Studying Perturbation Theory with Explorer EyeChem and VRML
Departament de Química, Universitat de les Illes Balears, E-07071,
Palma de Mallorca, SPAIN
(b,c) Department of Chemistry, Imperial College of Science, Technology and
Medicine, London, England, SW7 2AY
Abstract: The EyeChem
visualization environment was extended to study
well-known Diels-Alder reactions in a Perturbation Theory approach.
Virtual Reality Modelling Language (VRML)
molecular 3D data files of the transition states
and a reaction pathway animation were created.
In recent years, Computational Quantum Chemistry has become a
powerful tool for the study of many chemical reactions. Through the combined
use of increasingly faster computers and sophisticated programs, chemists
are now able to study various chemical properties, such as molecular structure
and chemical reactivity.
The corresponding emergence of visualization programs is allowing
chemists to better treat the quantum results, and consequently leads to
a better understanding of the molecular properties. Moreover, visualization
allows chemists to present their results in a highly comprehensible manner.
Some difficulties can arise, however, since all the theoretical calculations
imply the use of the "supermolecule approach" technique, that is, the treatment
of the two (or n) chemical moieties as a supermolecule by the program. For
instance, the calculation of the Diels-Alder reaction path requires that the
the diene and the dienophile be included in the same input file. In other
words, all the calculated molecular properties belong to the "supermolecule"
and not to the individual moieties.
Approach to the Perturbation theory
In studying the properties of one moiety being perturbed by the other
in the Diels-Alder reaction, one approach would be the calculation of
the Molecular Orbitals (MO) for each moiety (dieno and dienophile) instead of
the MO of the supermolecule (dieno plus dienophile). To achieve this, we first
performed a normal semi-empirical (see Results)
reaction coordinate calculation with the MOPAC-93-93  package
in order to obtain the minimum energy reaction
pathway (MERP). At every reaction coordinate, we then created two new
MOPAC-93 input files,
one for each moiety with the coordinates of the other
replaced by dummy atoms. Here, EyeChem
automated what would otherwise have been a very lengthy
and tedious process. We finally ran MOPAC-93 on each input file and generated graph
files for both the HOMO and LUMO MOs. Again EyeChem was used to visualize
the overlap of the frontier
MO of each moiety and to
create animations of the complete Diels-Alder reaction pathway.
This perturbation theory approach - the effect of the interaction of the MO of
the two components as a perturbation on each other - has been applied
to a wide range of well known Diels-Alder reactions 
(with C, Z and X-side
groups ) in order to better study the regioselectivity
of such reactions.
Molecular Modeling with EyeChem
is an Iris Explorer
module suite developed primarily to visualize
molecular models in a number of file formats including MOPAC-93. The
primary advantage of a visualization system such as Explorer is its
extensibility. For this paper EyeChem was extended
to run MOPAC-93, create animations, and create 3D files in the
Modelling Language (VRML) format.
VRML is basically a 3D metaphore
of HTML text. A VRML viewer such as SGI
acts as a helper application for World Wide Web (WWW) browsers. EyeChem
itself was extended into a VRML viewer.
EyeChem process of splitting each MERP into two moieties
and preparing all the visualizations for this
paper can be summarized as follows:
1) The HOMO/LUMO interactions of the diene and the dieneophile in their
transition state (TS) were visualized and saved as both gif images and VRML files.
2) The reaction coordinate output was read in and, for only one reaction coordinate,
the moiety to be replaced by dummy atoms was selected.
3) New MOPAC-93 input files for each reaction coordinate were automatically generated
with one of the moities in each input file containing the dummy atoms.
4) A single-point MOPAC-93 calculation on each input file generated the graph files.
5) Steps 2-4 were repeated for the other moiety.
One example QuickTime movie of a reaction pathway was prepared.
A QuickTime movie, although better than a static image,
conveys only one particular and unalterable viewpoint.
However movies are often created and viewed in EyeChem as a sequence of 3D
Such 3D movies can be viewed from any perspective and are thus preferable
to the conventional formats.
One example 3D VRML movie was created for this paper. It is
a sequence of VRML files viewable in
Twelve Diels-Alder reactions have been modeled using the AM1 SCF-MO semi-empirical
method implemented in MOPAC-93.
In every case the MERP has been found using the normal reaction coordinate technique.
Each TS has been calculated using the TS keyword.
VRML files and their corresponding GIF images showing
the frontier orbitals of each reaction have been prepared. Molecular coordinate
files in PDB format have also been prepared.
Reaction Pathway Animations
I. Reaction of 1-phenyl-butadiene and 1-phenyl-ethylene.
Example of a 1-C-substituted diene with a C-substituted dienophile, having
an observed ortho/meta adduct ratio of 8:1. In this case the MO overlapping
in the ortho TS is slightly better than in the meta TS.
II. Reaction of butadiene-1-carboxylic acid and 1-phenyl-ethylene.
Example of a 1-Z-substituted diene with a C-substituted dienophile, having an
observed ortho/meta adduct ratio of 6:1. No great differences are shown from
the visualization of the MO's.
III. Reaction of 1-methyl-butadiene and 1-phenyl-ethylene.
Example of a 1-X-substituted diene with a C-substituted dienophile. Here the
observed ratio is slightly favorable to the ortho adduct.
IV. Reaction of 2-phenyl-butadiene and 1-phenyl-ethylene.
Example of a 2-C-substituted diene with a C-substituted dienophile, having an
observed para/meta adduct ratio of 20:1. It can be seen that the overlap
contribution of the phenyl group is greater for the para TS than for the
V. Dimerization of 2-cyano-butadiene.
Example of a 2-Z-substituted diene with a C-substituted dienophile. In this
case we are considering the dimerization of 2-cyano-butadiene, with the
double bond (C1-C2) of one moiety as a dienophile. The observed product is
the para adduct, that shows the better overlap.
VI. Dimerization of 2-methoxy-butadiene.
Example of a 2-X-substituted diene with a C-substituted dienophile. As in
the previous reaction, we consider the dimerization of 2-methoxy-butadiene,
with the para adduct being the observed one. The para TS clearly shows the
interaction of the 2-methoxy group in the overlap.
VII. Reaction of 1-phenyl-butadiene acid and acrolein.
Example of a 1-C-substituted diene with a Z-substituted dienophile, where
the observed product is an ortho adduct. The ortho TS shows
the only suitable overlap.
VIII. Reaction of 1-cyano-butadiene and methyl acrylate.
Example of a 1-Z-substituted diene with a Z-substituted dienophile. In
this case, where two Z groups exist, both overlappings are very
IX. Reaction of 1-methyl-butadiene and acrylic acid.
Example of a 1-X-substituted diene with a Z-substituted dienophile. Same
case in our earlier example (see Abstract), where the most suitable
overlap is related to the ortho adduct.
X. Reaction of 2-phenyl-butadiene and cyano-ethylene.
Example of a 2-C-substituted diene with a Z-substituted dienophile,
with an observed para/meta ratio of 4:1. No substantial differences
can be seen between the MO of both TS.
XI. Dimerization of cyclopentadiene-2-carboxylic methyl ester
(formation of Thiele's ester).
Example of a 2-Z-substituted diene with a Z-substituted dienophile.
This case is especially remarkable due to the very rapid 1,5-sigmatropic
hydrogen shifts of the cyclopentadiene. This leads to the presence
of all three isomers in the reaction and could give a wide range of
products. We only present the MO of the TS leading to the observed
XII. Reaction of 2-methoxy-butadiene and carbonyl-acetylene.
Example of a 2-X-substituted diene with a Z-substituted dienophile,
in this case a substituted acetylene. Although the observed product
is the para adduct, only small differences can be seen between the
MO of both TS structures.
Perturbation Theory, chemists can obtain a much better understanding
of chemical reactions by visualizing the MO of each reactant
along the MERP. We are aware that key factors, in
addition MO overlapping, must be taken into account
when trying to explain regioselectivity.
The importance of 3D visualization, however, is clearly evident.
Moreover, new sophisticated VRML browsers as WWW helper
applications provide a novel chemical tool
useful for research and educational
References and notes:
1.. MOPAC-93-93: J. J. P. Stewart, Fujitsu Limited,
Tokyo, Japan, 1993. Available from Quantum Chemistry Program Exchange,
University of Indiana, Bloomington, IN.
2.. All examples are taken from Fleming, Ian.
"Frontier Orbitals and Organic Chemical Reactions" John Wiley
3.. Terminology is:
- C: An extra conjugation group.
- Z: An electron-withdrawing group.
- X: An electron-donating group.
4.. O. Casher and H. S. Rzepa, "Chemical Collaboratories using
World-Wide Web Servers and EyeChem Based Viewers",
J. Mol. Graphics,
to be published.