Journal of Mathematical Chemistry
, Volume 51, Issue 1, pp 297315
First online:
Entropic representation in the theory of molecular electronic structure
 Roman F. NalewajskiAffiliated withDepartment of Theoretical Chemistry, Jagiellonian University Email author
Abstract
The entropic perspective on the molecular electronic structure is investigated. Informationtheoretic description of electron probabilities is extended to cover the complex amplitudes (wave functions) of quantum mechanics. This analysis emphasizes the entropic concepts due to the phase part of electronic states, which generates the probability current density, thus allowing one to distinguish the information content of states generating the same electron density and differing in their current densities. The classical information measures of Fisher and Shannon, due to the probability/density distributions themselves, are supplemented by the nonclassical terms generated by the wavefunction phase or the associated probability current. A complementary character of the Fisher and Shannon information measures is explored and the relationship between these classical information densities is derived. It is postulated to characterize also their nonclassical (phase/currentdependent) contributions. The continuity equations of the generalized information densities are examined and the associated nonclassical information sources are identified. The variational rules involving the quantumgeneralized Shannon entropy, which generate the stationary and timedependent Schrödinger equations from the relevant maximum entropy principles, are discussed and their implications for the system “thermodynamic” equilibrium states are examined. It is demonstrated that the lowest, stationary “thermodynamic” state differs from the true ground state of the system, by exhibiting the spacedependent phase, linked to the modulus part of the wave function, and hence also a nonvanishing probability current.
Keywords
Electronic structure theory Information continuity equations Maximum entropy principle Nonclassical entropy Quantum Fisher information Quantum mechanics Schrödinger equation “Thermodynamic” states Title
 Entropic representation in the theory of molecular electronic structure
 Open Access
 Available under Open Access This content is freely available online to anyone, anywhere at any time.
 Journal

Journal of Mathematical Chemistry
Volume 51, Issue 1 , pp 297315
 Cover Date
 201301
 DOI
 10.1007/s1091001200849
 Print ISSN
 02599791
 Online ISSN
 15728897
 Publisher
 Springer Netherlands
 Additional Links
 Topics
 Keywords

 Electronic structure theory
 Information continuity equations
 Maximum entropy principle
 Nonclassical entropy
 Quantum Fisher information
 Quantum mechanics
 Schrödinger equation
 “Thermodynamic” states
 Industry Sectors
 Authors

 Roman F. Nalewajski ^{(1)}
 Author Affiliations

 1. Department of Theoretical Chemistry, Jagiellonian University, R. Ingardena 3, 30060, Cracow, Poland