Chapter 5 Orbital Interactions

We are going to do two things in this chapter. First show on to build up the MOs for "large" molecules from smaller fragments and, secondly, how the electronic structure - the electron count - determines the geometrical structure in molecules. We are going to do this with extremely simple and mostly hypothetical molecules composed solely of hydrogen atoms.

A. The H₃ System

We have seen this in some depth before with D_3h and D_h structures. Let us do D_3h from an orbital interaction perspective:

Suppose two H-H distances are longer than the other.

The <f₁|c₃> is smaller than before so 2a₁ lies lower than b₂. An alternative way to display the evolution of orbitals and their associated energies is by means of an orbital correlation diagram. This connects the energy of orbitals by means of a straight line along some distortion coordinate.

compd. e's shape H-H dist. (Å)

H₃⁺ 2 D_3h 0.872

H₃ 3 D_h 0.994

H₃^- 4 D_h 1.084

B. The H₄ System

We shall now look at the geometries associated with H₄. Lets start with a rectangle - D_2h symmetry.

NOTE:

H₂ = 0.741Å

H₂⁺ = 1.044Å

Notice that <f₁|f₂'> = <f₁'|f₂> = 0. We could also do an

orbital interaction diagram to get to the square D_4h geom-

etry, but it is more instructive to use an orbital correlation

diagram:

An alternative (and useful representation for the e_u set is a linear combination:

Now lets build up a T_d geometry:

An alternative way to write down the t₂ set is to take linear combinations of two members (there are several other useful forms actually associated with t₂)

And an orbital correlation diagram relating the D_4h square to the T_d geometry:

Putting this all together for H₄:

compd. e's relative stability

H₄²⁺ 2 T_d > D_4h D_2h

H₄ 4 D_2h >D_4h > T_d

H₄^2- 6 D_4h > D_2h > T_d

C. The H₆ System

There are several ways that one can partition this molecule:

We can use these MOs to determine stability patterns for a hypothetical - really bizarre - molecule - - flat AH₆