From: rparson@spot.Colorado.EDU (Robert Parson)
Subject: Selection Rules (was Re: Why are Glaciers blue?)
Date: 22 Aug 1998 20:23:30 GMT
In article <35D8C706.D89D7D81@ix.netcom.com>,
Eric Lucas <firstname.lastname@example.org> wrote:
>One is a vibrational transition (nuclear motion), the other is
>electronic. I guess I consider that a pretty big distinction. Why is
>this overtone of the vibrational transition forbidden?
It is forbidden in the harmonic approximation, in which the dipole
moment operator only connects states that differ by one vibrational
quantum. Classically this corresponds to the fact that a harmonic
oscillator has only a linear response - drive it at frequency omega_o,
and it vibrates at frequency omega_o. Deviations from the harmonic
approximation lead to absorption at the overtone frequencies, and,
in polyatomic molecules, to combination bands.
[Technical correction: there are actually two approximations involved
in the delta-v = 1 selection rule: the oscillator is treated as a
harmonic oscillator and the dipole moment is assumed to be
proportional to the bond length, as would be the case if the
dipole were simply due to fixed partial charges on the atoms. Deviations
from the first are called "mechanical anharmonicity", deviations from
the second are called "electrical anharmonicity", both give rise to
overtone absorption. ]
I can readily believe that when the OH bond in a water molecule becomes
involved in a hydrogen-bonding network, it will become less harmonic.
Probably both mechanical and electrical anharmonicity will increase:
the bond will 'soften' as you pull the H out, increasing mechanical
anharmonicity, and the charge distribution in the bond will reorganize
increasing the electrical anharmonicity. So it seems plausible
that overtone intensities would increase in the liquid.
>It involves a change in dipole moment, no? I thought the
>selection rules for vibrational modes were based entirely on dipole
>moments, whereas the selection rules for electronic transitions are
>associated with various quantum numbers in addition to dipole requirements?
The underlying principle is the same: the dipole moment must change
as the molecule does its thing. From a classical point of view it's
easier to see this in emission than in absorption: an oscillating
dipole moment represents accelerating charges which radiate.
For vibrations, the charges slosh back and forth as the bond stretches
and compresses - an oscillating dipoole. For rotations, the magnitude
of the dipole stays the same but its direction changes, i.e. the
projection of the dipole moment on a space-fixed axis oscillates.
For electronic transitions, you can visualize the electronic charge
cloud as pulsating in and out around fixed nuclei. In all cases
what you've got is a dipole radiator.