Question

Construct MO diagrams for H3+ using the D2h (linear) and D3h (cyclic) point groups. What MO diagram most closely matches the true geometery of H3+?

Answer 1

Let us first discuss the D3h cyclic point group.

A1’ corresponds to totally symmetric combination of atomic orbitals and E' corresponds to a degenerate set of molecular orbitals formed as a result of combination of 1s orbitals of each hydrogen atom. The projection operator method can be used to determine the combination of atomic orbitals here.

Now, let us see the D2h scheme for linear H3+. There are 3 AO corresponding to 3 H atoms. H carrying the positive charge can be taken as the central atom with one s orbital and is symmetrical (gerade). The other two can be taken as outer atoms that are far apart to interact with each other and hence have the same energy. They form group orbitals one of which is symmetrical (gerade) and the other is anti symmetrical (ungerade). The atomic orbitals can be mixed based on their symmetry. Orbitals can interact only if they have the same energy and symmetry. Hence the gerade (g) orbitals will interact while the ungerade (u) orbital remain as antibonding. Each outer hydrogen atom has one electron each which get paired in the bonding molecular orbital.