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In this paper we report detailed theoretical studies of formic acid-water clusters using a Gaussian implementation of Kohn-Sham density functional theory (DFT). Some MP2 calculations were made when necessary to make comparison. The newly developed Laplacian-dependent (LAP) functionals are extensively used although calculations with other traditional gradient-corrected functionals were also made for comparison. To assess our techniques we studied first the formic acid dimer. Good results for structures, vibrational frequencies and proton transfer barrier heights were achieved by the LAP functionals in contrary to other DFT methods, which usually give extremely low barrier heights. We obtained optimized structures of the formic acid-water clusters with up to 4 waters with many possible minimum energy states. The vibrational frequencies, successive hydration energy as well as the corresponding enthalpy were calculated. The interaction energy between formic acid and water was found to be larger than that of water-water. Ring-type structures are among the lowest in energy. Transition states were located for formic acid-water with various solvation patterns to study the effect of hydration on the proton transfer barrier. The transition state structures are of two fundamental types, i.e., a formic acid anion bound to H[sub 3]O[sup +]- and H[sub 5]O[sup +,sub 2]-centered structures, respectively. The proton transfer barrier is reduced by proper solvation of the transition states, notably to full and proper solvation of the hydrated proton units. [ABSTRACT FROM AUTHOR]

Explicit expressions of the mean spherical approximation (MSA) solvation thermodynamic functions, the Gibbs free energy, energy, enthalpy, entropy, apparent molar heat capacities, and partial molar volume are derived starting from the Helmholtz free energy. The thermodynamic consistency of the MSA solvation thermodynamic functions are discussed. The limiting behavior of the MSA solvation thermodynamic functions is compared to the Born theory. The effect of the solvent structure on the Gibbs and the Helmholtz free energy in the MSA is discussed. The results for alkali and halide ions in water are compared with experimental data. The apparent molar heat capacities at constant volume and pressure, and the partial molar volume are calculated along an isobaric line to the critical region of a dipolar liquid. Some recent experiments on solvation thermodynamics in the critical region are discussed. © 1995 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The density functional calculations using the Perdew nonlocal corrections to exchange and correlation have been carried out for a sequence of hydrated proton clusters. The optimized structures were obtained up to H13O+6. It is found that H3O+ is indeed the central unit in all the lowest energy structures we found. Our results support the argument that the structure with a four-coordinate first solvation shell is very unlikely in small hydrated proton clusters. The density functional calculations with the Perdew nonlocal corrections to exchange and correlation give somewhat shorter hydrogen bond lengths, but slightly longer chemical bond lengths as compared with the post-Hartree–Fock calculations. The harmonic vibrational frequencies and IR intensities of various vibrational modes have been generated for all the structures optimized. Results for small clusters are compared with the high resolution experimental spectroscopy studies of Yeh et al. and Begemann et al. Results for larger clusters are used to interpret the low resolution spectra of Schwartz. Very good accord with experimental results is obtained. The solvent effects on proton transfer energy barriers in clusters have been studied by designing a few model systems. The barrier is found to be very sensitive to the solvent configurations. When the solvent water is replaced by the classical partial charge model, a significant change of the barrier is observed, indicating that a quantitative treatment will ultimately require a good pseudopotential to properly account for the quantum nature of the solvent. A combined density functional and molecular dynamics simulation was used to calculate the proton transfer energy and free energy barrier in aqueous solution. The barrier is found to be 3 kcal/mol higher than in gas phase. Very large solvent fluctuation is observed which may have a significant influence on the reaction rate. [ABSTRACT FROM AUTHOR]

A self contained microscopic theory is described for ion solvation dynamics in dipolar fluids. The theory takes account of inertial and non-Markovian effects which are of critical importance for the fast initial phase of the relaxation of the ion–solvent energy. The theory also includes diffusional effects important at long times. The results obtained are shown to be in good agreement with recent computer simulation studies of ions in Stockmayer solvents. [ABSTRACT FROM AUTHOR]

The effect of ionic polarizability on properties of the electrical double layer is considered by extending a theory of Kusalik and Patey [J. Chem. Phys. 92, 1345 (1990)] to the case of an ion at a distance r from a charged macroion. The reference hypernetted-chain theory is solved for a fully molecular model of the double layer and the results are compared with previous results for an identical model without polarizability and with experimental data for double layers in alkali halide solutions. Polarizability is found to have a large effect on the differential capacitance at high surface charges and to make a substantial contribution to the experimentally observed asymmetry in this quantity. This effect is shown to have its origin, not in any structural change in the double layer, but in the contribution to the potential from the induced polarization of the ions themselves. [ABSTRACT FROM AUTHOR]

An approximate expression is derived for the dielectric function ε(k,ω). The theory includes inertial and non-Markovian effects and is free of adjustable parameters. For the k=0 case, detailed comparisons are made with computer simulation results for dipolar soft-sphere and Stockmayer fluids, and the theory is shown to be qualitatively sound at both low and high frequencies. The present approximation should be very useful in developing a theory of solvation dynamics which properly includes important inertial effects. [ABSTRACT FROM AUTHOR]

The frequency dependent conductivity, σ(ω), of model electrolyte solutions is investigated employing molecular dynamics simulations. Approximate analytical theories are also derived and evaluated. It is found that σ(ω) is generally not a simple function and that its detailed frequency dependence contains much useful information about the structure and dynamics of ionic solutions. By varying molecular and state parameters such as the dipole moment and moment of inertia of the solvent, the ionic charge, the solution density, etc., we are able to obtain a physical interpretation of the behavior of σ(ω). For example, very interesting dynamical solvation effects as well as features associated with ion pairs are identified and described. [ABSTRACT FROM AUTHOR]

The dielectric behavior of model electrolyte solutions is studied by molecular dynamics simulations. For the systems considered, it is found that the zero-frequency dielectric constant depends only on equilibrium properties and that there is no measurable ‘‘kinetic dielectric decrement.’’ A theoretical explanation of the simulation results is presented. It is argued that no kinetic dielectric decrement exists for spherical ions in solvents of arbitrary molecular symmetry. [ABSTRACT FROM AUTHOR]

It has long been thought that the total potential drop V across an isolated electrical double layer must be a monotonically increasing function of the surface charge density σ (i.e., ∂V/∂σ≥0). This result has been ‘‘established’’ by thermodynamic arguments of Landau and Lifshitz [Electrodynamics of Continuous Media (Pergamon, Oxford, 1960)] and by a more recent statistical mechanical method of Blum et al. [J. Chem. Phys. 72, 1902 (1981)]. Here we describe statistical mechanical analyses for both constant and fluctuating charge models. It is shown that the derivation of Blum et al. is in error and that correct statistical mechanical treatments do not determine the sign of ∂V/∂σ. However, some rigorous bounds for related quantities are found. We also point out a mathematical problem in the method of Landau and Lifshitz which appears to invalidate their argument. We conclude that at present there is no rigorous proof that ∂V/∂σ must be positive and that the existence of negative values cannot be ruled out. [ABSTRACT FROM AUTHOR]

General expressions in terms of van Hove time correlation functions are given for the wave vector frequency-dependent dielectric function of multicomponent mixtures. The van Hove functions are obtained by applying the Kerr approximation and the dielectric relaxation at zero wave vector is considered in detail. At this level of theory, the frequency-dependent dielectric constant depends upon the self-reorientational correlation times of the various species involved and upon the equilibrium pair correlation functions. It is shown that if the self-correlation times are assumed to be given by the Stokes–Debye relationship, and if the equilibrium direct correlation functions obey certain relatively weak conditions, then for particles of equal size (i.e., the self-correlation times are the same for all species) the dielectric relaxation behavior can be described by a simple Debye formula with a single concentration-dependent relaxation time. This observation is independent of the number of components, of the concentration, and of the molecular dipole moments of the different species present. It may help explain why for some binary mixtures of polar molecules experimental measurements indicate only a single relaxation channel. The exact Kerr result for binary mixtures is expressed explicitly as the sum of two Lorentzians, and some numerical results are given for solutions of dipolar hard spheres of different diameter. [ABSTRACT FROM AUTHOR]

The dielectric relaxation theory of electrolyte solutions is formulated in terms of solvent–solvent, ion–ion, and ion–solvent van Hove time correlation functions. General wave vector frequency-dependent expressions are given for the longitudinal components of the relevant (i.e., polarization–polarization, current–current, current–polarization, polarization–current) time correlation functions and of the susceptibility, dielectric, and conductivity tensors. The Kerr theory relating the distinct and self parts of the van Hove functions is extended to mixtures of molecular fluids and solved explicitly in the k→0 limit for solutions of spherical ions (assuming that the self part of the van Hove functions is given by Fick’s law) immersed in polar solvents. At this level of theory, the van Hove functions, the time correlation functions and the susceptibilities are all found to depend upon coupled ion–solvent motion. However, the dynamical coupling terms are shown to cancel exactly in the final expressions for the conductivity and dielectric constant yielding relatively simple results. Specifically, the conductivity obtained is independent of frequency and is related to the self diffusion constants of the ions by the Nernst–Einstein expression. If a spherical diffusor model is chosen for the solvent, then the frequency-dependent dielectric constant is given by a Debye-type formula with a concentration dependent relationship connecting the Debye and self reorientational relaxation times of the solvent.These results are discussed in the context of previous theories and experimental observations. It is shown that, although obviously oversimplified, the present theory does qualitatively predict the correct concentration dependence of the observed relaxation times for a number of salt solutions. [ABSTRACT FROM AUTHOR]

Potentials of mean force for pairs of charged and neutral macroparticles immersed in simple dipolar hard sphere and waterlike solvents are obtained using the reference hypernetted-chain theory. In general, the results depend rather strongly upon both the solvent and the size of the macroparticles. For smaller neutral macroparticles, the potential of mean force in both solvents is essentially a short-ranged hydrophobic interaction with very little structure. For larger neutral particles in water, short-ranged structural effects likely due to solvent ordering near the flatter surfaces are evident. For charged macroparticles, the potential of mean force is found to be essentially a superposition of three distinct contributions: a short-ranged structural contribution which clearly depends upon the granular nature of the solvent; a repulsive ‘‘cavity’’ term which decays asymptotically as r-4; and of course there is the long-ranged Coulombic interaction. At intermediate separations, this repulsion is the principal correction to Coulomb’s law and it is shown to be much more important in molecular solvents than predicted by comparable dielectric continuum calculations. Furthermore, it is shown that this contribution can be represented with reasonable accuracy by simple analytical approximations. [ABSTRACT FROM AUTHOR]

Explicit expressions are given for the Fourier–Laplace transform of the van Hove function for fluids of particles interacting through orientation dependent pair potentials. The expressions are obtained from the Kerr approximation together with diffusion models for the self part of the van Hove function and apply at all frequencies and wavelengths. Both spherical (scalar diffusion constants) and nonspherical (tensorial diffusion constants) diffusors are considered and the theory is applied to k-dependent dielectric relaxation and ion solvation dynamics. The required equilibrium structure is obtained using the hypernetted chain (HNC) or reference hypernetted chain (RHNC) theories and Kerr/RHNC(HNC) results are given for fluids of dipolar hard spheres, dipolar hard ellipsoids, and water-like particles. Comparisons are made with earlier work based upon coupling equilibrium theories, such as the mean spherical approximation (MSA) for dipolar hard spheres with a dynamical equation of the Smoluchowski–Vlasov (SV) type. It is shown that for spherical diffusors with the self part of the van Hove function treated at the Fick–Debye level, the SV and Kerr equations are in fact equivalent. However, even for spherical diffusors, the results obtained can differ substantially depending upon the equilibrium theory and/or the molecular model employed. For nonspherical diffusors, the anisotropy of the rotational diffusion tensor can also be an important parameter influencing the k-dependent dielectric relaxation. [ABSTRACT FROM AUTHOR]

This paper is concerned with rotational motion and the coupling between rotational and translational motion in molecular fluids. The van Hove angular space–time correlation function is expanded in a basis set of rotational invariants and some properties of the expansion are discussed. General expressions for collective reorientational time correlation functions and relaxation times are given in terms of the expansion coefficients. It is shown that this expansion allows the Kerr and Vineyard approximations which relate the distinct and self parts of the van Hove function to be cast in tractable form and Fourier–Laplace space solutions can be obtained for all frequencies and wave vectors. General solutions are given as well as explicit results for the simpler but important k=0 case. The dielectric relaxation of polar–nonpolarizable molecules is discussed and both infinite samples and the reaction field boundary conditions sometimes employed in the computer simulation of polar fluids are considered. It is shown that in the Kerr theory the frequency dependent dielectric constant ε(ω) is correctly independent of the boundary conditions applied. This is not true of the Vineyard approximation. Applying the Kerr theory and using a result for the self part of the van Hove function recently given by Caillol, we investigate the dielectric relaxation of both spherical and nonspherical diffusors. The nonspherical model is that of Berne and Pecora and couples the rotational and translational diffusion. It is found that within the Kerr approximation spherical diffusors behave as Debye dielectrics at all frequencies. However, in the nonspherical case ε(ω) can deviate substantially from the Debye result and we conclude that for highly anisotropic diffusors the coupling between rotational and translational motion can significantly contribute to the observed dielectric relaxation. [ABSTRACT FROM AUTHOR]

A model for association in a nonprimitive ionic solution is presented. It consists of a mixture of hard sphere ions and dipoles with sticky interactions. This model can be solved analytically in the mean spherical approximation (MSA). We consider first the case in which the stickinesses between ions, the ion–dipole, and the dipole–dipole have spherical symmetry. In this case, the solution for the unrestricted case is given formally. Much simpler formulas can be obtained in the case of equal ionic sizes, which however are different from the size of the dipole. If the size of ions is equal, and also equal to the size of the dipole, then we get a cubic equation for the ion–dipole parameter b2 and a quadratic equation for ion–ion parameter b. We found that the spherical stickiness between the ion–dipole and the dipole–dipole has very little effect on the directional correlation of the ion–dipole and the dipole–dipole. So we further consider the case in which the stickiness is directional. In this case, the solution is obtained for all equal sizes. Finally we compute the thermodynamic properties. [ABSTRACT FROM AUTHOR]

The previously obtained solution of the mean spherical approximation (MSA) for an arbitrary mixture of ions and dipoles is discussed in the case of the low ionic densities (up to 3 M however). In this case, the solution is obtained by solving a system of only three algebraic equations for three parameters, an ion–ion scaling parameter Γ, an ion–dipole scaling parameter B10, and finally a dipole–dipole parameter b2. The thermodynamic properties, however, are better expressed in terms of a shifted screening parameter Γsj. The pair correlation functions and thermodynamics are discussed. The thermodynamics is known to agree fairly with more accurate theories like the LHNC. An attempt to fit the experimental hydration free energies shows that this simple model overestimates the structure breaking effect of the ions. If we empirically adjust this effect for one ion, then we get a surprisingly good correlation for monovanlent ions. The results for the pair correlation functions for the dipole–dipole and ion–dipole are reasonable. However the ion–ion correlation function exhibits the low density pathology of the MSA. [ABSTRACT FROM AUTHOR]

Activity coefficients are calculated for model aqueous alkali halide solutions. The theoretical results are found to be very sensitive to details of the interionic potential employed and good agreement with experiment is obtained by simply superimposing an additional r -n repulsive interaction upon charged hard sphere potentials. The ‘‘best fits’’ to the experimental data involve interesting changes in the solution structure. In particular, our results suggest that the strong deviations from limiting behavior observed for some alkali halide solutions (e.g., NaCl) are closely associated with structures involving solvent separated as opposed to contact ion pairs. [ABSTRACT FROM AUTHOR]

In this paper the ab initio potential of mean force for the formic acid-water system is calculated in a Monte Carlo simulation using a classical fluctuating charge molecular mechanics potential to guide Monte Carlo updates. The ab initio energies in the simulation are calculated using density-functional theory (DFT) methods recently developed by Salahub et al. [J. Chem. Phys. 107, 6770 (1997)] to describe hydrogen-bonded systems. Importance sampling methods are used to investigate structural changes and it is demonstrated that using a molecular mechanics importance function can improve the efficiency of a DFT simulation by several orders of magnitude. Monte Carlo simulation of the system in a canonical ensemble at T=300 K reveals two chemical processes at intermediate time scales: The rotation of the H[sub 2]O bonded to HCOOH, which takes place on a time scale of 3 ps, and the dissociation of the complex which occurs in 24 ps. It is shown that these are the only important structural "reactions" in the formic acid-water cluster which take place on a time scale shorter than the double transfer of the proton. © 2000 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The structural, vibrational, and electronic properties of solid nitromethane under hydrostatic pressure of up to 20 GPa have been studied using density functional theory. The changes of cell volume, the lattice constants, and the molecular geometry of solid nitromethane under hydrostatic loading are examined, and the bulk modulus B0 and its pressure derivative B0' are fitted from the volume-pressure relation. Our theoretical results are compared with available experiments. The change of electron band gap of nitromethane under high pressure is also discussed. Based on the optimized crystal structures, the vibrational frequencies for the internal and lattice modes of the nitromethane crystal at ambient and high pressures are computed, and the pressure-induced frequency shifts of these modes are discussed.