20.4 Heteronuclear Diatomic Molecules 865
PROBLEMS
Section 20.4: Heteronuclear Diatomic Molecules
20.25Describe the bonding in the possible molecule LiB. Do
you think the molecule could exist?
20.26For a heteronuclear diatomic molecule, sketch the orbital
region for the LCAOMO
ψc 1 ψ 2 sA+c 2 ψ 2 pzA+c 1 ψ 2 sB−c 2 ψ 2 pzBwherec 1 is slightly larger thanc 2 and both are positive.
Take thezaxis as the bond axis. Determine whether this
orbital is an eigenfunction of̂iand of̂σh. Give the
eigenvalues if it is an eigenfunction.20.27Using the modified valence-bond method, describe the
bonding of the gaseous NaCl molecule. Predict whether
the coefficient of the covalent term or the ionic term will
be larger. Look up the electronegativity of sodium if
necessary.
20.28By analogy with the 2sphybrid orbitals, sketch the
orbital region of the two 3sphybrid orbitals.
20.29Using the molecular orbital method, describe the bonding
of an NaCl molecule in the gas phase. Predict what the
bonding molecular orbitals will look like if optimized.
20.30Describe the bonding in the carbon monoxide molecule
using the valence-bond method. Include ionic terms.
20.31Give a qualitative description of the bonding of the BN
molecule using molecular orbitals. Compare it with
diatomic carbon.
20.32The dipole moment of the HCl molecule in its ground
state equals 1.1085 Debye and the internuclear distance
equals 127.455 pm. Estimate the percent ionic character
and the values of the coefficients of the covalent and
ionic terms in the modified valence-bond wave
function.
20.33The dipole moment of the HF molecule in its ground state
equals 1.82 Debye and the internuclear distance equals
91.68 pm. Estimate the percent ionic character and the
values of the coefficients of the covalent and ionic terms
in the modified valence-bond wave function.
20.34Using average bond energies from Table 20.4 calculate
the electronegativity differences for H and C and for H
and N. Compare with the values in Table A.21 of the
appendix.
20.35Using average bond energies from Table 20.4, calculate
the electronegativity differences for C and N and for C
and F. Compare with the values in Table A.21 in the
appendix.
20.36Using average bond energies from Table 20.4, calculate
the electronegativity differences for O and N and for O
and Cl. By subtraction find the electronegativity
difference for N and Cl. Compare with the values in
Table A.21 in the appendix.
20.37Using average bond energies from Table 20.4, calculate
the electronegativity differences for H and N and for H
and F. Compare with the values in Table A.21 in the
appendix.Summary of the Chapter
In this chapter, we have discussed the quantum mechanics of electrons in diatomic
molecules using the Born–Oppenheimer approximation, which is the assumption that
the nuclei are stationary as the electrons move. With this approximation the time-
independent Schrödinger equation for the hydrogen molecule ion, H+ 2 , can be solved
without further approximation to give energy eigenvalues and orbitals that depend on
the internuclear distance.
Linear combinations of atomic orbitals, called LCAOMOs, provide approximate rep-
resentations of molecular orbitals for H+ 2. The ground-state LCAOMO, called theσg 1 s
function, is a sum of the 1satomic orbitals for each nucleus, and is called a bonding orbital.
The first excited-state LCAOMO, called theσ∗u 1 sfunction, is an antibonding orbital.
An approximate wave function for a diatomic molecule is a product of LCAOMOs
similar to those of H+ 2. The ground state of the H 2 molecule corresponds to the electron
configuration (σg 1 s)^2. A wave function with a single configuration can be improved
by adding terms corresponding to different electron configurations. This procedure