From Electronegativity towards Reactivity-Searching for a Measure of Atomic Reactivity.

Sture Nordholm

doi:10.3390/molecules26123680

Abstract

Pauling introduced the concept of electronegativity of an atom which has played an important role in understanding the polarity and ionic character of bonds between atoms. We set out to define a related concept of atomic reactivity in such a way that it can be quantified and used to predict the stability of covalent bonds in molecules. Guided by the early definition of electronegativity by Mulliken in terms of first ionization energies and Pauling in terms of bond energies, we propose corresponding definitions of atomic reactivity. The main goal of clearly distinguishing the inert gas atoms as nonreactive is fulfilled by three different proposed measures of atomic reactivity. The measure likely to be found most useful is based on the bond energies in atomic hydrides, which are related to atomic reactivities by a geometric average. The origin of the atomic reactivity is found in the symmetry of the atomic environment and related conservation laws which are also the origin of the shell structure of atoms and the periodic table. The reactive atoms are characterized by degenerate or nearly degenerate (several states of the same or nearly the same energy) ground states, while the inert atoms have nondegenerate ground states and no near-degeneracies. We show how to extend the use of the Aufbau model of atomic structure to qualitatively describe atomic reactivity in terms of ground state degeneracy. The symmetry and related conservation laws of atomic electron structures produce a strain (energy increase) in the structure, which we estimate by use of the Thomas-Fermi form of DFT implemented approximately with and without the symmetry and conservation constraints. This simplified and approximate analysis indicates that the total strain energy of an atom correlates strongly with the corresponding atomic reactivity measures but antibonding mechanisms prevent full conversion of strain relaxation to bonding.

Highlights

Linus Pauling was, for most chemists of the past century, instrumental in establishing the link between quantum mechanics and chemical bonding [1]
The last of them, based on hydride bond energies and geometric averaging, will be our currently recommended measure, but we recognize a non-uniqueness as in the case of electronegativity. We show how such atomic reactivity can be understood as a quantum mechanical consequence of conservation laws acting on the motion of the electrons in an atom
The analysis that follows uses a semiclassical form of quantum mechanics, which includes this early form of density functional theory (TF-DFT), implemented approximately, but we suggest that it provides a useful insight into the strain energies of atoms

Summary

Introduction

Linus Pauling was, for most chemists of the past century, instrumental in establishing the link between quantum mechanics and chemical bonding [1]. In the connection to development of the VB theory, Pauling proposed that atoms could be assigned a property of “electronegativity”, the power of an atom in a molecule to attract electrons to itself, which could be relied upon to explain the direction and magnitude of the transfer of electrons when two atoms of different electronegativity EN formed a polar covalent bond [6] He introduced a measure of EN determined from the assumption that the bond energy Eb(AB) of atoms A and B would exceed the average of the bond energies Eb(AA) and Eb(BB) by an amount proportional to the square of the difference in electronegativity ∆EN = EN(A)-EN(B). This idea was a few years later taken up by Mulliken who proposed a measure for the electronegativity EN(A) directly from single atom properties, i.e., as the average of the first ionization energy and the electron affinity (defined as the first ionization energy of the negative ion A−) of the atom A [7]

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