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Orbital symmetry conservation and frontier orbital control in the reactions of organic radical cations
Tefra/w&wVol 41.No. I. pp. 145,o 161.19X5 Printedin GreatBntaln.
Am
FmmTIEP
oD4o-l020;8553.00 + .oo c 1985Pergamon Press Ltd
mBITAL
mBITAL
SRagipY
axmoL
m m
ccels~vAIIm
-10ns
omnxc
OF
CATION
mumAt
Ian R. Dunkin*
of Pure and Applied
Department
295 Cathedral
Chemistry, University of Street, Glasgow GI 1XL
and Lester Department
of
Chemistry,
University
of
(Received
Andrew
Virginia,
in UK
Strathclyde
Charlottesville,
5 November
Virginia
22901
19R4)
Abstract: Electrocyclic ring-opcninga, cpcloreversions, cycloadditions, and sigmatropic rearrangements of organic radical cations are discussed in terms of a simple qualitative theory, based on orbital s-etry conservation or is placed on the photofrontier orbital interactions. Special emphasis numerous examples of which have chemical reactions of the radical cations, recently been discovered experimentally. The theoretical models are in good radical cation rearrgeneral accord with the apparent facility with which angements and fragmentations have been observed to take place, and provide swe detailed predictions, especially with respect to stereochemistry, for further experimental testing.
Organic methods a
radical
for
cations
generating
thorough
investigation
I-irradiation
of
vacuum-u.v.
irradiation
As
a result
variety that
of
of have
been
illustrate
of
familiar
the
resemblance
between
cations,
orbital
interactions
radical
cation
specific
class
recent
regard
to
to
the
control
paper,
we have
the
radical
play
a part
likely
area,
the
which
of
cation
hitherto
thin
type
it
reaction
processes (i)
of
and (iii) has
the type
to provide (ii)
been
ie
there
is
species
and those
orbital
sywoetry
largely
145
that
been During
sac
therefore,
is
province
1.
of
for
physical
the
theoretical with
extension
theoretical
organic
the
over
In writing
experiments
caongst
of
particularly
a simple
qualitative
the
discussed
more general
an elclentary
interest
doublet
deliberations
would be helpful,
further
of
or frontier
and stereochemistry
already
to
cation
a superficial
whether
have
a
such as are
leaat
in Table
to promote
spectroscopists.
at
exaplified
to encourage
intended
neutral
became apparent
What follows,
the proceesee
of radical
pathways
pathways
can undergo
Some of
examples
rearrangements.7,16-lg
unlikely
reactions,
theory,
allowed
in Ar matricea.4t5
cations
and cycloreversions,
Hence
include
eimultaneous
the selection
reveal
shifts,
the
however,
purpose:
pericyclic
will
several allowing
methods
ionization radical
1, where
or triplet
in detemining
These
thus
or Ar matricea,1*3
that
the question
transformations.
to cover
a threefold
of
sigmatropic
praxpta
radical
and
Table
molecules.
Considerationa
findings,
cation
this
singlet
of
resemblance
made.
and fragmentations.
shown in Table
at
uncharged
reactions
photochemical
predictions
promising
the
models
are
be Freon
apparent
rearrangerents
ring-openings, of
electrocpclic
the
becoming
A glance
reactions. of
orbital
of
typical.
of
but
been developed,
and two-photon
deposition,4 is
with mass-spectrwetry,
have alao to
X-irradiation
or postulated
and this
experimental as
it
matrices
photochemietry
photochemical
cheaietry
radical
guidance
studies,
electrocyclic
in
known in connection
their
and Ar-matrix
observed is
best
matrices,182
facile
what
analoguea
of
Freon
recent
very
are
them in low-temperature
of this
model
aimed at testing chemists
in this
chemists
and
146
I. R. DUNKIN and L. ANDREWS
TABLE 1.
Poatulated
and observed
photoprocessee
of radical
cationa.
(Ref.
2.
0 ’
l+-
=_
(Refa.
\
&+_ 6”_ 84”_ a+’
6)
cl+* -
7 and 8)
(Ref.
11)
(Ref.
12)
(Ref.
13)
(Ref.
9)
(Ref.
141
(Ref.
15)
Orbital symmetry conservation and frontier orbital control
147
GElmRAL coesIDxRATIons
Dercriptions frontier
orbital
currency
of
symbols
of
depicted phase
mechanistic these
have
a singly
parent
promotion
of
occupied unoccupied
the
the
to
that
the
two
within
of
aa (n,n),
of
the
of
their
and
elcctrocyclic special in
two
orbitals,
not
included
on ground
both
for
Cyclobutene 1” Figure to
is
for
the
the
orbital the
C-C
they by
point
symmetry
are
Table
that
cyclic
of
these
doubly
It
8o.e
of
lowest
excited
statea
classification
or (~,a*)
paper.
remove
polyenes
on the other,
will
the
be seen
later
restrictions
ring-openinge
were
23
Since
have been publirhed Fxcaples
of
first
proposed
then,
similar
by several
photochemical
1-3,
versions
5,
of
the excited
correlatione
(CS),
(r,n*), reactant
and
on
neutral
of
by Woodward and treatments,of
groups,7*l+lg
electrocyclic
and 7).
those
state
to
of
the
broken
Ihe
with
processes
rchemes we outline
previously
advanced,
and are
correlations.
(S:
are
for
the
included.
of
element the
that
into
openings
product
labels lower
are
while
these
orbital6 to
of
elaborated
orbitala during the
(i)
opening,
appropriate
part
The correlations
opening,
orbital.9
conrotatory
splmctry In the
the
orbitals,
relating
and (ii)
is maintained
disrotatory
the molecular
are
Each of
[cyclobutene]+‘.
transform
[cyelobutene]*’
the TT and n*
antisymmetrical)
Alternative
alno
they
(91 - 14). A:
of
and product,
reactant,
and also
and conrotatory
states will
reactant
symmetry is maintained,
is maintained.
symmetry that,
and d),
symmetrical;
the ring-opening
both
For
four n orbital6
disrotatory (u,w)
(a
for
for
reaction.
ti:d,b)
orbital8
indicate
the is
symmetry
both
depicts,
Es (mirror)
(&:g’,&“; for
respect
in
labels
axial)
that with
energy
in the SOnO to the
clcctrocyclic
1 (Reactions
orbital
the set
where
groups
correlations
prototype
cations
highest
by
REAcTxms
and to emphasize
bond
symmetry
correlations
ground
the
radical
one attained
exist.
from the simpler
involved
opening,
aseumption
These
the
Q2 (two-fold
two
in
to
derived neutral
orbital,
the simple
thin
they each is
[buta-1,3-diene]+’
directly
product,
or
region
the ground-state
and aa (n,+)
throughout
likely
correlations.
found
description
that
states:
from
h.
is
cation
occupied
adequate
Abrahamson.
The top section
with
disrotatory where
state
completeness
,--*
classified
the
and
1 shows the important
most
associated
of
radical
essentially
[buta-1,3-d&w]+‘.
orbital6
ia
are
differ
are
spanetry
to an unshaded
atate
excited
the electron
otherwise
and higher
in
singly
of
be adopted
Longuet-Higgins
cations
do
and
orbital8
their
cations
(RCHO) of a
on the one hand,
atate
treatments
processes
emphasis
radical
below
by
a shaded
configuration-intcraction,3b*7
which might
cyclohexa-1,3-diene,
cyclobutene, Aof fmann22
the general
molecular
a ground
electronic
by promotion
or (a,~)
these
symmetry
of
naenclature
to indicate
radical
orbital
possessing
a fully
and will
paths
of
exenple,
occupied
KLEccRocTcL1c
Orbital
now part
standard
instance,
fra
feature For
valence
considerable
(a,~),
reaction
special
low-lying
Although
validity,
existence
photochemical
solely
a change
are
the
atomic
the highest
relatively
(LUMO).
an approximate
adopted
orbital8
on symmetry conservation,19
-
for
(SOnO).
the SOHO, the other
inclusion
states
orbital
fra
an electron
orbital
requiree
the
MO theory,
a consequence
have
orbital
baaed
In the Figures,
now conventional,
molecular
Ar
of
-
continuity21
in the wave-function.
onc electron
generally
paths
phase
We have
treatments.
is
of
occupied
of
a8
phare
reaction
chemistry.
aa cabinations
context
molecule.
cations
ha8
of
the
of
or orbital
known
and,
a change
removal
control
organic
well
properties;
Within
of
the orbital
schematically
denotes
by
of
interactiona,
Figure
for
1,
each of
rely
which hare
to
on the the 8-e
the transformation. (n,rr*)
state
of
I. R. DUNKINand L. ANDREWS
148 FIGURE 1.
/
Orbital
correlations
for
the electrocyclic
opening
-1” \
of
[cyclobutene]+’
d+’
c
-
-c2
A(b)
I% LB3
A iaIr)
Sial
S iall
Albl
CS
- c2
A loll)
S(a)
S ial)
A(b)
A (all)
S la)
S loll
A Ibl
u’3
r2 !PI
-
rL,\_ (i)
sia’)
S(a)
Disrotatory
A---
TP
A-
-
opening
J4 Q*
ol,
C, (mirror)
1’.
A YL -4-s Y, X
H
s4
u
s+---
(ii)
---
---
+ +-+
-A
Y,
_X,
+s
Yq
+--+
+-
IH,H~
hn7
GS
symmetry maintained.
Conrotatory
opening -
1’.
-
GS
C2 (two-fold
-
axial)
X
(u,rd
-SC HE
symmetry maintained.
+I+*
)n( urn
A-
lv
s-
X
-s
v4
-A
b
+s?$ X Q s+ 4-A v,
7TA4
GS
Irr,rd
+-
X+
_X_
-
+ XXh,rf)
HE
-3t + b,rrl.
X
+ 4k GS
Orbital symmetry conservation and frontier orbltal control
149
1. R. DUNKIN and L. ANDREWS
150
[cyclobutene]+’
should
transform
(Q,w)
state
only
(u,w)
state
which correlates
both
modes
of
into
a highly
excited
associated
with
into
the ground state
(HE) state;
directly
ring-opening
particular
directly
excited
with
the product
are photochemically
state
involved.
a ground
while
state
of
[buta-1,3-diene]+.
the conrotatory
ground state.
allowed,
Moreover,
state-ground
for
In this
the preferred
neither
it
model,
is
the
therefore,
pathway depending
disrotatory
correlation,
and the
opening,
nor conrotatory
on the
opening
corresponding
to
a favourable
are displayed
more compactly
is
thermal
reaction. The
relationships
correlation
shown
diagrams
derived
directly
frw
but more realistic As
first
1,
can
thus
configuraton
aw2,
the
symmetrical
state
lowest
mainly
barrier
in a disrotatory
(rr,n*) The
energy
state
of
path
is
followed,
should although
be
by
in
the
the
state
The
thus
likely
to
be
the
unlikely
and
for
(n,n)
states,
state
should
an
open
with
the
(conrotation).
barrier
the conrotatory
in reality,
the
down to
pathway has
either
energy
of
in the
dropping
correlates
ring-closure
to occur
(w,n*)
correlation
in contrast,
a substantial lower
the same
which has
disrotatory state,
lower energy
reasoning,
and thus ground
the
state
[cyclobutene]+‘,
alternative
involve
of
of energy barriers
[cyclobutene]*’
or with
will
states
by conrotation,
The (VT,+) of
for
radicals,23
of
as state
show correlations,
configuration-interaction, rule
indication
(U,W)
process.
of
and ally1
a qualitative
By similar
the
Broken lines
to open predasinantly
is
unfavourable
2.
a non-crossing
surmounted.
barrier
from
Figure
in the absence
The ground state
favoured.
disrotation
of
observe
(disrotation)
this
energetically
proceed
likely
be
and (ii),
the cyclopropyl
give
the ground state
but
therefore
for
is
to
product
fras
lines)
be seen that
manner.
the
ring-opening
(i)
would obtain
basis
electronic
appreciable
that
explained
It
1,
portion
(solid
on this
pathways.
Figure
left-hand
Figure
constructed
various
in
the
correlations
bymmetry.23 diagrams
in
whichever
pathway,
vould
and by conrotation
which
,3-diene]+‘ ,
[buta-l
be expected frm
the
to
(n,w)
state. We should excited
not
states
vibrationally
excited
blurred
if
energy,
this
which
electronic the
happens
of
likely
to
with
the
energy be
ground
expected,
state
therefore,
Cyclohexa-1,3-diene
the
electrocyclic
the
reverse
tetraene]+* centre
,
diagrams,
states
labels
(rn)
lowest
three
the
(w,w*)
system.
the
the
(w,w*)
the
reverse
above,
for
ring-opening
will
highest
of
of
the
first
of
are
identified
the orbitals
These
lead
vhich
should
by their of
in order From the
electronic
are
states
undergo
This
applies
to
in these
in is
directly
state,
the
which is
radical
cations.
may be worked out
and
that,
for
is
and
[octa-1,3,5,7-
diagrrrms shown in Figure by Shida -* et
for
the
four
shown,
the
state,
and
five-electron
transformations seven-electron
and ring-closure. for
(n,w)
six-carbon
those
2 at
In these
conventional
cations
the
disrotatory
the eight-carbon
expected
al 7
making use of the
the ground state,
ring-opening
reactions
initial
manner.
polyene
given
predwinantly
while both
that
For each of
may be deduced
will
cyclic
configurations,
energy,
the
asslnning
(w,w*)
[cyclobutene]*-
correlation
w-systems.
increasing
of
of differences
and [cycloocta-1,3,5-triene]+‘,
be compared to
transformations,
stereospecificity
state
be
vibrational
[cyclobutene]*‘,
[hexa-1,3,5-triene]+’
diagrcrms it
and (w,w)
conrotatory
of
to the
conjugated of
for
[cyclohexa-1,3-diene]+’
ring-closures
excess
in a disrotatory
above
the
will
states
can correlate
is met by the
and higher
described
or to
High stereospecificity
the reactant
stereospecifically
to those
openings
hold.
condition
Upper
states
effect
paths.
of
similar
the
nround state
state
this
2,
reactions.
a consequence kinetic
cycloocta-1,3,5-triene]+‘,
reactions,
state.
as
subsequent reaction
excited
these excited
the considerable
states
the
lower
amongst the various
In the ring-opening
to undergo
states,
excited
available
lowest
the product.
respectively.
and right,
to
Distinctions
reduce
on the the
in all
decay
Additionally,
the
in Figure
‘*,
for
in will
correctly
correlations
for
present
where
of
stereosoecificity
extent.
a cation,
barriers
found
ordered
Orbital
be of
high
non-radiative
ground state.
to a large
may well
heights
are
expect undergo
electronic
excitation
most
states
necessarily
may readily
and
system,
As suggested
processes
uhere
the
Orbital symmetry conservation and frontier orbital control
lowest
excited
condition
rtate
obtains
1,3-diene]+’
and
(~2y:r,rf)
of
,
its
the and
Generalized cations
the reactant
the
reverse
we have
presented
the
in Table
2.
Electrons
4n+3 (n-1,2,3...)
t
Ring-opening
reverse
the product
(w,w)
stereochemistry
ground
(u2vl?z)
ring-opening
for
be
state
state. of
of
This
[cyclohexa-
the (n,w)
state
reaction.
elaborated
[cyclobutene]*‘,
readily
of
the
[cyclohexa-1,3-
extended
to
electrocpclic
higher
systems.
reactions
of
radical
2.
Pavoured
electrocyclic
modes for
radical
cations.
Excited
Ground State
(n:1,2,3...)
the
conrotatory
may
1 ;;;::::::;;I
4n+l
with
of
the
[cycloocta-1,3,5-triene]+.
TABLE
No.of
and and its
which
for
directly
ring-opening
reaction,
treatment
predictions
are
correlates
disrotatory
[cycloocta-1,3,5-triene]+-
Obviously diene]+’
of
in
151
1
State
(a,lr)
I
h,n)
I
conrotatory?
1
conrotatory!
1
h,n*) disrotatory
diarotatory
disrotatory
conrotatory
conrotatory
conrotatory
disrotatory
II Ring-closure
only.
only
CICLORgVBRSIOHS AND CYCUIADDITIONS
Symmetry enunciated
rules
by
cation
reactions
radical
cations
are
that
The [2+2]+’
the
;
Subscripts denotes
labels
c and
diagram,
transformation, occupied
found,
orbital
as
reversion ground favoured
shown of
or
to
is
to
denote
occupied
orbital
of
With
part
of
should The
reverse
ethylene
of
with
were
first
radical
cycloreversions
for
of
no corresponding
amongst the orbital6
more
reaction,
and the h,fl)
The
state
readily the state
the
from
of
(I_T,@)
cycloaddition,
[ethylene]+‘.
thus nc state in the a doubly
has only
correlations
suggest state
the
with
cation etate
or
plane.
involved
correlate
radical set
the
mirror
to construct
correlations
[2+2]*’ of
this
directly
must
a unique
symmetry with
respectively;
In order
because
and
which are broken
to
molecule,
of
[ethylene]*’
of mirror
refer
[cyclobutane]*’
3.
cycloreversion of
retention
ethylene.
constraint,
Figure
the
to the two wbonds
neutral
molecule, this
occur
of
we know of
cycloaddition
place
and
that,
ethylene
Rround state
take
to note
neutral
states.
Examples but
correlations
and parallel
cation
orbitals.
molecules
to the analogous
+ ethylene.
[2+2]*’
neceseary
lower
”
their
and vr,, that
the
the
neutral rules
and A (antisymmetrical)
or nc* in
sections.
cis-cis
assumed
these
established.
and
to the ring
of
of
8 and 9),
[ethylene
MO’s
[ethylene]+’
[cyclobutane]*’
(a,a)
for
used
of it
of
f
corresponding are
a doubly
in the n,
well
S (symmetrical)
n are
following
1 (Reactions
reasonably
perpendicular
cycloreversions
Adaptations
the
Table
relevant
the
the w orbital
correlation
electron
the
processes
to a plane
and
[cyclobutane]+’
, and Both
ethylene.
in
in
have been
3 shows
[cyclobutane]+’
formed
found
reaction:
Figure
cycloadditions and Woodward.
presented
are
cycloadditions
respect
for
Hoffmann
that
one is
cyclo-
than from the is
especially
I. R. DUNKINand L. ANDREWS
152 FIGURE 3.
Orbital
and atate
[ethylene]*’
correlations
and ethylene,
for and for
the ~:pclorevereion the csrresponding
of [cpclobutane]+ [2+2]+’
+* W
e
l-l’
CH,=CH-j+’
Orbital
H
+
correlations
S-
State
correlations
=A
v
into
cycloaddition.
CH,=CH,
Orbital symmetry conservation
The
sclme conclusion
consideration
of has
[ethylene]+’ shows
how
state
neutral
its
frontier
faoour
a cis-trana
the
(a,~)
of
course,
state formidable
JWXJRF, 4.
regard
orbital
the
favour
It
between
cycloaddition
should
-
n-orbital
sis-tie
the
at
(n,n*)
between the
energy
state
of
ground
state
reached that
more
the
than
orbital
ethylene
the
of
and the interactions
such
frontier and the
orbital ground
for
(n,n*)
interactions state
of
the
are,
state
of
(GSI
Favourable (u,w)
state
frontier of
orbital
[ethylene]*’
interactions and the
ground
cis - trans
for
the
state
ground of
also state
ethylene.
state
ethylene.
or
4
ground
ground
cis - cis
FIGURE 5.
of
a reaction
5).
Favourable
by
state
SOnO. Figure
and either
requirements
quickly
(n,+)
[ethylene]*’
Frontier
geometric
153
may be be noted
lower
cycloaddition.
although
[ethylene]+‘, (Figure
cpcloaddition
[2*2]+’
vacant
the
[ethylene]+’
CH,=CH,
the
interactions.
interactions
[2+2]+’ of
to
orbital
LUHO -
molecule
or
with
frontier
and frontier orbital control
1. R. DUNKINand L. ANDREWS
154
FIGtIlE 6.
Orbital
correlations
corresponding
[2+4]+’
for
the
cycloreoereion
n
c’d
bs
0
A-
S-
\\\
/ / J/
of [cyclohcrene]*’
end the
cpcloadditioos.
+
CH2=CHJ+’
Orbital symmetry conservation and frontier orbital control
r24+1+*cvcloreoersions Analysis
of
considerably orbital8
shows
but
orbital
possibility
Broken
of
denote
Fran the orbital
shown
in
Figure butadiene
ethylene
(ce).
The
immediately electron
spectra
orbital
of
clear
is
than 1.5
the
for
difference
left-hand
of
(S) state
and
of
the
the
[butadiene]*’ [ethylene]+’
of of
(w,W)A
state and
is
11.5
the
species,
adopted
it
should
These
this
on this
since
side
the
of
be noted
that
probably
lie
of
Figure
the
states
two (U,n) close
7 is
of
may not be
fra
the photo-
10.5 eV for
are
It
a lower
of butadiene
suggest,
states
the
therefore,
the most likely.
[cyclohexene]” are
in energy,
is
energy
is
possible:
with
On more
symmetric
the antisymnetric
the two. the of
state
especially
correlation
and
diagram should
[cyclohexene]+’
ethylene,
State
the w
butadiene.
that
the
cis-cis Other
favourable.
as discussed
readily
undergo
leads
cycloaddition
[2+4]*’ processes
above
all
to the conclusion
cycloreversion
have higher
to ground of
butadiene
energy
barriers
overcome.
FIGUE?, 7.
used to
1.5 eV cclmpares with
These data
of
are
and cationic
potential
of
shown as correlation
the diagrm
are
6
the orbitals,
(ne),
derived
ionization
side
very
retained
ethylene
difference
and ~1 of butadiene.
ordering
of
and
symmetry is
subscripts
respectively,
first
[ethylene]+’
the state
values
and neutral
this
nlus
Figure
ethylene
potentials
more
pathways.
forms of
diagram,
is
there
to the correlations
neutral
and yl,
the right-hand
the
Figure,
that
~2
by the
The relevant
Moreover,
for
of (cb),
[butadiene]*’
butadiene,
mirror
rise
are
direction.
or into
we can construct
states
~2
either
reaction
which
ionization
eV for
ethylene.
(A).
lower
of
on vertical
eV between
the
except
Interpretation that
2.5
antisymmetric
being
of
states
side
straightforward,
state
that
of
the ordering
and
and neutral
than
aide
butadiene
in
suggested
6,
and buta-1,3-diene.25
and 9.0
the ground
lower
baeed
are
Figure
right-hand
cationic
in
cpcloadditions
Not only
and ethylene
symmetry give
of
ordering
ia
ethylene
[ethylene]+’
eV
larger that
of
ethylene,
that,
pair
but
that
place
plausible
reaction,
the sac
On the
reactions.
[butadiene]*’
the number of
cis-cis
with
and the corresponding
[2+2]” may take
correlations
(nb),
relative
obvious,
into
correlations
7.
neutral
the
reactions
the
orbital6
identify
of
increases for
lines
crossings
lines.
diagram
that
distinct
correlations
avoided
solid
two
or [cyclohexene]*.
than
may deccrmpose either
and this
throughout. but
cycloreoersion
complicated
involved,
[cyclohexene]+. butadiene;
and cvcloadditions.
the
more
15s
correlations
corresponding
[2+4]
for ‘*
the cycloreversion
of
[cyclohexene]+’
and the
cycloadditions.
(Gs),b h, fl&, hrrl,,
hf.rr’ll,,
+
l
(GSI,,
+ ES),,,
(GZ&, + (GSb
@s&b+ (GS),
state and to
I. R. DUNKIN and L. ANDREWS
156
Similar
state
correlations
of
frontier
orbital
predictions detail
in
is
interactions
for
example
of are
interactions,
included
preferred
set
3.
additions
is
ground
reactione
for
state-ground butadiene
TABLE
3.
No.of Electrons = m+n-1
Cycloreversion
cycloadditions the consideration
the 8me is
stereochemical
that
some of
the ground state
reaction
Predictions
and ethylene. baaed
on
the of
for
frontier
the
orbital
with
of
of
-
these
is
likely
It likely
a distinct
There
except is
correlate
is most
there
for to
interactions,
cia-trans
favourable.
cations.
cations,
and this
orbital
or
unfavourable,
states
be especially
reactions,
the
-
are geometrically
and radical
7),
routea
excited
and the corresponding
or frontier
stereoapecificity
these
for
cycloadditions
preferred
lowest
will of
[m+n]+*
are,
of course.
directly is
amongst this
similarity however,
to reduced
Sme
in a tie-ciq
to be found.
latter
Finally,
between
no direct
charge-transfer
lead
are
trane-trane
the
ground
pairs
such as
etereoapecificity
species.
Orbitally preferred stereochemistry of [m+n]” cycloadditions and the corresponding cycloreversions. The cycloadditions are between two ground rtate reactants or between one excited state and one ground state. Ground State
cis-cis or trans-trans
(n=1,2..)
-
(Figure
reactions
5
4n*5
betveen
symmetry nodele
rings
molecules
correlations
cis-tranr
(n=1,2..)
yields
simplification
and cycloreversiona,
where the
degree
that,
neutral
3
4n+3
the
[butadiene]*’
orbitally
products
[ethylene]*’ state
for
difference
outcomes
in small
.!I high
out
state and
in the ground
t
that
both
however,
3.
the
hand -
state
worth pointing
predictions
of
by orbital
Some of
on the other
vith
group of it
Table
predicted
or cycloreversions
processes, manner
in Table
stereochemical
as
in
and that
and tram-tram
and cycloadditions.
cyc loreversions, out
intereating
cis-tram
cycloeddition, cycloadditions
[24]+’
The penalty
cycloadditions
[2+4]*’
cycloreversions
The
the
for
the [z+z]+’
manner.
and butadiene
stereochemistry
for
in the
a much simpler
lost,
[ethylene]+’
General
may be constructed
As shown above
and cycloreversions.
Excited
cir-trane
(a,.+)
1
(u,u)
t
1
cis-cis t or trane-trans
4-I
State
(o,n)
cis-trans
1
cis-cist Or
tram-tram
1
hf,R)
i
-
1
I cis-cis or tram-tram8
I
tie-trans
cis-trans
tie-cis or trana-tranb
only.
-
II Cycloaddition
only.
1- I
cis-cis Or
trams-trams
1
(lr,le) cis-cis I or trans-trans
c cis-trans
cis-cis or trans-trann
tie-trans
Orbital symmetry
PIcuuE
Favourahle
8.
A-shifts
conservation
frontier of
orbital
order
[1,3]
and frontier orbital control
interactions
and
for
157
radical
cation
sigmatropic
[1,5].
Il. 31
r.
iG.9
SOMO
h-r,’
HOMO
-.
>
Ground
and
Cw,n*)
(u,w)
states
atate
-
-
antarafacial
euprafacial
- +* 3 1
r
Il.51
CH3
CH3
IGSI
SOMO
hrl
HOMO
$$
/
LUMO $$
LUMO Ground
and
HOMO (w,n)
states
LUMO $$
-
suprafacial
SOMO -#$j
HOMO (w,n*)
LUMO state
-
antarafacial
I. R. DUNKIN and L. ANDREWS
158
SIGMATROPIC SEIFTS
The
orbital
Woodward
and
correlations
control
based
straightforward indicate
cat ions,
cations
are
Radical
cation
the
found
stages
respectively.
early
C-H
of
(n,n*)
for
oethylene
it
8,
are
with
for
shifts. phase
of
first
The most
continuity
sigmatropic
sipatropic
by
and state
shifts
ehifts
to in
in radical
1,5
may be considered rr-system,
states
lie
below
of
that
pathway
for
the
of
the
and
are
(n,rrl
orbital6
and
to be in
the radical model of
of
(a,~)
H-shift
is
are, the
states,
mutatis
the
the w-system
than where overlap
the [1,3]
reversed,
states,
of
orbital
pathvay
ground
tvo
is
hydrogen-shifts
states
frontier
for
which
[penta-1,3-diene]+‘,
the (w,n*)
preferences in
and [1,5] and
energy
between
the u-bond
the appropriate
preferences
ground
[1,3]
In the
a lover
orbital
These
state.
for
features
between of
as a” interaction
and (ii)
[prope”e]*’
the SOnO’s.
overlap
beginning
antarafacial
is
Orbitally of order
capable
respect
example,
included
to
inversion,
and
mutandis,
and anatarafacial
the for
for
reaction
is as
pathways
is is
able
to
possible
are doubled
migrate with
the
in
an
methyl
or
in number and become
4.
preferred [i, j] .
stereochemirtry
of radical
I
sigmatropic
supra-supra or antara-antara
supra-eupra or antara-antara .
shifts
(w,n*)
supra-antara
I
supra-antara
cation
Bxcited State (vr,lrl
(a,lr)
supra-aupra or antara-antara
(n=1,2..)
if
&.
own configuration,
the poesible
in Table
supra-antara
4
(n=1,2..)
of its
Ground State
i+j
4”+4
Excnnples of
and
shift
clear
the (n,+)
group
manner
TABLE 4.
4”+2
is
or orbital
treatment
with
orbital
* migrating
groups,
which
r1,3
the original
positive the
was dealt
systems,
to sigmatropic
interactions
following
the most striking
suprafacial
H-shift.
the
inapplicable
approach.
excited
which
indicates
Figure
route
antarafacial
those
above,
state. If
the
molecules
4-7).
order
(i)
two
LllMO’s,
unfavourable
suprafacial
of
lowest
the reaction,
From
[1,5]
and
o-bond
geometrically
former
neutral
in the reacting
orbital
In
a sigmatropic
As noted
negative.
the
shifts
are
frontier
1 (Reactions
of
low energy
stages the
syetry
the
in
rymetry
8 shows H0!40- or SOHO-LIMO interactions
states
are
low
pathways.
in the molecule.
Figure
cations
and
in Table
shifts
of of
adopted
sigmatropic
early
ground
energy
we have
moieties
broken.
on conservation
lowest
radical
The
sigmatropic Because
models make use of
the
separate
of
Hof fmann .26
I
eupra-antara
I
supra-antara
supra-supra or antara-antara
Orbital symmetry
Radical
cation
The an
ally1
sinmatropic
prototype radical
depicted
in
ahifts
radical
an ally1
9.
The
suprafacial-suprafacial the
(n,n*)
IO the
The
latter
general
state,
radical
Extension given
in
pathways
should
Table are
significant
4.
the
i,j
with
fra
FIGURR 9.
SOMO-LIJMOinteractions
the
molecule
is
4 other
Pwourable
is
Pore
likely
lowest
two
orbital of
to
drop
systems
down
leads eo1e
to
be
excited
thia
to
the
to of
the the
(n,n)
I
shift
is
for
the
radical
always
cation
-3
1
+*
\
I
I
Cation LUMO Ground
and
(n,r)
etatea
Radical LUMO
Cation HOMO -
auprafacial-ruprafacial
Radical SOMO
\ I
I
I I Cation LUMO
(rr,d)
atate
while
state.
generalized orbitally
Radical LUMO ,
the
manner.
Perhaps
followed.
0
Radical ,
are in
manner,
[3,3].
0
I
between syota
rearrange
states.
interactions
order
1
SOMO HOMO
higher
unlikely
\ +c-
IGSI (ml
in should
a ruprafacial-suprafacial
the
shift
interaction
suprafacial-antarafacial
cycloreversions,
and
frontier
rigmatropic
the
antarafacial-antarafacial) farourable
and
that
of
as
[hexa-l,%diene]+‘
less
to
cycloadditione
or
treated
shift.
discussion
Table
one
of
unlikely in
unfaoourable
of
HO?40- and states
sigmatropic
preceding
As
may be
The (w,rr)
only
the
159
rearrangement
gewetrically
therefore,
geometrically feature
photochemically,
the
rearrange
cation
of
and
and frontier orbital control
f3.3‘1.
Cope
cation.
ground
(or
state
order
cation
and
Figure
of
conservation
-
suprafacial-antarafacial
rules favoured the
most
possible
1. R. DUNKIN and L. ANDREWS
160
concLus1oIIs
In the cation The
foregoing
sections,
electrocyclic theory
is
based
models,
which
radical
cations
are
electron
from
(SOMO).
As
relatively from
a
the
result
highest of
the
of
ground
state
are
and
are
them.
in
energy very
a recurring not
fra and facile
the
the
qualitative loosely
and
extensive
consistent pathways
reactions
are
meantime,
there
patterns can
occur
concerted is
every
or sign
of for
that
the
the
are
together neutral
lowest
of
the
that
fact
can excited to
photochemistry
be of
etates,
organic
and
the
be
favoured
product
ground
electron, There
cations
are
higher
rationalization can
of
undergo.
reactions, indeed,
whether whether
cations
is
the In
experimentally.
radical
of
reactions
unpaired
these and,
neutral
molecules.
cations
demonstrated
to
generally
will
radical
in
and
states
a general
found
The
leads
cycloreversion
of
radical
be
excited
neutral
form
that
LOHO.
stereochemistry
state
because
parents,
two
remain
excited
reactions with
the
pathways and
two
an electron
states
cations
an
orbital
possess of
excited
on the
different
of
occupied
SOHO to
radical
two
Organic
removal
cations
the
lowest
possible
rearrangements
all
the
for
reactant
stereospecificity
stepwise
from
interaction
by
prmotion
low-lying
and
state
their
by
cycloaddition,
correlations
photochemical
or
the
properties,
theory,
radical
attained
radical
molecules.
a singly
few restrictions
are
between
than
leaving the
since
excited
bound
MO theory,
SORO,
electrocyclic,
Such
neutral
relatively
cations,
symetry the
analogous
more
different
a rich
the
field
investigation.
This University these
in
there
orbital
in
thus
organic
rearrangements.
frontier
of
may be
the
two
of
sigmatropic
derived,
predictions
that
correlations
feature.
found
Whether
for
radical
or
direct
cations,
indications
the
of
in
Moreover,
to and
theoretical is
orbital-phase
of
orbital
these
or
configuration, which
theory
and
reactions are
molecule,
states,
state
the
reactions
different
radical
in mongst
which
electronic
occupied
qualitative
conservation
analogous
neutral
excited
doublet
photochemical
of
this
the
atater
parent
doubly
differences
each
the
a simple cycloreoersions,
symmetry
for
ground
doublet
Foremost
for
established doublet
HOHO of
significant
have
on orbital
well
molecules. the
throughout
low-lying
existence
presented
cycloadditions,
have the
we have
reactions,
paper of
institutions
was
written
Strathclyde, are
while as
thanked
one
Visiting for
of
the
Scholar their
authors in
assistance.
(I.R.D.)
Chemistry
at
was the
on
leave
University
of
absence
of Virginia.
from
the Both
Orbital symmetry
1. 2. 3. 4.
5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19.
20.
21. 22. 23. 24. 25. 26.
conservation
and frontier orbital control
T. Shida, E. Haselbaeh, And T. Belly, Acc.Chti.Re~., l7, 180 (1984). C. Sandorfy, Can.J.SpectroAc., l0, 85 (1965). (a) U. Klemm, Dissertation, University of BAAAl (1981). (b) T. Bully, S. Nitsche, K. Roth, And E. Raselbach, to be published. L. Andrewa, Annu.Rev.PhyA.Chem., 30, 79 (1979); and in “HoleculAr Ions : Spectroscopy, Structure and Chemistry,” cd. T. A. Miller And V. F.. Bondybey, Amsterdam North-Holland, (1983) p.91. B. J. KelA~ll and L. Andrews, J.Chem.PhyA., 76, 5005 (1982). E. HAAelbAch, T. Bally, R. Grchwind, U. Klcma, And 2. Lanyiova, Chiaia 33, 405 (1979). -I T. Shida, T. Kate, And Y. NoAAka, J.Phy~.Chm., 81, 1095 (1977). B. J. KelAAll and L. Andrevs, J.PhyA.Cbem., g, 2723 (1984). I. R. Dunkin, L. Andrews, J. T. Lurito, And B. J. Kelsall, to be published. T. Shida, personal collmunication. T. Shida, Y. Egawa, H. Kubodera, And T. Kate, J.Ch~.PhpA., 73, 5963 (1980). 8. J. Kelsall and L. Andrews, J.Am.Cher.Soc., 105, 1413 (198fl. B. J. KelAAll And L. Andrevs, unpublished work. L. AndrewA, I. R. Dunkin, B. J. Kelsall, and J. T. Lurito, to be published. T. Shida, T. UoPoAe, and N. One, J.PhyA.Chem., in preae. J. H. Kim And E. R. Thornton, J.Am.Chem.Soc., 97, 1865 (1975). N. L. Bauld And J. CeAAAc, J.Aa.Chu.Soc., 99, 23 (1977). E. Raselbach, T. Bally, and 7.. LAnyiovA, Aelv.Chim.ActA, 62, 57 (1979). (A) R. Aoffmann and R. B. Woodward, Acc.Chea.ReA., 1, 17 (1968). (b) R. B. Woodvard and R. Hoffmann, “The ConAervAti& of Orbital SFetry,” Verlag ChemieAcademic Press, New York (1970). (a) K. Fukui and M. Pujimoto, in “MechAnismA of MOleCular Migrations,” ed. B.S.ThyAgArajan, Interscience, New York, ~01.2, p.113 (1968). (b) K. Fukui, “Theory of Orientation and Stereoselection”, Springer, Berlin (1975). W. A. Goddard III, J.Am.Chem.Soc., 94, 793 (1972). R. B. Woodward and R. Hoffmann, J.Am.Chem.Soc., 87, 395 (1965). H. C. Longuet-Higgins And E. W. Abrahmron, J.Am.Chem.Soc., 87, 2045 (1965). R. HOffmAnn And R. B. Woodward, J.Am.Chem.Soe., 87, 2046 (1965). R. H. White, T. A. Carlson, And D. P. Spears, J.ElecCron., 2, 59 (1974). R. B. Wocdward and R. Hoffmann, J.Am.Chem.Soc., 87, 2511 (1965).
161
Am
FmmTIEP
oD4o-l020;8553.00 + .oo c 1985Pergamon Press Ltd
mBITAL
mBITAL
SRagipY
axmoL
m m
ccels~vAIIm
-10ns
omnxc
OF
CATION
mumAt
Ian R. Dunkin*
of Pure and Applied
Department
295 Cathedral
Chemistry, University of Street, Glasgow GI 1XL
and Lester Department
of
Chemistry,
University
of
(Received
Andrew
Virginia,
in UK
Strathclyde
Charlottesville,
5 November
Virginia
22901
19R4)
Abstract: Electrocyclic ring-opcninga, cpcloreversions, cycloadditions, and sigmatropic rearrangements of organic radical cations are discussed in terms of a simple qualitative theory, based on orbital s-etry conservation or is placed on the photofrontier orbital interactions. Special emphasis numerous examples of which have chemical reactions of the radical cations, recently been discovered experimentally. The theoretical models are in good radical cation rearrgeneral accord with the apparent facility with which angements and fragmentations have been observed to take place, and provide swe detailed predictions, especially with respect to stereochemistry, for further experimental testing.
Organic methods a
radical
for
cations
generating
thorough
investigation
I-irradiation
of
vacuum-u.v.
irradiation
As
a result
variety that
of
of have
been
illustrate
of
familiar
the
resemblance
between
cations,
orbital
interactions
radical
cation
specific
class
recent
regard
to
to
the
control
paper,
we have
the
radical
play
a part
likely
area,
the
which
of
cation
hitherto
thin
type
it
reaction
processes (i)
of
and (iii) has
the type
to provide (ii)
been
ie
there
is
species
and those
orbital
sywoetry
largely
145
that
been During
sac
therefore,
is
province
1.
of
for
physical
the
theoretical with
extension
theoretical
organic
the
over
In writing
experiments
caongst
of
particularly
a simple
qualitative
the
discussed
more general
an elclentary
interest
doublet
deliberations
would be helpful,
further
of
or frontier
and stereochemistry
already
to
cation
a superficial
whether
have
a
such as are
leaat
in Table
to promote
spectroscopists.
at
exaplified
to encourage
intended
neutral
became apparent
What follows,
the proceesee
of radical
pathways
pathways
can undergo
Some of
examples
rearrangements.7,16-lg
unlikely
reactions,
theory,
allowed
in Ar matricea.4t5
cations
and cycloreversions,
Hence
include
eimultaneous
the selection
reveal
shifts,
the
however,
purpose:
pericyclic
will
several allowing
methods
ionization radical
1, where
or triplet
in detemining
These
thus
or Ar matricea,1*3
that
the question
transformations.
to cover
a threefold
of
sigmatropic
praxpta
radical
and
Table
molecules.
Considerationa
findings,
cation
this
singlet
of
resemblance
made.
and fragmentations.
shown in Table
at
uncharged
reactions
photochemical
predictions
promising
the
models
are
be Freon
apparent
rearrangerents
ring-openings, of
electrocpclic
the
becoming
A glance
reactions. of
orbital
of
typical.
of
but
been developed,
and two-photon
deposition,4 is
with mass-spectrwetry,
have alao to
X-irradiation
or postulated
and this
experimental as
it
matrices
photochemietry
photochemical
cheaietry
radical
guidance
studies,
electrocyclic
in
known in connection
their
and Ar-matrix
observed is
best
matrices,182
facile
what
analoguea
of
Freon
recent
very
are
them in low-temperature
of this
model
aimed at testing chemists
in this
chemists
and
146
I. R. DUNKIN and L. ANDREWS
TABLE 1.
Poatulated
and observed
photoprocessee
of radical
cationa.
(Ref.
2.
0 ’
l+-
=_
(Refa.
\
&+_ 6”_ 84”_ a+’
6)
cl+* -
7 and 8)
(Ref.
11)
(Ref.
12)
(Ref.
13)
(Ref.
9)
(Ref.
141
(Ref.
15)
Orbital symmetry conservation and frontier orbital control
147
GElmRAL coesIDxRATIons
Dercriptions frontier
orbital
currency
of
symbols
of
depicted phase
mechanistic these
have
a singly
parent
promotion
of
occupied unoccupied
the
the
to
that
the
two
within
of
aa (n,n),
of
the
of
their
and
elcctrocyclic special in
two
orbitals,
not
included
on ground
both
for
Cyclobutene 1” Figure to
is
for
the
the
orbital the
C-C
they by
point
symmetry
are
Table
that
cyclic
of
these
doubly
It
8o.e
of
lowest
excited
statea
classification
or (~,a*)
paper.
remove
polyenes
on the other,
will
the
be seen
later
restrictions
ring-openinge
were
23
Since
have been publirhed Fxcaples
of
first
proposed
then,
similar
by several
photochemical
1-3,
versions
5,
of
the excited
correlatione
(CS),
(r,n*), reactant
and
on
neutral
of
by Woodward and treatments,of
groups,7*l+lg
electrocyclic
and 7).
those
state
to
of
the
broken
Ihe
with
processes
rchemes we outline
previously
advanced,
and are
correlations.
(S:
are
for
the
included.
of
element the
that
into
openings
product
labels lower
are
while
these
orbital6 to
of
elaborated
orbitala during the
(i)
opening,
appropriate
part
The correlations
opening,
orbital.9
conrotatory
splmctry In the
the
orbitals,
relating
and (ii)
is maintained
disrotatory
the molecular
are
Each of
[cyclobutene]+‘.
transform
[cyelobutene]*’
the TT and n*
antisymmetrical)
Alternative
alno
they
(91 - 14). A:
of
and product,
reactant,
and also
and conrotatory
states will
reactant
symmetry is maintained,
is maintained.
symmetry that,
and d),
symmetrical;
the ring-opening
both
For
four n orbital6
disrotatory (u,w)
(a
for
for
reaction.
ti:d,b)
orbital8
indicate
the is
symmetry
both
depicts,
Es (mirror)
(&:g’,&“; for
respect
in
labels
axial)
that with
energy
in the SOnO to the
clcctrocyclic
1 (Reactions
orbital
the set
where
groups
correlations
prototype
cations
highest
by
REAcTxms
and to emphasize
bond
symmetry
correlations
ground
the
radical
one attained
exist.
from the simpler
involved
opening,
aseumption
These
the
Q2 (two-fold
two
in
to
derived neutral
orbital,
the simple
thin
they each is
[buta-1,3-diene]+’
directly
product,
or
region
the ground-state
and aa (n,+)
throughout
likely
correlations.
found
description
that
states:
from
h.
is
cation
occupied
adequate
Abrahamson.
The top section
with
disrotatory where
state
completeness
,--*
classified
the
and
1 shows the important
most
associated
of
radical
essentially
[buta-1,3-d&w]+‘.
orbital6
ia
are
differ
are
spanetry
to an unshaded
atate
excited
the electron
otherwise
and higher
in
singly
of
be adopted
Longuet-Higgins
cations
do
and
orbital8
their
cations
(RCHO) of a
on the one hand,
atate
treatments
processes
emphasis
radical
below
by
a shaded
configuration-intcraction,3b*7
which might
cyclohexa-1,3-diene,
cyclobutene, Aof fmann22
the general
molecular
a ground
electronic
by promotion
or (a,~)
these
symmetry
of
naenclature
to indicate
radical
orbital
possessing
a fully
and will
paths
of
exenple,
occupied
KLEccRocTcL1c
Orbital
now part
standard
instance,
fra
feature For
valence
considerable
(a,~),
reaction
special
low-lying
Although
validity,
existence
photochemical
solely
a change
are
the
atomic
the highest
relatively
(LUMO).
an approximate
adopted
orbital8
on symmetry conservation,19
-
for
(SOnO).
the SOHO, the other
inclusion
states
orbital
fra
an electron
orbital
requiree
the
MO theory,
a consequence
have
orbital
baaed
In the Figures,
now conventional,
molecular
Ar
of
-
continuity21
in the wave-function.
onc electron
generally
paths
phase
We have
treatments.
is
of
occupied
of
a8
phare
reaction
chemistry.
aa cabinations
context
molecule.
cations
ha8
of
the
of
or orbital
known
and,
a change
removal
control
organic
well
properties;
Within
of
the orbital
schematically
denotes
by
of
interactiona,
Figure
for
1,
each of
rely
which hare
to
on the the 8-e
the transformation. (n,rr*)
state
of
I. R. DUNKINand L. ANDREWS
148 FIGURE 1.
/
Orbital
correlations
for
the electrocyclic
opening
-1” \
of
[cyclobutene]+’
d+’
c
-
-c2
A(b)
I% LB3
A iaIr)
Sial
S iall
Albl
CS
- c2
A loll)
S(a)
S ial)
A(b)
A (all)
S la)
S loll
A Ibl
u’3
r2 !PI
-
rL,\_ (i)
sia’)
S(a)
Disrotatory
A---
TP
A-
-
opening
J4 Q*
ol,
C, (mirror)
1’.
A YL -4-s Y, X
H
s4
u
s+---
(ii)
---
---
+ +-+
-A
Y,
_X,
+s
Yq
+--+
+-
IH,H~
hn7
GS
symmetry maintained.
Conrotatory
opening -
1’.
-
GS
C2 (two-fold
-
axial)
X
(u,rd
-SC HE
symmetry maintained.
+I+*
)n( urn
A-
lv
s-
X
-s
v4
-A
b
+s?$ X Q s+ 4-A v,
7TA4
GS
Irr,rd
+-
X+
_X_
-
+ XXh,rf)
HE
-3t + b,rrl.
X
+ 4k GS
Orbital symmetry conservation and frontier orbltal control
149
1. R. DUNKIN and L. ANDREWS
150
[cyclobutene]+’
should
transform
(Q,w)
state
only
(u,w)
state
which correlates
both
modes
of
into
a highly
excited
associated
with
into
the ground state
(HE) state;
directly
ring-opening
particular
directly
excited
with
the product
are photochemically
state
involved.
a ground
while
state
of
[buta-1,3-diene]+.
the conrotatory
ground state.
allowed,
Moreover,
state-ground
for
In this
the preferred
neither
it
model,
is
the
therefore,
pathway depending
disrotatory
correlation,
and the
opening,
nor conrotatory
on the
opening
corresponding
to
a favourable
are displayed
more compactly
is
thermal
reaction. The
relationships
correlation
shown
diagrams
derived
directly
frw
but more realistic As
first
1,
can
thus
configuraton
aw2,
the
symmetrical
state
lowest
mainly
barrier
in a disrotatory
(rr,n*) The
energy
state
of
path
is
followed,
should although
be
by
in
the
the
state
The
thus
likely
to
be
the
unlikely
and
for
(n,n)
states,
state
should
an
open
with
the
(conrotation).
barrier
the conrotatory
in reality,
the
down to
pathway has
either
energy
of
in the
dropping
correlates
ring-closure
to occur
(w,n*)
correlation
in contrast,
a substantial lower
the same
which has
disrotatory state,
lower energy
reasoning,
and thus ground
the
state
[cyclobutene]+‘,
alternative
involve
of
of energy barriers
[cyclobutene]*’
or with
will
states
by conrotation,
The (VT,+) of
for
radicals,23
of
as state
show correlations,
configuration-interaction, rule
indication
(U,W)
process.
of
and ally1
a qualitative
By similar
the
Broken lines
to open predasinantly
is
unfavourable
2.
a non-crossing
surmounted.
barrier
from
Figure
in the absence
The ground state
favoured.
disrotation
of
observe
(disrotation)
this
energetically
proceed
likely
be
and (ii),
the cyclopropyl
give
the ground state
but
therefore
for
is
to
product
fras
lines)
be seen that
manner.
the
ring-opening
(i)
would obtain
basis
electronic
appreciable
that
explained
It
1,
portion
(solid
on this
pathways.
Figure
left-hand
Figure
constructed
various
in
the
correlations
bymmetry.23 diagrams
in
whichever
pathway,
vould
and by conrotation
which
,3-diene]+‘ ,
[buta-l
be expected frm
the
to
(n,w)
state. We should excited
not
states
vibrationally
excited
blurred
if
energy,
this
which
electronic the
happens
of
likely
to
with
the
energy be
ground
expected,
state
therefore,
Cyclohexa-1,3-diene
the
electrocyclic
the
reverse
tetraene]+* centre
,
diagrams,
states
labels
(rn)
lowest
three
the
(w,w*)
system.
the
the
(w,w*)
the
reverse
above,
for
ring-opening
will
highest
of
of
the
first
of
are
identified
the orbitals
These
lead
vhich
should
by their of
in order From the
electronic
are
states
undergo
This
applies
to
in these
in is
directly
state,
the
which is
radical
cations.
may be worked out
and
that,
for
is
and
[octa-1,3,5,7-
diagrrrms shown in Figure by Shida -* et
for
the
four
shown,
the
state,
and
five-electron
transformations seven-electron
and ring-closure. for
(n,w)
six-carbon
those
2 at
In these
conventional
cations
the
disrotatory
the eight-carbon
expected
al 7
making use of the
the ground state,
ring-opening
reactions
initial
manner.
polyene
given
predwinantly
while both
that
For each of
may be deduced
will
cyclic
configurations,
energy,
the
asslnning
(w,w*)
[cyclobutene]*-
correlation
w-systems.
increasing
of
of differences
and [cycloocta-1,3,5-triene]+‘,
be compared to
transformations,
stereospecificity
state
be
vibrational
[cyclobutene]*‘,
[hexa-1,3,5-triene]+’
diagrcrms it
and (w,w)
conrotatory
of
to the
conjugated of
for
[cyclohexa-1,3-diene]+’
ring-closures
excess
in a disrotatory
above
the
will
states
can correlate
is met by the
and higher
described
or to
High stereospecificity
the reactant
stereospecifically
to those
openings
hold.
condition
Upper
states
effect
paths.
of
similar
the
nround state
state
this
2,
reactions.
a consequence kinetic
cycloocta-1,3,5-triene]+‘,
reactions,
state.
as
subsequent reaction
excited
these excited
the considerable
states
the
lower
amongst the various
In the ring-opening
to undergo
states,
excited
available
lowest
the product.
respectively.
and right,
to
Distinctions
reduce
on the the
in all
decay
Additionally,
the
in Figure
‘*,
for
in will
correctly
correlations
for
present
where
of
stereosoecificity
extent.
a cation,
barriers
found
ordered
Orbital
be of
high
non-radiative
ground state.
to a large
may well
heights
are
expect undergo
electronic
excitation
most
states
necessarily
may readily
and
system,
As suggested
processes
uhere
the
Orbital symmetry conservation and frontier orbital control
lowest
excited
condition
rtate
obtains
1,3-diene]+’
and
(~2y:r,rf)
of
,
its
the and
Generalized cations
the reactant
the
reverse
we have
presented
the
in Table
2.
Electrons
4n+3 (n-1,2,3...)
t
Ring-opening
reverse
the product
(w,w)
stereochemistry
ground
(u2vl?z)
ring-opening
for
be
state
state. of
of
This
[cyclohexa-
the (n,w)
state
reaction.
elaborated
[cyclobutene]*‘,
readily
of
the
[cyclohexa-1,3-
extended
to
electrocpclic
higher
systems.
reactions
of
radical
2.
Pavoured
electrocyclic
modes for
radical
cations.
Excited
Ground State
(n:1,2,3...)
the
conrotatory
may
1 ;;;::::::;;I
4n+l
with
of
the
[cycloocta-1,3,5-triene]+.
TABLE
No.of
and and its
which
for
directly
ring-opening
reaction,
treatment
predictions
are
correlates
disrotatory
[cycloocta-1,3,5-triene]+-
Obviously diene]+’
of
in
151
1
State
(a,lr)
I
h,n)
I
conrotatory?
1
conrotatory!
1
h,n*) disrotatory
diarotatory
disrotatory
conrotatory
conrotatory
conrotatory
disrotatory
II Ring-closure
only.
only
CICLORgVBRSIOHS AND CYCUIADDITIONS
Symmetry enunciated
rules
by
cation
reactions
radical
cations
are
that
The [2+2]+’
the
;
Subscripts denotes
labels
c and
diagram,
transformation, occupied
found,
orbital
as
reversion ground favoured
shown of
or
to
is
to
denote
occupied
orbital
of
With
part
of
should The
reverse
ethylene
of
with
were
first
radical
cycloreversions
for
of
no corresponding
amongst the orbital6
more
reaction,
and the h,fl)
The
state
readily the state
the
from
of
(I_T,@)
cycloaddition,
[ethylene]+‘.
thus nc state in the a doubly
has only
correlations
suggest state
the
with
cation etate
or
plane.
involved
correlate
radical set
the
mirror
to construct
correlations
[2+2]*’ of
this
directly
must
a unique
symmetry with
respectively;
In order
because
and
which are broken
to
molecule,
of
[ethylene]*’
of mirror
refer
[cyclobutane]*’
3.
cycloreversion of
retention
ethylene.
constraint,
Figure
the
to the two wbonds
neutral
molecule, this
occur
of
we know of
cycloaddition
place
and
that,
ethylene
Rround state
take
to note
neutral
states.
Examples but
correlations
and parallel
cation
orbitals.
molecules
to the analogous
+ ethylene.
[2+2]*’
neceseary
lower
”
their
and vr,, that
the
the
neutral rules
and A (antisymmetrical)
or nc* in
sections.
cis-cis
assumed
these
established.
and
to the ring
of
of
8 and 9),
[ethylene
MO’s
[ethylene]+’
[cyclobutane]*’
(a,a)
for
used
of it
of
f
corresponding are
a doubly
in the n,
well
S (symmetrical)
n are
following
1 (Reactions
reasonably
perpendicular
cycloreversions
Adaptations
the
Table
relevant
the
the w orbital
correlation
electron
the
processes
to a plane
and
[cyclobutane]+’
, and Both
ethylene.
in
in
have been
3 shows
[cyclobutane]+’
formed
found
reaction:
Figure
cycloadditions and Woodward.
presented
are
cycloadditions
respect
for
Hoffmann
that
one is
cyclo-
than from the is
especially
I. R. DUNKINand L. ANDREWS
152 FIGURE 3.
Orbital
and atate
[ethylene]*’
correlations
and ethylene,
for and for
the ~:pclorevereion the csrresponding
of [cpclobutane]+ [2+2]+’
+* W
e
l-l’
CH,=CH-j+’
Orbital
H
+
correlations
S-
State
correlations
=A
v
into
cycloaddition.
CH,=CH,
Orbital symmetry conservation
The
sclme conclusion
consideration
of has
[ethylene]+’ shows
how
state
neutral
its
frontier
faoour
a cis-trana
the
(a,~)
of
course,
state formidable
JWXJRF, 4.
regard
orbital
the
favour
It
between
cycloaddition
should
-
n-orbital
sis-tie
the
at
(n,n*)
between the
energy
state
of
ground
state
reached that
more
the
than
orbital
ethylene
the
of
and the interactions
such
frontier and the
orbital ground
for
(n,n*)
interactions state
of
the
are,
state
of
(GSI
Favourable (u,w)
state
frontier of
orbital
[ethylene]*’
interactions and the
ground
cis - trans
for
the
state
ground of
also state
ethylene.
state
ethylene.
or
4
ground
ground
cis - cis
FIGURE 5.
of
a reaction
5).
Favourable
by
state
SOnO. Figure
and either
requirements
quickly
(n,+)
[ethylene]*’
Frontier
geometric
153
may be be noted
lower
cycloaddition.
although
[ethylene]+‘, (Figure
cpcloaddition
[2*2]+’
vacant
the
[ethylene]+’
CH,=CH,
the
interactions.
interactions
[2+2]+’ of
to
orbital
LUHO -
molecule
or
with
frontier
and frontier orbital control
1. R. DUNKINand L. ANDREWS
154
FIGtIlE 6.
Orbital
correlations
corresponding
[2+4]+’
for
the
cycloreoereion
n
c’d
bs
0
A-
S-
\\\
/ / J/
of [cyclohcrene]*’
end the
cpcloadditioos.
+
CH2=CHJ+’
Orbital symmetry conservation and frontier orbital control
r24+1+*cvcloreoersions Analysis
of
considerably orbital8
shows
but
orbital
possibility
Broken
of
denote
Fran the orbital
shown
in
Figure butadiene
ethylene
(ce).
The
immediately electron
spectra
orbital
of
clear
is
than 1.5
the
for
difference
left-hand
of
(S) state
and
of
the
the
[butadiene]*’ [ethylene]+’
of of
(w,W)A
state and
is
11.5
the
species,
adopted
it
should
These
this
on this
since
side
the
of
be noted
that
probably
lie
of
Figure
the
states
two (U,n) close
7 is
of
may not be
fra
the photo-
10.5 eV for
are
It
a lower
of butadiene
suggest,
states
the
therefore,
the most likely.
[cyclohexene]” are
in energy,
is
energy
is
possible:
with
On more
symmetric
the antisymnetric
the two. the of
state
especially
correlation
and
diagram should
[cyclohexene]+’
ethylene,
State
the w
butadiene.
that
the
cis-cis Other
favourable.
as discussed
readily
undergo
leads
cycloaddition
[2+4]*’ processes
above
all
to the conclusion
cycloreversion
have higher
to ground of
butadiene
energy
barriers
overcome.
FIGUE?, 7.
used to
1.5 eV cclmpares with
These data
of
are
and cationic
potential
of
shown as correlation
the diagrm
are
6
the orbitals,
(ne),
derived
ionization
side
very
retained
ethylene
difference
and ~1 of butadiene.
ordering
of
and
symmetry is
subscripts
respectively,
first
[ethylene]+’
the state
values
and neutral
this
nlus
Figure
ethylene
potentials
more
pathways.
forms of
diagram,
is
there
to the correlations
neutral
and yl,
the right-hand
the
Figure,
that
~2
by the
The relevant
Moreover,
for
of (cb),
[butadiene]*’
butadiene,
mirror
rise
are
direction.
or into
we can construct
states
~2
either
reaction
which
ionization
eV for
ethylene.
(A).
lower
of
on vertical
eV between
the
except
Interpretation that
2.5
antisymmetric
being
of
states
side
straightforward,
state
that
of
the ordering
and
and neutral
than
aide
butadiene
in
suggested
6,
and buta-1,3-diene.25
and 9.0
the ground
lower
baeed
are
Figure
right-hand
cationic
in
cpcloadditions
Not only
and ethylene
symmetry give
of
ordering
ia
ethylene
[ethylene]+’
eV
larger that
of
ethylene,
that,
pair
but
that
place
plausible
reaction,
the sac
On the
reactions.
[butadiene]*’
the number of
cis-cis
with
and the corresponding
[2+2]” may take
correlations
(nb),
relative
obvious,
into
correlations
7.
neutral
the
reactions
the
orbital6
identify
of
increases for
lines
crossings
lines.
diagram
that
distinct
correlations
avoided
solid
two
or [cyclohexene]*.
than
may deccrmpose either
and this
throughout. but
cycloreoersion
complicated
involved,
[cyclohexene]+. butadiene;
and cvcloadditions.
the
more
15s
correlations
corresponding
[2+4]
for ‘*
the cycloreversion
of
[cyclohexene]+’
and the
cycloadditions.
(Gs),b h, fl&, hrrl,,
hf.rr’ll,,
+
l
(GSI,,
+ ES),,,
(GZ&, + (GSb
@s&b+ (GS),
state and to
I. R. DUNKIN and L. ANDREWS
156
Similar
state
correlations
of
frontier
orbital
predictions detail
in
is
interactions
for
example
of are
interactions,
included
preferred
set
3.
additions
is
ground
reactione
for
state-ground butadiene
TABLE
3.
No.of Electrons = m+n-1
Cycloreversion
cycloadditions the consideration
the 8me is
stereochemical
that
some of
the ground state
reaction
Predictions
and ethylene. baaed
on
the of
for
frontier
the
orbital
with
of
of
-
these
is
likely
It likely
a distinct
There
except is
correlate
is most
there
for to
interactions,
cia-trans
favourable.
cations.
cations,
and this
orbital
or
unfavourable,
states
be especially
reactions,
the
-
are geometrically
and radical
7),
routea
excited
and the corresponding
or frontier
stereoapecificity
these
for
cycloadditions
preferred
lowest
will of
[m+n]+*
are,
of course.
directly is
amongst this
similarity however,
to reduced
Sme
in a tie-ciq
to be found.
latter
Finally,
between
no direct
charge-transfer
lead
are
trane-trane
the
ground
pairs
such as
etereoapecificity
species.
Orbitally preferred stereochemistry of [m+n]” cycloadditions and the corresponding cycloreversions. The cycloadditions are between two ground rtate reactants or between one excited state and one ground state. Ground State
cis-cis or trans-trans
(n=1,2..)
-
(Figure
reactions
5
4n*5
betveen
symmetry nodele
rings
molecules
correlations
cis-tranr
(n=1,2..)
yields
simplification
and cycloreversiona,
where the
degree
that,
neutral
3
4n+3
the
[butadiene]*’
orbitally
products
[ethylene]*’ state
for
difference
outcomes
in small
.!I high
out
state and
in the ground
t
that
both
however,
3.
the
hand -
state
worth pointing
predictions
of
by orbital
Some of
on the other
vith
group of it
Table
predicted
or cycloreversions
processes, manner
in Table
stereochemical
as
in
and that
and tram-tram
and cycloadditions.
cyc loreversions, out
intereating
cis-tram
cycloeddition, cycloadditions
[24]+’
The penalty
cycloadditions
[2+4]*’
cycloreversions
The
the
for
the [z+z]+’
manner.
and butadiene
stereochemistry
for
in the
a much simpler
lost,
[ethylene]+’
General
may be constructed
As shown above
and cycloreversions.
Excited
cir-trane
(a,.+)
1
(u,u)
t
1
cis-cis t or trane-trans
4-I
State
(o,n)
cis-trans
1
cis-cist Or
tram-tram
1
hf,R)
i
-
1
I cis-cis or tram-tram8
I
tie-trans
cis-trans
tie-cis or trana-tranb
only.
-
II Cycloaddition
only.
1- I
cis-cis Or
trams-trams
1
(lr,le) cis-cis I or trans-trans
c cis-trans
cis-cis or trans-trann
tie-trans
Orbital symmetry
PIcuuE
Favourahle
8.
A-shifts
conservation
frontier of
orbital
order
[1,3]
and frontier orbital control
interactions
and
for
157
radical
cation
sigmatropic
[1,5].
Il. 31
r.
iG.9
SOMO
h-r,’
HOMO
-.
>
Ground
and
Cw,n*)
(u,w)
states
atate
-
-
antarafacial
euprafacial
- +* 3 1
r
Il.51
CH3
CH3
IGSI
SOMO
hrl
HOMO
$$
/
LUMO $$
LUMO Ground
and
HOMO (w,n)
states
LUMO $$
-
suprafacial
SOMO -#$j
HOMO (w,n*)
LUMO state
-
antarafacial
I. R. DUNKIN and L. ANDREWS
158
SIGMATROPIC SEIFTS
The
orbital
Woodward
and
correlations
control
based
straightforward indicate
cat ions,
cations
are
Radical
cation
the
found
stages
respectively.
early
C-H
of
(n,n*)
for
oethylene
it
8,
are
with
for
shifts. phase
of
first
The most
continuity
sigmatropic
sipatropic
by
and state
shifts
ehifts
to in
in radical
1,5
may be considered rr-system,
states
lie
below
of
that
pathway
for
the
of
the
and
are
(n,rrl
orbital6
and
to be in
the radical model of
of
(a,~)
H-shift
is
are, the
states,
mutatis
the
the w-system
than where overlap
the [1,3]
reversed,
states,
of
orbital
pathvay
ground
tvo
is
hydrogen-shifts
states
frontier
for
which
[penta-1,3-diene]+‘,
the (w,n*)
preferences in
and [1,5] and
energy
between
the u-bond
the appropriate
preferences
ground
[1,3]
In the
a lover
orbital
These
state.
for
features
between of
as a” interaction
and (ii)
[prope”e]*’
the SOnO’s.
overlap
beginning
antarafacial
is
Orbitally of order
capable
respect
example,
included
to
inversion,
and
mutandis,
and anatarafacial
the for
for
reaction
is as
pathways
is is
able
to
possible
are doubled
migrate with
the
in
an
methyl
or
in number and become
4.
preferred [i, j] .
stereochemirtry
of radical
I
sigmatropic
supra-supra or antara-antara
supra-eupra or antara-antara .
shifts
(w,n*)
supra-antara
I
supra-antara
cation
Bxcited State (vr,lrl
(a,lr)
supra-aupra or antara-antara
(n=1,2..)
if
&.
own configuration,
the poesible
in Table
supra-antara
4
(n=1,2..)
of its
Ground State
i+j
4”+4
Excnnples of
and
shift
clear
the (n,+)
group
manner
TABLE 4.
4”+2
is
or orbital
treatment
with
orbital
* migrating
groups,
which
r1,3
the original
positive the
was dealt
systems,
to sigmatropic
interactions
following
the most striking
suprafacial
H-shift.
the
inapplicable
approach.
excited
which
indicates
Figure
route
antarafacial
those
above,
state. If
the
molecules
4-7).
order
(i)
two
LllMO’s,
unfavourable
suprafacial
of
lowest
the reaction,
From
[1,5]
and
o-bond
geometrically
former
neutral
in the reacting
orbital
In
a sigmatropic
As noted
negative.
the
shifts
are
frontier
1 (Reactions
of
low energy
stages the
syetry
the
in
rymetry
8 shows H0!40- or SOHO-LIMO interactions
states
are
low
pathways.
in the molecule.
Figure
cations
and
in Table
shifts
of of
adopted
sigmatropic
early
ground
energy
we have
moieties
broken.
on conservation
lowest
radical
The
sigmatropic Because
models make use of
the
separate
of
Hof fmann .26
I
eupra-antara
I
supra-antara
supra-supra or antara-antara
Orbital symmetry
Radical
cation
The an
ally1
sinmatropic
prototype radical
depicted
in
ahifts
radical
an ally1
9.
The
suprafacial-suprafacial the
(n,n*)
IO the
The
latter
general
state,
radical
Extension given
in
pathways
should
Table are
significant
4.
the
i,j
with
fra
FIGURR 9.
SOMO-LIJMOinteractions
the
molecule
is
4 other
Pwourable
is
Pore
likely
lowest
two
orbital of
to
drop
systems
down
leads eo1e
to
be
excited
thia
to
the
to of
the the
(n,n)
I
shift
is
for
the
radical
always
cation
-3
1
+*
\
I
I
Cation LUMO Ground
and
(n,r)
etatea
Radical LUMO
Cation HOMO -
auprafacial-ruprafacial
Radical SOMO
\ I
I
I I Cation LUMO
(rr,d)
atate
while
state.
generalized orbitally
Radical LUMO ,
the
manner.
Perhaps
followed.
0
Radical ,
are in
manner,
[3,3].
0
I
between syota
rearrange
states.
interactions
order
1
SOMO HOMO
higher
unlikely
\ +c-
IGSI (ml
in should
a ruprafacial-suprafacial
the
shift
interaction
suprafacial-antarafacial
cycloreversions,
and
frontier
rigmatropic
the
antarafacial-antarafacial) farourable
and
that
of
as
[hexa-l,%diene]+‘
less
to
cycloadditione
or
treated
shift.
discussion
Table
one
of
unlikely in
unfaoourable
of
HO?40- and states
sigmatropic
preceding
As
may be
The (w,rr)
only
the
159
rearrangement
gewetrically
therefore,
geometrically feature
photochemically,
the
rearrange
cation
of
and
and frontier orbital control
f3.3‘1.
Cope
cation.
ground
(or
state
order
cation
and
Figure
of
conservation
-
suprafacial-antarafacial
rules favoured the
most
possible
1. R. DUNKIN and L. ANDREWS
160
concLus1oIIs
In the cation The
foregoing
sections,
electrocyclic theory
is
based
models,
which
radical
cations
are
electron
from
(SOMO).
As
relatively from
a
the
result
highest of
the
of
ground
state
are
and
are
them.
in
energy very
a recurring not
fra and facile
the
the
qualitative loosely
and
extensive
consistent pathways
reactions
are
meantime,
there
patterns can
occur
concerted is
every
or sign
of for
that
the
the
are
together neutral
lowest
of
the
that
fact
can excited to
photochemistry
be of
etates,
organic
and
the
be
favoured
product
ground
electron, There
cations
are
higher
rationalization can
of
undergo.
reactions, indeed,
whether whether
cations
is
the In
experimentally.
radical
of
reactions
unpaired
these and,
neutral
molecules.
cations
demonstrated
to
generally
will
radical
in
and
states
a general
found
The
leads
cycloreversion
of
radical
be
excited
neutral
form
that
LOHO.
stereochemistry
state
because
parents,
two
remain
excited
reactions with
the
pathways and
two
an electron
states
cations
an
orbital
possess of
excited
on the
different
of
occupied
SOHO to
radical
two
Organic
removal
cations
the
lowest
possible
rearrangements
all
the
for
reactant
stereospecificity
stepwise
from
interaction
by
prmotion
low-lying
and
state
their
by
cycloaddition,
correlations
photochemical
or
the
properties,
theory,
radical
attained
radical
molecules.
a singly
few restrictions
are
between
than
leaving the
since
excited
bound
MO theory,
SORO,
electrocyclic,
Such
neutral
relatively
cations,
symetry the
analogous
more
different
a rich
the
field
investigation.
This University these
in
there
orbital
in
thus
organic
rearrangements.
frontier
of
may be
the
two
of
sigmatropic
derived,
predictions
that
correlations
feature.
found
Whether
for
radical
or
direct
cations,
indications
the
of
in
Moreover,
to and
theoretical is
orbital-phase
of
orbital
these
or
configuration, which
theory
and
reactions are
molecule,
states,
state
the
reactions
different
radical
in mongst
which
electronic
occupied
qualitative
conservation
analogous
neutral
excited
doublet
photochemical
of
this
the
atater
parent
doubly
differences
each
the
a simple cycloreoersions,
symmetry
for
ground
doublet
Foremost
for
established doublet
HOHO of
significant
have
on orbital
well
molecules. the
throughout
low-lying
existence
presented
cycloadditions,
have the
we have
reactions,
paper of
institutions
was
written
Strathclyde, are
while as
thanked
one
Visiting for
of
the
Scholar their
authors in
assistance.
(I.R.D.)
Chemistry
at
was the
on
leave
University
of
absence
of Virginia.
from
the Both
Orbital symmetry
1. 2. 3. 4.
5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19.
20.
21. 22. 23. 24. 25. 26.
conservation
and frontier orbital control
T. Shida, E. Haselbaeh, And T. Belly, Acc.Chti.Re~., l7, 180 (1984). C. Sandorfy, Can.J.SpectroAc., l0, 85 (1965). (a) U. Klemm, Dissertation, University of BAAAl (1981). (b) T. Bully, S. Nitsche, K. Roth, And E. Raselbach, to be published. L. Andrewa, Annu.Rev.PhyA.Chem., 30, 79 (1979); and in “HoleculAr Ions : Spectroscopy, Structure and Chemistry,” cd. T. A. Miller And V. F.. Bondybey, Amsterdam North-Holland, (1983) p.91. B. J. KelA~ll and L. Andrews, J.Chem.PhyA., 76, 5005 (1982). E. HAAelbAch, T. Bally, R. Grchwind, U. Klcma, And 2. Lanyiova, Chiaia 33, 405 (1979). -I T. Shida, T. Kate, And Y. NoAAka, J.Phy~.Chm., 81, 1095 (1977). B. J. KelAAll and L. Andrevs, J.PhyA.Cbem., g, 2723 (1984). I. R. Dunkin, L. Andrews, J. T. Lurito, And B. J. Kelsall, to be published. T. Shida, personal collmunication. T. Shida, Y. Egawa, H. Kubodera, And T. Kate, J.Ch~.PhpA., 73, 5963 (1980). 8. J. Kelsall and L. Andrews, J.Am.Cher.Soc., 105, 1413 (198fl. B. J. KelAAll And L. Andrevs, unpublished work. L. AndrewA, I. R. Dunkin, B. J. Kelsall, and J. T. Lurito, to be published. T. Shida, T. UoPoAe, and N. One, J.PhyA.Chem., in preae. J. H. Kim And E. R. Thornton, J.Am.Chem.Soc., 97, 1865 (1975). N. L. Bauld And J. CeAAAc, J.Aa.Chu.Soc., 99, 23 (1977). E. Raselbach, T. Bally, and 7.. LAnyiovA, Aelv.Chim.ActA, 62, 57 (1979). (A) R. Aoffmann and R. B. Woodward, Acc.Chea.ReA., 1, 17 (1968). (b) R. B. Woodvard and R. Hoffmann, “The ConAervAti& of Orbital SFetry,” Verlag ChemieAcademic Press, New York (1970). (a) K. Fukui and M. Pujimoto, in “MechAnismA of MOleCular Migrations,” ed. B.S.ThyAgArajan, Interscience, New York, ~01.2, p.113 (1968). (b) K. Fukui, “Theory of Orientation and Stereoselection”, Springer, Berlin (1975). W. A. Goddard III, J.Am.Chem.Soc., 94, 793 (1972). R. B. Woodward and R. Hoffmann, J.Am.Chem.Soc., 87, 395 (1965). H. C. Longuet-Higgins And E. W. Abrahmron, J.Am.Chem.Soc., 87, 2045 (1965). R. HOffmAnn And R. B. Woodward, J.Am.Chem.Soe., 87, 2046 (1965). R. H. White, T. A. Carlson, And D. P. Spears, J.ElecCron., 2, 59 (1974). R. B. Wocdward and R. Hoffmann, J.Am.Chem.Soc., 87, 2511 (1965).
161