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Full-Text Articles in Physical Sciences and Mathematics
Kink-Based Path Integral Calculations Of Atoms He-Ne, Randall W. Hall
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
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
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
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
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
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
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
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
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
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 …