Randall W. Hall

The Aperiodic Crystal Picture and Free Energy Barriers in Glasses

The aperiodic crystal picture associates the glass transition with freezing into a nonperiodic structure. Dynamics in the glassy state involves activated jumps between different aperiodic free energy minima. Activation barriers may be estimated through the use of freezing theory and the theory of dense solids. The results resemble, but are distinct from, free volume theory. Reasonable fits to experimental data are obtained.

Density functional calculation of the structure and electronic properties of Cu(n)O(n) (n = 1-8) clusters.

Ab initio simulations and calculations were used to study the structures and stabilities of copper oxide clusters, Cu(n)O(n) (n = 1-8). The lowest energy structures of neutral and charged copper oxide clusters were determined using primarily the B3LYP/LANL2DZ model chemistry. For n ≥ 4, the clusters are nonplanar. Selected electronic properties including atomization energies, ionization energies, electron affinities, and Bader charges were calculated and examined as a function of n.

Constructing explicit magnetic analogies for the dynamics of glass forming liquids

By defining a spatially varying replica overlap parameter for a supercooled liquid referenced to an ensemble of fiducial liquid state configurations, we explicitly construct a constrained replica free energy functional that maps directly onto an Ising Hamiltonian with both random fields and random interactions whose statistics depend on the liquid structure. Renormalization group results for random magnets when combined with these statistics for the Lennard-Jones glass suggest that discontinuous replica symmetry breaking would occur if a liquid with short range interactions could be equilibrated at a sufficiently low temperature where its mean field configurational entropy would vanish, even though the system strictly retains a finite configurational entropy.

The treatment of exchange in path integral simulations via an approximate pseudopotential

An approximate form that includes the effects of exchange is suggested for the short time propagator used in path integral simulations. The form is inspired physically by the approximation made in Hartree–Fock treatments of atoms and molecules. The approximate propagator is used with quantitative accuracy in two systems: an ideal gas of fermions localized in a three‐dimensional harmonic well and the triplet state of the sodium dimer.

Structure of XeN+ clusters (N=3–30): Simulation and experiment

We present an experimental and computational study of the photoabsorption line shape of XeN+ clusters. Positively charged xenon clusters have a unique feature not seen in lighter rare gas cation clusters: there are two families of isomers whose ground states consist of neutral atoms surrounding either a linear trimer ion core or a linear tetramer ion core. Interconversion of these two isomers is possible at temperatures as low as 60 K. The combination of simulation and experiment demonstrates the existence of these two families of isomers and their manifestation in the photoabsorption spectra. Clusters present, in general, either of the two cores depending on the number of atoms along the axis that contains the ion core.

Electronic properties of small neutral and charged beryllium clusters

We determine the atomic and electronic structures for neutral and singly positively charged beryllium clusters containing from two to six atoms using density functional theory in the local spin density approximation. Ions are moved with a steepest descent method and the electronic wave functions optimized using a fictitious dynamics with simulated annealing, as conceived by Car and Parrinello [Phys. Rev. Lett. 55, 2471 (1985)]. Shell-like orbitals, filling angular momentum states in the order: 1s 1p 2s 1d are obtained. We employ a Mulliken population analysis using an atomic basis to examine how the shell orbitals arise from atomic orbitals. This analysis also allows us to associate the electron density distribution and, in the case of a charged cluster, the distribution of the hole with atomic sites and with regions of overlap between atom pairs. We show quantitatively that the contribution to the bonding density from delocalization of the 1s state is hampered by the appearance of the antibonding 2s stat...

An adaptive, kink-based approach to path integral calculations

A kink-based expression for the canonical partition function is developed using Feynman’s path integral formulation of quantum mechanics and a discrete basis set. The approach is exact for a complete set of states. The method is tested on the 3×3 Hubbard model and overcomes the sign problem seen in traditional path integral studies of fermion systems. Kinks correspond to transitions between different N-electron states, much in the same manner as occurs in configuration interaction calculations in standard ab initio methods. The different N-electron states are updated, based on which states occur frequently during a Monte Carlo simulation, giving better estimates of the true eigenstates of the Hamiltonian.

Solvent Influence on Atomic Spectra: The Effect of Finite Size

Time dependent Hartree theory is used to determine the solvent effect on atomic spectra for a given solvent configuration. Configuration averaging is performed as in the mean spherical approximation, resulting in an upper bound to the polarizability. Comparisons are made with previous, more approximate theories, including path integral treatments. It is found that deviations from previous theories can be significant in certain regimes.

The Exchange Potential in Path Integral Studies: Analytical Justification

We present analytical justification for our previously described exchange pseudopotential. We show how the fermi quantum partition function can be constructed from the Boltzmann (distinguishable particle) wave functions if the states that correspond to like‐spin electrons occupying the same quantum state are excluded. A class of weighting functions that satisfy this constraint approximately is discussed. Our previous pseudopotential falls under this class. Essentially, our pseudopotential forces the unwanted states to have high energy and, hence, to make negligible contribution to the partition function. Exchange potentials of the form discussed in this article should be useful for studying systems where the (allowed) correlated Boltzmann wave functions have negligible amplitude for like‐spin fermion–fermion distances less than the diameter of the individual particle wave packets. For example, in the case of two spin‐up (or spin‐down) fermions, if one fermion is located at r, then ‖Ψ(r,q)‖2 is negligible ...

Tight-binding Simulations of Argon Cation Clusters

A simple, semiempirical model was used to study the ground and excited state properties of argon cation clusters at 60 K. The model is a tight-binding Hamiltonian whose parameters are determined from atomic and diatomic properties. Monte Carlo simulations were used to calculate the average properties of these clusters. The photoabsorption spectrum was in good agreement with previous calculations and experiments. The splitting of the photoabsorption spectrum for clusters with greater than 14 atoms was investigated. The two excited states corresponding to the splitting arise from a 3-atom ion core, perturbed by a 4th atom, with solvation from the remaining atoms. The perturbation of the 3-atom ion core by the 4th atom is of the form ψion core±ψ4. The splitting can be decomposed into a contribution solely from the 4 atom wave functions (75% of the splitting) and to additional solvation stabilization of the low energy excited state over the high energy excited state (25%).