*From*: "Joerg-Ruediger Hill" <jxh %-% at %-% msi-eu.com>*Subject*: Re: CCL:Theta_0 values for polyatomics*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 jxh %-% at %-% msi-eu.com | nal opinions and no offi- D-82008 Unterhaching | | cal statements of Molecu- Germany | http://www.msi.com/ | lar Simulations Inc. -------------------------------------------------------------------------