21.10 More Advanced Treatments of Molecular Electronic Structure. Computational Chemistry 913
Include a specification of the molecular geometry, which
means the shape of the molecule not including the
nonbonding electron pairs.
a.Sulfur hexafluoride, SF 6.
b.Xenon difluoride, XeF 2.
c.Phosphorus trichloride, PCl 3.21.78The methylene radical (carbene), CH 2 , is said to be
linear, whereas CCl 2 is thought to be bent, with a bond
angle near 120◦. Assuming this to be true, describe the
bonding in both molecules and explain the difference in
shape. Which molecule will have unpaired electrons?
21.79The crystal field theory is an approximate theory for
complex ions with a transition metal atom in the center
and several atoms or groups (ligands) bonded around it.
The ligands are approximately represented as point
charges.
a.If six negative charges are octahedrally arranged
about an iron(II) ion, say which of the real 3dorbitals
will have their energies raised by a greater amount and
which will have their energies raised by a lesser
amount.
b.If the energy difference in part a is small, the 3d
orbitals will be occupied as though they were at the
same energy, and if the energy difference is large, the
lower-energy 3dorbitals will be preferentially
occupied in the ground-state. In each case, use Hund’s
first rule to determine the number of unpaired 3d
electrons in the iron.
21.80Calculations^24 indicate that the C–H bonds in methane
might have the opposite polarity from that predicted by
the electronegativity difference, with each bond having a
dipole moment possibly as large as 1.67 debye with a net
positive charge on the carbon atom. If each sigma C–H
bonding orbital is represented by
C(ψ 2 sp (^3) C+cHψ 1 sH)
estimate the value of the coefficientcH, assuming the
bond polarity given above. Neglect the overlap integral in
the calculation.
21.81The infrared spectrum of methonium ion, CH+ 5 , has
recently been observed.^25 Using one of the available
computational chemistry programs, carry out a
semiempirical or ab initio calculation to find its
(^24) A. E. Reed and F. Weinhold,J. Chem. Phys., 84 , 2428 (1986).
(^24) S. Borman,Chem. Eng. News, 83 , 45, July 25, 2005.
equilibrium conformation and its predicted infrared
spectrum.
21.82Using one of the available computational chemistry
programs, carry out a semiempirical or ab initio
calculation on the hydroxyl radical, OH, to obtain its
LCAOMOs and its electronic spectrum.
21.83The hydroxyl radical, OH, is important in atmospheric
chemistry. Describe the bonding in this radical using
hybrid orbitals as appropriate. What orbital is occupied
by the unpaired electron?
21.84Using one of the available computational chemistry
programs, carry out a semiempirical or ab initio
calculation on the cyclopropenyl cation, C 3 H+ 3 , to obtain
its equilibrium conformation, its LCAOMOs, and its
electronic spectrum.
21.85The dipole moment of chloromethane is 1.87 debye.
Assume that the C–H bond has length 111 pm and that the
C–Cl bond has length 178 pm. Estimate the net charge on
each atom, assuming a tetrahedral molecular geometry
and assuming that the carbon atom has a net charge
of zero.
21.86Compare the electronic structures of BeH 2 ,BH 2 ,CH 2
and H 2 O. How many unpaired electrons are there in
BH 2? How many in CH 2? Explain your answer.
21.87Consider the two molecules, BH 3 and NH 3.
a.Describe the bonding in each, using the simple
LCAOMO approach of using two atomic orbitals in
each LCAOMO. Use the appropriate hybrid atomic
orbitals in the LCAO molecular orbitals.
b.Explain why the molecules have different shapes.
c.In the gas phase, a mixture of these two substances
undergoes a Lewis acid-base reaction to form an
adduct with a coordinate covalent bond. Describe the
bonding in this molecule, using the simple LCAOMO
approach with the appropriate hybrid atomic
orbitals.
d.Compare the adduct of part c to ethane, C 2 H 6.
e.Would the adduct of part c be polar or nonpolar?
Justify your answer in terms of electronegativity and
in terms of orbital energy levels.
f.To which point group does each molecule
belong?