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

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.