Potential energy surfaces for small alcohol dimers I: methanol and ethanol

Potential energy landscapes for homogeneous dimers of methanol and ethanol were calculated using counterpoise (CP) corrected energies at the MP26-311+G(2df,2pd) level. The landscapes were sampled at approximately 15 dimer separation distances for different relative monomer geometries, or routes, given in terms of a relative monomer yaw, pitch, and roll and the spherical angles between the monomer centers (taken as the C atom attached to the O). The 19 different routes studied for methanol and the 22 routes examined for ethanol include 607 CP corrected energies. Both landscapes can be adequately represented by site-site, pairwise-additive models, suitable for use in molecular simulations. A modified Morse potential is used for the individual pair interactions either with or without point charges to represent the monomer charge distribution. A slightly better representation of the methanol landscape is obtained using point charges, while the potential energy landscape of ethanol is slightly better without point charges. This latter representation may be computationally advantageous for molecular simulations because it avoids difficulties associated with long-range effects of point-charge-type models.     

Using multipole point charge distributions to provide the electrostatic potential in the variational explicit polarization (X-Pol) potential

The equations defining the variational explicit polarization (X-Pol) potential introduced in earlier work are modified in the present work so that multipole point charge distributions are used instead of Mulliken charges to polarize the monomers that comprise the system. In addition, when computing the electrostatic interaction between a monomer whose molecular orbitals are being optimized and a monomer whose electron density is being used to polarize the first monomer, the electron densities of both monomers are represented by atom-centered multipole point charge distributions. In the original formulation of the variational X-Pol potential, the continuous electron density of the monomer being optimized interacts with external Mulliken charges, but this corresponds to the monopole truncation in a multipole expansion scheme in the computation of the Fock matrix elements of the given monomer. The formulation of the variational X-Pol potential introduced in this work (which we are calling the “multipole variational X-Pol potential”) represents the electron density of the monomer whose wave function is being variationally optimized in the same way that it represents the electron densities of external monomers when computing the Coulomb interactions between them.     

Electrostatic water models

The possiblity of creating a useful model for the electrostatic potential around the water molecule is examined from two different starting points. It is suggested that the simplest and most accurate model will have three point charges on the nuclei together with a diffuse Gaussian charge centered near the nuclear center of the charge. This will represent the lone-pair cloud, include the penetration effects, and improve the representation of the electron density. The alternative use of atomic dipoles is explored but seen to be less effective.     

A practical procedure for the determination of electrostatic charges of large molecules

Summary A practical procedure for the precise determination of electrostatic charges, which are evaluated by fitting the rigorous quantum mechanical molecular electrostatic potential to a monopole-monopole expression, is presented. The proposal of this procedure arises from the study of the minimum requirements necessary to obtain reliable electrostatic charges. Such a study is focused on: (i) the dependence of the electrostatic charges on the set of points where the quantum mechanical and the monopole-monopole molecular electrostatic potentials are fitted; thus, both the influence of the number of points and their distribution in layers located out of the van der Waals radii of the atoms are examined, and (ii) the reliability of the use of fractional models for the evaluation of electrostatic charges of large molecules. Results point out that the optimum number of points is defined by a density of points ranging from 0.45 to 0.60 points/Ų when four layers (separated by 0.2 Å) are considered. Nevertheless, the use of only two layers (separated by 0.4 Å) for large molecules is recommended, thus enabling one to obtain reliable charges at a reduced computational cost. Moreover, results justify the use of fractional models for the determination of electrostatic charges of extremely large molecules, even when aromatic structures exist.     

On the representation of electrostatic fields around ab initio charge distributions

Summary We compare two methods (Mulliken charges and a distributed multipole analysis, DMA) of representing an ab initio charge distribution for calculating the electrostatic field and potential outside the molecule, using pyrimidine and the RNA base uracil as examples. This is done using a 3-D graphical display of the electrostatic fields, which, when used with real-time rotation, zooming and clipping, has many advantages for qualitatively assessing the electrostatic interactions of a molecule. The errors involved in using Mulliken point charges may be of similar magnitude to the total electrostatic field in regions which are important in recognition processes. The DMA representation automatically includes the anisotropic electrostatic effects of non-spherical features in the charge distribution of each atom, and yet the displayed electrostatic fields around the atoms which have lone-pair density do not show marked anisotropy.     

Modeling of the mutual molecular polarization with an electronegativity equalization approach

A model for the mutual polarization of two approaching molecules is proposed, exploiting the principle of electronegativity equalization. The deformation of the electronic density of one molecule is the response to the perturbation of its chemical potential due to the electrostatic potential of the other molecule. The electronic densities, the density deformations, and the electrostatic potentials of both molecules are described with a previously developed asymptotic density model (ADM ). The ADM model allows a partitioning of all relevant properties in terms of atomic quantities. The perturbation of the chemical potential is given in atomic resolution, and the change of the electronic density is represented in terms of atomic charges. A hardness tensor, which determines the changes of the atomic chemical potentials due to the changes of the atomic charges, is modeled consistently with the ADM and earlier approaches. The results of the model, the changes of atomic charges within the molecules due to their mutual interaction, are compared with the changes of atomic charges obtained from population analysis of ab initio calculations. © 1995 John Wiley & Sons, Inc.     

Packaging of a flexible polyelectrolyte inside a viral capsid: effect of salt concentration and salt valence

The effect of salt on the location and structure of a flexible polyelectrolyte confined inside a viral capsid and the Donnan equilibrium of the salt across the capsid have been examined using a coarse-grained model solved by Monte Carlo simulations. The polyelectrolyte was represented by a linear jointed chain of charged beads, and the capsid was represented by a spherical shell with embedded charges. At low salt concentration, the polyelectrolyte was strongly adsorbed onto the inner capsid surface, whereas at high salt concentration it was located preferentially in the central part of the capsid. Under the condition of equal Debye screening length, the electrostatic screening increased as the valence of the polyelectrolyte counterion was increased. The distribution of the small cations and anions was unequal across the capsid. An excess of polyelectrolyte counterions occurred inside the capsid, and the excess increased with the salt concentration. A simplified representation of the small ions through the use of the screened Coulomb potential provided only a qualitatively correct picture; the electrostatic screening originating from the small ions was exaggerated.     

SPC cluster modeling of metal oxides: ways of determining the values of point charges in the embedded cluster model

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Ewald mesh method for quantum mechanical calculations

The Fourier transform Coulomb (FTC) method has been shown to be effective for the fast and accurate calculation of long-range Coulomb interactions between diffuse (low-energy cutoff) densities in quantum mechanical (QM) systems. In this work, we split the potential of a compact (high-energy cutoff) density into short-range and long-range components, similarly to how point charges are handled in the Ewald mesh methods in molecular mechanics simulations. With this linear scaling QM Ewald mesh method, the long-range potential of compact densities can be represented on the same grid as the diffuse densities that are treated by the FTC method. The new method is accurate and significantly reduces the amount of computational time on short-range interactions, especially when it is compared to the continuous fast multipole method.     

Electrostatic and covalent contributions in the coordination bonds of transition metal complexes

To develop a molecular mechanics force field for modeling complexes of transition metals and organic ligands, the electrostatic and covalent contributions in the coordination bonds were investigated using quantum mechanical density functional theory and model complexes of glyoxal diimine and the 2+ cations of the first row transition metals. The VDD and Hirshfeld charges are found to be closely correlated with the extent of the electron transfer between the ligands and the cations. Assuming the electrostatic contribution can be represented by the atomic partial charges, the covalent contributions in the coordination bonds are estimated to be in a range of 54-92% for the systems calculated. A simple force field was parametrized to validate the partial charge representation.     

Discrete charge effects on the Donnan potential and surface potential of a soft particle

The Donnan potential and surface potential of soft particles (i.e., polyelectrolyte-coated hard particles) in an electrolyte solution play an essential role in their electric behaviors. These potentials are usually derived via a continuum model in which fixed charges inside the surface layer are distributed with a continuous charge density. In this paper, for a plate-like soft particle consisting of a cubic lattice of fixed point charges, on the basis of the linearized Poisson–Boltzmann equation, we derive expressions for the electric potential distribution in the regions inside and outside the surface layer. This expression is given in terms of a sum of the screened Coulomb potentials produced by the point charges within the surface layer. We show that the deviation of the results of the discrete charge model from those of the continuous charge model becomes significant as the ratio of the lattice spacing to the Debye length becomes large.     

VESPA: A new,fast approach to electrostatic potential-derived atomic charges from semiempirical methods

An improved semiempirical method for computing electrostatic potential-derived atomic charges is described. It includes a very fast algorithm for the generation of the grid points around the molecule and the calculation of the electrostatic potential at these points. The dependency of the atomic point charges obtained on the number of grid points used in the fitting procedure is examined. For “buried” atoms a high density grid is necessary. It is possible to obtain 6–31G*-quality atom-centered point charges, even for phosphorus compounds, using AM1 or PM3. This approach can therefore be recommended for general use in QSAR or molecular mechanics for any organic and bioorganic system up to about 200 atoms. © 1997 by John Wiley & Sons, Inc. J Comput Chem 18: 744–756, 1997     

Energy decomposition in molecular complexes: implications for the treatment of polarization in molecular simulations

This study examines the contribution of electrostatic and polarization to the interaction energy in a variety of molecular complexes. The results obtained from the Kitaura-Morokuma (KM) energy decomposition analysis at the HF/6-31G(d) level indicate that, for intermolecular distances around the equilibrium geometries, the polarization energy can be determined as the addition of the polarization energies of interacting blocks, as the mixed polarization term is typically negligible. Comparison of KM and QM/MM results shows that the electrostatic energy determined in the KM method is underestimated (in absolute value) by QM/MM methods. The reason of such underestimation can be attributed to the simplified representation of treating the interaction between overlapping charge distribution by the interaction of a QM molecule with a set of point charges. Nevertheless, the polarization energies calculated by KM and QM/MM methods are in close agreement. Finally, a consistent, automated strategy to derive charge distributions that include implicitly polarization effects in pairwise, additive force fields is presented. The strategy relies in the simultaneous fitting of electrostatic and polarization energies computed by placing a suitable perturbing particle at selected points around the molecule. The suitability of these charges to describe molecular interactions is discussed.     

Surface properties of fluids of charged platelike colloids

Surface properties of mixtures of charged platelike colloids and salt in contact with a charged planar wall are studied within density functional theory. The particles are modeled by hard cuboids with their edges constrained to be parallel to the Cartesian axes corresponding to the Zwanzig model [J. Chem. Phys. 39, 1714 (1963)] and the charges of the particles are concentrated at their centers. The density functional applied is an extension of a recently introduced functional for charged platelike colloids. It provides a qualitative approach because it does not determine the relation between the actual and the effective charges entering into the model. Technically motivated approximations, such as using the Zwanzig model, are expected not to influence the results qualitatively. Analytically and numerically calculated bulk and surface phase diagrams exhibit first-order wetting for sufficiently small macroion charges and isotropic bulk order as well as first-order drying for sufficiently large macroion charges and nematic bulk order. The asymptotic wetting and drying behaviors are investigated by means of effective interface potentials which turn out to be asymptotically the same as for a suitable neutral system governed by isotropic nonretarded dispersion forces. Wetting and drying points as well as predrying lines and the corresponding critical points have been located numerically. A crossover from monotonic to nonmonotonic electrostatic potential profiles upon varying the surface charge density has been observed. Nonmonotonic electrostatic potential profiles are equivalent to the occurrence of charge inversion. Due to the presence of both the Coulomb interactions and the hard-core repulsions, the surface potential and the surface charge do not vanish simultaneously, i.e., the point of zero charge and the isoelectric point of the surface do not coincide.     

A Universal and Straightforward Approach to Include Penetration Effects in Electrostatic Interaction Energy Estimation

To compensate for the lack of the explicit treatment of charge penetration in classical force fields, we propose a new charge‐distribution model based on a promolecule augmented with point charges (aug‐PROmol). It relies on a superposition of spherical atomic electron densities obtained for each chemical element from SCF energy optimized atomic orbitals. Atomic densities are further rescaled by partial point charges computed from fits to the molecular electrostatic potential. Aug‐PROmol was tested on the S66 benchmark dataset extended to nonequilibrium geometries (J. Chem. Theory Comput., 2011, 7, 3466). The model does not need any additional parametrization other than point charges. Despite its simplicity, aug‐PROmol approximates the electrostatic energy with good agreement (RMSE=0.76 kcal mol^?1 to DFT‐SAPT with B3LYP/aug‐cc‐pVTZ).     

Effect of discrete macroion charge distributions in solutions of like-charged macroions

The effect of replacing the conventional uniform macroion surface charge density with discrete macroion charge distributions on structural properties of aqueous solutions of like-charged macroions has been investigated by Monte Carlo simulations. Two discrete charge distributions have been considered: point charges localized on the macroion surface and finite-sized charges protruding into the solution. Both discrete charge distributions have been examined with fixed and mobile macroion charges. Different boundary conditions have been applied to examine various properties. With point charges localized on the macroion surface, counterions become stronger accumulated to the macroion and the effect increases with counterion valence. As a consequence, with mono- and divalent counterions the potential of mean force between two macroions becomes less repulsive and with trivalent counterions more attractive. With protruding charges, the excluded volume effect dominates over the increased correlation ability; hence the counterions are less accumulated near the macroions and the potential of mean force between two macroions becomes more repulsive/less attractive.     

The effect of isodensity surface sampling on ESP derived charges and the effect of adding bondcenters on DMA derived charges

The effect of sampling the electrostatic potential around a molecule on the quality of electrostatic potential derived charges is investigated. In addition, the effect of the number of expansion sites in a Distributed Multipole Analysis (DMA) on the quality of charges fitted to the DMA derived electrostatic potential is investigated. Sampling on constant electron density surfaces gives a better fit between the quantum mechanical potential and the potential derived from the fitted charges, compared to sampling on a van der Waals surface composed of intersecting spheres. The fit between the electrostatic potential derived from point charges and the quantum mechanical potential becomes poorer with increasing quality of the employed basis set. The inclusion of bondcenters into the calculations improves the fit between the Quantum Mechanical (QM) electrostatic potential and the DMA derived potential. The number of expansion sites needed for an accurate approximation of the QM electrostatic potential increases with increasing quality of the used basis set.     

Model calculation of the spin density for trapped muonium in ionic solids

A previously developed perturbation formula for calculating the spin density of trapped normal muonium in diamond is applied to the trapped muonium in the ionic solids of MgO, KCl and KBr. To obtain an improved molecular electrostatic potential (MEP) inside the cubic lattice, we performed MO calculations using clusters of MgO, KCl and KBr with additional surrounding point charges. Calculated spin densities (ƒ-values) in these potentials are compared with experimental results. We also report ab initio UHF MO calculations for these clusters with a trapped hydrogen atom at the centre of the clusters.     

原子簇量子化学从头算的自洽晶体场模型

本文提出一种收敛的点电荷和Hartree-Fock表面势构成的自洽晶体场Madelung势用于原子簇量子化学从头计算。前者的计算类似于核吸引积分的单电子积分, 后者可以通过点群对称性操作从原子簇内的积分矩阵元得到。点电荷的大小和原子簇内对应的原子电荷相等, 其数目以晶体场势收敛为标准确定。介绍加速计算的程序技巧。该模型用于高温超导体YBa2Cu3O7的全电子从头计算并得到一些新结果。