system. These two features are known to benefit from multipolar electrostatics. Here the electrostatic interaction is governed by atomic multipole moments obtained from topologically partitioned ab initio electron densities. The non-electrostatic terms are modeled with Lennard-Jones parameters adjusted to fit the experimental liquid density. All σ values are incrementally increased by one single scaling factor. We report on how the presence of multipolar electrostatics influences the local structure, dynamics and thermodynamics of the liquid compared to electrostatics by atomic point charges. The point charge force field exaggerates the number of π-stacked dimers in the liquid, and underestimates the number of hydrogen-bonded dimers. The effect of the temperature on the local structure of liquid imidazole was analysed using radial and spatial distribution functions.     

Electrostatic potentials and fields from density expansions of deformed atoms in molecules

The exact representation of the molecular density by means of atomic expansions, consisting in spherical harmonics times analytical radial factors, is employed for the calculation of electrostatic potentials, fields, and forces. The resulting procedure is equivalent to an atomic multipolar expansion in the long-range regions, but works with similar efficiency and accuracy in the short-range region, where multipolar expansions are not valid. The performances of this procedure are tested on the calculation of the electrostatic potential contour maps and electrostatic field flux lines of water and nitrobenzene, computed from high-quality molecular electron densities obtained with Slater basis sets.     

Atomic multipoles and perpendicular electrostatic forces in diatomic and planar molecules

Current methods for assigning atomic multipoles focus on reproduction of the molecular electrostatic potential. Another aspect of electrostatic interaction, which is usually overlooked, is the forces that an external electric field exerts on the nuclei of a molecule. In a self-consistent theory, both the electrostatic potential and force should be accounted for. However, in general it is not easy to meet this requirement for the force. For planar molecules, though, a formal solution is available in terms of atomic multipoles that are extracted from the molecular multipolar tensors. These Force-Related (FR) atomic multipoles are discussed in detail for some typical diatomics and planar polyatomics, and are shown to provide a solid uniform framework for treating both aspects of the electrostatics. In contrast, the commonly used potential-derived charges (i.e., the atomic charges obtained by fitting the electrostatic potential) can yield large deviations with respect to electrostatic forces on the nuclei, even when the electrostatic potential is very well reproduced.     

Continuum treatment of electronic polarization effect

A continuum treatment of electronic polarization has been explored for in molecular mechanics simulations in implicit solvents. The dielectric constant for molecule interior is the only parameter in the continuum polarizable model. A value of 4 is found to yield optimal agreement with high-level ab initio quantum mechanical calculations for the tested molecular systems. Interestingly, its performance is not sensitive to the definition of molecular volume, in which the continuum electronic polarization is defined. In this model, quantum mechanical electrostatic field in different dielectric environments from vacuum, low-dielectric organic solvent, and water can be used simultaneously in atomic charge fitting to achieve consistent treatment of electrostatic interactions. The tests show that a single set of atomic charges can be used consistently in different dielectric environments and different molecular conformations, and the atomic charges transfer well from training monomers to tested dimers. The preliminary study gives us the hope of developing a continuum polarizable force field for more consistent simulations of proteins and nucleic acids in implicit solvents.     

Optimization of a molecular mechanics force field for type-II polyoxometalates focussing on electrostatic interactions: a case study

In this study, we have focussed on type-II polyanions such as [M(7)O(24)](6-), and we have developed and validated optimized force fields that include electrostatic and van der Waals interactions. These contributions to the total steric energy are described by the nonbonded term, which encompasses all interactions between atoms that are not transmitted through the bonds. A first validation of a stochastic technique based on genetic algorithms was previously made for the optimization of force fields dedicated to type-I polyoxometalates. To describe the new nonbonded term added in the functional, a fixed-charged model was chosen. Therefore, one of the main issues was to analyze that which partial atomic charges could be reliably used to describe these interactions in such inorganic compounds. Based on several computational strategies, molecular mechanics (MM) force field parameters were optimized using different types of atomic charges. Moreover, the influence of the electrostatic and van der Waals buffering constants and 1,4-interactions scaling factors used in the force field were also tested, either being optimized as well or fixed with respect to the values of CHARMM force field. Results show that some atomic charges are not well adapted to CHARMM parameters and lead to unrealistic MM-optimized structures or a MM divergence. As a result, a new scaling factor has been optimized for Quantum Theory of Atoms in Molecules charges and charges derived from the electrostatic potential such as ChelpG. The force fields optimized can be mixed with the CHARMM force field, without changing it, to study for the first time hepta-anions interacting with organic molecules.     

Comparison of charge models for fixed-charge force fields: small-molecule hydration free energies in explicit solvent

In molecular simulations with fixed-charge force fields, the choice of partial atomic charges influences numerous computed physical properties, including binding free energies. Many molecular mechanics force fields specify how nonbonded parameters should be determined, but various choices are often available for how these charges are to be determined for arbitrary small molecules. Here, we compute hydration free energies for a set of 44 small, neutral molecules in two different explicit water models (TIP3P and TIP4P-Ew) to examine the influence of charge model on agreement with experiment. Using the AMBER GAFF force field for nonbonded parameters, we test several different methods for obtaining partial atomic charges, including two fast methods exploiting semiempirical quantum calculations and methods deriving charges from the electrostatic potentials computed with several different levels of ab initio quantum calculations with and without a continuum reaction field treatment of solvent. We find that the best charge sets give a root-mean-square error from experiment of roughly 1 kcal/mol. Surprisingly, agreement with experimental hydration free energies does not increase substantially with increasing level of quantum theory, even when the quantum calculations are performed with a reaction field treatment to better model the aqueous phase. We also find that the semiempirical AM1-BCC method for computing charges works almost as well as any of the more computationally expensive ab initio methods and that the root-mean-square error reported here is similar to that for implicit solvent models reported in the literature. Further, we find that the discrepancy with experimental hydration free energies grows substantially with the polarity of the compound, as does its variation across theory levels.     

Solution of the nonlinear Poisson-Boltzmann equation using pseudo-transient continuation and the finite element method

The nonlinear Poisson-Boltzmann (PB) equation is solved using Newton-Krylov iterations coupled with pseudo-transient continuation. The PB potential is used to compute the electrostatic energy and evaluate the force on a user-specified contour. The PB solver is embedded in a existing, 3D, massively parallel, unstructured-grid, finite element code. Either Dirichlet or mixed boundary conditions are allowed. The latter specifies surface charges, approximates far-field conditions, or linearizes conditions "regulating" the surface charge. Stability and robustness are proved using results for backward Euler differencing of diffusion equations. Potentials and energies of charged spheres and plates are computed and results compared to analysis. An approximation to the potential of the nonlinear, spherical charge is derived by combining two analytic formulae. The potential and force due to a conical probe interacting with a flat plate are computed for two types of boundary conditions: constant potential and constant charge. The second case is compared with direct force measurements by chemical force microscopy. The problem is highly nonlinear-surface potentials of the linear and nonlinear PB equations differ by over an order of magnitude. Comparison of the simulated and experimentally measured forces shows that approximately half of the surface carboxylic acid groups, of density 1/(0.2 nm2), ionize in the electrolyte implying surface charges of 0.4 C/m2, surface potentials of 0.27 V, and a force of 0.6 nN when the probe and plate are 8.7 nm apart.     

Electrostatic calculation of linear and non-linear optical properties of ice Ih,II, IX and VIII

Macroscopic first- and third-order susceptibilities of ice Ih, ice II, ice IX and ice VIII are calculated using static and frequency-dependent electronic and static vibrational molecular (hyper)polarizabilities at the MP2 level. The molecular properties are in good agreement with experiment and with high-level ab initio calculations. Intermolecular electrostatic and polarization effects due to induced dipoles are taken into account using a rigorous local-field theory. The electric field due to permanent dipoles is used to calculate effective in-crystal (hyper)polarizabilities. The polarizability depends only weakly on the permanent field, but the dipole moment and the hyperpolarizabilities are strongly affected. The calculated linear susceptibility is in good agreement with available experimental data for ice Ih, and the third-order susceptibility for a third harmonic generation experiment is in reasonable agreement with experimental values for liquid water. The molecular vibrational contributions have a small effect on the susceptibilities. The electric properties of a water tetramer are calculated and used to estimate the effect of non-dipolar interactions on the susceptibilities of ice Ih, which are found to be small.     

A force field for molecular simulation of tetrabutylphosphonium amino acid ionic liquids

An all-atom force field was set up for a new class of ionic liquids (ILs), tetrabutylphosphonium amino acid, on the basis of the AMBER force field with determining parameters related to the phosphorus atom and modifying several parameters. Ab initio quantum chemical calculations were employed to obtain molecular geometries, infrared frequencies, and torsion energy profiles. Atom partial charges were obtained by using the one-conformation, two-step restraint electrostatic potential approach. Molecular dynamics simulation was carried out in the isothermal-isobaric ensemble for 14 tetrabutylphosphonium amino acid ILs at two temperatures to validate the force field against the experimental densities and heat capacities at constant pressure. Computed thermodynamic properties are in good agreement with available experimental values. Moreover, radial distribution functions were investigated to depict the microscopic structures of these ILs.     

Liquid-structure forces and electrostatic modulation of biomolecular interactions in solution

Molecular interactions in solution are controlled by the bulk medium and by the forces originating in the structured region of the solvent close to the solutes. In this paper, a model of electrostatic and liquid-structure forces for dynamics simulations of biomolecules is presented. The model introduces information on the microscopic nature of the liquid in the vicinity of polar and charged groups and the associated non-pairwise character of the forces, thus improving upon conventional continuum representations. The solvent is treated as a polar and polarizable medium, with dielectric properties described by an inhomogeneous version of the Onsager theory. This treatment leads to an effective position-dependent dielectric permittivity that incorporates saturation effects of the electric field and the spatial variation of the liquid density. The non-pairwise additivity of the liquid-structure forces is represented by centers of force located at specific points in the liquid phase. These out-of-the-solute centers are positioned at the peaks of liquid density and exert local, external forces on the atoms of the solute. The density is calculated from a barometric law, using a Lennard-Jones-type solute-liquid effective interaction potential. The conceptual aspects of the model and its exact numerical solutions are discussed for single alkali and halide ions and for ion-pair interactions. The practical aspects of the model and the simplifications introduced for efficient computation of forces in molecular solutes are discussed in the context of polar and charged amino acid dimers. The model reproduces the contact and solvent-separated minima and the desolvation barriers of intermolecular potentials of mean force of amino acid dimers, as observed in atomistic dynamics simulations. Possible refinements based on an improved treatment of molecular correlations are discussed.     

Electrostatics of proteins in dielectric solvent continua. I. Newton's third law marries qE forces

The authors reformulate and revise an electrostatic theory treating proteins surrounded by dielectric solvent continua [B. Egwolf and P. Tavan, J. Chem. Phys. 118, 2039 (2003)] to make the resulting reaction field (RF) forces compatible with Newton's third law. Such a compatibility is required for their use in molecular dynamics (MD) simulations, in which the proteins are modeled by all-atom molecular mechanics force fields. According to the original theory the RF forces, which are due to the electric field generated by the solvent polarization and act on the partial charges of a protein, i.e., the so-called qE forces, can be quite accurately computed from Gaussian RF dipoles localized at the protein atoms. Using a slightly different approximation scheme also the RF energies of given protein configurations are obtained. However, because the qE forces do not account for the dielectric boundary pressure exerted by the solvent continuum on the protein, they do not obey the principle that actio equals reactio as required by Newton's third law. Therefore, their use in MD simulations is severely hampered. An analysis of the original theory has led the authors now to a reformulation removing the main difficulties. By considering the RF energy, which represents the dominant electrostatic contribution to the free energy of solvation for a given protein configuration, they show that its negative configurational gradient yields mean RF forces obeying the reactio principle. Because the evaluation of these mean forces is computationally much more demanding than that of the qE forces, they derive a suggestion how the qE forces can be modified to obey Newton's third law. Various properties of the thus established theory, particularly issues of accuracy and of computational efficiency, are discussed. A sample application to a MD simulation of a peptide in solution is described in the following paper [M. Stork and P. Tavan, J. Chem. Phys., 126, 165106 (2007).     

Multi-layer coarse-graining polarization model for treating electrostatic interactions of solvated α-conotoxin peptides

A multi-layer coarse-graining (CG) model is presented for treating the electrostatic interactions of solvated α-conotoxin peptides. According to the sensitivity to the electrostatic environment, a hybrid set of electrostatic parameters, such as secondary-structure- and residue-based dipoles, and atom-centered partial charges, are adopted. For the polarization "inert" secondary-structures and residues, the fragment dipole moments are distributed within narrow ranges with the magnitude close to zero. The coarse-graining fragment dipoles are parameterized from a large training set (10,000 configurations) to reproduce the electrostatic features of molecular fragments. In contrast, the electrostatically "sensitive" atoms exhibit large fluctuations of charges with the varied environments. The environment-dependent variable charges are updated in each energetic calculation. The electrostatic interaction of the whole chemical system is hence partitioned into several sub-terms coming from the fragment dipole-dipole, (fragment) dipole-(atom) charge, and atom charge-charge interactions. A large number of test calculations on the relative energies of cyclo-peptide conformers have demonstrated that the multi-layer CG electrostatic model presents better performance than the non-polarized force fields, in comparison with the density-functional theory and the fully polarized force field model. The selection of CG fragment centers, mass or geometric center, has little influence on the fragment-based dipole-dipole interactions. The multi-layer partition of electrostatic polarization is expected to be applied to many biologically interesting and complicated phenomena.     

Accurate solution of multi-region continuum biomolecule electrostatic problems using the linearized Poisson-Boltzmann equation with curved boundary elements

We present a boundary-element method (BEM) implementation for accurately solving problems in biomolecular electrostatics using the linearized Poisson-Boltzmann equation. Motivating this implementation is the desire to create a solver capable of precisely describing the geometries and topologies prevalent in continuum models of biological molecules. This implementation is enabled by the synthesis of four technologies developed or implemented specifically for this work. First, molecular and accessible surfaces used to describe dielectric and ion-exclusion boundaries were discretized with curved boundary elements that faithfully reproduce molecular geometries. Second, we avoided explicitly forming the dense BEM matrices and instead solved the linear systems with a preconditioned iterative method (GMRES), using a matrix compression algorithm (FFTSVD) to accelerate matrix-vector multiplication. Third, robust numerical integration methods were employed to accurately evaluate singular and near-singular integrals over the curved boundary elements. Fourth, we present a general boundary-integral approach capable of modeling an arbitrary number of embedded homogeneous dielectric regions with differing dielectric constants, possible salt treatment, and point charges. A comparison of the presented BEM implementation and standard finite-difference techniques demonstrates that for certain classes of electrostatic calculations, such as determining absolute electrostatic solvation and rigid-binding free energies, the improved convergence properties of the BEM approach can have a significant impact on computed energetics. We also demonstrate that the improved accuracy offered by the curved-element BEM is important when more sophisticated techniques, such as nonrigid-binding models, are used to compute the relative electrostatic effects of molecular modifications. In addition, we show that electrostatic calculations requiring multiple solves using the same molecular geometry, such as charge optimization or component analysis, can be computed to high accuracy using the presented BEM approach, in compute times comparable to traditional finite-difference methods.     

Molecular mechanics of organic halides. V. Conformational equilibria in solution

With a view of using data on solutions and liquids for parameter fitting in molecular mechanical force fields, Abraham's theory of solvation is incorporated in the force field procedure. Geometries and bond moments are estimated internally, partial account being taken of bond–bond induction, and used to calculate the intramolecular electrostatic energy, dipole moment, and the dipole and quadrupole terms in the solvation energy. Three dielectric constants are used, one for the solute in the vapor, one for the solution, and one for the intramolecular space through which dipole–dipole interactions take place. Examples are given, including such where computation differs with measurement, to illustrate the performance of the scheme.     

Polarizable and nonpolarizable force fields for alkyl nitrates

Quantum-chemistry-based many-body polarizable and two-body nonpolarizable atomic force fields were developed for alkyl nitrate liquids and pentaerythritol tetranitrate (PETN) crystal. Bonding, bending, and torsional parameters, partial charges, and atomic polarizabilities for the polarizable force field were determined from gas-phase quantum chemistry calculations for alkyl nitrate oligomers and PETN performed at the MP2/aug-cc-pvDz level of theory. Partial charges for the nonpolarizable force field were determined by fitting the dipole moments and electrostatic potential to values for PETN molecules in the crystal phase obtained from molecular dynamics simulations using the polarizable force field. Molecular dynamics simulations of alkyl nitrate liquids and two polymorphs of PETN crystal demonstrate the ability of the quantum-chemistry-based force fields to accurately predict thermophysical and mechanical properties of these materials.