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Hierarchies of quantum chemical descriptors induced by statistical analyses of domain occupation number operators

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Abstract
As approximations to the wave functions governing quantum chemical systems become more and more complex, it is becoming increasingly important to devise descriptors that help understand the practical results of those approximations by condensing information in insightful ways. Quantum chemical descriptors that are able to capture the statistical signatures of quantum chemical interactions provide such conceptual building blocks. Central to an understanding of these descriptors is the concept of a "domain occupation number operator," which allows the so-called "real space" and Hilbert space partitionings to be treated on the same footing. Many of the existing descriptors can be expressed as the (central) densities and density cumulants associated with the domain operators. These densities can be obtained by successive differentiation of generating functions, effectively structuring domain associated densities into hierarchies. Not only do the resulting hierarchies indicate how many of the previously reported descriptors are related, they also show which areas have not yet been explored. This article is categorized under: Electronic Structure Theory > Ab Initio Electronic Structure Methods
Keywords
MAXIMUM PROBABILITY DOMAINS, MANY-PARTICLE SYSTEMS, ELECTRON, LOCALIZATION FUNCTION, MULTICENTER BOND INDEXES, REAL-SPACE, HARTREE-FOCK, DELOCALIZATION INDEXES, POPULATION ANALYSIS, DENSITY-MATRICES, VALENCE INDEXES, (de)localization and fluctuation, domains, moments and cumulants, occupation number operator, quantum chemical descriptors

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MLA
Acke, Guillaume, et al. “Hierarchies of Quantum Chemical Descriptors Induced by Statistical Analyses of Domain Occupation Number Operators.” WILEY INTERDISCIPLINARY REVIEWS-COMPUTATIONAL MOLECULAR SCIENCE, vol. 10, no. 4, 2020, doi:10.1002/wcms.1456.
APA
Acke, G., De Baerdemacker, S., Martin Pendas, A., & Bultinck, P. (2020). Hierarchies of quantum chemical descriptors induced by statistical analyses of domain occupation number operators. WILEY INTERDISCIPLINARY REVIEWS-COMPUTATIONAL MOLECULAR SCIENCE, 10(4). https://doi.org/10.1002/wcms.1456
Chicago author-date
Acke, Guillaume, Stijn De Baerdemacker, Angel Martin Pendas, and Patrick Bultinck. 2020. “Hierarchies of Quantum Chemical Descriptors Induced by Statistical Analyses of Domain Occupation Number Operators.” WILEY INTERDISCIPLINARY REVIEWS-COMPUTATIONAL MOLECULAR SCIENCE 10 (4). https://doi.org/10.1002/wcms.1456.
Chicago author-date (all authors)
Acke, Guillaume, Stijn De Baerdemacker, Angel Martin Pendas, and Patrick Bultinck. 2020. “Hierarchies of Quantum Chemical Descriptors Induced by Statistical Analyses of Domain Occupation Number Operators.” WILEY INTERDISCIPLINARY REVIEWS-COMPUTATIONAL MOLECULAR SCIENCE 10 (4). doi:10.1002/wcms.1456.
Vancouver
1.
Acke G, De Baerdemacker S, Martin Pendas A, Bultinck P. Hierarchies of quantum chemical descriptors induced by statistical analyses of domain occupation number operators. WILEY INTERDISCIPLINARY REVIEWS-COMPUTATIONAL MOLECULAR SCIENCE. 2020;10(4).
IEEE
[1]
G. Acke, S. De Baerdemacker, A. Martin Pendas, and P. Bultinck, “Hierarchies of quantum chemical descriptors induced by statistical analyses of domain occupation number operators,” WILEY INTERDISCIPLINARY REVIEWS-COMPUTATIONAL MOLECULAR SCIENCE, vol. 10, no. 4, 2020.
@article{8689182,
  abstract     = {As approximations to the wave functions governing quantum chemical systems become more and more complex, it is becoming increasingly important to devise descriptors that help understand the practical results of those approximations by condensing information in insightful ways. Quantum chemical descriptors that are able to capture the statistical signatures of quantum chemical interactions provide such conceptual building blocks. Central to an understanding of these descriptors is the concept of a "domain occupation number operator," which allows the so-called "real space" and Hilbert space partitionings to be treated on the same footing. Many of the existing descriptors can be expressed as the (central) densities and density cumulants associated with the domain operators. These densities can be obtained by successive differentiation of generating functions, effectively structuring domain associated densities into hierarchies. Not only do the resulting hierarchies indicate how many of the previously reported descriptors are related, they also show which areas have not yet been explored. This article is categorized under: Electronic Structure Theory > Ab Initio Electronic Structure Methods},
  articleno    = {e1456},
  author       = {Acke, Guillaume and De Baerdemacker, Stijn and Martin Pendas, Angel and Bultinck, Patrick},
  issn         = {1759-0876},
  journal      = {WILEY INTERDISCIPLINARY REVIEWS-COMPUTATIONAL MOLECULAR SCIENCE},
  keywords     = {MAXIMUM PROBABILITY DOMAINS,MANY-PARTICLE SYSTEMS,ELECTRON,LOCALIZATION FUNCTION,MULTICENTER BOND INDEXES,REAL-SPACE,HARTREE-FOCK,DELOCALIZATION INDEXES,POPULATION ANALYSIS,DENSITY-MATRICES,VALENCE INDEXES,(de)localization and fluctuation,domains,moments and cumulants,occupation number operator,quantum chemical descriptors},
  language     = {eng},
  number       = {4},
  pages        = {29},
  title        = {Hierarchies of quantum chemical descriptors induced by statistical analyses of domain occupation number operators},
  url          = {http://dx.doi.org/10.1002/wcms.1456},
  volume       = {10},
  year         = {2020},
}

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