Orbital contraction and covalent bonding

According to Ruedenberg’s classic treatise on the theory of chemical bonding K. Ruedenberg, Rev. Mod. Phys. 34, 326–376 (1962), orbital contraction is an integral consequence of covalent bonding. While the concept is clear, its quantification by quantum chemical calculations is not straightforward, except for the simplest of molecules, such as H2+ and H2. This paper proposes a new, yet simple, approach to the problem, utilizing the modified atomic orbital (MAO) method of Ehrhardt and Ahlrichs Theor. Chim. Acta 68, 231 (1985). Through the use of MAOs, which are an atom-centered minimal basis formed from the molecular and atomic density operators, the wave functions of the species of interest are re-expanded, allowing the computation of the kinetic energy (and any other expectation value) of free and bonded fragments. Thus, it is possible to quantify the intra- and interfragment changes in kinetic energy, i.e., the effects of contraction. Computations are reported for a number of diatomic molecules H2, Li2, B2, C2, N2, O2, F2, CO, P2, and Cl2 and the polyatomics CH3–CH3, CH3–SiH3, CH3–OH, and C2H5–C2H5 (where the single bonds between the heavy atoms are studied) as well as dimers of He, Ne, Ar, and the archetypal ionic molecule NaCl. In all cases, it is found that the formation of a covalent bond is accompanied by an increase in the intra-fragment kinetic energy, an indication of orbital contraction and/or deformation.