Summary of geometries and frequencies



And now summary of the responses to experimental geometries and vibr
 spectra
 Original question from jkl { *at * } 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 { *at * } ccl.net. I summarize if there is good response.
  Jan Labanowski
  jkl { *at * } ccl.net
  ---------------------------------------------
 Answers: (Big Thanks to all of who responded...):
 ----------------------------------------------
 From: Chris D Paulse <cpaulse { *at * } magnus.acs.ohio-state.edu
 Message-Id: <9208091900.AA11695 { *at * } top.magnus.acs.ohio-state.edu
 Subject: Re: harmonic frequences and geometries
 To: jkl { *at * } 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 { *at * } um.cc.umich.edu Sun Aug  9 15:54:36 1992
 Date: Sun, 9 Aug 92 15:48:40 EDT
 From: Kurt.Hillig { *at * } um.cc.umich.edu
 To: jkl { *at * } 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 { *at * } organik.uni-erlangen.de
 Message-Id: <9208100749.AA08115 { *at * } derioc1.organik.uni-erlangen.de
 Subject: Re: harmonic frequences and geometries
 To: jkl { *at * } 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