More insight in multiple bonding with valence bond theory

An original procedure is proposed, based on valence bond theory, to calculate accurate dissociation energies for multiply bonded molecules, while always dealing with extremely compact wave functions involving three valence bond structures at most. The procedure consists of dividing the bond-breaking into sequential steps, thus breaking one by one the separate components of the multiple bond. By using the breathing-orbital valence bond method (Hiberty and Shaik, 2002), it is ensured that both static and dynamic differential electron correlations are taken into account in each step. The procedure is illustrated for typical examples of multiply bonded molecules, N2, C2 and CO. The so-calculated total dissociation energies are at par with accurate calculations by state-of-the-art standard methods in the same basis set. The procedure also allows one to get some deep insight into the properties of the individual bonds that constitute the multiple bond. A so-called quasi-classical state is defined, in which the electrons of the bond under study have only one spin arrangement pattern, αβ, thus disabling the exchange of the two spin arrangements that is necessary for a covalent bonding interaction to take place. Taking this quasi-classical state as a non-bonded reference, one may estimate the “in-situ bonding energy” of an individual bond, as calculated at the molecular equilibrium geometry and in the presence of the other electrons. The procedure may also be used to assess the preferred bond length of an individual bond, which is shown to amount to 1.33 Å for the σ bond of N2, while the π bonds get stronger and stronger as the interatomic distance is shortened. Another application is the calculation of the resonance energy arising from the mixing of the ionic components of an individual bond to its covalent component, and the comparison of this resonance energy with the in-situ bonding energy. This shows that the σ bond of N2 and C2 is a classical covalent bond. On the other hand, the π bonds have a substantial resonance energy that put them close to the category of charge-shift bonds.