More insight in multiple bonding with valence bond theory

Abstract

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 (P.C. Hiberty, S. Shaik, Theor.Chem. Acc. 108 (2002) 255-272), 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, N 2 , C 2 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, α β, thus disabling the exchange of the two spin arrangements that is necessary for a covalent bonding interaction to take place. Taking this quasiclassical 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 N 2 , 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 N 2 and C 2 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.

The Chemical Bond in C2

“…Very recently, a theoretical study by Hendrick et al. appeared where the nature of the bonding in N 2 , C 2 and CO was analyzed with VB methods . The authors introduced a stepwise procedure for breaking the triple bond in N 2 and the alleged quadruple bond in C 2 , which gives numerical values for each in‐situ bond.…”

Clarifying the quantum mechanical origin of the covalent chemical bond

“…In two-electron bonds, it is the interference between ( ↑ − ↓ ) and ( ↓ − ↑ ) states built from fragment-localized orbitals (in a valence-bond picture) which gives rise to covalent stabilization. Multiple bonds have access to even more states (within a few kcal/mol of the ground state) 45 . It is important to note that for charge-shift bonds like in F 2 , significant stabilization is also gained by the relaxation of the requirement of fragment locality, which results in a wavefunction (in a generalized valence-bond picture) in which both ionic and covalent structures are present.…”

A view of covalent and ionic bonding from Maximum Probability Domains

“…The ELF basins have indeed a quite different physical meaning [37], and may or may not match the chemists' expectation of visualizing a volume that could be associated to the space-localization of the bonding electron pair(s). In the case of N 2 , in a paper to be found in this same special issue [38], one of us has indeed shown that the p bonds in dinitrogen have substantially charge-shift character. It is known that charge-shift bonds lead to very small disynaptic basins, if any, and that a substantial part of the bonding density is found in these cases in the monosynaptic basins associated to the lone pairs [39].…”