From quantum alchemy to Hammett's equation: Covalent bonding from atomic energy partitioning

TL;DR

This paper introduces a simple analytical model to estimate covalent bond energies based on atomic charges, aligning with Hammett's equation, and provides accurate estimates for diatomic molecules with p-block elements.

Contribution

The paper presents a novel, intuitive approximation for covalent bond energies using atomic energy partitioning, calibrated for p-block diatomics, connecting quantum chemistry with classical models.

Findings

Accurate bond energy estimates for hydrogen-saturated diatomics.

Model's response to nuclear charge variation is near-linear.

Simple formulas for substitution effects in bond energies.

Abstract

We present an intuitive and general analytical approximation estimating the energy of covalent single and double bonds between participating atoms in terms of their respective nuclear charges with just three parameters, $[{E_\text{AB} \approx a - b Z_\text{A} Z_\text{B} + c (Z_\text{A}^{7/3} + Z_\text{B}^{7/3})}]$. The functional form of our expression models an alchemical atomic energy decomposition between participating atoms A and B. After calibration, reasonably accurate bond energy estimates are obtained for hydrogen-saturated diatomics composed of $p$-block elements coming from the same row $2\le n\le 4$ in the periodic table. Corresponding changes in bond energies due to substitution of atom B by C can be obtained via simple formulas. While being of different functional form and origin, our model is as simple and accurate as Pauling's well-known electronegativity model. Analysis indicates that the model's response in covalent bonding to variation in nuclear charge is near-linear -- which is consistent with Hammett's equation.