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Physical Sciences and Mathematics Commons™
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Full-Text Articles in Physical Sciences and Mathematics
Using Genetic Algorithms To Map First-Principles Results To Model Hamiltonians: Application To The Generalized Ising Model For Alloys, Gus L. W. Hart, Volker Blum, Michael J. Walorski, Alex Zunger
Using Genetic Algorithms To Map First-Principles Results To Model Hamiltonians: Application To The Generalized Ising Model For Alloys, Gus L. W. Hart, Volker Blum, Michael J. Walorski, Alex Zunger
Faculty Publications
The cluster expansion method provides a standard framework to map first-principles generated energies for a few selected configurations of a binary alloy onto a finite set of pair and many-body interactions between the alloyed elements. These interactions describe the energetics of all possible configurations of the same alloy, which can hence be readily used to identify ground state structures and, through statistical mechanics solutions, find finite-temperature properties. In practice, the biggest challenge is to identify the types of interactions which are most important for a given alloy out of the many possibilities. We describe a genetic algorithm which automates this …
How To Choose One-Dimensional Basis Functions So That A Very Efficient Multidimensional Basis May Be Extracted From A Direct Product Of The One-Dimensional Functions: Energy Levels Of Coupled Systems With As Many As 16 Coordinates, Richard Dawes, Tucker Carrington Jr.
How To Choose One-Dimensional Basis Functions So That A Very Efficient Multidimensional Basis May Be Extracted From A Direct Product Of The One-Dimensional Functions: Energy Levels Of Coupled Systems With As Many As 16 Coordinates, Richard Dawes, Tucker Carrington Jr.
Chemistry Faculty Research & Creative Works
In this paper we propose a scheme for choosing basis functions for quantum dynamics calculations. Direct product bases are frequently used. The number of direct product functions required to converge a spectrum, compute a rate constant, etc., is so large that direct product calculations are impossible for molecules or reacting systems with more than four atoms. It is common to extract a smaller working basis from a huge direct product basis by removing some of the product functions. We advocate a build and prune strategy of this type. the one-dimensional (1D) functions from which we build the direct product basis …