Electron flow and electronegativity equalization in the process of bond formation

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Abstract
Charge‐constrained calculations make it possible to rigorously analyze electron flow and electronegativity equalization in the process of bond formation. Such an analysis is performed for the prototypical H2, HF, and LiH molecules. As the bonds are stretched, the dependence of the electronegativity difference on the extent of charge transfer undergoes a transition from approximate linearity to a steplike discontinuous character. With the help of the second‐order perturbation theory, the bondhardness is related to the matrix elements of the fragment‐electron‐count operator and is shown to increase exponentially with the bond length R at the dissociation limit. For polar bonds, the magnitude of the in situ electronegativity difference Δχ AB decreases quickly with R due to the decreasing polarization of the fragments. However, Δχ AB levels off for large distances, and most of the reduction in charge transfer that accompanies bonddissociation can be attributed to the dramatic increase in the bondhardness. The charge‐constrained calculations provide both the evidence and explanation for the energy derivative discontinuities that are observed in isolated atoms and molecules.