Randall B. Shirts

Periodic boundary condition induced breakdown of the equipartition principle and other kinetic effects of finite sample size in classical hard-sphere molecular dynamics simulation

We examine consequences of the non-Boltzmann nature of probability distributions for one-particle kinetic energy, momentum, and velocity for finite systems of classical hard spheres with constant total energy and nonidentical masses. By comparing two cases, reflecting walls (NVE or microcanonical ensemble) and periodic boundaries (NVEPG or molecular dynamics ensemble), we describe three consequences of the center-of-mass constraint in periodic boundary conditions: the equipartition theorem no longer holds for unequal masses, the ratio of the average relative velocity to the average velocity is increased by a factor of [N/(N-1)]1/2, and the ratio of average collision energy to average kinetic energy is increased by a factor of N/(N-1). Simulations in one, two, and three dimensions confirm the analytic results for arbitrary dimension.

Noncontact Dipole Effects on Channel Permeation. V. Computed Potentials for Fluorinated Gramicidin

Experimental and theoretical calculations indicate that the dipole moment of the four Trp side chains in gramicidin A (gA) channels modify channel conductance through long-range electrostatic interactions. Electrostatic ion/side-chain interaction energies along the channel were computed with CHARMM using ab initio atom charges for native and 4-, 5-, or 6-fluorinated Trp side chains. The bulk water reaction to the polar side chains was included using the method of images as implemented by, and channel waters in idealized structures were included. Ion/Trp interaction energies were approximately -0.6 kcal/mol throughout the channel for all four of the native Trp pairs. Channel waters produced a modest reduction in the magnitude of interactions, essentially offsetting images representing the bulk water outside the channel. The effects of side-chain fluorination depended on ring position and, to a lesser extent, residue number. Compared with native Trp, 5-fluorination reduces the translocation barrier with minor effects on the exit barrier. In contrast, 6-fluorination primarily reduces exit barrier. 4-Fluorination produces a more complex double-well energy profile. Effects of measured side-chain movements resulting from fluorination or change in lipid bilayer were negligible whereas thermal side chain librations cause large effects, especially in the region of the ion-binding sites.

Conformational Sensitivity of Polyether Macrocycles to Electrostatic Potential: Partial Atomic Charges, Molecular Mechanics, and Conformational Prediction

Molecular recognition (whether by enzymes, the immune system, or chelating ligands) depends critically on molecular conformation. Molecular mechanics predicts energetically favorable molecular conformations by locating low energy conformations using an empirical fit of molecular potential energy as a function of internal coordinates. Molecular mechanics analysis of 18-crown-6 demonstrates that the nonbonded term (primarily the electrostatic part) is the largest contributor to the conformational energy. Nevertheless, common methods of treating the electrostatic interaction for 18-crown-6 yield inconsistent values for conformational energies partly because partial charges assigned to each atom can change with conformation due to through-space inductive effects which are not considered in most molecular mechanics programs. Similar findings from several other groups are reviewed to support our conclusions. We argue for care and caution in predicting conformational preferences of molecules with two or more highly polar atoms. We also discuss the desirability of using an empirical method of partial charge determination such as the charge equilibration algorithm of Rappé and Goddard (or a suitable generalization which includes polarization) as a method of including these effects in molecular mechanics and molecular dynamics calculations.

Semiclassical quantization of a nonintegrable system: Pushing the Fourier method into the chaotic regime

Semiclassical Einstein–Brillouin–Keller (EBK) quantization of the nonintegrable Henon–Heiles Hamiltonian succeeds using the Fourier transform method of Martens and Ezra. Two innovations are required for this success: (1) the use of tunneling corrected quantizing actions obtained from an approximate, one‐dimensional Hamiltonian and (2) exploitation of intermediate‐time approximate quasiperiodicity or ‘‘vague tori’’ wherein the Fourier transform of chaotic motion over 10–100 vibrational periods allows the determination of frequencies and amplitudes which approximate motion during the time interval. Approximate tori, actions, and EBK energy levels are then straightforward. We use an interpolation method to smooth over small resonance zones that are not expected to be important quantum mechanically.

Deviations from the Boltzmann distribution in small microcanonical quantum systems: Two approximate one-particle energy distributions

The Boltzmann distribution, which accurately describes the exponential energy dependence of the canonical ensemble, only describes the distribution of one-particle energies for a microcanonical system in the large system limit. We present two distribution functions which closely approximate the distribution of allowed one-particle energies in weakly coupled microcanonical quantum systems. One function is exact for a set of identical harmonic oscillators. The second function is a generalization of work by Andersen et al. [J. Chem. Phys. 114, 6518 (2001)] and is exact for a system with constant microcanonical heat capacity. We compare these two functions with enumerated probabilities for three model systems. The model system distributions and both approximate functions become exponential for large systems but differ from the Boltzmann distribution most dramatically at high energy, for which states can be considerably less populated than predicted by the Boltzmann distribution. Corrections to the Boltzmann distribution may be important in unimolecular reactions, fragmentation dynamics, and in the spectroscopy of nanoclusters.

Solid + liquid phase equilibria and solid-compound formation for hexafluorobenzene + p-dioxane and + each of several related ethers

Abstract Solid + liquid phase diagrams have been obtained from cooling and warming curves for hexafluorobenzene + p-dioxane and + tetrahydrofuran. An incongruently melting solid addition compound forms with p-dioxane mixtures. No compound forms with tetrahydrofuran. Exploratory measurements show that no compound forms with hexafluorobenzene + tetrahydropyran or + 1,2-dimethoxyethane. The results suggest that compound formation results from a combination of favorable packing geometry and weak eletrostatic interactions rather than from charge-transfer.

Anomalous line shapes caused by charge transfer in low-pressure discharges

Abstract Doppler profiles are calculated for initial velocity distributions after charge transfer collisions. Such profiles are applied to emissions from excited Fe + following Ar + -Fe collisions, assuming an energy-independent cross section. It is shown that exoergic charge transfer processes may give significantly non-Gaussian line shapes with lines that are flatter and wider than would be expected from a Maxwellian distribution. Endoergic charge transfer processes, however, will give Gaussian line shapes with a linewidth described by a temperature only slightly below the source temperature. For exoergic reactions, our results differ slightly from results obtained using an adaptation of the method developed by Biondi and coworkers for dissociative recombination.

Solid + liquid phase equilibria and solid-compound formation in mixtures of phosphorus oxychloride with a Group IVA tetrachloride

Abstract Solid + liquid phase diagrams have been obtained from cooling and warming curves for binary mixtures formed from POCl 3 + SnCl 4 , + GeCl 4 , + SiCl 4 , and + CCl 4 . A congruently melting compound of empirical formula SnCl 4 · 2POCl 3 forms. The other mixtures show no compound formation. Solid solutions form over a considerable part of the composition range for POCl 3 + CCl 4 . Exploratory measurements show no compound formation between SnBr 4 and POCl 3 or Sn(CH 3 ) 4 and POCl 3 . A comparison is made between the experimental freezing curves for SiCl 4 and GeCl 4 in POCl 3 with the curves calculated assuming ideal-mixture behavior. Both mixtures show positive deviations from Raoults law. The deviations are larger for SiCl 4 + POCl 3 suggesting less attraction between unlike molecules than in GeCl 4 + POCl 3 . The lack of compound formation of phosphorus oxychloride with all the tetrachlorides except that of tin and the deviations from ideal-mixture behavior are explained in terms of steric effects and the electron-accepting ability of the Group IVA elements.

Solid/liquid phase equilibria and solid compound formation in mixtures of hexafluorobenzene with nitrogen containing compounds

Thermal methods have been used to determine with high precision the solid/liquid phase equilibria diagrams for mixtures of hexafluorobenzene with N-methylmorpholine, N-methylpiperidine and NN′-dimethylpiperazine. Solid addition compounds form in all three systems. Exploratory measurements show that hexafluorobenzene does not form solid addition compounds with triethylamine, acetonitrile or NN-dimethylacetamide. A comparison of the phase diagrams for a number of systems containing hexafluorobenzene suggests that compound formation with hexafluorobenzene results from a combination of favorable packing geometry and electrostatic interactions.

An improved model to calculate equilibrium constants for formation of peroxy radical–water complexes

Recent experimental results show that the kinetics of some radical–radical reactions important for atmospheric pollution formation are faster when a radical–molecule complex forms as one step in the reaction mechanism. Calculated radical–molecule equilibria are needed to accurately describe the concentrations of complexes formed in these experiments as well as in the atmosphere. Here we report calculation of the equilibrium constant for complexation of hydroperoxy (HO2·) and 2-hydroxyethylperoxy radicals (HOCH2CH2O2·) with one water molecule by directly calculating the canonical partition function of the reactant and product species. We demonstrate the accuracy of the calculation using formation of the water dimer as a test case. Ab initio calculations provide the binding energy, rotational constants, and vibrational frequencies of both monomers and complexes. We demonstrate the failure of the harmonic approximation in the partition function for describing the low-frequency vibrational modes of the complexes. Instead, we model one dissociative hydrogen bond mode using a Lennard-Jones 6–3 potential and the other low-frequency vibrational modes using one- and twofold hindered rotors. The contributions of weakly bound states of the long-range dipole–dipole potential (Lennard-Jones 6–3) and of vibration–rotation coupling are not as important as the contribution of twofold hindered rotors. We also discuss methods for including multiple hydrogen-bonding configurations (local minima) when calculating equilibrium constants for formation of complexes.