Scaleadaptive tensor algebra for local manybody methods of electronic structure theory
Abstract
While the formalism of multiresolution analysis (MRA), based on wavelets and adaptive integral representations of operators, is actively progressing in electronic structure theory (mostly on the independentparticle level and, recently, secondorder perturbation theory), the concepts of multiresolution and adaptivity can also be utilized within the traditional formulation of correlated (manyparticle) theory which is based on second quantization and the corresponding (generally nonorthogonal) tensor algebra. In this paper, we present a formalism called scaleadaptive tensor algebra (SATA) which exploits an adaptive representation of tensors of manybody operators via the local adjustment of the basis set quality. Given a series of locally supported fragment bases of a progressively lower quality, we formulate the explicit rules for tensor algebra operations dealing with adaptively resolved tensor operands. The formalism suggested is expected to enhance the applicability and reliability of local correlated manybody methods of electronic structure theory, especially those directly based on atomic orbitals (or any other localized basis functions).
 Authors:
 ORNL
 Publication Date:
 Research Org.:
 Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Oak Ridge Leadership Computing Facility (OLCF)
 Sponsoring Org.:
 USDOE
 OSTI Identifier:
 1136372
 DOE Contract Number:
 DEAC0500OR22725
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: International Journal of Quantum Chemistry
 Country of Publication:
 United States
 Language:
 English
Citation Formats
Liakh, Dmitry I. Scaleadaptive tensor algebra for local manybody methods of electronic structure theory. United States: N. p., 2014.
Web. doi:10.1002/qua.24732.
Liakh, Dmitry I. Scaleadaptive tensor algebra for local manybody methods of electronic structure theory. United States. doi:10.1002/qua.24732.
Liakh, Dmitry I. 2014.
"Scaleadaptive tensor algebra for local manybody methods of electronic structure theory". United States.
doi:10.1002/qua.24732.
@article{osti_1136372,
title = {Scaleadaptive tensor algebra for local manybody methods of electronic structure theory},
author = {Liakh, Dmitry I},
abstractNote = {While the formalism of multiresolution analysis (MRA), based on wavelets and adaptive integral representations of operators, is actively progressing in electronic structure theory (mostly on the independentparticle level and, recently, secondorder perturbation theory), the concepts of multiresolution and adaptivity can also be utilized within the traditional formulation of correlated (manyparticle) theory which is based on second quantization and the corresponding (generally nonorthogonal) tensor algebra. In this paper, we present a formalism called scaleadaptive tensor algebra (SATA) which exploits an adaptive representation of tensors of manybody operators via the local adjustment of the basis set quality. Given a series of locally supported fragment bases of a progressively lower quality, we formulate the explicit rules for tensor algebra operations dealing with adaptively resolved tensor operands. The formalism suggested is expected to enhance the applicability and reliability of local correlated manybody methods of electronic structure theory, especially those directly based on atomic orbitals (or any other localized basis functions).},
doi = {10.1002/qua.24732},
journal = {International Journal of Quantum Chemistry},
number = ,
volume = ,
place = {United States},
year = 2014,
month = 1
}

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