The gross selection rule for vibrational
transitions is that the electric dipole moment of the molecule
must change in the course of the vibrational motion.
e.g. homonuclear diatomics are infrared inactive - stretching
of the bond does not alter the dipole moment of the molecule,
it remains at zero. However, heteronuclear diatomics may be
infrared active, as bond stretching increases the distance between
the positive and negative ends of the molecule, increasing its
Note that this selection rule does not
require a molecule to possess a permanent electric dipole moment,
the change may be from a state without a dipole moment to a
state with one.
The specific vibrational selection rule in terms of the quantum
number ν is:
The gaps between vibrational energy levels are larger than those
between rotational energy levels, to the extent that at room
temperature molecules are almost always in their vibrational
ground state, ν = 0. Thus a vibrational spectrum commonly
consists of only one line, corresponding to the transition from
ν = 0 to ν = 1. This is called the fundamental
transition. Other transitions are only weakly observed,
due to the tiny populations of the lower states in these transitions.
Note that as a result of our approximations, the implication
is that the energy terms of allowed vibrational transition are
a constant value:
which further indicates that the spectrum should always consist
of a single line anyway.
However, the approximation of the potential energy curve to
a parabola is an approximation, and the breakdown of
this approximation leads to the transitions lying at slightly
different frequencies in reality. Thus several lines may
be observed in the spectrum, particularly if the molecule is
formed in some vibrationally excited states (ν > 0)
as transitions from these states will then have greater intensities
than would normally be the case.