Method for Slater-Type Density Fitting for Intermolecular Electrostatic Interactions with Charge Overlap. I. The Model.

The effects of charge overlap, or charge penetration, are neglected in most force fields and interaction terms in QM/MM methods. The effects are however significant at intermolecular distances near the van der Waals minimum. In the present study, we propose a method to evaluate the intermolecular Coloumb interaction using Slater-type functions, thus explicitly modeling the charge overlap. The computational cost of the method is low, which allows it to be used in large systems with most force fields as well as in QM/MM schemes. The charge distribution is modeled as a distributed multipole expansion up to quadrupole and Slater-type functions of angular momentum up to L = 1. The exponents of the Slater-type functions are obtained using a divide-and-conquer method to avoid the curse of dimensionality that otherwise is present for large nonlinear optimizations. A Levenberg-Marquardt algorithm is applied in the fitting process. A set of parameters is obtained for each molecule, and the process is fully automated. Calculations have been performed in the carbon monoxide and the water dimers to illustrate the model. Results show a very good accuracy of the model with relative errors in the electrostatic potential lower than 3% over all reasonable separations. At very short distances where the charge overlaps is the most significant, errors are lower than 8% and lower than 3.5% at distances near the van der Waals minimum.

Dielectric response from lattices of dipoles with fixed orientation.

The properties of dipolar cubic lattices are studied and the paradox of how to obtain a long range polarization in such lattices is resolved by choosing a proper shape of the total system. It has been shown that large but finite number of aligned dipoles prefer to exist as needle shaped macroscopic particles [M. Yoon and D. Tománek, J. Phys.: Condens. Matter 22, 455105 (2010)]. The total energy for a particle in such a system has one short range contribution depending on the packing (the chosen lattice) and one long range term depending on the dipole density of the system. We show that the latter term corresponds exactly to the polarization term from a dielectric medium embedding a sphere of the considered system. There is no need to include a dielectric medium in this modeling and the "dielectric stabilization" is generated solely by the dipoles of the system.

Calculation of the molecular and atomic properties of selected anions in water.

The polarizability and other properties have been studied for F(-), Cl(-), Br(-), and HCOO(-) in water using a combined quantum chemical statistical mechanics simulation model that explicitly takes into account the Pauli repulsion as well as the electrostatic coupling between the QM system and the classical surroundings. It is shown that the surrounding molecules significantly reduce both the polarizability and the size of the anions. For the formate ions, local properties have been computed.

Structural Anisotropy in Polar Fluids Subjected to Periodic Boundary Conditions.

A heuristic model based on dielectric continuum theory for the long-range solvation free energy of a dipolar system possessing periodic boundary conditions (PBCs) is presented. The predictions of the model are compared to simulation results for Stockmayer fluids simulated using three different cell geometries. The boundary effects induced by the PBCs are shown to lead to anisotropies in the apparent dielectric constant and the long-range solvation free energy of as much as 50%. However, the sum of all of the anisotropic energy contributions yields a value that is very close to the isotropic one derived from dielectric continuum theory, leading to a total system energy close to the dielectric value. It is finally shown that the leading-order contribution to the energetic and structural anisotropy is significantly smaller in the noncubic simulation cell geometries compared to when using a cubic simulation cell.

An exact calculation of the van der Waals interaction between two spheres of classical dipolar fluid.

An exact treatment of the van der Waals interaction between two spherical dielectric bodies possessing purely classical degrees of freedom is presented. The spheres are described by multipole expansions of their fluctuating charge distributions, and the correlation between the fluctuations are taken into account using classical electrostatics and statistical mechanics. The presented approach avoids both the assumption of pairwise additivity of Hamaker theory and the implicit linear response assumption of Lifshitz theory. The resulting equations are solved numerically for D/a ≥ 0.01, where a is the radius of the spheres and D is their minimum separation, for a system with ε = 80, and the results are compared to the analytical Hamaker formula with a Hamaker constant calculated from Lifshitz theory.

A NEMO potential that includes the dipole-quadrupole and quadrupole-quadrupole polarizability.

To increase the accuracy of molecular force fields a systematical and balanced improvement of the various terms included is needed. In this work, we have followed this strategy to improve the quality of the NEMO potential for the formaldehyde dimer by introducing local quadrupole moments and higher-order polarizabilities. It is found that inclusion of the quadrupole moment significantly improves the interaction potential. Furthermore, the inclusion of higher-order polarizabilities up to quadrupole-quadrupole polarizability is shown to give a better description of the intermolecular interaction. In addition, it is demonstrated that localized properties based on MP2 densities reproduces the BSSE corrected MP2 interaction energy at large intermolecular separations. This is not the case for HF-SCF based properties.

Two-center potential correlations and its use to determine effective ion-ion interactions and dielectric permittivities in dipolar solvents.

General expressions for two-center electrostatic potential correlations and its use to determine (i) the effective interaction between simple ions in a dipolar solvent and (ii) the dielectric permittivity of the solvent are proposed. Such two-center potential correlations were determined from Monte Carlo simulations of spherically confined dipolar particles embedded in a dielectric medium described by using an image charge approximation. The deduced dielectric permittivities increased with increasing dipolar moment, and at large dipole moments the effective interaction displayed an attractive first minimum.

Bulk simulation of polar liquids in spherical symmetry.

Molecular simulations of strongly coupled dipolar systems of varying size have been carried out, using particles confined inside a dielectric cavity and an image charge approach to treat the dielectric response from the surroundings. A simple method using penalty functions was employed to create an isotropic and homogeneous distribution of particles inside the cavity. The dielectric response of the molecular system was found to increase as the number of particles N was increased. Nevertheless, a significant surface effect remained even for the largest systems (N=10,000), manifesting itself through a decrease in the dielectric constant of the system as the confining surface was approached. The surface effect was significantly reduced by using a negative dielectric constant of the surrounding dielectric medium, although accomplishing a full dielectric solvation of the molecular system was not possible.

Retardation effects breaking long-range orientational ordering in dipolar fluids.

A strongly coupled dipolar fluid confined in a sphere has been examined by Monte Carlo simulations using a modified distance-dependent pair interaction to emulate retardation effects. The effective dipole-dipole interaction and a property closely related to Kirkwood's g-factor have been analyzed for potentials with different distances at which the retardation effects became effective. The retardation effects were found to break the otherwise long-range structural ordering occurring in strongly coupled dipolar fluids.

Nondielectric long-range solvation of polar liquids in cubic symmetry.

Long-range solvation properties of strongly coupled dipolar systems simulated using the Ewald and reaction field methods are assessed by using electric fluctuation formulas for a dielectric medium. Some components of the fluctuating electric multipole moments are suppressed, whereas other components are favored as the boundary of the simulation box is approached. An analysis of electrostatic interactions in a periodic cubic system suggests that these structural effects are due to the periodicity embedded in the Ewald method. Furthermore, the results obtained using the reaction field method are very similar to those obtained using the Ewald method, an effect which we attribute to the use of toroidal boundary conditions in the former case. Thus, the long-range solvation properties of polar liquids simulated using either of the two methods are nondielectric in their character.

Electric multipole moment fluctuations in polar liquids.

A general expression for the distribution of the fluctuating 2(l)-pole moment M(l) of a spherical sample of dielectric material is derived on the basis of dielectric theory combined with statistical mechanics. The formulas are compared with results from computer simulations of a weakly coupled Stockmayer fluid and the agreement is shown to be excellent. Furthermore, we calculate the size of the coupling, quantified through the free energy of solvation A(solv), of the fluctuating electric moments to a surrounding dielectric medium. It turns out that the contribution to A(solv) from each fluctuating electric moment actually increases with increasing order l of the moment, resulting in a formally infinite free energy of solvation. We also present a correction to A(solv) for molecular media, which shows that the molecular nature of the surrounding medium effectively suppresses the divergence in the solvation free energy.

Induction correction model for rotation of two or three dihedral angles.

In a previous work we have introduced an intramolecular induction correction model. In this work we have used the model to calculate the total dipol moment of six molecules as a function of two or three dihedral angles that are simultaneously varied in the molecules. It is found that the induction model behaves very well for the systems studied when compared with a regular force field model where fixed charges and dipoles are rotated along with the atoms of the molecules. This suggests that the proposed induction correction model can be used to model systems containing several dihedral angles around which rotations are performed.

Inclusion of the quadrupole moment when describing polarization. The effect of the dipole-quadrupole polarizability.

A method to compute distributed dipole-quadrupole polarizabilities is suggested. The method is based on numerical differentiation of distributed quadrupole moments, using finite field perturbation calculations. It is tested using two different multicenter multipole expansions, and compared with results using polarizabilities obtained via the uncoupled Hartree-Fock approximation. The accuracy of these dipole-quadrupole polarizabilities are tested for different molecules and basis sets, by comparing the induced electrostatic potential of the Hartree-Fock density with the induced electrostatic potential of the polarization models. This is done by perturbing the molecules with an external homogeneous field and with an external dipole. It is found that inclusion of the dipole-quadrupole polarizability significantly improves the accuracy of the response of the molecule to these external perturbations. This suggests that inclusion of higher-order induced moments can be of importance when improving the description of intermolecular interactions using force fields.

Accuracy of typical approximations in classical models of intermolecular polarization.

One of the largest limitations of standard molecular-mechanics force fields is the neglect of intermolecular polarization. Several attempts to cure this problem have been made, but the results have not always been fully satisfactory. In this paper, we present a quantitative study of the fundamental approximations that underlie polarization models for classical force fields. The induced charge density of a large set of molecular dimers is compared to supermolecular calculations for a hierarchy of simplified models. We study the effect of the Pauli principle, the local inhomogeneity of the electric field, the intramolecular coupling of the polarization response, and the fact that the induced density is a continuous function. We show that standard point-polarizability models work rather well, despite their lack of all these effects, because (1) there is a systematic error cancellation between the neglect of effects of the Pauli principle and the locally inhomogeneous electric field, and (2) the lack of intramolecular coupling and the use of a dipole expansion of the induced density have only minor effects on the polarization. However, the cancellation in (1) is not perfect, and therefore polarizable force-fields could be improved if both effects are explicitly treated.

An intramolecular induction correction model of the molecular dipole moment.

A model for intramolecular polarization is presented. It is used to describe the changes in the molecular charge distribution occurring as a response to changes of dihedral angles in the molecule. The model is based on a multicenter multipole distribution of the molecular charge distribution. The electric field from this charge distribution induce dipole moments in the same molecule. The model contains atom type parameters to describe the damping of the electric field. A total of four atom types are used. The parameters are fitted to a calibration set with various functional groups, and tested against a validation set. The error obtained for the calibration set is reduced by 92% and by 88% for the validation set, if compared to an accurate state-of-the-art force field. It is shown that rotating the non-polarizable multicenter multipole distribution for the equilibrium geometry gives too large dipole moments for dihedral angles deviating from the equilibrium geometry. This will lead to too large long-range attractions in simulations. This problem is overcome by using the dipole polarizability correction suggested here, which gives dipole moments very close to the Hartree-Fock dipole moments obtained from reference calculations.

Simulations of the absorption and fluorescence of indole in aqueous solution and at a nonpolar/polar interface.

Theoretical results are presented on the absorption and fluorescence of indole in aqueous solution as well as at the air/water surface. We use a combined quantum chemical statistical mechanical model with explicit solvent. An approximate ab initio complete active space self-consistent field description of the indole molecule is used, coupled to a discrete polarizable water medium. From the bulk simulations, strong support is found for the interchange mechanism, which explains the unusual solvent shift of the fluorescence of indole or tryptophan in a polar surrounding by a solvent induced switch of the fluorescing state. Two mechanisms are given to explain the different shifts for indole at the interface. First, a dielectric depletion effect, which is expected from the reduction of the amount of polar media. Second, an interface-specific effect, which derives from the stronger hydrogen bond formation at the surface. The latter effect acts to increase the shift for both absorption and emission at the surface as compared to the bulk. From these results, the intrinsic probe photophysics of tryptophan in proteins is discussed in terms of the properties of the protein/solvent interface and the orientation of the amino acid.

Planar or nonplanar: what is the structure of urea in aqueous solution?

A combined quantum chemical statistical mechanical method has been used to study the solvation of urea in water, with emphasis on the structure of urea. The model system consists of three parts: a Hartree-Fock quantum chemical core, 99 water molecules described with a polarizable force-field, and a dielectric continuum. A free-energy profile along the transition of urea from planar to a nonplanar structure is calculated. This mode in aqueous solution is found to be floppy. That is, the structure of urea in water is not well-defined because the planar to nonplanar transition requires an energy of the order of the thermal energy at room temperature. We discuss the implications of this finding for simulation studies of urea in polar environments like water and proteins.

Formation of ferroelectric domains observed in simulation of droplets of dipolar particles.

In this work it is shown that domains of ordered dipoles are formed in large droplets made from dipolar particles provided that the dipole-dipole interaction between nearest neighbors is larger than the thermal energy. The size of the domains grows almost linearly with the size of the droplets for droplets containing 1000-30 000 particles. The largest domains occupy around 25-35% of the droplet volume. The total dipole moment of a domain is of the order of 3-10% of the maximum dipole moment possible if all dipoles in the domain were parallel. The finding offers an explanation to the observation that different boundary conditions yield different long-range order for dipolar liquids and challenges the present view of a short-range dipolar order in polar solvents.

Many-Body Polarization, a Cause of Asymmetric Solvation of Ions and Quadrupoles.

Three models are used to study the effect of many-body polarization in the solvation of non-dipolar molecules and ions in water. Two of the models are very simplified and are used to show a number of basic principles of correlation of solvent degrees of freedom and asymmetric solvent structures. These principles are used to interpret results from the third model: an accurate simulation of para-benzoquinone (PBQ) in aqueous solution with a combined quantum chemical statistical mechanical solvent model with an explicit solvent. It is found that nonzero polarizability of PBQ introduces correlation in the solvent degrees of freedom through the many-body nature of the polarization. The fluctuating electric field from the solvent on the solute increases in magnitude with the correlation. Solvent effects are hence modified. This correlation is not described within the mean-field approximation. In practice, the correlation will show up as an increased probability for asymmetric solvation of the molecule.