comparison betweem EXP and Compuation

 On Thu, 28 Aug 1997, Dr. Adel El-Azhary wrote:
 > Dear CCL members:
 > I sent an e-mail to ccl yesterday but it looks like that it was not
 > So my apologies if you receive it twice. My question is that I am doing
 > calculation on some small molecules for which effective, substituted,
 > or equilibrium experimental geometries are available. So which of these
 is the
 > best to be comapred to the calculated geometry.
 This is a good question. Too often, we compare computed molecular
 structure with experimental value without concerning whether they are
         First of all, WHAT IS A MOLECULE? (see, Gribov, L. A.
 J. Mol. Struc. 1993,300,415). There is one quite accuarte definition:
 it is the smallest particle of the substance made up of eletrons and
 nuclei of a definit mass. This definition can be expressed mathematically
 by the schrodinger equation. However, we must reduce to classical
 expresions if we want to compare calculated structure with a real
 experiment. We have to use classic models, different models for
 different experiments.
         Let us start from several experimental procedures obtaining
 the information of molecular structure. Two kinds of operational bond
 lengths R(0) and R(s) may be derived directly from rotational and
 rotation-vibrational spectroscopy. The R(0) structure is derived from
 the ground state rotational constants B(0) directly, or more usually with
 assumptions about some of the structural parameters. When the rotational
 constants for various isotopic species are observed, the substituted
 structure R(s) can be determined by Kraitchman method. When vibrational
 (both harmonic and anharmonic) properties are recorded, one may obtained
 equilibrium structure R(e) with some approximation. Only is the R(e)
 really comparable with the value from quantum mechanical calculations,
 which give the distance between equilibrium nuclear position R(e).
   X-ray or neutron diffraction experiments give the average nuclear
 positions at thermal equilibrium, and from which the average nuclear
 the internuclear distance R(alpha) is defined. When we refer to the
 structure at 0 K, we get R(z) structure, which may derived from
 rotational and rotation-vibrational spectroscopy.
         Gas phase electron diffraction experiments give the thermal
 average value of internuclear distance: R(g) structure.
         The relationship and interconversion of those strcutures may be
 formulated by classical approximation (see reference cited in the end
 of this message). MM3(96) version will print out all those structures.
 If you are using molecular mechanical method, MM3(96) is a good option.
 you can compare your calculated results with  comparable experimental
 data. Other molecular mechanical packages, as I know, do not realized
 the difference. If you are talking about QM calculation, of course,
 experimental equilibrium structure is first choice. However, if it is
 not available, R(s) structure is close to R(e). I have derived a formula
 R(s) =[R(z) + R(e)]/2 . R(z) comes third, then R(alpha), and finally
 R(g). Note that QM results are base sets and correlation dependent, and
 convergence should be considered in the comparison.
 a) Kuchitus, K. in Accurated Molecular Structures, Ed Domenicano, A et al.
 Oxford Science Publication, 1992.
 b) Ma, B.; et al. J. Physical chem. 1996, 100, 8763.
                  J. Am. Chem. Soc. 1997, 119, 2570.
                  J. Mol. Struc. In press ( the issure dedicated to Dr.
 Dr. Buyong Ma             buyong -8 at 8-
 Computational Center for Molecular Structure and Design
 Department of Chemistry
 University of Georgia
 Athens, Georgia 30602 USA            Voice (706) 542-2044