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LBL-12809
Preprin
t c.o---'
ITlI
Lawrence
Berkeley
Laboratory
Ii:I
UNIVERSITY
OF
CALIFORNIA
Materials &
Molecular
Research Division
Submitted
to
the
Journal
of
the
American
Chemical
Society
A
METHOD
FOR
CONSTRUCTING ISOMERIZATION REACTIONS
K.
Balasubramanian
May
1981
TWO-WEEK
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Prepared
for
the U.S. Department
of
Energy under Contract W-7405-ENG-48
DISCLAIMER
This document was prepared as an account
of
work sponsored by the United States
Government. While this document
is
believed
to
contain correct information, neither the
United States Government nor any agency thereof, nor the Regents
of
the University of
California, nor any
of
their employees, makes any warranty, express or implied, or
assumes any legal responsibility for the accuracy, completeness, or usefulness
of
any
information, apparatus, product, or process disclosed, or represents that its use would not
infringe privately owned rights. Reference herein to any specific commercial product,
process, or service by its trade name, trademark, manufacturer, or otherwise, does not
necessarily constitute or imply its endorsement, recommendation, or favoring by the
United States Government or any agency thereof, or the Regents
of
the University of
California. The views and opinions
of
authors expressed herein do not necessarily state or
reflect those
of
the United States Government or any agency thereof or the Regents
of
the
University
of
California.
A Method
for
Constructing
Isomerization
Reactions
K.
Balasubramanian
Department
of
Chemistry
and
Lawrence
Berkeley
Laboratory,
University
of
California,
Berkeley,
CA
94720
Abstract
LBL-12809
A
method
is
formulated
for
enumerating
and
constructing
isomerization
reactions
of
molecules
exhibiting
large
amplitude
non-rigid
motions.
This
method
not
only
enumerates
the
isomers
of
non-rigid
molecules
and
the
corresponding
rigid
molecules
but
also
the
symmetry
species
spanned
by
the
equivalent
structures
whose
representative
is
an
isomer.
Conse-
quently,.
using
the
method
of
correlating
the
symmetry
species
of
a
group
to
the
symmetry
species
of
its
subgroup
the
splitting
patterns
of
isomers
of
non-rigid
molecule
to
those
of
rigid
molecule
are
obtained.
This
provides
an
elegant
method
for
both
enumerating
and
constructing
reaction
graphs.
The
method
is
illustrated
with
examples.
This
work was
supported
by
the
Director,
Office
of
Energy
Research,
Office
of
Basic
Energy
Sciences,
Chemical
Sciences
Division
of
the
U.S.
Department
of
Energy
under
Contract
Number W-7405-ENG-48.
1.
Introduction
1-7
In
recent
years
several
papers
have
appeared
that
concern
representations
and
enumerations
of
dynamic
processes
in
molecules
exhibiting
large
amplitude
motions.
The
inter-relationship
among a
set
of
rigid
isomers
that
are
transformable
into
one
another
by
non-rigid
symmetry
operations
can
be
described
by
the
associated
diagram
called
a
reaction
graph.
A
reaction
graph
as
formulated
in
reference
7b
is
a
diagram
with
vertices
and
edges,
vertices
representing
isomers
of
the
rigid
molecules
and
the
edges
representing
interconversions
of
such
rigid
isomers
by
operations
in
the
rotation
group
of
the
non-rigid
molecule.
There
are
several
other
topological
schemes
and
representa-
tions
of
processes
of
interest
in
dynamic
stereochemistry.
An
excellent
. 1
review
of
such
schemes
can
be
found
in
the
papers
of
Mis10w
or
the
4
recent
book
by
Balaban.
Several
such
chemical
applications
of
graph
theory
can
be
found
in
the
papers
of
Randic.
3
It
is
known
that
the
isomers
of
molecules
can
be
characterized
and
enumerated
very
elegantly
.
10-13
harnessing
the
symmetry
of
the
unsubst~tuted
molecule.
The
combinatorial
structures
constructed
using
the
symmetry
of
the
molecule
are
generators
and
enumerators
of
such
phenomena.
One
combinatorial
structure
is
the
well-known
cycle
index
of
a
group,4,12-16
which
is
the
generator
of
isomers.
The
cycle
indices
have
been
employed
in
chemical
applications
by
1
3-11
.
several
authors.'
In
th~s
paper
we
introduce
and
use
a more
general
and
powerful
generator
called
a
generalized
character
cycle
index
(hereafter
abbreviated
as
GCCI). A
GCCI
is
a
cycle
index
that
also
has
the
character
of
the
irreducible
representation
to
which
it
corresponds.
Consequently,
GCCI's
are
generators
of
not
only
isomers
(patterns
in
2
