Physical Chemistry Third Edition

20.4 Heteronuclear Diatomic Molecules 861

The designations g and u are not used because the orbitals are not eigenfunctions of

the inversion operator, but we use the * symbol to designate an antibonding orbital.

The bond order is 3, the same as in N 2. The bonding and antibonding effects in the

lowest-energy four orbitals approximately cancel, so we can use the alternative electron

configuration

(1sC)^2 (1sO)^2 (2sC)^2 (2sO)^2 (π 2 px)^2 (π 2 py)^2 (σ 2 pz)^2

The coefficients of the oxygen orbitals are greater in the bonding orbitals, so the

bonding electrons contribute a net negative charge at the oxygen end of the molecule.

The oxygen nucleus has two more protons than the carbon nucleus, and this contributes

a net positive charge at the oxygen end, which slightly more than cancels the charge

due to the electrons. The dipole moment of the CO molecule is rather small, about

0.1 Debye. The carbon end is negative, and it is this end that coordinates to transition

metal atoms in various complexes, including the iron atom in hemoglobin in cases of

CO poisoning.

EXAMPLE20.13

Assuming the alternate electron configuration with eight electrons occupying nonbonding 1s

and 2sorbitals and making zero net contribution to the dipole moment and assuming that the

coefficients of the atomic orbitals in all three of the bonding molecular orbitals are the same,

estimate the values of the coefficients corresponding to the experimental value of the dipole

moment of the CO molecule.

Solution

The experimental bond length is 1.128 Å1.128× 10 −^10 m.

μexp 0. 1 D 3. 336 × 10 −^31 Cm

The dipole moment is equal to the net charge at one end of the dipole times the bond length. The

charge at the carbon end of the molecule is (6e− 4 e− 6 x^2 e)ifCCis the coefficient of the

carbon orbital in the bonding LCAOMOs.

Carbon:(6e− 4 e− 6 CC^2 e)(1. 128 × 10 −^10 m) 3. 336 × 10 −^31 Cm

CC 0. 575

Neglecting the overlap integrals, if COis the oxygen coefficient

C^2 C+CO^2  1

C^2 O 1 −C^2 C 1 − 0. 330  0. 670

CO 0. 818

This corresponds to the greater electronegativity of oxygen.

Exercise 20.19

a.Calculate the dipole moment that would occur for CO if the electrons were equally shared.

b.Write an improved electron configuration using 2sphybrid orbitals to make the sigma bond

and for the unshared valence electrons.