Summary
Extensions of the "Distributed Approximating Functional” (DAF) approach to approximating functions and their derivatives are given. The method, although inherently approximate, can be made arbitrarily accurate, numerically stable, and computationally efficient by appropriate choice of parameters. It also provides approximate representations of quantum operators which are analytic and which can be accurate. Differences between the DAFs and more standard basis set approaches are discussed in order to clarify the properties of the DAFs. Some illustrative examples are given.
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References
The discrete grid DAF was first introduced in: D.K. Hoffman, N. Nayar, O.A. Sharafeddin and D.J. Kouri, J. Phys. Chem. 95 (1991) 8299; D.K. Hoffman and D.J. Kouri, ibid. 96 (1992) 1179.
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Supported in part under National Science Foundation Grant CHE92-01967.
The Ames Laboratory is operated for the Department of Energy by Iowa State University under Contract No 2-7405-ENG82.
Supported under National Science Foundation Grants CHE-8907429 and CHE-9403416.
Supported under R.A. Welch Foundation Grant E-0608.
Supported under National Science Foundation Grants CHE-8907429 and CHE-9403416.
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Hoffman, D.K., Marchioro, T.L., Arnold, M. et al. Variational derivation and extensions of distributed approximating functionals. J Math Chem 20, 117–140 (1996). https://doi.org/10.1007/BF01165159
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DOI: https://doi.org/10.1007/BF01165159