On phase-equilibria in molecules

Roman F Nalewajski

doi:10.1007/s10910-013-0280-2

Abstract

Information theory (IT) is applied to explore electronic phase-equilibria in molecules. The modulus and phase parts of electronic states, giving rise to the particle probability and current densities, respectively, delineate two basic degrees-of-freedom in the generalized (quantum) IT treatment of molecular states. The classical and non-classical contributions to the resultant information content are accounted for in the complementary Shannon and Fisher measures. These quantum descriptors are then applied in the “vertical” information principles, which determine the density-constrained molecular equilibria. A close parallelism between the vertical maximum-entropy and minimum-energy principles of quantum mechanics and their thermodynamic analogs is emphasized. The relation between the probability and phase distributions in the “horizontal” (probability-unconstrained) equilibria is examined and solutions of the (energy-unconstrained) orbital variational rules for the extremum entropy/information are shown to involve the spatial phase related to electron density. Selected properties of such molecular equilibrium states are explored.

Highlights

The information theory (IT) [1,2,3,4,5,6,7,8] is one of the youngest branches of the applied probability theory in which the probability ideas have been introduced into the fieldR
J Math Chem (2014) 52:588–612 of communication, control, and data processing. These classical information concepts have been successfully applied to explore the molecular electron probabilities and the system chemical bonds, e.g., [9,10,11,12,13,14,15,16,17,18,19,20]. Both the electron density or its shape factor, the probability distribution determined by the wave-function modulus, and the system current distribution, related to the gradient of the wavefunction phase, contribute to the resultant information content of molecular states
In what follows we examine the associated solutions of the complementary energyunconstrained entropy/information principles for the system equilibrium phase

Summary

Introduction

The information theory (IT) [1,2,3,4,5,6,7,8] is one of the youngest branches of the applied probability theory in which the probability ideas have been introduced into the field. The system electron distribution, related to the wave-function modulus, reveals the probability (classical) aspect of the molecular information content [1,2,3,4,5,6], while the phase(current) facet of the molecular state gives rise to the quantum (non-classical) entropy/information terms [9,10,21,22]. Together these two contributions allow one to monitor the full information content of the non-equilibrium (variational) quantum states, providing the complete information description of their evolution towards the final equilibrium

Molecular equilibria

N-electron extension

Conclusion