Physical Chemistry Third Edition

20.4 Heteronuclear Diatomic Molecules 853

2 p

2 s

1 s

Li atomic

orbitals

Molecular

orbitals

H atomic

orbitals

1 s

2   

1   

3   

Orbital energy (schematic)

Figure 20.14 Correlation Diagram for the Lithium Hydride Molecule.

nonbonding electrons and two bonding electrons for a single bond, in contrast with the

He 2 molecule, which has two bonding and two antibonding electrons, for a bond order

of zero.

Hybrid Orbitals

We would like to have a simple method of predicting roughly what an optimized

orbital wave function for a given molecule should be without doing any calculations.

The SCF results for LiH suggest a pattern that we can use for such predictions. We

want to construct a wave function that is approximately the same as that of Eq. (20.4-5)

but contains linear combinations of no more than two atomic orbitals.

The 1σLCAOMO is nearly the same as the 1slithium orbital, so we replace this

LCAOMO by the 1slithium orbital, a nonbonding orbital. The 2σorbital contains

three atomic orbitals with coefficients that are appreciably nonzero. The coefficients

of the 2slithium and 2pzlithium orbitals in the 2σLCAOMO are roughly the same

magnitude with opposite signs. To a usable approximation, we will replace these two

atomic orbitals by ahybrid atomic orbital:

ψ 2 sp(1)c 1 (−ψ 2 s+ψ 2 pz) (20.4-6)

wherec 1 is a normalizing constant that can be shown to be equal to

√

1 /2. The desig-

nation 2spmeans that the new atomic orbital is a linear combination of the 2sanda2p

orbital, and the 1 subscript indicates that this is the first orbital of this type. Since we

can define two independent linear combinations from two functions, there is another

2 sphybrid orbital:

ψ 2 sp(2)c 2 (−ψ 2 s−ψ 2 pz) (20.4-7)