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At least 19 recordsLinked to original sources
arXiv1995

Monte-Carlo studies of bosonic van der Waals clusters

In a previous paper (http://www.phys.uri.edu/people/nightingale/publications.html, chem-ph/9406003) we developed a form of variational trial wave function and applied it to van der Waals clusters: five or less atoms of Ar and Ne modeled by the Lennard-Jones potential. In addition, we tested the trial functions for a hypothetical, light atom resembling Ne but with only half its mass. We did not study atoms such as He with larger de Boer parameters, i.e., systems in which the zero point energy plays a more important role relative to the potential energy. This is the main purpose of the present paper. In fact, we study clusters to the very limit where the zero-point energy destroys the ground state as a bound state. A simple picture of this un-binding transition predicts the power law with which the energy vanishes as the de Boer parameter approaches its critical value and the power of the divergence of the the size of the clusters in this limit. Our numerical results are in agreement with these predictions.

chem-ph↗
arXiv1996

Theory of DDT in Unconfined Flames

This paper outlines a theoretical approach for predicting the onset of detonation in unconfined turbulent flames which is relevant both to problems of terrestrial combustion and to thermonuclear burning in Type Ia supernovae. Two basic assumuptions are made: 1) the gradient mechanism is the inherent mechanism that leads to DDT in unconfined conditions, and 2) the sole mechanism for preparing the gradient in induction time is by turbulent mixing and local flame quenching. The criterion for DDT is derived in terms of the one-dimensional detonation wave thickness, the laminar flame speed, and the laminar flame thickness in the reactive gas. This approach gives a lower-bound criterion for DDT for conditions where shock preheating, wall effects, and interactions with obstacles are absent. Regions in parameter space where unconfined DDT can and cannot occur are determined. A subsequent paper will address these issues specifically in the astrophysical context.

astro-ph↗
arXiv1994

Monte Carlo Studies of the Orientational Order-Disorder Phase Transition in Solid Ammonium Chloride

Monte Carlo methods are used to study the phase transition in ammonium chloride from the orientationally ordered $δ$ phase to the orientationally disordered $γ$ phase. An effective pair potential is used to model the interaction between ions. Thermodynamic properties are computed in the canonical and isothermal-isobaric ensembles. Each ammonium ion is treated as a rigidly rotating body and the lattice is fixed in the low-temperature CsCl geometry. A simple extension of the Metropolis Monte Carlo method is used to overcome quasiergodicity in the rotational sampling. In the constant-$NVT$ calculations the lattice is held rigid; in the constant-$NpT$ calculations the lattice parameter is allowed to fluctuate. In both ensembles the order parameter rapidly falls to zero in the range (200 - 250)K, suggesting that the model disorders at a temperature in fair agreement with the experimental disordering temperature (243K). Peaks in the heat capacity and thermal expansivity curves are also found in the same temperature range.

chem-ph↗
arXiv1994

Tests of Dielectric Model Descriptions of Chemical Charge Displacements in Water

A dielectric model of electrostatic solvation is applied to describe potentials of mean force in water along reaction paths for: a) formation of a sodium chloride ion pair; b) the symmetric SN2 exchange of chloride in methylchloride; and c) nucleophilic attack of formaldehyde by hydroxide anion. For these cases simulation and XRISM results are available for comparison. The accuracy of model predictions varies from spectacular to mediocre. It is argued that: a) dielectric models are physical models, even though simplistic and empirical; b) their successes suggest that second-order perturbation theory is a physically sound description of free energies of electrostatic solvation; and c) the most serious deficiency of the dielectric models lies in the definition of cavity volumes. Second-order perturbation theory should therefore be used to refine the dielectric models. These dielectric models make no attempt to assess the role of packing effects but for solvation of classical electrostatic interactions the dielectric models sometimes perform as well as the more detailed XRISM theory.

chem-ph↗
arXiv1994

Optical response of C60 and C70 fullerenes: Exciton and lattice fluctuation effects

Molecular exciton effects in the neutral and maximally doped C60 (C70) are considered using a tight binding model with long-range Coulomb interactions and bond disorder. By comparing calculated and observed optical spectra, we conclude that relevant Coulomb parameters for the doped cases are about half of those of the neutral systems. The broadening of absorption peaks is well simulated by the bond disorder model.

chem-ph↗
arXiv1994

Theoretical calculation of the water ion product K_W

A dielectric solvation model is applied to the prediction of the equilibrium ionization of liquid water over a wide range of density and temperature with the objective of calibrating that model for the study of ionization in water of organic acids, {\it e.g.\/}, proteins and nucleic acids. The model includes an approximate description of the polarizability of the dissociating water molecule. The calculated pK$_W$ are very sensitive to the value of the radii that parameterize the model. The radii required for the spherical molecular volumes of the water molecule in order to fit the experimental ion product are presented and discussed. These radii are larger than those commonly used. They decrease with increasing density as would be guessed but the rate of decrease is slight. They increase with increasing temperature, a variation opposite to what would be guessed if radii were strictly viewed as a distance of closest approach. The molecular theoretical principles that might provide an explanation of the thermodynamic state dependence of these radii are discussed.

chem-ph↗
arXiv1994

Transferable Tight-Binding Potential for Hydrocarbons

A transferable tight-binding potential has been constructed for heteroatomic systems containing carbon and hydrogen. The electronic degree of freedom is treated explicitly in this potential using a small set of transferable parameters which has been fitted to small hydrocarbons and radicals. Transferability to other higher hydrocarbons were tested by comparison with ab initio calculations and experimental data. The potential can correctly reproduce changes in the electronic configuration as a function of the local bonding geometry around each carbon atom. This type of potential is well suited for computer simulations of covalently bonded systems in both gas-phase and condensed-phase systems.

chem-ph↗
arXiv1994

Theoretical Study of Time-Resolved Fluorescence Anisotropy from Coupled Chromophore Pairs

Calculations of time-resolved fluorescence anisotropy from a pair of chromophores coupled by an excitation transfer interaction are presented. For the purpose of investigating the effects of nuclear motion on the energy transfer and anisotropy, an illustrative model is developed that provides each chromophore with a single intramolecular vibrational mode. Account is taken of non-instantaneous excitation and time- and frequency-resolved detection. Effects of excitation pulse duration, detection window duration and frequency resolution, and excitation transfer coupling strength on the time-resolved anisotropy are examined in detail. Effects of vibrational relaxation and dephasing are also examined using a simplified Redfield description of the effects of coupling to a thermal bath.

chem-ph↗
arXiv1994

Funnels, Pathways and the Energy Landscape of Protein Folding: A Synthesis

The understanding, and even the description of protein folding is impeded by the complexity of the process. Much of this complexity can be described and understood by taking a statistical approach to the energetics of protein conformation, that is, to the energy landscape. The statistical energy landscape approach explains when and why unique behaviors, such as specific folding pathways, occur in some proteins and more generally explains the distinction between folding processes common to all sequences and those peculiar to individual sequences. This approach also gives new, quantitative insights into the interpretation of experiments and simulations of protein folding thermodynamics and kinetics. Specifically, the picture provides simple explanations for folding as a two-state first-order phase transition, for the origin of metastable collapsed unfolded states and for the curved Arrhenius plots observed in both laboratory experiments and discrete lattice simulations. The relation of these quantitative ideas to folding pathways, to uni-exponential {\em vs.} multi-exponential behavior in protein folding experiments and to the effect of mutations on folding is also discussed. The success of energy landscape ideas in protein structure prediction is also described. The use of the energy landscape approach for analyzing data is illustrated with a quantitative analysis of some recent simulations, and a qualitative analysis of experiments on the folding of three proteins. The work unifies several previously proposed ideas concerning the mechanism protein folding and delimits the regions of validity of these ideas under different thermodynamic conditions.

chem-ph↗
arXiv1995

Chemistry of Nanoscale Semiconductor Clusters

The ground state structures of small silicon clusters are determined through exhaustive tight-binding molecular dynamics simulation studies. These simulations revealed that \Si{11} is an icosahedron with one missing cap, \Si{12} is a complete icosahedron, \Si{13} is a surface capped icosahedron, \Si{14} is a 4-4-4 layer structure with two caps, \Si{15} is a 1-5-3-5-1 layer structure, and \Si{16} is a partially closed cage consisting of five-membered rings. The characteristic feature of these clusters is that they are all surface. Smalley and co-workers discovered that chemisorption reactivities of silicon clusters vary over three orders of magnitude as a function of cluster size. In particular, they found that \Si{33}, \Si{39}, and \Si{45} clusters are least reactive towards various reagents compared to their immediate neighbors in size. We provide insights into this observed reactivity pattern through our stuffed fullerene model. This structural model consists of bulk-like core of five atoms surrounded by fullerene-like surface. Reconstruction of the ideal fullerene geometry gives rise to four-fold coordinated crown atoms and $π$-bonded dimer pairs. This model yields unique structures for \Si{33}, \Si{39}, and \Si{45} clusters without any dangling bonds and thus explains their lowest reactivity towards chemisorption of closed shell reagents. We also explain why a) these clusters are substantially unreactive compared to bulk surfaces and b) dissociative chemisorption occurs on bulk surfaces while molecular chemisorption occurs on cluster surfaces. Finally, experiments on Si$_x$X$_y$ (X = B, Al, Ga, P, As, AlP, GaAs) are suggested as a means of verifying the proposed model.

chem-ph↗
arXiv1996

On a Thomas-Fermi model of "hollow" atom

A Thomas-Fermi model of a spherical shell of positive charge is investigated, under various boundary conditions. The electron distribution and the ionization charge are given particular attention.

chem-ph↗
arXiv1996

A Variational Approach to the Structure and Thermodynamics of Linear Polyelectrolytes with Coulomb and Screened Coulomb Interactions

A variational approach, based on a discrete representation of the chain, is used to calculate free energy and conformational properties in polyelectrolytes. The true bond and Coulomb potentials are approximated by a trial isotropic harmonic energy containing force constants between {\em all}monomer-pairs as variational parameters. By a judicious choice of representation and the use of incremental matrix inversion, an efficient and fast-convergent iterative algorithm is constructed, that optimizes the free energy. The computational demand scales as $N^3$ rather than $N^4$ as expected in a more naive approach. The method has the additional advantage that in contrast to Monte Carlo calculations the entropy is easily computed. An analysis of the high and low temperature limits is given. Also, the variational formulation is shown to respect the appropriate virial identities.The accuracy of the approximations introduced are tested against Monte Carlo simulations for problem sizes ranging from $N=20$ to 1024. Very good accuracy is obtained for chains with unscreened Coulomb interactions. The addition of salt is described through a screened Coulomb interaction, for which the accuracy in a certain parameter range turns out to be inferior to the unscreened case. The reason is that the harmonic variational Ansatz becomes less efficient with shorter range interactions. As a by-product a very efficient Monte Carlo algorithm was developed for comparisons, providing high statistics data for very large sizes -- 2048 monomers. The Monte Carlo results are also used to examine scaling properties, based on low-$T$ approximations to end-end and monomer-monomer separations. It is argued that the former increases faster than linearly with the number of bonds.

chem-ph↗
arXiv1994

Recent Developments in Supersymmetric Quantum Mechanics

Some recent results in supersymmetric quantum mechanics are presented. New semi-classical approximation formulas for Witten's realization of supersymmetric quantum mechanics are discussed. Implications of the supersymmetric structure of Pauli's Hamiltonian are also considered. In particular, the paramagnetisation of a non-interacting electron gas is related to a modified version of Witten's index. We also show that the supersymmetry in this system provides a new counter example for the paramagnetic conjecture.

cond-mat↗
arXiv1995

Coadsorption of Copper and Sulfate on Au(111) Electrodes: Monte Carlo Simulation of a Lattice-Gas Model

We report ground-state calculations and Monte Carlo simulations for a lattice-gas model of the underpotential deposition of copper on Au(111) in sulfate-containing electrolytes. In a potential range of approximately 100$\sim$150 mV, this system exhibits a $(\sqrt3\!\times\!\sqrt3)$ mixed phase with 2/3 monolayer (ML) copper and 1/3 ML sulfate. Our simulation results agree well with experimental results and with other theoretical work.

cond-mat↗
arXiv1995

On thermoelastic phenomena around orientational ordering transition in crystalline C60

Thermoelastic phenomena associated with orientational phase transition in solid C60 are considered. Coupling of the order parameter with elastic strain is analyzed in the Landau theory of phase transitions. Wide range of possible coexistence of the FCC phase with SC one in C60 has been found from 260 K down to critical temperature 160 K of the instability of high-symmetry phase. The specific heat, thermal expansion coefficient and isothermal compressibility for low-symmetry phase are calculated as function of temperature and pressure in an agreement with reported data. Applicability of the Landau theory to ordering transition in fullerenes is discussed.

cond-mat↗
arXiv1995

Exciton effects and nonlinear optical response in soliton lattice states of doped conjugated polymers

Exciton effects on conjugated polymers are investigated in the soliton lattice system. We use the Su-Schrieffer-Heeger model with long-range Coulomb interactions treated by the single-excitation configuration-interaction method. The soliton band is present in the Peierls gap of the doped system. There appears a new kind of the exciton where an electron-hole pair is excited between the soliton band and the continuum states. We find that the oscillator strengths accumulate rapidly at this exciton as the soliton concentration increases. The contribution from the lowest exciton is more than 90% at the 10% doping. The third-harmonic generation (THG) at off-resonance frequencies is calculated as functions of the soliton concentration and the chain length of the polymer. The optical nonlinearity by the THG at the 10% doping increases by the factor about 10^2 from that of the neutral system.

cond-mat↗
arXiv1996

Electronic Structures in C60-Polymers (review)

Variations in the band structures of C60-polymers are studied, when conjugation conditions and the electron number are changed. We use a semiempirical model with the Su-Schrieffer-Heeger type electron-phonon interactions. In the neutral one-dimensional C60-polymer, electronic structures change among direct-gap insulators and the metal, depending on the degree of conjugations. High pressure experiments could observe such pressure-induced metal-insulator transitions. The C60-polymer doped with one electron per one molecule is always a metal. The energy difference between the highest-occupied state and the lowest-unoccupied state of the neutral system becomes smaller upon doping owing to the polaron effects. When the C60-polymer is doped with two electrons per one C60, the system is insulating. When the conjugation in the direction of the polymer chain is smaller, it is a direct-gap insulator. The energy gap becomes indirect when the conjugation is stronger. We also study the antiferromagnetic phase of AC60 by using a tight-binding model with long-range Coulomb interactions. The antiferromagnetism is well described by the model. The comparison with the photoemission studies shows that the new band around the Fermi energy of the AC60 phase can be explaind by the extremely large intrusion of an energy level into the gap of the neutral system. This indicates that the interaction effects among electrons are important in doped C60-polymers.

cond-mat.mtrl-sci↗