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Information distance analysis of molecular electron densities
Author(s) -
Nalewajski Roman F.,
Świtka Elžbieta,
Michalak Artur
Publication year - 2002
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.10100
Subject(s) - chemistry , entropy (arrow of time) , statistical physics , electron density , configuration entropy , kullback–leibler divergence , charge density , molecule , electron , atomic physics , physics , quantum mechanics , mathematics , statistics
The information‐theoretic basis of the Hirshfeld partitioning of the molecular electronic density into the densities of the “stockholder” atoms‐in‐molecules (AIM) is summarized. It is argued that these AIM densities minimize both the directed divergence (Kullback–Leibler) and divergence (Kullback) measures of the entropy deficiency between the AIM and their free atom analogs of the promolecule. The local equalization of the information distance densities of the Hirshfeld components, at the local value of the corresponding global entropy deficiency density, is outlined and several approximate relations are established between the alternative local measures of the missing information and the familiar function of a difference between the molecular and promolecule densities. Various global (of the system as a whole) and atomic measures of the entropy deficiency or the displacements relative to the isoelectronic promolecule, defined for densities or probabilities (shape functions) in both the local resolution and the Hirshfeld AIM discretization, are introduced and tested. This analysis is performed also for the valence electron (frozen‐core) approximation. Illustrative results for representative linear molecules, including diatomics, triatomics, and tetraatomics, are reported. They are interpreted as complementary characteristics of changes in the net AIM charge distribution and of the displacements in the information content of the electron distributions of bonded atoms. These numerical results confirm the overall similarity of the stockholder AIM to their free atom analogs and reflect the information displacements due to the AIM polarization and charge transfer in molecules. They also demonstrate the semiquantitative nature of the approximate relations established between the entropy deficiency densities and the related functions involving the density difference function. This development extends the range of interpretations based on the density difference diagrams into probing the associated information displacements in a molecule accompanying the formation of the chemical bonds. © 2002 John Wiley & Sons, Inc. Int J Quantum Chem, 2002