Sherwin J. Singer

Density functional theory of nonuniform polyatomic systems. I. General formulation

We extend the density functional theory of nonuniform fluids to the cases of systems composed of polyatomic species. By the method of Legendre transforms, one demonstrates the existence of a free energy density functional where the densities refer to the locations of interaction sites (not full molecular coordinates). A variational principle for the free energy is derived. The methodology retains nearly all the mathematical simplicity of the traditional theory of atomic fluids. Thus, it may provide a practical route to deriving mean field theories of assembly and phase transitions in complex systems. Certain nonlinearities intrinsic to polyatomic systems and absent in simple fluids become apparent in our analysis. These features are associated with the entropy density functional for systems with bonding constraints. They must be carefully assessed in accurate applications.

Free energy functions in the extended RISM approximation

It is shown that the free energies associated with the solutions of extended RISM integral equations can be obtained in closed form thus avoiding the necessity of numerical coupling parameter integrations. In addition, variational principles are deduced which provide a basis for efficient algorithms to solve extended RISM integral equations.

Density functional theory of nonuniform polyatomic systems. II. Rational closures for integral equations

With the density functional theory outlined in paper I, we address and formally solve the nonlinear inversion problem associated with identifying the entropydensity functional for systems with bonding constraints. With this development, we derive a nonlinear integral equation for the average site density fields of a polyatomic system. When external potential fields are set to zero, the integral equation represents a mean field theory for symmetry breaking and thus phase transformations of polyatomic systems. In the united atom limit where the intramolecular interaction sites become coincident, the mean field theory becomes identical to that developed for simple atomic systems by Ramakrishnan, Yussouff, and others. When the external potential fields are particle producing fields (in the sense introduced long ago by Percus), the integral equation represents a theory for the solvation of a simple spherical solute by a polyatomic solvent. In the united atom limit for the solvent, the theory reduces to the hypernetted chain (HNC) integral equation. This reduction is not found with the so‐called ‘‘extended’’ RISM equation; indeed, the extended RISM equation—the theory in which the HNC closure of simple systems is inserted directly into the Chandler–Andersen (i.e., RISM or SSOZ) equation—behaves poorly in the united atom limit. The integral equation derived herein with the density functional approach however suggests a rational closure of the RISM equation which does pass over to the HNC theory in the united atom limit. The new integral equation for pair correlation functions arising from this suggested closure is presented and discussed.

Potential models for simulations of the solvated proton in water

Analytical potential models are designed for simulations of water with excess protons. The potentials describe both intramolecular and intermolecular interactions, and allow dissociation and formation of the species (H2O)nH+. The potentials are parametrized in the form of interactions between H+ and O2− ions, with additional three-body (H–O–H) interaction terms and self-consistent treatment of the polarizability of the oxygen ions. The screening of electrostatic interactions caused by the overlap of the electron clouds in the real molecules is modeled by functions modifying the electric field at short distances. The model was derived by fitting to the potential surface of the H5O2+ ion and other species, as obtained from ab initio MP2 calculations employing an extensive basis set. Emphasis was put on modeling the potential-energy surface for the proton-transfer reaction. Potential-surface profiles, geometry-optimized structures and formation energies of H5O2+, protonated water clusters [H+(H2O)n, n=2–4] a...

Theory of diatomic molecule photodissociation: Electronic angular momentum influence on fragment and fluorescence cross sections

We present a general theory of the photodissociation of diatomic molecules in the presence of nonadiabatic interactions between dissociative electronic states. Nonadiabatic couplings exert a profound influence on the photodissociation process when the molecule dissociates to atoms with nonvanishing electronic angular momentum, even if there are no ordinary curve crossings. Nonadiabatic interactions in this latter situation couple adiabatic molecular states which would otherwise be degenerate at infinite internuclear separation. Methods are developed for properly including nonadiabatic interactions in an exact or approximate calculation of photodissociation transition amplitudes for the production of the atomic fragments in particular fine structure levels. We derive differential cross sections for photofragment production and general expressions describing the detection of fragments by any secondary process, such as spontaneous emission, occurring during or after the breakup of the diatom. These expressio...

On the use of graph invariants for efficiently generating hydrogen bond topologies and predicting physical properties of water clusters and ice

Water clusters and some phases of ice are characterized by many isomers with similar oxygen positions, but which differ in direction of hydrogen bonds. A relationship between physical properties, like energy or magnitude of the dipole moment, and hydrogen bond arrangements has long been conjectured. The topology of the hydrogen bond network can be summarized by oriented graphs. Since scalar physical properties like the energy are invariant to symmetry operations, graphical invariants are the proper features of the hydrogen bond network which can be used to discover the correlation with physical properties. We demonstrate how graph invariants are generated and illustrate some of their formal properties. It is shown that invariants can be used to change the enumeration of symmetry-distinct hydrogen bond topologies, nominally a task whose computational cost scales like N2, where N is the number of configurations, into an N ln N process. The utility of graph invariants is confirmed by considering two water clusters, the (H2O)6 cage and (H2O)20 dodecahedron, which, respectively, possess 27 and 30 026 symmetry-distinct hydrogen bond topologies associated with roughly the same oxygen atom arrangements. Physical properties of these clusters are successfully fit to a handful of graph invariants. Using a small number of isomers as a training set, the energy of other isomers of the (H2O)20 dodecahedron can even be estimated well enough to locate phase transitions. Some preliminary results for unit cells of ice-Ih are given to illustrate the application of our results to periodic systems.

Short H-bonds and spontaneous self-dissociation in (H2O)20: Effects of H-bond topology

There are 30026 symmetry-distinct ways to arrange 20 water molecules in a dodecahedral cage with nearly optimum hydrogen bond lengths and angles, analogous to the arrangements that give rise to the zero-point entropy in ice-Ih. The energy of hydrogen bond isomers in (H2O)20, assumed to be similar in the past, differs by up to 70 kcal/mol. The isomers differ widely in their hydrogen bond lengths, some exhibiting bond lengths as short as ∼2.4 A. The differences among the isomers extends to their chemical properties: In some arrangements one or more water molecules spontaneously self-dissociate, giving rise to spatially separated excess proton and hydroxyl ion units in the cluster. Isomers that exhibit these unusual properties can be identified by features of their hydrogen bond topology.

A density functional treatment of the hard dumbbell freezing transition

We present the first implementation of our density functional theory [J. Chem. Phys. 85, 5971, 5977 (1986)] to investigate a fluid–solid phase transition. In this theory, designed specifically for polyatomic systems, the entropy functional with bonding constraints is treated exactly, and approximations are generated by truncating expansions of the intermolecular interaction part of the free‐energy density functional. We examine the theory resulting from the quadratic truncation of the interaction free energy, and determine the resulting phase diagram for hard dumbbell molecules. The results for short bond lengths are in accord with known trends from experiment and simulation. However, the theory predicts no plastic crystal transition for hard dumbbells with a bond length that might characterize nitrogen, for which the experimental β phase is a plastic crystal. Reasons for this behavior are discussed.

Monte Carlo study of fluid-plastic crystal coexistence in hard dumbbells

The fluid‐cubic plastic crystal coexistence curve for the hard dumbbell model is determined from Monte Carlo simulations. A transition to a stable plastic crystal phase is found for reduced bond lengths L/σ<0.4. A metastable plastic crystal is observed at slightly longer bond lengths. Orientational correlations in both the fully ordered and plastic crystal phase are examined. This is the first calculation of the complete coexistence curve between two phases as a function of particle anisotropy. This information permits detailed comparison with several recent density functional theory predictions for the same transition.

The water–amorphous silica interface: Analysis of the Stern layer and surface conduction

To explain why dynamical properties of an aqueous electrolyte near a charged surface seem to be governed by a surface charge less than the actual one, the canonical Stern model supposes an interfacial layer of ions and immobile fluid. However, large ion mobilities within the Stern layer are needed to reconcile the Stern model with surface conduction measurements. Modeling the aqueous electrolyte-amorphous silica interface at typical charge densities, a prototypical double layer system, the flow velocity does not vanish until right at the surface. The Stern model is a good effective model away from the surface, but cannot be taken literally near the surface. Indeed, simulations show no ion mobility where water is immobile, nor is such mobility necessary since the surface conductivity in the simulations is comparable to experimental values.