Fundamental aspects of electrostatic interactions and charge renormalization in electrolyte systems

The consistent inclusion of ion-ion correlations and molecular solvent effects in electrolyte theory can be expressed in a physical formalism, where the particles acquire a renormalized charge density and where they interact electrostatically via a generalized screened Coulomb potential. The latter usually decays for large distances r like a Yukawa function exp(-κr)/r, where 1/κ is the decay length (normally different from the Debye length), but, for smaller r, the screened Coulomb potential is a more complicated function. The resulting electrostatic theory, “Yukawa electrostatics”, differs in many important aspects from ordinary (unscreened) Coulomb electrostatics. In the present paper, we give illustrations and explanations of some important differences between Coulomb and Yukawa electrostatics. The effective “Yukawa charge” of a particle differs from the ordinary Coulombic charge. Furthermore, contributions from multipoles of all orders contribute, in general, to the leading asymptotic term in the potential for large r, which decays like exp(-κr)/r. Thus, the electrostatic potential from, for example, an electroneutral molecule with an internal charge distribution has generally the same range as the potential from an ion. Some implications of these facts are pointed out. The presentation is based on exact statistical mechanical analysis where all particles are treated on the same fundamental level, but the main focus lies on physical consequences and interpretations of the theory. The text was submitted by the author in English.     

Force related atomic multipoles in planar molecules. Derivation of atomic quadrupole and octupole moments

Atomic multipoles as defined by current methods generally do not account for forces in molecules that arise from external electrostatic fields. It is pointed out that such forces and the electrostatic potential that the molecule itself generates are both determined by the molecular multipolar tensors. The latter constitute therefore the fundamental molecular constants that determine the molecular electrostatics apart from polarization. In general the multipolar tensors include contributions from the atomic multipoles and their fluxes. In planar molecules, however, the perpendicular charge flux is zero by symmetry. This gives rise to a (previously introduced) formalism that extracts analytical, force-related, atomic multipoles from the molecular multipolar tensors. This formalism is extended in this work to include force-related (FR) atomic quadrupoles and octupoles in planar molecules. The properties of the FR atomic multipoles, including their perpendicular fluxes, are discussed and some formal theoretical and computational advantages that characterize them are indicated. As an example, the electrostatics of OCS, including the molecular electrostatic potential and the forces on the nuclei due to an external point charge, is discussed.     

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.     

A regularized and renormalized electrostatic coupling Hamiltonian for hybrid quantum-mechanical-molecular-mechanical calculations

We describe a regularized and renormalized electrostatic coupling Hamiltonian for hybrid quantum-mechanical (QM)-molecular-mechanical (MM) calculations. To remedy the nonphysical QM/MM Coulomb interaction at short distances arising from a point electrostatic potential (ESP) charge of the MM atom and also to accommodate the effect of polarized MM atom in the coupling Hamiltonian, we propose a partial-wave expansion of the ESP charge and describe the effect of a s-wave expansion, extended over the covalent radius r(c), of the MM atom. The resulting potential describes that, at short distances, large scale cancellation of Coulomb interaction arises intrinsically from the localized expansion of the MM point charge and the potential self-consistently reduces to 1r(c) at zero distance providing a renormalization to the Coulomb energy near interatomic separations. Employing this renormalized Hamiltonian, we developed an interface between the Car-Parrinello molecular-dynamics program and the classical molecular-dynamics simulation program Groningen machine for chemical simulations. With this hybrid code we performed QM/MM calculations on water dimer, imidazole carbon monoxide (CO) complex, and imidazole-heme-CO complex with CO interacting with another imidazole. The QM/MM results are in excellent agreement with experimental data for the geometry of these complexes and other computational data found in literature.     

An investigation of the image potential at the semiconductor/electrolyte interface employing nonlocal electrostatics

Using recent developments of solid state and surface physics, the image potential (IP) energy is calculated for a test charge situated in an electrolyte near the surface of a doped semiconductor electrode. The effect of the structure of the semiconductor and solvent on the electrostatics is addressed through the static dielectric function ϵ(q). Specifically discussed in light of the results are implications for ion adsorption to the electrode and reorganization energy. At lower ionic strengths (1:1 electrolytes at a maximum of 0.1 M were considered) the IP is found to be a rather sensitive function of the ϵ(q) of both the solvent and SC, and a wide variety of behavior is displayed. In opposition to simplistic classical treatments, image potentials corresponding to repulsion of the charge from the electrode are sometimes found even for highly doped semiconductors. At higher ionic strengths the image potential behavior is predominantly repulsive. The approach shows a host of concerns that have hitherto received little or no consideration for the semiconductor electrode/electrolyte interface. Treatments of the image potential energy for the metal electrode/electrolyte interface have appeared previously and comparisons to this interface are made.     

Solvent-averaged potentials for alkali-, earth alkali-, and alkylammonium halide aqueous solutions

We derive effective, solvent-free ion-ion potentials for alkali-, earth alkali-, and alkylammonium halide aqueous solutions. The implicit solvent potentials are parametrized to reproduce experimental osmotic coefficients. The modeling approach minimizes the amount of input required from atomistic (force field) models, which usually predict large variations in the effective ion-ion potentials at short distances. For the smaller ion species, the reported potentials are composed of a Coulomb and a Weeks-Chandler-Andersen term. For larger ions, we find that an additional, attractive potential is required at the contact minimum, which is related to solvent degrees of freedom that are usually not accounted for in standard electrostatics models. The reported potentials provide a simple and accurate force field for use in molecular dynamics and Monte Carlo simulations of (poly-)electrolyte systems.     

Scalable improvement of SPME multipolar electrostatics in anisotropic polarizable molecular mechanics using a general short‐range penetration correction up to quadrupoles

We propose a general coupling of the Smooth Particle Mesh Ewald SPME approach for distributed multipoles to a short‐range charge penetration correction modifying the charge‐charge, charge‐dipole and charge‐quadrupole energies. Such an approach significantly improves electrostatics when compared to ab initio values and has been calibrated on Symmetry‐Adapted Perturbation Theory reference data. Various neutral molecular dimers have been tested and results on the complexes of mono‐ and divalent cations with a water ligand are also provided. Transferability of the correction is adressed in the context of the implementation of the AMOEBA and SIBFA polarizable force fields in the TINKER‐HP software. As the choices of the multipolar distribution are discussed, conclusions are drawn for the future penetration‐corrected polarizable force fields highlighting the mandatory need of non‐spurious procedures for the obtention of well balanced and physically meaningful distributed moments. Finally, scalability and parallelism of the short‐range corrected SPME approach are addressed, demonstrating that the damping function is computationally affordable and accurate for molecular dynamics simulations of complex bio‐ or bioinorganic systems in periodic boundary conditions. © 2016 Wiley Periodicals, Inc.     

Atomic forces for geometry‐dependent point multipole and Gaussian multipole models

In standard treatments of atomic multipole models, interaction energies, total molecular forces, and total molecular torques are given for multipolar interactions between rigid molecules. However, if the molecules are assumed to be flexible, two additional multipolar atomic forces arise because of (1) the transfer of torque between neighboring atoms and (2) the dependence of multipole moment on internal geometry (bond lengths, bond angles, etc.) for geometry‐dependent multipole models. In this study, atomic force expressions for geometry‐dependent multipoles are presented for use in simulations of flexible molecules. The atomic forces are derived by first proposing a new general expression for Wigner function derivatives . The force equations can be applied to electrostatic models based on atomic point multipoles or Gaussian multipole charge density. Hydrogen‐bonded dimers are used to test the intermolecular electrostatic energies and atomic forces calculated by geometry‐dependent multipoles fit to the ab initio electrostatic potential. The electrostatic energies and forces are compared with their reference ab initio values. It is shown that both static and geometry‐dependent multipole models are able to reproduce total molecular forces and torques with respect to ab initio, whereas geometry‐dependent multipoles are needed to reproduce ab initio atomic forces. The expressions for atomic force can be used in simulations of flexible molecules with atomic multipoles. In addition, the results presented in this work should lead to further development of next generation force fields composed of geometry‐dependent multipole models. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2010     

Effects of the Bead‐Solvent Interaction on the Dynamics of Macromolecules, 1

Summary: Hamiltonian dynamics and a chain model are used to study the dynamics of macromolecules immersed in a solution. From the Hamiltonian of the overall system, “macromolecule + solvent,” a master and a Fokker‐Planck equation are then derived for the phase‐space distribution of the macromolecule. In the Fokker‐Planck equation, all the information about the interaction among the beads of the macromolecule as well as the effects of the surrounding solvent is described by friction tensors, which are expressed in terms of the bead‐solvent interaction and the dynamic structure factor of the solvent. To explore the influence of the bead‐solvent potential on the dynamics of macromolecules, the friction tensors are calculated for a dumbbell molecule and for three choices of the interaction (Yukawa, Born‐Mayer, and Lennard‐Jones). Expressions are derived, in particular, for the friction tensor coefficients of the center‐of‐mass and the relative coordinates of the dumbbell. For the long‐term behaviour of the internal momentum autocorrelation function, moreover, an “algebraic decay” is found, in contrast to the (unphysical) exponential decay as known from phenomenological theory.

Yukawa, Born‐Mayer and Lennard‐Jones bead‐solvent interaction potentials.     

Atomic partitioning of two-center potentials for slater basis

In a previous paper we have shown that the long-range potential generated by the two-center distributions can be written as a sum of two multipolar expansions centered at the terminal atoms and defined so that the two series of multipoles be minimal. In this paper we show that both charge distributions and short-range potentials can also be separated in atomic contributions in a way consistent with the above mentioned partition of the long-range potentials.     

Series approach to modeling ion size effects for asymmetric electrolytes in the diffuse double layer

The theory of the diffuse layer for asymmetric electrolytes is reconsidered with emphasis on the effects of ion size on the diffuse layer potential drop and differential capacity. For asymmetric 2:1 and 1:2 electrolytes, this potential drop is expressed in terms of a polynomial with a linear, quadratic, and cubic term in the corresponding estimate in the Gouy-Chapman theory. Optimal polynomial coefficients and model validation for 2:1 electrolytes are provided by least-squares regression of Monte Carlo data obtained for a restricted electrolyte in a primitive solvent. These coefficients are then expressed as simple functions of the parameters commonly associated with the mean spherical approximation. The series approach accurately describes potential drops and differential capacities of the diffuse layer for 2:1 and 1:2 electrolytes for the chosen assumptions.     

Self-consistent Ornstein-Zernike approximation for the Yukawa fluid with improved direct correlation function

Thermodynamic consistency of the mean spherical approximation as well as the self-consistent Ornstein-Zernike approximation (SCOZA) with the virial route to thermodynamics is analyzed in terms of renormalized gamma-ordering. For continuum fluids, this suggests the addition of a short-ranged contribution to the usual SCOZA direct correlation function, and the shift of the adjustable parameter from the potential term to this new term. The range of this contribution is fixed by imposing consistency with the virial route at the critical point. Comparison of the results of our theory for the hard-core Yukawa potential with the simulation data show very good agreement for cases where the liquid-vapor transition is stable or not too far into the metastable region with respect to the solid state. In the latter case for extremely short-ranged interactions discrepancies arise.     

First-principles calculation of local atomic polarizabilities

Common methods of determining atomic polarizabilities suffer from the inclusion of nonlocal effects such as charge polarization. A new method is described for determining fully ab initio atomic polarizabilities based on calculating the response of atomic multipoles to the local electrostatic potential. The localized atomic polarizabilities are then used to calculate induction energies that are compared to ab initio induction energies to test their usefulness in practical applications. These polarizabilities are shown to be an improvement over the corresponding molecular polarizabilities, in terms of both absolute accuracy and the convergence of the multipolar induction series. The transferability of localized polarizabilities for the alkane series is also discussed.     

Canonical two‐range addition theorem for slater‐type orbitals

The radial Slater‐type orbitals (STO) ${r^\mu }{e^{ - \alpha r}}$ can be simply obtained by repeated parametric differentiation of the Yukawa Potential $({e^{ - \alpha r}}/r)$ with respect to α. A new compact two‐range addition theorem (AdT) for the STO is herein derived by explicit parametric differentiation of the well‐known Yukawa AdT. The resulting addition formula is combined with the single‐range AdT for solid spherical harmonics $({r^l}Y_l^m(\hat r))$ to present a new AdT for three‐dimensional spherical coordinate STOs. We advance the proposition that this formula is “canonical” in the same sense that the Laplace expansion of the Coulomb potential is considered canonical. We demonstrate how this procedure can be employed for all exponential‐type orbitals. © 2012 Wiley Periodicals, Inc.