Entropic concepts in electronic structure theory

Roman F Nalewajski

doi:10.1007/s10698-012-9168-7

Abstract

It is argued that some elusive “entropic” characteristics of chemical bonds, e.g., bond multiplicities (orders), which connect the bonded atoms in molecules, can be probed using quantities and techniques of Information Theory (IT). This complementary perspective increases our insight and understanding of the molecular electronic structure. The specific IT tools for detecting effects of chemical bonds and predicting their entropic multiplicities in molecules are summarized. Alternative information densities, including measures of the local entropy deficiency or its displacement relative to the system atomic promolecule, and the nonadditive Fisher information in the atomic orbital resolution(called contragradience) are used to diagnose the bonding patterns in illustrative diatomic and polyatomic molecules. The elements of the orbital communication theory of the chemical bond are briefly summarized and illustrated for the simplest case of the two-orbital model. The information-cascade perspective also suggests a novel, indirect mechanism of the orbital interactions in molecular systems, through “bridges” (orbital intermediates), in addition to the familiar direct chemical bonds realized through “space”, as a result of the orbital constructive interference in the subspace of the occupied molecular orbitals. Some implications of these two sources of chemical bonds in propellanes, π-electron systems and polymers are examined. The current–density concept associated with the wave-function phase is introduced and the relevant phase-continuity equation is discussed. For the first time, the quantum generalizations of the classical measures of the information content, functionals of the probability distribution alone, are introduced to distinguish systems with the same electron density, but differing in their current(phase) composition. The corresponding information/entropy sources are identified in the associated continuity equations.

Highlights

For the chemical understanding of molecular electronic structure it is vital to interpret the system equilibrium electron density qðrÞ 1⁄4 NpðrÞ in terms of pieces representing the relevant subsystems, e.g., Atoms-in-Molecules (AIM) (Bader 1990), functional groups or other pieces of interest, e.g., the r and p electrons in benzene, and through such intuitive concepts as multiplicities of the internal and external chemical bonds, describing the bonding pattern between these molecular fragments (Nalewajski 2006a, 2010a, 2012a)
In Orbital Communication Theory (OCT), which regards a molecule as the communication network in Atomic Orbital (AO) resolution, with AO constituting both the elementary ‘‘emitters’’ and ‘‘receivers’’ of the electron AOassignment signals, the typical descriptors of the channel average ‘‘noise’’ and the information flow constitute adequate Information Theory (IT) descriptors of the molecular overall entropy covalency and information ionicity, due to all chemical bonds in the system under consideration
By shaping the input signal in these networks and ‘‘reducing’’ (Nalewajski 2006a) the resolution level of these AO probabilities, it is possible to extract the interal and external IT descriptors of specific bonds in molecular fragments, e.g., the localized bond multiplicities of diatomic subsystems, as well as measures of the information coupling between bonds located in different parts of the molecule

Summary

Introduction

For the chemical understanding of molecular electronic structure it is vital to interpret the system equilibrium electron density qðrÞ 1⁄4 NpðrÞ in terms of pieces representing the relevant subsystems, e.g., Atoms-in-Molecules (AIM) (Bader 1990), functional groups or other pieces of interest, e.g., the r and p electrons in benzene, and through such intuitive concepts as multiplicities (orders) of the internal (intra-subsystem) and external (interfragment) chemical bonds, describing the bonding pattern between these molecular fragments (Nalewajski 2006a, 2010a, 2012a). The semantics of these traditional chemical descriptors is not sharply defined in modern quantum mechanics, quite useful definitions are available from several alternative perspectives (Nalewajski 2012a), which reflect the accepted chemical intuition quite well. Since these chemical concepts do not represent specific observables, i.e., specific quantum mechanical operators, they have to be classified as Kantian noumenons of chemistry (Parr et al 2005). This article summarizes the diverse IT perspectives on the molecular electronic structure, in which the molecular states, their electron distributions and probability currents carry the complete information about the system bonding patterns. Some of these chemical characteristics are distinctly ‘‘entropic’’ in character, being primarily designed to reflect the ‘‘pairing’’ patterns between electrons, rather than the molecular energetics

Objectives

Conclusion