Minimum-cross-entropy estimation of atomic charge densities from scattering factors

Antolín, J.; Cuchí, J. C.; Angulo, J. C.

doi:10.1088/0953-4075/32/3/003

Cited by 13 publications

(7 citation statements)

References 30 publications

(32 reference statements)

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“…The Kullback‐Leibler divergence or relative entropy 14 is perhaps the most important non symmetric divergence measure in the Information Theory, being defined as which embodies the well known Shannon entropy 1, which constitutes a global measure of the spread of the distribution over its whole domain. The KL divergence, as well as its symmetrized version have been extensively studied and applied in a great variety of fields such as, for instance, minimum cross entropy estimation 36 or indexing and image retrieval 37.…”

Section: Dissimilarity Measures: the Jensen‐shannon Divergencementioning

confidence: 99%

Generalized Jensen divergence analysis of atomic electron densities in conjugated spaces

Angulo

López-Rosa

Antolín

et al. 2010

Int J of Quantum Chemistry

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Several measures of divergence have been used in the past to quantify the dissimilarity between two or more one-particle atomic densities. The advantages and difficulties of them to capture the differences among different atomic systems in the position and momentum spaces are studied. One of these measures, the Jensen-Shannon divergence, is generalized giving rise to a one-parameter divergence, the Jensen-Rényi divergence, here proposed for a deep study of atomic systems, improving the above previous results. The versatility and power of this divergence is applied to compare different neutral atoms, their composing subshells and each of those atomic densities computed within different models. The parameter of the Jensen-Rényi Divergence allows also to emphasize the study in relevant specific regions of both conjugated spaces.

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Section: Dissimilarity Measures: the Jensen‐shannon Divergencementioning

confidence: 99%

Generalized Jensen divergence analysis of atomic electron densities in conjugated spaces

Angulo

López-Rosa

Antolín

et al. 2010

Int J of Quantum Chemistry

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“…The KL divergence constitutes an essential tool within the information theory, as shown by its applications for obtaining minimum cross entropy estimations and for determining atomic [36] and molecular [37] properties, among others. More recent applications include the introduction of an informational quantum dissimilarity measure to study the relativistic effects on the electron density [15], or the employment of KL measures to analyze molecular reaction paths [38].…”

Section: Jensen-shannon and Kullback-leibler Divergencesmentioning

confidence: 99%

Jensen–Shannon and Kullback–Leibler divergences as quantifiers of relativistic effects in neutral atoms

Martín

López-Rosa

Angulo

et al. 2015

Chemical Physics Letters

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“…Especially remarkable is its property of non-negativity, and the minimum null value is reached only for identical distributions ρ 1 = ρ 2 . The KL relative entropy constitutes an essential tool within information theory, as shown by its applications for obtaining minimum cross-entropy estimations and for determining atomic [28] and molecular [29] properties, among others. More recent applications include the introduction of an informational quantum dissimilarity measure to study the relativistic effects on the electron density [16], or the employment of KL measures to analyze molecular reaction paths [30].…”

Section: Jensen-shannon and Jensen-fisher Divergencesmentioning

confidence: 99%

Relativistic global and local divergences in hydrogenic systems: A study in position and momentum spaces

et al. 2014

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Relativistic effects in one-particle densities of hydrogenic systems are quantified by means of global and local density functionals: the Jensen-Shannon and the Jensen-Fisher divergences, respectively. The Schrödinger and Dirac radial densities are compared, providing complementary results in position and momentum spaces. While the electron cloud gets compressed towards the origin in the Dirac case, the momentum density spreads out over its domain, and the raising of minima in position space does not occur in the momentum space. Regarding the dependence on the nuclear charge and the state quantum numbers for all divergences here considered, as well as their mutual interconnection, accurate powerlike laws y ≈ Cx a are found systematically. The parameters {C,a} defining the respective dependences are extremely sensitive to the closeness of the system to the ground and/or the circular state. Particularly interesting are the analyses of (i) the plane subtended by the Jensen-Shannon and Jensen-Fisher divergences, in a given space (position or momentum), and (ii) either of the above two divergences in the position-momentum plane. These kinds of results show the complementary role of global and local divergences and that of both conjugate spaces.

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Minimum-cross-entropy estimation of atomic charge densities from scattering factors

Cited by 13 publications

References 30 publications

Generalized Jensen divergence analysis of atomic electron densities in conjugated spaces

Generalized Jensen divergence analysis of atomic electron densities in conjugated spaces

Jensen–Shannon and Kullback–Leibler divergences as quantifiers of relativistic effects in neutral atoms

Relativistic global and local divergences in hydrogenic systems: A study in position and momentum spaces

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