Subject: Re: CCL:Theta_0 values for polyatomics

From: "Joerg-Ruediger Hill" <[email-masked]>
Date: Wed, 5 Jul 2000 08:58:47 +0200

Hi,
> In the simple case of a diatomic molecule, we know that the internuclear
> distance re (well depth) and r0 (zero-point corrected) differ slightly due
> to the anharmonicity of the potential function. That's why r0 > re. But,
> you can 'estimate' the difference r0 - re fairly easily. (One can easily
> see the difference by just looking at the energy vs distance plot).
>
> In the most complex case of polyatomics, you have 3N-5 or 3N-6 degrees of
> freedom. For the simpler case of a bent triatomic molecule as for example
> H2O, you have a Theta_e angle that you calculate by minimizing the energy,
> but an experimentalist should be measuring a Theta_0 value. Most of the
> time, calculations compare their theta_e results with an experimental
> theta number, whatever its subscript. I know the difference between
> theta_e and theta_0 should be very small in most triatomics, but sometimes
> an experiment may report both values, their difference being as much as 1
> degree.
>
> I want to find out how I can 'correct' a theta_e value I calculate in some
> level of theory, to theta_0, by incorporating in some way (which one?) the
> zero-point contributions.
>
> As one can see, this is a special case in a big problem which will be more
> and more evident in the future, as calculations become more and more
> accurate. To what degree of accuracy are experimental and theoretical
> results comparable, since 'theory decides what is measurable', but on the
> other hand we don't really measure EXACTLY the same thing?

The differences between equilibrium structures as calculated by computational
chemistry methods and "measured" structures are well understood and there
is a strict theoretical framework for calculating them, although it is very
expensive (you need third derivatives) and therefore not very widely done=2E
As a starting point you might want to check out:

J.-R. Hill, J. Sauer, and R. Ahlrichs
Ab Initio Calculation of Nuclear Motion Corrections to the Geometries of
Water, Methanol and Silanol
Mol. Phys. 73(2) (1991), 335 - 348

and references therein. The entire theoretical derivation can be found in:

M. Toyama and T. Oka and Y. Morino
Effect of vibration and rotation on the internuclear distance
J. Mol. Spectrosc. 13 (1964), 193

Hope this helps
J=F6rg-R=FCdiger Hill

-------------------------------------------------------------------------
Dr. Joerg-Ruediger Hill  | Phone +49 89 61459-413 | The opinions  expressed in
Molecular Simulations    | Fax   +49 89 61459-400 | this message are my perso-
Inselkammerstrasse 1     | E-mail [email-masked]  | nal opinions  and no offi-
D-82008 Unterhaching     |                        | cal statements of  Molecu-
Germany                  | http://www.msi.com/    | lar Simulations Inc.
-------------------------------------------------------------------------