Physical Sciences and Mathematics Commons^™

The Treatment Of Exchange In Path Integral Simulations Via An Approximate Pseudopotential, Randall W. Hall

Randall W. Hall

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 q u a n t i t a t i v e accuracy in two systems: an ideal gas of fermions localized in a three‐dimensional harmonic well and the triplet state of the sodium dimer.

Path Integral Study Of The Correlated Electronic States Of Na4–Na6, Randall W. Hall

Randall W. Hall

Feynman’s path integral formulation of quantum mechanics is used to study the correlated electronic states of Na4–Na6. Two types of simulations are performed: in the first, the nuclei are allowed to move at finite temperature in order to find the most stable geometries. In agreement with previous calculations, we find that planar structures are the most stable and that there is significant vibrational amplitude at finite temperatures, indicating that the Born–Oppenheimer surface is relatively flat. In the second type of simulation, the nuclei are held fixed at symmetric and asymmetric geometries and the correlated electron density is found. Our results …

Simulation Of Electronic And Geometric Degrees Of Freedom Using A Kink-Based Path Integral Formulation: Application To Molecular Systems, Randall Hall

Randall W. Hall

A kink-based path integral method, previously applied to atomic systems, is modified and used to study molecular systems. The method allows the simultaneous evolution of atomic and electronic degrees of freedom. Results for CH4, NH3, and H2O demonstrate this method to be accurate for both geometries and energies. Comparison with DFT and MP2 level calculations show the path integral approach to produce energies in close agreement with MP2 energies and geometries in close agreement with both DFT and MP2 results.

Constructing Explicit Magnetic Analogies For The Dynamics Of Glass Forming Liquids, Jacob D. Stevenson, Aleksandra M. Walczak, Randall W. Hall, Peter G. Wolynes

Randall W. Hall

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 …

Microscopic Theory Of Network Glasses, Randall Hall, Peter Wolynes

Randall W. Hall

A theory of the glass transition of network liquids is developed using self-consistent phonon and liquid state approaches. The dynamical transition and entropy crisis characteristic of random first-order transitions are mapped as a function of the degree of bonding and density. Using a scaling relation for a soft-core model to crudely translate the densities into temperatures, theory predicts that the ratio of the dynamical transition temperature to the laboratory transition temperature rises as the degree of bonding increases, while the Kauzmann temperature falls explaining why highly coordinated liquids are “strong” while van der Waals liquids without coordination are “fragile.”

An Adaptive, Kink-Based Approach To Path Integral Calculations, Randal W. Hall

Randall W. Hall

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 …

Divergence, Recombination And Retention Of Functionality During Protein Evolution, Yanong O. Xu, Randall W. Hall, Richard A. Goldstein, David D. Pollock

Randall W. Hall

We have only a vague idea of precisely how protein sequences evolve in the context of protein structure and function. This is primarily because structural and functional contexts are not easily predictable from the primary sequence, and evaluating patterns of evolution at individual residue positions is also difficult. As a result of increasing biodiversity in genomics studies, progress is being made in detecting context-dependent variation in substitution processes, but it remains unclear exactly what context-dependent patterns we should be looking for. To address this, we have been simulating protein evolution in the context of structure and function using lattice models …

Kink-Based Path Integral Calculations Of Atoms He-Ne, Randall W. Hall

Randall W. Hall

An adaptive, kink-based path integral formalism is used to calculate the ground state energies of the atoms He–Ne. The method uses an adaptive scheme to virtually eliminate the sign difficulties. This is done by using a Monte Carlo scheme to identify states that contribute significantly to the canonical partition function and then include them in the wavefunctions to calculate the canonical averages. The calculations use the 6-31G basis set and obtain both precision and accuracy.

Kink-Based Path Integral Calculations Of Atoms He-Ne, Randall W. Hall

Randall W. Hall

An adaptive, kink-based path integral formalism is used to calculate the ground state energies of the atoms He–Ne. The method uses an adaptive scheme to virtually eliminate the sign difficulties. This is done by using a Monte Carlo scheme to identify states that contribute significantly to the canonical partition function and then include them in the wavefunctions to calculate the canonical averages. The calculations use the 6-31G basis set and obtain both precision and accuracy.

Simulation Of Electronic And Geometric Degrees Of Freedom Using A Kink-Based Path Integral Formulation: Application To Molecular Systems, Randall W. Hall

Randall W. Hall

A kink-based path integral method, previously applied to atomic systems, is modified and used to study molecular systems. The method allows the simultaneous evolution of atomic and electronic degrees of freedom. Results for CH4, NH3, and H2O demonstrate this method to be accurate for both geometries and energies. Comparison with DFT and MP2 level calculations show the path integral approach to produce energies in close agreement with MP2 energies and geometries in close agreement with both DFT and MP2 results.

Constructing Explicit Magnetic Analogies For The Dynamics Of Glass Forming Liquids, Jacob D. Stevenson, Aleksandra M. Walczak, Randall W. Hall, Peter G. Wolynes

Randall W. Hall

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 …

Microscopic Theory Of Network Glasses, Randall W. Hall, Peter G. Wolynes

Randall W. Hall

A theory of the glass transition of network liquids is developed using self-consistent phonon and liquid state approaches. The dynamical transition and entropy crisis characteristic of random first-order transitions are mapped as a function of the degree of bonding and density. Using a scaling relation for a soft-core model to crudely translate the densities into temperatures, theory predicts that the ratio of the dynamical transition temperature to the laboratory transition temperature rises as the degree of bonding increases, while the Kauzmann temperature falls explaining why highly coordinated liquids are “strong” while van der Waals liquids without coordination are “fragile.”

An Adaptive, Kink-Based Approach To Path Integral Calculations, Randal W. Hall

Randall W. Hall

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 …

Divergence, Recombination And Retention Of Functionality During Protein Evolution, Yanong O. Xu, Randall W. Hall, Richard A. Goldstein, David D. Pollock

Randall W. Hall

We have only a vague idea of precisely how protein sequences evolve in the context of protein structure and function. This is primarily because structural and functional contexts are not easily predictable from the primary sequence, and evaluating patterns of evolution at individual residue positions is also difficult. As a result of increasing biodiversity in genomics studies, progress is being made in detecting context-dependent variation in substitution processes, but it remains unclear exactly what context-dependent patterns we should be looking for. To address this, we have been simulating protein evolution in the context of structure and function using lattice models …

Simulation Of Electronic And Geometric Degrees Of Freedom Using A Kink-Based Path Integral Formulation: Application To Molecular Systems, Randall W. Hall

Randall W. Hall

A kink-based path integral method, previously applied to atomic systems, is modified and used to study molecular systems. The method allows the simultaneous evolution of atomic and electronic degrees of freedom. Results for CH4, NH3, and H2O demonstrate this method to be accurate for both geometries and energies. Comparison with DFT and MP2 level calculations show the path integral approach to produce energies in close agreement with MP2 energies and geometries in close agreement with both DFT and MP2 results.

Constructing Explicit Magnetic Analogies For The Dynamics Of Glass Forming Liquids, Jacob D. Stevenson, Aleksandra M. Walczak, Randall W. Hall, Peter G. Wolynes

Randall W. Hall

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 …

An Adaptive, Kink-Based Approach To Path Integral Calculations, Randal W. Hall

Randall W. Hall

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 …

Divergence, Recombination And Retention Of Functionality During Protein Evolution, Yanong O. Xu, Randall W. Hall, Richard A. Goldstein, David D. Pollock

Randall W. Hall

We have only a vague idea of precisely how protein sequences evolve in the context of protein structure and function. This is primarily because structural and functional contexts are not easily predictable from the primary sequence, and evaluating patterns of evolution at individual residue positions is also difficult. As a result of increasing biodiversity in genomics studies, progress is being made in detecting context-dependent variation in substitution processes, but it remains unclear exactly what context-dependent patterns we should be looking for. To address this, we have been simulating protein evolution in the context of structure and function using lattice models …

Computational Studies Of The Role Of Metal Oxides In Combustion-Generated Environmentally Persistent Free Radicals, Randall Hall

Randall W. Hall

No abstract provided.

Density Functional Calculation Of The Structure And Electronic Properties Of CuNON (N = 1−8) Clusters, Gyun-Tack Bae, Randall W. Hall, Barry Dellinger

Randall W. Hall

A Kink-Based Path Integral Method For Multi-Electron Systems, Randall Hall

Randall W. Hall

No abstract provided.

Density Functional Calculation Of The Structure And Electronic Properties Of CuNON (N = 1−4) Clusters, Gyun-Tack Bae, Randall W. Hall

Randall W. Hall

Ab Initio Study Of The Formation And Degradation Reactions Of Chlorinated Phenols, Cheri A. Mcferrin, Randall W. Hall, Barry Dellinger

Randall W. Hall

Intermolecular Forces And The Glass Transition, Randall W. Hall, Peter G. Wolynes

Randall W. Hall

Ab Initio Study Of The Formation And Degradation Reactions Of Semiquinone And Phenoxyl Radicals, Randall W. Hall, Cheri A. Mcferrin, Barry Dellinger

Randall W. Hall

Structural Characterization Of Al10O6IBu16(Μ-H)2, A High Aluminum Content Cluster:  Further Studies Of Methylaluminoxane (Mao) And Related Aluminum Complexes, Feng-Jeng Wu, Larry S. Simeral, Anthony A. Mrse, Jan L. Eilertsen, Lacramioara Negureanu, Zhehong Gan, Frank R. Fronczek, Randall W. Hall, Leslie G. Butler

Randall W. Hall

Formation And Stabilization Of Persistent Free Radicals, Barry Dellinger, Slawomir Lomnicki, Lavrent Khachatryan, Zofia Maskos, Randall W. Hall, Julien Adounkpe, Cheri Mcferrin, Hieu Truong

Randall W. Hall

Methyaluminoxane (Mao) Polymerization Mechanism And Kinetic Model From Ab Initio Molecular Dynamics And Electronic Structure Calculations, Lacramioara Negureanu, Randall W. Hall, Leslie G. Butler, Larry A. Simeral

Randall W. Hall

Ab Initio And 1H Nmr Study Of The Zn(Ii) Complexes Of A Nido- And A Closo-Carboranylporphyrin, Petia Bobadova-Parvanova, Yuko Oku, Anura Wickramasinghe, Randall W. Hall, Graca H. Vicente

Randall W. Hall

Tools And Strategies For Processing Diffusion-Ordered 2d Nmr Spectroscopy (Dosy) Of A Broad, Featureless Resonance: An Application To Methylaluminoxane (Mao), Jan Lasse Eilertsen, Randall W. Hall, Larry S. Simeral, Leslie G. Butler

Randall W. Hall