Physical interpretation of information entropy: Numerical evidence of the Collins conjecture

Esquivel, Rodolfo O.; Rodríguez, Ana L.; Sagar, Robin P.; Hô, Minhhuy; Smith, Vedene H.

doi:10.1103/physreva.54.259

Cited by 68 publications

(50 citation statements)

References 25 publications

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“…Correlation energy has been related to the entropy of entanglement [2] by Collins [3], and this conjecture has been assessed on a series of light atomic ions by Esquivel et al [4]. Relations with the correlation strength have been also established by Ziesche [5], while many other works have been focused on the link between the nonidempotency of the one-particle density matrix and complexity measures (see, for example, Nagy and Romera [6] and other references therein).…”

Section: Introductionmentioning

confidence: 99%

Shannon Entropy in Atoms: A Test for the Assessment of Density Functionals in Kohn-Sham Theory

Amovilli

Floris

2018

Computation

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Electron density is used to compute Shannon entropy. The deviation from the Hartree-Fock (HF) of this quantity has been observed to be related to correlation energy. Thus, Shannon entropy is here proposed as a valid quantity to assess the quality of an energy density functional developed within Kohn-Sham theory. To this purpose, results from eight different functionals, representative of Jacob's ladder, are compared with accurate results obtained from diffusion quantum Monte Carlo (DMC) computations. For three series of atomic ions, our results show that the revTPSS and the PBE0 functionals are the best, whereas those based on local density approximation give the largest discrepancy from DMC Shannon entropy.

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Section: Introductionmentioning

confidence: 99%

Shannon Entropy in Atoms: A Test for the Assessment of Density Functionals in Kohn-Sham Theory

Amovilli

Floris

2018

Computation

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“…It is natural to use some information-theoretic principle (19)(20)(21)(22)(23)(24)(25)(26) for this purpose. And here is where density-functional theory (DFT) (27,28) helps.…”

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confidence: 99%

Information theory, atoms in molecules, and molecular similarity

Nalewajski

Parr²

2000

Proc. Natl. Acad. Sci. U.S.A.

344

278

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Using information theory, it is argued that from among possible definitions of what an atom is when it is in a molecule, a particular one merits special attention. Namely, it is the atom defined by the “stockholders partitioning” of a molecule invented by Hirshfeld [(1977) Theor. Chim. Acta 44, 129]. The theoretical tool used is the minimum entropy deficiency principle (minimum missing information principle) of Kullback and Liebler [(1951) Ann. Math. Stat. 22, 79]. A corresponding analysis is given of the problem of assessing similarity between molecules or pieces of molecules.

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“…correlation energy and entropy [36][37][38][39][40]. This idea underlies several recent studies, including that by Delle Site that also uses Shannon entropic indices albeit directly on the electron density [41][42][43].…”

Section: Theoretical Aspectsmentioning

confidence: 93%

Performance of Shannon-entropy compacted N-electron wave functions for configuration interaction methods

et al. 2016

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Physical interpretation of information entropy: Numerical evidence of the Collins conjecture

Cited by 68 publications

References 25 publications

Shannon Entropy in Atoms: A Test for the Assessment of Density Functionals in Kohn-Sham Theory

Shannon Entropy in Atoms: A Test for the Assessment of Density Functionals in Kohn-Sham Theory

Information theory, atoms in molecules, and molecular similarity

Performance of Shannon-entropy compacted N-electron wave functions for configuration interaction methods

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