Essentials of Computational Chemistry

560 APPENDIX B
Linear
molecule?
no
Presence
of C n axis?
yes
Multiple C n
axes, n ≥ 3?
no
Presence
of S 2n axis?
yes
S 2n
yes
yes
no
no
T, O, and I
Presence
of s h ?
no
Presence
of n s v ?
no
no
Presence
of s h ?
Presence
of s h ?
nC 2 axes
perpendicular
to C n axis?
yes
yes
C nh
C ∞v
Presence of
inversion
center?
yes
Presence
of s h ?
Presence
of n s d ?
C n C nv D n
Figure B.2 Flow chart for point-group assignment. A symmetry plane that is perpendicular to a
proper axis of rotation is a σh plane, one that includes the unique proper axis of rotation is a σv plane,
and one that includes the highest order proper axis of rotation and bisects the remaining two-fold axes
of rotation is a σd plane
a minimal basis set representation, but the dxy orbital on oxygen or the antisymmetric
combination of two p y orbitals on the H atoms would belong to this irrep in a polarized
basis set representation). The b1 irrep includes orbitals that are inverted by rotation and
reflection through the σxz symmetry plane, but left unchanged by reflection through the σyz
symmetry plane, and the b2 irrep includes orbitals that are inverted by rotation and reflection
through the σyz symmetry plane, but left unchanged by reflection through the σxz symmetry
plane.
no
no
yes
no
no
yes
yes
D ∞h
C s
no
yes
yes
C i
C 1
D nh
D nd