Intrinsic Resolution of Molecular Electronic Wave Functions and Energies in Terms of Quasi-atoms and Their Interactions

Abstract

A general intrinsic energy resolution has been formulated for strongly correlated wave functions in the full molecular valence space and its subspaces. The information regarding the quasi-atomic organization of the molecular electronic structure is extracted from the molecular wave function without introducing any additional postulated model state wave functions. To this end, the molecular wave function is expressed in terms of quasi-atomic molecular orbitals, which maximize the overlap between subspaces of the molecular orbital space and the free-atom orbital spaces. As a result, the molecular wave function becomes the superposition of a wave function representing the juxtaposed nonbonded quasi-atoms and a wave function describing the interatomic electron migrations that create bonds through electron sharing. The juxtaposed nonbonded quasi-atoms are shown to consist of entangled quasi-atomic states from different atoms. The binding energy is resolved as a sum of contributions that are due to quasi-atom formation, quasiclassical electrostatic interactions, and interatomic interferences caused by electron sharing. The contributions are further resolved according to orbital interactions. The various transformations that generate the analysis are determined by criteria that are independent of the working orbital basis used for calculating the molecular wave function. The theoretical formulation of the resolution is quantitatively validated by an application to the C molecule.

Eliminating symmetry problems in electronegativity equalization and correcting self‐interaction errors in conceptual DFT

“…Based on the fact that c‐DFT has accepted the role of ionic structures for calculating bond polarities and net atomic charges, we assume that the localized electron‐pair bond X:Y consists of three main contributions: the covalent X–Y, and the ionic X + Y: − and X: − Y + structures. The total energy of the molecule is not minimized by charge transfer alone, but by the sum of bond energy contributions of all relevant covalent and ionic structures . The relevant structures must be selected according to the strict Wigner‐Witmer rules .…”

“…Mulliken, Ruedenberg, Klopman, Ferreira, Zhang et al, and James et al highlighted the importance of ionic valence‐structures in bonding. Ionic structures introduce intra‐atomic pair‐density and pair‐repulsion by “sharing‐penetration” even into homonuclear bonds, for example, in H 2 , O 2 , F 2 , or Cl 2 . The admixture of ionic structures is necessary for obtaining reasonable results for F 2 , Cl 2 , ClF, HOF, and other molecules, which otherwise are calculated non‐bonded, for example, at the Valence Bond single configuration level of theory .…”

Plädoyer für eine duale Molekülorbital/Valenzbindungs‐Kultur

“…Daher kann man eine CMO‐basierte CASSCF‐Wellenfunktion transformieren, um einen genaueren Einblick in die Bindungsverhältnisse im Molekül zu erhalten. Dies soll am Beispiel des C 2 ‐Moleküls erläutert werden, dessen elektronische Struktur Gegenstand heftiger Debatten war und ist . Können wir die Bindungsverhältnisse in diesem kleinen Molekül visuell klar darstellen und mit seiner wesentlichen Eigenschaft, seiner enormen Reaktivität, korrelieren?…”

“…Diese Elektronenkonfigurationen können zu individuellen Elektronendichten führen, sodass Aussagen über chemische Motive wie innere Elektronen, freie Elektronenpaare und Bindungen möglich werden. Als neue Methode kommt das dynamische Voronoi‐Metropolis‐Sampling (DVMS) hinzu, mit dem man ebenfalls chemische Motive aus akkuraten Wellenfunktionen ableiten kann . Beide genannten Methoden ergeben für das Wassermolekül zwei äquivalente Rabbit‐Ear‐Elektronenpaare und für Ethylen zwei gebogene Bindungen.…”

Quantifying the Role of Orbital Contraction in Chemical Bonding

“…As part of his classic analysis of the H accounts for 21 kcal/mol out of the 64 kcal/mol of chemical binding. 11,14 Other studies by Ruedenberg 6,[15][16][17][18][19] and Kutzelnigg 8,9 showed that, for many molecules, orbital contraction is the dominant change in the electron potential energy term on bond formation. Constrained variational calculations for molecules in small basis sets 20,21 suggested that orbital contraction could typically be responsible for 25% or more of the chemical binding energy.…”