21.8 Applications of Symmetry to Molecular Orbitals 895
Table 21.2 SCF Orbitals for H 2 OMO c 1 sO c 2 sO c 2 pzO c 2 pyO c 2 pxO ca 1 cb 2(^1) a 1 1.000 0.015 0.003 0 0 − 0. 004 0
(^2) a 1 − 0. 027 0.820 0.132 0 0 0.152 0
(^1) b 2 0 0 0 0.624 0 0 0.424
(^3) a 1 − 0. 026 − 0. 502 0.787 0 0 0.264 0
(^1) b 1 0 0 0 0 1.000 0 0
(^4) a 1 0.08 0.84 0.70 0 0 − 0. 75 0
(^2) b 2 0 0 0 0.99 0 0 − 0. 89
From M. Pitzer and D. P. Merrifield,J. Chem. Phys., 52 , 4782 (1970).
the lowest-energy orbitals at the top of the table. The orbital designations are explained
in Appendix H. There are ten electrons, so that by the Aufbau principle each of the
first five orbitals is occupied by two electrons. The 1a 1 orbital is nearly the same as the
nonbonding inner-shell oxygen 1sorbital. The 1b 1 orbital is identical with the oxygen
2 pxorbital, and contains a lone pair. The other occupied orbitals extend over the entire
molecule.
Exercise 21.15
Sketch an approximate orbital region for the 1b 2 LCAOMO in Table 21.2. Is this a bonding, a
nonbonding, or an antibonding orbital?
This description is somewhat different from the ideas presented in a general chemistry
course and with our earlier simple description, in which four electrons are shared
between pairs of atoms and four electrons constitute two “lone pairs.” If energy-
localized orbitals are formed, they have orbital regions primarily concentrated between
pairs of atoms and correspond to localized sigma bonds between the oxygen atom and
the hydrogen atoms.^9
PROBLEMS
Section 21.8: Applications of Symmetry to
Molecular Orbitals
21.40Construct symmetry-adapted basis orbitals for the BeH 2
molecule from the minimal basis set used in Section 21.1.
How do the LCAOMOs in Table 21.1 relate to these basis
orbitals?
21.41List the symmetry operations that belong to
trans-1,3-butadiene in its equilibrium nuclear
conformation. Construct a set of symmetry-adapted basis
orbitals for the delocalized pi orbitals of this molecule.
Specify the symmetry operators of which each of the
basis orbitals is an eigenfunction and give the
corresponding eigenvalues.
21.42List the symmetry operations that belong to
cis-1,3-butadiene in its equilibrium nuclear conformation.
Construct a set of symmetry-adapted basis orbitals for the
delocalized pi orbitals of this molecule. Specify the
symmetry operators of which each of the basis orbitals is
an eigenfunction and give the corresponding eigenvalues.
(^9) I. N. Levine,op. cit., pp. 513–514 (note 2).