Kudos to Robert. I think he is right. Assuming that the potential is the
same, sampling slightly different bond lengths will obviously give rise to
slightly different polarizabilities...
Branko
-----Original Message-----
From: Robert Hinde [mailto:[log in to unmask]]
Sent: Thursday, June 13, 2002 8:53 PM
To: [log in to unmask]
Subject: polarizability of H2 isotopomers
Daniel Willey wrote:
> Does any one happen to know the polarizability of molecular deuterium,
> D2? And, if you don't know it, is there any reason to expect it to be
> very different form the polarizability of H2?
In response, Branko Ruscic wrote:
> Good question. As you expected, polarizabilities of H2 and D2 are not
> very different. The average static polarizability (alpha bar) ever so
> slightly decreases in going from H2 through HD to D2:
>
> H2 0.803 Angstroms^3
> HD 0.798 Angstroms^3
> D2 0.793 Angstroms^3
>
> [see J. Rychlewski, Mol. Phys. 41, 833 (1980)]
>
> My take on this: it's small because its not a true isotopic effect,
> which would be dependent on the zero-point-energies; rather it's
> basically a non-Born-Oppenheimer effect, related to the fact that the
> electronic potential curve for different isotopes is ever so slightly
> different, and hence it's expected to be small.
I disagree... I think the bulk of these (admittedly small) changes is
precisely due to zero-point effects. The polarizability of H2, even in the
Born-Oppenheimer approximation, depends on the internuclear distance; if
memory serves me correctly, there is an old paper by Kolos and Wolniewicz
that shows the distance dependence of the H2 polarizability. Different
isotopomers of H2 sample different ranges of bond lengths in the v=0
vibrational level and therefore have different expectation values of the
polarizability.
If both parallel and perpendicular components of the polarizability varied
linearly with bond length near the equilibrium bond length, then within the
Born-Oppenheimer approximation the polarizability would be almost exactly
the same for all isotopomers of H2 (neglecting minor effects from mechanical
anharmonicity of the v=0 wavefunction). But it turns out that the bond
length dependence of the polarizability is not quite linear near the
equilibrium bond length; furthermore, it is rather different for the
parallel and perpendicular components of the polarizability.
Cheers,
RJH
=====
Robert J. Hinde
Department of Chemistry
University of Tennessee
Knoxville, TN 37996-1600
865-974-4840 voice
865-974-3454 fax
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http://proton.chem.utk.edu/~hinde/
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