Topological analysis of electron density in depleted homopolar chemical bonds

Abstract

Except for the case of van der Waals interactions, homopolar bonds are covalent and therefore a concentration of the electron density is expected at the bond midpoint. Many experimental and theoretical studies have reported standard deformation density maps and molecular density minus spherical atoms densities, which show a depletion of electron density between formally covalently bonded atoms. For example, electron deficits are found in the theoretical map of the FF bond in F2, in the experimental map of the NN bond in carbonohydrazide, and in the experimental and theoretical maps of the OO bond in 1,2,7,8‐tetraaza‐4,5,10,11‐tetraoxatricyclo[6.4.1.1]tetradecane. Other partitioning schemes, such as subtraction of valence state atoms rather than spherical atoms from the total density, have been proposed to interpret these unexpected features. In the present work we examine these electronically depleted covalent bonds on the basis of the topological analysis of the electron localization function (ELF) of theoretically calculated electron densities. The attractors of ELF determine basins that are either core or valence basins. The valence basins are characterized by the number of core basins with which they share a common boundary, and this number is called the synaptic order. Disynaptic valence basins have been found for the FF bond in F2, for the NN bond in carbonohydrazide and for the OO bond in 1,2,7,8‐tetraaza‐4,5,10,11‐ tetraoxatricyclo[6.4.1.1]tetradecane. In the case of F2, polarization functions increase the V(F, F′) basin population, whereas accounting for the Coulomb correlation lowers this basin population. The results calculated for F2 are compared with those obtained for other diatomic molecules, such as N2 and O2, and the ELF picture of the bond compared with the molecular orbital analysis. In the case of carbonohydrazyde, the V(N, N′) basin population is the lowest among all the populations of the disynaptic valence basins present in the molecule, in good agreement with the experimental observations. Analogous results are obtained for the V(O, O′) basin population in 1,2,7,8‐tetraaza‐4,5,10,11‐ tetraoxatricyclo[6.4.1.1]tetradecane. Population fluctuation analysis indicates a strong delocalization of the electron density toward lone pairs and adjacent bonds. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 1517–1526, 1999

Topological analysis of the electron delocalization range

“…A symmetry‐restricted Hartree–Fock (RHF) wavefunction placing two electrons in a bonding orbital is unstable relative to an symmetry‐broken unrestricted HF singlet with spin‐up and spin‐down electrons localized to different atoms . Previous studies have show how covalent bond dissociation leads to bifurcation of ELF bonding basins and considered the role of nondynamical correlation in this process . However, these studies could not effectively treat singlet H 2 , as the ELF from single‐determinant calculations is identically 1 at all points in space and all bond lengths .…”

Comments on the nature of the bonding in oxygenated dinuclear copper enzyme models

“…The topological analysis of the ELF function [24] has been extensively used for bonding analysis [25][26][27][28][29][30][31][32][33]. Indeed, ELF is interpretable in term of an excess of kinetic energy due to the Pauli repulsion [34].…”

A quantitative measure of bond polarity from the electron localization function and the theory of atoms in molecules

“…This term, which is de®ned from the ELF analysis alone, has already been used implicitly as a substitute for the bond order [21,42]. The combined ELF/AIM analysis now allows the introduction of a bond polarity index as…”