The echinos model of cluster electronic structure: What is angle strain?

Abstract

According to Molecular Orbital Valence Bond (MOVB) theory (based on a fusion of MO and VB concepts) a molecule can be viewed as a composite of two or more fragments and the total wavefunction is a linear combination of substates, called bond diagrams, each of which is a pictorial representation of a distinct, symmetry-consistent way of connecting fragments by bonds or antibonds. In any cluster, the atomic orbitals (AOs) can be partitioned into radial and tangential AOs with the former interacting to produce the symmetry adapted MOs of the needle (N) fragment and the latter interacting to yield the symmetry adapted MOs of the surface (S) fragment. A cluster is then a species in which electrons are deposited in the needle and surface fragments with coordinate-type bonds connecting these two fragments and with ligands attaching themselves on the composite NS system via covalent bonds. This MOVB Echinos (Greek sea urchin) model is applied to the problem of “angle strain”. Contrary to common intuition, it is concluded that cyclopropane is strained relative to cyclohexane because, while overall bonding is stronger in cyclopropane, the amount of atomic excitation needed for bond making is disproportionately large. The reason behind this is an odd-even distinction of rings which originates from the fact that odd members have coupled Hückel and Möbius, whereas even members have coupled Hückel and Hückel needle and surface AO rings, respectively. The implication is that σ bonds are not system-invariant, i.e. the CC and CH bonds of cyclopropane and cyclohexane are completely different from one another. MOVB theory explains the interplay of atom excitation (investment) and bond making (return) which is actually what determines “stability”, and can be used to answer some vexing questions. Why is cubane so much more strained than cyclopropane? Why does replacement of C by Si sometimes increase (e.g. cyclopropane) and sometimes decrease (e.g. cubane) strain? Why is tetrahedral N 4 so unstable but tetrahedral P 4 a stable allotrope? Why do metal atoms form stable three-dimensional clusters, i.e. why does strain disappear in metallic systems? What is wrong with current approaches which have failed to provide us with a clear understanding of strain, as is now well recognized?