866 20 The Electronic States of Diatomic Moleculesis called using configuration interaction (CI), and can introduce dynamical electron
correlation. Most of the information about a one-term LCAOMO wave function is
contained in the specification of the electron configuration, which is constructed for
the ground state by the Aufbau principle, much as with atoms. Molecular term symbols
can be assigned much as with atoms.
In the valence-bond method, bonding factors are included in the wave function
instead of molecular orbitals. A bonding factor represents electron sharing between
nuclei by containing two “covalent” terms, with each electron occupying an orbital on
one nucleus in one term and on the other nucleus in the other term. Ionic terms, with
both electrons on the same nucleus, can also be included.
An approximate molecular orbital wave function for the LiH molecule was con-
structed using hybrid orbitals calledsphybrids, which are a linear combination of
sandpatomic orbitals on the same nucleus. A bonding molecular orbital made from
a2sphybrid on the Li nucleus and a 1sorbital on the H nucleus provides an adequate
description of the bonding in LiH.
Criteria for a good bonding LCAOMO were presented, based on results of Hartree–
Fock calculations: A good bonding LCAOMO is formed from a pair of atomic orbitals
with roughly equal energies, considerable overlap, and the same symmetry about the
bond axis. The use of hybrid orbitals in forming such LCAOMOs was discussed.
The use of electronegativity, an empirical parameter, to estimate bond polarity was
discussed. The use of the valence-bond method for heteronuclear diatomic molecules
was discussed, including the addition of a single ionic term to give bond polarity.ADDITIONAL PROBLEMS
20.38Predict what will be formed if a hydrogen molecule ion in
the state corresponding to theπu 2 pyLCAOMO
dissociates.
20.39Describe the bonding in the possible molecule BeC using
the molecular orbital method. Do you think the molecule
could exist in the ground state? If not, is there an excited
configuration that could correspond to a bound molecule?
Why do you think that the simple valence-bond method
would not be appropriate for this molecule?
20.40Describe the bonding in the boron nitride (BN) molecule
using both the molecular orbital method and the
valence-bond method. Compare the BN molecule with
diatomic carbon.
20.41Identify each statement as either true or false. If a
statement is true only under special circumstances, label
it as false.
a.Use of the Born–Oppenheimer approximation
prevents one from studying the motion of the nuclei in
a molecule.
b.The total electronic angular momentum of a diatomic
molecule is a good quantum number.c.The orbital angular momentum of the electrons of a
diatomic molecule is a good quantum number.d.The component on the bond axis of the orbital angular
momentum of an electron in a diatomic molecule is a
good quantum number.e.Hybrid orbitals are used to allow reasonable
approximate molecule orbitals to be written as linear
combinations of only two atomic orbitals.f. Every orbital must be an eigenfunction of every
operator that belongs to the molecule.g.The simple valence-bond method does not include any
dynamical electron correlation.h.Molecular orbital methods without configuration
interaction can include dynamical electron
correlation.i.Configuration interaction can introduce dynamical
electron correlation.j.The use of bond energy data is the only means of
evaluating electronegativity differences.