From jkl@ccl.net Fri Aug 14 04:26:55 1992
Date: Fri, 14 Aug 1992 04:26:50 -0400
From: jkl@ccl.net
To: chemistry@ccl.net
Subject: Summary of geometries and frequencies
Status: RO

And now summary of the responses to experimental geometries and vibr spectra
Original question from jkl@ccl.net:
-------------------------- 
 Dear Netters
 I am trying to compare performance of a few quantum methods on the
 following molecules: CH3CH2OH (still popular...), HCOOH, CH3OH, CH3NH2
 and maybe CH3COOH.
 
 First geometries. These are popular molecules, however, the experimental
 gas phase geometries listed in Landolt-Bornstein, Harmony et al. - J.Phys.
 Chem.Ref.Data, and few papers from J.Mol.Spect. list only bond lengths
 and valence angles. As to valence angles, some are given indirectly
 as "tilt of the internal methyl group rotation axis". On the other hand,
 in papers of the Pople's group and in Hehre et al. "Bible", there are
 additional angles (usually angles between bisectors of H-X-H angles and X-Y
 bonds). I understand that "tilt" is good only for idealized equilateral
 methyls, which do not come this way from geometry optimization. 
 How these angles with bisectors were derived from experimental information,
 or maybe, I was looking in the wrong book? I could not find anything in the
 Landolt-Bornstein on these. Is there a trick to convert the "tilt" of the
 methyl group to these values? Also, I could not find anything on torsional
 angles for these molecules beside general statements about what are the likely
 conformations.
 
 Now frequences. I could find frequences for all above except CH3CH2OH
 in the Pople et al paper in Int.Quant.Chem.-Quant.Chem.Symp., 15, 269(1981).
 I do not know when to find ethanol. I will search Chem.Abs, but if good soul
 knows, I will be thankful. However, it looks like all these frequences are
 the plain experimental ones. Are there harmonically corrected experimental
 frequences for these? If so let me know... please...
 
 Send responese to jkl@ccl.net. I summarize if there is good response.
 Jan Labanowski
 jkl@ccl.net
 ---------------------------------------------

Answers: (Big Thanks to all of who responded...):

----------------------------------------------

From: Chris D Paulse <cpaulse@magnus.acs.ohio-state.edu
Message-Id: <9208091900.AA11695@top.magnus.acs.ohio-state.edu
Subject: Re: harmonic frequences and geometries
To: jkl@ccl.net
Date: Sun, 9 Aug 92 15:00:45 EDT

The geometries of these molecules obtained by experimential techniques are most
likely incomplete due to the fact that they are obtained from the rotational
constants of a wide variety of isotopomers.  In the case of planar molecules,
only two of the three rotational constants are independent of one another,
which certainly limits the amount of experimental data available for an
empirical least squares fit.  In the case of most of the molecules you mentioned
their high resolution rotational spectra will be dominated
by splittings due to torsional-rotational interactions (ethanol has two
independent internal nearly free rotors which complicate its spectrum
tremendously).  So it seems without looking at the references that a number
of simplifying assumptions were probably used in obtaining a spectroscopic
geometry for the molecule.  On the other hand, it should be possible to find
accurate spectroscopic geometries for both the cis and trans forms of formic
acid, as my old boss did some of the work on this.

Beware that most experimental geometries you find in the literature will not
be directly comparable to those obtained via an ab initio calculation.  Perhaps
the most common geometry is r_0, which is just obtained from fitting the
geometrical parameters to the uncorrected rotational constants for a series
of isotopomers and represents an average geometry in the ground vibrational
state.  The substitution geometry r_s comes closer to the r_e geometry, but
if any of the nuclei lie close to the three principal axes, it is bound to
have large error.  Perhaps the most unreliable is the r_\alpha, which is
a _thermally_ averaged geometry obtained by electron diffraction (contributions
from any of the vibrational states populated at the temperature of the
experiment).  In my experience, often crystallographic geometries are 
more accurate than these.

You have unfortunately chosen, with the exception of formic acid, molecules
which present signifigant challenges to experimentalists in terms of the
deduction of an equilibrium geometry from observed spectra.  This is of
course due to the large amplitude motion that most of these molecules undergo
in their lower energy states.

As for vibrational frequencies, not only is it true that the experimental numbers
have to be corrected for vibrational anharmonicity, but with a large number of
modes (molecules with 5 atoms), the possibility of strong resonances becomes
important (these won't show up in your ab initio results).  Also, don't believe
that the experimental assignments of each mode for the molecule are definitive.
There are often ambiguities and errors in assigments of vibrational bands,
especially in low resolution spectra.

hope this helps,
Chris Paulse

------------------------------------------------------

>From Kurt.Hillig@um.cc.umich.edu Sun Aug  9 15:54:36 1992
Date: Sun, 9 Aug 92 15:48:40 EDT
From: Kurt.Hillig@um.cc.umich.edu
To: jkl@ccl.net

Jan -
 
    WRT  "I am trying to compare performance of a few quantum methods on the
 following molecules: CH3CH2OH (still popular...), HCOOH, CH3OH, CH3NH2
 and maybe CH3COOH...."
 
The gas-phase structural data are almost certainly done by microwave
spectroscopy (there is probably also electron-diffraction structure data
for many of these, but I'm an ex-MWer, not an EDer).  MW structures are
not equilibrium structures, but rather represent an "average" over the
zero-point vibrational motion in the ground vibrational state.  (Rarely
one obtains enough information from the spectra of excited vibrational
states to make a harmonic-approximation correction to get a "closer-to-
equilibrium" structure, but this is very hard work.)
 
  MW structures are usually obtained by least-squares fitting of the atomic
coordinates to experimentally determined moments of inertia of the normal
and several isotopically-substituted species.  Often, one finds that not
all of the atomic sites can be substituted - sometimes the isotopes are
too expensive, or the chemistry to make a selective substitution is too
hard.  Then too, there are vibrational and mechanical problems which sometimes
pop up; for example in N2O, a heavier isotope (14N-15N-16O) has a smaller
moment of inerta than a lighter one (14N-14N-16O), implying an imaginary
coordinate for the central Nitrogen.
 
  When problems such as these come up in a MW structure determination, they
are usually resolved by making assumptions about the structure, and using
these as constraints in the fit.  Typical assumptions include local C3v
symmetry of methyl groups (i.e. all C-H bond lengths and H-C-H angles are
identical), overall symmetry (e.g. Cs symmetry for CH3COOH) etc.  I believe
the Harmony et. al. paper you refer to discusses this; see also Schwendeman
in "Critical Evaluation of Chemical and Physical Structural Data", D. Lide and
M.A.Paul, Eds, Nat. Acad. Sci. 1974.  Even today, with much more sophisti-
cated experimental methods, MWers still run into these problems; for a
typical current example (hopefully intelligible to the non-spectroscopist)
see Oh et. al., J. Molec. Spec 153, 497-510 (1992).
 
  Hope this helps.
 
  - Kurt Hillig
    Department of Chemistry
    University of Michigan

-------------------------------------------------

From: Paul Schleyer <pvrs@organik.uni-erlangen.de
Message-Id: <9208100749.AA08115@derioc1.organik.uni-erlangen.de
Subject: Re: harmonic frequences and geometries
To: jkl@ccl.net
Date: Mon, 10 Aug 92 9:49:12 METDST
Organization: Institut fuer Organische Chemie, Universitaet Erlangen-Nuernberg
Postal-Address: Henkestrasse 42, D-8520 Erlangen, Bundesrepublik Deutschland
Phone: +49/9131/852536
Fax:   +49/9131/859132
 
Dear Dr. Labanowski,
We have run all of these at MP2/6-31G* opt at least, and freqs at HF at
least (see Angew. Chem,  Int. Ed., 1992, 31, 314). Please contact Dr. Nico
van Eikema Hommes to arrange transfer of the archive entries.
                                   Paul Schleyer