experiment and (large scale) computer modell ing is emerging as an increasingly powerfultool. Below we comment in
someVlLhatgreater detail on the various application areas.
Some of the project leaders have graciously provided us with
feature articles of their work. These appear as case studies
under the various research areas listed below.
Reports and manuscripts/1000 CPU hrs.
40
30
II
20
o
1993
1992
Fig. 9.
Chemistry
This is the research field that consumes the largest number of
experimentalists
GPU hrs and more than twice as many GRA Y GPU hrs. as the
scopists, but reaction mechanisms are also investigated.
Approximately 40% of the GRA Y time used is for applications
second largest group greater consumer
Physics -
which, however,
is a
of IBM time. At least 80% of the time is
used for quantum mechanical calculations, the remainder is
molecular mechanics and molecular dynamics simulatiom;.
The calculations
fall into two categories:
support and interpretation
the computational
of experimental
results, and pure
are mainly structural chemists and spectro-
using the (commercial)
program system Gaussian,
but the
majority of time goes to proprietary or public domain software.
The theoretical studies include investigations
of catalytic pro-
cesses on metal surfaces as well as methods development
for calculations on molecules containing heavy atoms.
theoretical simulations and the development of methods. The
Statistics:
Number of projects: 33.
GRA Y time used 1993: 5756 hrs.
Students in projects: 10 dr. scient. 4 dr. ing., 7 cand scient.
Published papers: 24
Reports and manuscripts:
IBM time used 1993: 9804 hrs.
58
Microwave Studies Aided by Ab Initio Calculations with
Thiiranemethanethiol as an Example
By Harald Møllendal
Department of Chemistry, University of Oslo
Introduction
Microwave (MW) spectra of gaseous molecules, radicals and ions can be routinely measured with an
almost unparalleled accuracy - seven significant digits, or better. The MW spectra arise when molecules
change their rotational energy, e.g. when they are itradiated by MW radiation. The spectra depend first of
all on the principal moments of inertia of the gaseous compound. The parameterized
quantum mechanic-
al theory, which is used to fit the spectra, works very well in most cases. The spectra are usually fitted to
within their extremely high accuracy yielding effective principal moments of inertia and some other parameters. The combination of high experimental accuracy, and a theory that exploits this accuracy fully, is
an idealone. This fortunate combination exists in MW spectroscopy.
The most important use made of the high-accuracy
geometrical
principal moments of inertia is to calculate the
structure, the way the atoms bu ild up a molecule.
Structures
derived in this manner are
generally considered to be the most accurate ones available.
All bodies have three principal moments of inertia. When two of them are identical, which is the case
--
Fig. 1.
A small portion of
the MWabsorption spectrum of
thiiranemethanethiol. Absorption
transitions are displayed downwards. The noise
fevei is practically
unnoticeable on
this recording,
which contains
assigned signals
from all three
hydrogen-bonded
conformers
shown in Fig. 2.
26300
~
g
/
}
'.
H bond inner
--
Fig. 2.
The four
conformers of
thiiranemethanethiol
which were
assigned by MW
spectroscopy.
!
H bond outer 2
H bond outer 1
!
Conformer IV
for compounds with high symmetry, the
resulting MW spectrum is generally quite
"0
relatively easy to interpret to exceedingly
complex. Unfortunately,
the latter is
often the case. When this occurs, all the
~~
C1
H1
~
81
/~
help a "desperate" MW spectroscopist
can get is deeply appreciated. 8uch a
nobody
thought
/
C2 -C3
H4
helping hand has come in recent years
from a source
II
/
.,~
the case for at least 99.99% of all compounds, the spectra can vary from being
H3
H2
simple and easy to analyse. If all three
moments of inertia are different which is
Fig. 3.
Atom numbering.
/ ~/
82
H5
~H6
might
even be considered on ly a decade ago.
High-Ievel ab initio computations
are
now appearing as an increasingly important toer in the analysis of complex MW spectra, such as the one
chosen as our example - that of thiiranemethanethiol.
The title compound
(see Fig. 1) has many thousarid
MW transitions - of weak, intermediate
and
strong intensities - scattered in a seemingly random manner throughout the entire MW spectral region.
Their analysis is a work worthy of a Champollion,
the man who deciphered the hieroglyphs of Egypt.
It has been known, of course, since the work of Egil Hylleraas in the 1920s that any MW spectrum
including that of thiiranemethanethiol
can be computed to anydegree
of accuracy starting with the known
masses and charges of the electrons and nuclei involved, i.e. starting from the first principles or ab initio.
8ince his work, however, it has also been know!'} that computations
within an extreme accuracy would be so large and demanding
could 'even dream of now - and in all future!
Chemical
aiming to reproduce MW spectra to
that they would exceed anything one
Problem
All chemical, physical and biological properties a molecule possesses are derived from its geometrical
structure. 8tructural studies are therefore the most fundamental studies that can be made. Once the
structure has been elucidated, all the other properties of a compound will be better understood.
Thiiranemethanethiol
was not chosen because of its complex MW spectrum, but because it presents
an interesting structural problem. There are two ~inds of problems associated with this molecule: the first
one is associated with the orientation of the atoms or groups of atoms within the molecule itself. Referring
to Fig. 2, one can see that four forms called confQrmers are drawn for this entity. These conformers arise
when one rotates around the 81-C1 and/or the C1-C2 bonds (see Fig. 3 for atom enumeration). This
rotation can succinctly be expressed in the values thatthe H1-81-C1-C2
and 81-C1-C2-C3
dihedral
angles take. (The angle between the H1-81-C1
plane of atoms and the 81-C1-C2
plane is called the
dihedral angle.) An infinite number of such forms (and dihedral angles) is of course conceivable, but only
a few of them are stable, i.e. they represent minima on an energy surface, called the conformational
energysurface.
The four conformers depicted in this figure turned out to be stable. Analysis of this kind is
called conformational analysis, and it was for his fundamental contribution to this field of chemistry that
Odd Hassel was awarded his Nobel Prize, the on ly one given to a Norwegian scientist for work conducted in this country.
The second kind of problem this molecule presents, involves intramolecular hydrogen bonding.
When hydrogen is bonded to an electronegative atom such as sulphur (81) as is the case in our model
compound, it may participate in intramolecular hydrogen bonding provided that other electronegative
atoms (such as 82) are not far away in the same molecule. This type of interaction is of enormous importance in all fields of natural sciences, and it is especially important in biology where it holds the DNA helices together, folds proteins into their active form, etc. It is an effect one would like to know as much about
as possible.
Experience has told us that three different kinds of hydrogen bonding can exist in thiiranemethanethiol. The first kind is a 81-H1 ... 82 hydrogen bond which is present in the H bond innerconformer.
The
approximate value of the H1-81-C1-C2
dihedral angle is -600 and the 81-C1-C2-G3
dihedral angle is
about -300 in this conformer. In the second kind, the H1 atoms interacts with the so-called pseudo-n electrons present along the C2-82 edge of the molecule's C282C3-ring.
which is characterised
This is the case in H bond outer 1,
by having the two quoted dihedral angles equal to about +600 and -1500, respecti-
vely. The third type of intramolecular
hydrogen bond, where the H1 atom interacts with the pseudo-n
electrons along the C2-G3 edge of the ring is found in H bond outer 2 (dihedral angles: approximately
-600 and +900, respectively). A fourth conformer, denoted Conformer IV in Fig. 1, was also found in the
course of the analysis. It has no internal hydrogen bond and its two characteristic
dihedral angles are
.
now approximately 180° and 90°, respectively. More conformers, perhaps as many as nine (or more?),
are presumed to be stable, but they are also thought to be of higher energy than the four identified conformers. They could not be assigned in the MW spectrum because their spectra were toa weak.
Calculation Methods
The ab initio calculations
I
presented
in this study were all made on the CRAY-YMP
computer
in
Trondheim, employing the GAUSSIAN 92 program package which is renowned for being both highly
advanced and user-friendly. It has, among many other things, provisions for searching for minima on the
conformational energy surface, i.e. a search for stable conformers. In order to be useful for the assignment of the complex MW spectrum observed for thiiranemethanethiol,
the computations had to meet the
following three requirements:
accurate predictions of the geometry of each conformer, accurate predicti-
ons of the dipole moments and its components along the principal inertial axis, and finally, accurate predictions of energy differences between the conformers. In order to fulfil these requirements, areasonably
accurate wave function has to be selected. General experience shows that the so-called 6-31G* basis
set, when used in so-called perturbation
computations
up to the second order, yields good geometri es
and dipole moments, while energy differences are in most cases, but not always, in good agreement with
experiments.
One would always like to use a better (read larger) basis set, but the computational
are al ready high with this basis set, and a compromise
between convenience
costs
and expected accuracy
must be found. The chosen MP2/6-31 G* computations represent such a compromise. The computer
time required for each conformer in the MP2/6-31G* computations was 10-15 hours, when allowance
was made for a full optimisation of the geometry. This is necessary when high accuracy is required.
Ideally, we would like to know the whole conformational energy surface, because of its importance for
the chemical properties of the compound. This would have required computations to be made for all combi nations of the H1-S1-C1-C2
and S1-C1-C2-C3
can even dream of today. A compromise
dihedral angles, which is far beyond anything one
would be toget an estimate of this energy surface. This could
have been obtained from 50-1 00 optimisations,
instead of the four we made, and would have required
approximately 1000 hours of cpu time on the Cray computer. This is, of course, beyond the present practical possibilities, but I think it provides an idea of what tomorrow's computations wililook like.
Results
Experience has taught us that the ab initio predictions
at the advanced
MP2/6-31 G* level of theory of
principal moments of inertia would surely be correct to within better than 4-5%, and are likely to be co rrect to within 2-3%. This puts limits on the frequency
ranges we have to search through to obtain an
assignment of the spectrum. Moreover, we were confident that the dipole moment and its components
along the principal axis of the molecule, would be correctly predicted to within better than 20%. The intensities could therefore be predicted rather satisfactorily.
With these predictions as the starting poirit, we
were able to assign MW spectra of the four conformers shown in Fig. 2. The assignment would probably
have taken much longer time if the ab initio computations were not available. Perhaps we would not have
succeeded at all!
In Table 1 the computed dihedral angles referred to above are selected from the full structure given in
Ref. 1. The experimental and calculated rotational constants (the rotational constant is equal to a constant divided by the corresponding
principal moment of inertia) of one of the conformers,
H bond outer 1,
are shown in Table 2. Note that the differences are less than about 1%. This small difference certainly
accelerated the first assignments. The agreemeht between the experimental and calculated rotational
constants for the remaining three conformers was equally satisfactory.1
Table 1. Dihedralangles obtained in the MP2/6c31G*
computations for the four conformers of thiiranemethanethiol, as depicted in Fig. 1. A full structure is given in
Ref. 1.
Table 2. Experimental and calculated (MP2/6.-31G*)
values for the rotationalconstants of the ground vibrational state of the H bond outer 1 of thiiranemethanethiol.
Uncertainties represent one standard deviation. The
Dihedral angle: H1-S1-C1-C2
Canfarmer
rotationalconstants are equal to a constant divided by
the principalmoments of inertia.Rotationalconstants for
allfourconformersassigned for thiiranemethanethiol,as
wellas other parameters of interest are given in Ref. 1.
H band inner
--
S1-C1-C2-C3
-61.4
-32.9
H band auter 1
62.1
H band auter 2
-62.8
-156.5
86.6
Canfarmer
166.7
80.6
IV
AdMHz
BdMHz
CdMHz
Experimental
Calculated
7 354.852 2(23)
7 418.1
1 727.44609(54)
1 708.4
1 483.416 07(56)
1 471.5
It is possible to obtain an accurate geometrical structure for all four conformers of thiiranemethanethiol using moments of inertia obtained from MW spectroscopy, but this requires several isotopic species of .
the compound. A study of isotopic species is at present tedious and costly. The structure computed for
I
molecules similar to our example at the high MP2/6-31 G* level are generally found to be remarkably close to the best examples provided by MW spectroscopy.
This is also probably the reason for the good
agreement between the calculated and experimental rotational constants referred to above (Table 2).
The calculated structures of the four conformers are therefore considered to be plausible structures believed to be Glose to those that might be derived from MW spectroscopy sometimes in the future.
In Table 3 the experimental and computed energy differences between the conformers are listed. In
order to obtain the experimental
energy differences,
However, in the case of thiiranemethanethiol
electrical
dipole moments
have to be used.
the dipole moments could not be obtained owing to too low
intensities. The values obtained in the MP2/6-31 G* computations were therefore employed. It is seen in
Table 3 that H bond outer 2 is the most stable conformer, and that this was correctly predicted in the ab
initio computations.
It should be admitted that at the outset of the MW investigation,
cussed here, this correctprediction
for reasons not dis-
was not thought to be trustworthy.
Another finding in Table 3 deserves comment. The energy of H bond inner is computed to be incorrect by about 6 kJ mol-1 , while the remaining energy differences are correct to within experimental uncertainty. Improvement of the theoretical results in the case of H bond innercan of course be made; however, this would require more elaborate computations.
is impossible to say.
How much more elaborate they would have to be,
Conclusions
We have found that high-Ievel calculations are helpful in assigning MW spectra, as exemplified above. In
particular one can get good estimates of the principal moments of inertia (in most cases better than 3%)
and the dipole moments if calculations are made at the 6-31 G* level of theory, or at a higher level. Energy
differences between conformers are often correctly computed to within the experimental uncertainty at
this level of theory. However, they may occasionally be unreliable in a way ane cannot predict in ad-
vance.
.
The fact thatit has been possible to perform ab initio computations
almost as a matter of routine, and
the fact that high-Ievel calculations yield results that may be a fine starting point in the MW investigation,
has changed the way we normally work in the MW lab. Today we always make ab initio predictions before we start working on a MW spectrum. The more advanced (read larger) the computations
better starting points we get. This again will result in less labour for the experimentalists.
Ab initio computations
are, the
have now attained such a high quality that they are useful for most branches of
chemistry. At the same time programs like GAUSSIAN are sa user- friendly that calculations are easy to
make even for unskilled chemists. A large increase in such computations is foreseen in the coming
years. In fact, what we are seeing today is no less than a "conquest" of chemistry by ab initio calculations.
A good thing is now happening: Fast computers as well as excellent programs are now becoming available to most chemists. Time has come that everybody can (and certainly should!) take part in utilising this
magnificent new tool for gaining deeper insight into all aspects of chemistry. We have already much to be
grateful for, and much more to expect!
Reference
1. K.-M. Marstokk, H. Møllendal and Y. Stenstrøm, Acta Chem. Scand., submitted for publication.
Table 3. Experimental and calculated (MP2/6-31G*)
energy differences in kJ mor1 (relative to H band outer
2). Uncertainties represent ane standard deviation.
H band auler 2
H band auler 1
Experimenlal
0.0
Calculaled
0.0
H band inner
1.4(3)
0.8
7.2
Canfarmer IV
3.5(4)
3.9
0.9(3)
.
.