L8 QMOT: Building from Fragments

Qualitative Molecular Orbital Theory

What is the first step to work out the orbital interactions of molecules of several atoms

Break it into fragments. Don’t need to follow any chemical rules but ideally keep the symmetry of the molecule. A single plane ought to be a symmetry element of both fragments (in this case down the middle)

Drawing H₃ triangular geometry orbitals

Draw the bonding/antibonding combinations as necessary for each fragment and determine their symmetry in the plane. Only orbitals of the same symmetry will combine. The antisymmetric orbital does not combione and for this molecule just happens to have the same energy as the out of phase combination of the other orbitals.

Drawing linear H₃ orbitals list of steps

Drawing linear H₃ orbitals

Make sure when listing multiple symmetries that you say which order they are in.

Correlating the orbitals from these different geometries

During the bending of the terminal atoms, any symmetry planes which remain lead to the same symmetry being shown from the orbitals.

The orbital energies change as you bend H₃ as the bonding/antibonding interactions strengthen.

What happens when you decrease the angle further

The orbital energies change again. You can tell which orbital was which originally as their symmetries are preserved, as the symmetry cannot change without being symmetric and anti-symmetric at the same time.

Why is the preferred geometry for H₃⁺ not less than 60 degrees

The exchange integral H_AB goes way up at low internuclear distances, the proprtionality to the overlap integral stops.

What generally determines the preferred geometry in temrs of orbaital energies

The most stable geometry is typically the one with the lowest energy HOMO. If you add more electrons to H₃, the lower HOMO wins out even though the lowest energy electrons went up in energy.

AH₃ orbital diagram - how do we adapt the diagram to draw the H₃ fragment

Reduce the stabilisation/destabiliastion as the orbitals are further apart.

Drawing the AH₃ orbitals - why do some orbitals with the same symmetry have zero overlap

They have a different number of nodes:

Top left 1:0 bottom right

Bottom left 0:1 Top right

(nodes come about from changes in sign)

Combining the AH₃ orbitals

Combine orbitals with the same symmetry as usual

Remember that the electronegativity of the atom affects the relative energy levels of the orbitals on the left.