Paul Siders

A model for orientation effects in electron‐transfer reactions

A method for solving the single‐particle Schrodinger equation with an oblate spheroidal potential of finite depth is presented. The wave functions are then used to calculate the matrix element T_BA which appears in theories of nonadiabatic electron transfer. The results illustrate the effects of mutual orientation and separation of the two centers on TBA. Trends in these results are discussed in terms of geometrical and nodal structure effects. Analytical expressions related to T_BA for states of spherical wells are presented and used to analyze the nodal structure effects for T_BA for the spheroidal wells.

Semiclassical quantization of multidimensional systems

Low order classical perturbation theory is used to obtain semiclassical eigenvalues for a system of three anharmonically coupled oscillators. The results in the low energy region studied here agree well with the ’’exact’’ quantum values. The latter had been calculated by matrix diagonalization using a large basis set.

MOLECULAR HARTREE-FOCK MODEL OF CALCIUM CARBONATE

Abstract Calculated properties of calcium carbonate monomers and dimers are presented. Properties of the dimer are compared to properties of calcite and of the cleavage surface of calcite. Protonation and hydration of calcium carbonate are discussed. The calcium carbonate dimer is a model for some features of the calcite surface.

A simple classical model of infrared multiphoton dissociation

The classical mechanics of a system of two nonlinearly coupled oscillators driven by an oscillating electric field is studied. The presence of quasiperiodic and chaotic motion in the unforced system is shown to influence the nature of energy absorption. Two essentially different types of behavior are observed. In the first, energy is exchanged in a multiply periodic manner between the system and the forcing field. In the second regime, the energy exchange is erratic and a statistical analysis of a family of trajectories shows the role of the chaotic motion in the unforced system in the dissociation process. A theory for rate of photodissociation is presented and results are compared with those obtained from an ensemble of exact classical trajectories.

Conformational free energy of alkylsilanes by nonequilibrium-pulling Monte Carlo simulation

The stationary phase in supercritical fluid chromatography includes alkylsilanes, bearing typically 18-carbon alkane chains, bonded to silica. The silanes are in contact with supercritical carbon dioxide. Interaction of the stationary phase with analytes from the mobile phase depends on conformation of the silanes, whether they form a collapsed layer between the silica and the carbon dioxide or are extended into the carbon dioxide. Although equilibrium conformation of alkylsilanes can be determined by equilibrium Monte Carlo (MC) simulation, that is hampered by slow relaxation of the chains. An alternative is to pull alkylsilanes from collapsed to extended conformations, then calculate free energy change from the Jarzynski equality. This work compares conformational results from equilibrium MC simulation to free energies from nonequilibrium pulling simulations. Because both equilibrium and nonequilibrium simulations are faster for shorter silanes, this work also compares results from 8-carbon and 18-carbon silanes. Free energies from nonequilibrium pulling predict that alkylsilanes tend to bend over and form a layer between silica and carbon dioxide. Results from equilibrium simulations are qualitatively consistent with results from nonequilibrium pulling. Longer-chain silanes have greater tendency to extend slightly into the carbon dioxide.

The Kirkwood superposition approximation for hard rods at high pressure

We examine the influence of the Kirkwood superposition approximation in the Yvon–Born–Green equation for the pair distribution function of a system of hard rods. We construct a linearization of the difference–differential form of the Yvon–Born–Green equation with Kirkwood superposition. By examining the Laplace transform of the linear equation, we construct the pair distribution functions essentially exactly, and predict a threshold for transition from damped to undamped oscillatory pair distribution functions. We show explicitly the closure for which this linear equation is exactly the Yvon–Born–Green equation. We compare the results to those obtained with the exact closure, and to numerical results obtained from the full nonlinear equation with Kirkwood closure. From these studies, we are able to show that it is the long‐range, non‐nearest‐neighbor coupling, present both in the Kirkwood and linearized closures, that is responsible for the transition to undamped oscillatory pair distribution functions in the dimension d=1. We speculate on the relevance of this result to the behavior of the Yvon–Born–Green equation in d=2,3.

Statistical thermodynamics of hard spheres in a narrow cylindrical pore

Statistical thermodynamics of hard spheres in a narrow right-circular cylindrical pore have been studied by the transfer-matrix method. The diameter of the pore is of the order of the particle diameter. The chemical potential and density calculated from the eigenvalues of the transfer operator show that there is no phase transition.

Simulated molecular-scale interaction of supercritical fluid mobile and stationary phases

In supercritical fluid chromatography, molecules from the mobile phase adsorb on the stationary phase. Stationary-phase alkylsilane-terminated silica surfaces might adsorb molecules at the silica, among the silanes, on a silane layer, or in pore space between surfaces. Mobile phases of carbon dioxide, pure and modified with methanol, and stationary phases were simulated at the molecular scale. Classical atomistic force fields were used in Gibbs-ensemble hybrid Monte Carlo calculations. Excess adsorption of pure carbon dioxide mobile phase peaked at fluid densities of 0.002-0.003Å-3. Mobile phase adsorption from 7% methanol in carbon dioxide peaked at lower fluid density. Methanol was preferentially adsorbed from the mixed fluid. Surface silanes prevented direct interaction of fluid-phase molecules with silica. Some adsorbed molecules mixed with tails of bonded silanes; some formed layers above the silanes. Much adsorption occurred by filling the space between surfaces in the stationary-phase model. The distribution in the stationary phase of methanol molecules from a modified fluid phase varied with pressure.

Thermodynamic self-consistency for hard spheres at low density

We consider the conditions on the triplet‐distribution function g(3), and the pair‐distribution g(2), sufficient that thermodynamic quantities calculated from g(2) be state functions. We show that g(3) cannot be, even to first order in density, equivalent to the Kirkwood superposition approximation. We obtain a g(3) that does yield a thermodynamically self‐consistent g(2), to second order in density. We show that this g(2) differs little from the exact g(2), at that order. We also examine the low‐density behavior of a partially self‐consistent closure in which angular correlations appear explicitly. The latter closure is found to describe three‐particle correlations well when two of the particles are in contact. A principal conclusion which follows from these studies is that the criterion of thermodynamic self‐consistency is useful as a constraint in constructing closures, although it does not in itself determine a closure.

Computer quadrature programs for the determination of best-fit acid dissociation and complex formation constants

Abstract Two new computer programs are introduced which determine “best-fit” acid dissociation constants for di-, tri- and tetra-dentate ligands, and “best-fit” complex formation constants for complexes having a maximum order of two, three, or four. The programs find the constants which minimize the numerically integrated area between the experimental and theoretical (Bjerrum) formation curves.