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Orbital Correspondence Analysis in Maximum Symmetry.

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Orbital Correspondence Analysis in Maximum Symmetry[**]
By E. Amitai Haleviy]
The use of Orbital Correspondence Analysis in Maximum Symmetry (OCAMS) for determining
the allowed course of a reaction is described in terms of the familiar “A, S” notation. Several
well known thermal and photochemical reactions are used as examples : Polyene cyclization;
the fragmentation and dimerization of cyclobutadiene; [.4 + A2] cycloaddition; the isomerization
of Dewar-benzene. The relation of OCAMS to the classical correlation procedures of Woodward
and Hoffmann and of Longuet-Higgins and Abrahamson is brought out, as are the sources
of the occasionally contradictory predictions of OCAMS and of the classical procedures.
1. Introduction
Although the recognition that symmetry is an important
factor in chemical reactivity goes back nearly half a century[’],
it was only after the appearance on these pages of Woodward
and Hoffann’s classic paperl21that considerations of symmetry became an essential component of the way nearly all
chemists, organic chemists in particular, think about reaction
mechanism.
Since then, developments in the field have been so rapid
and so diverse that the proposal of yet another, formally
different, approach to the subjectc3’ cannot but be greeted
with reserve. Even after the theoretical soundness of the new
method has been established14], its proponent is apt to be
asked :
1 ) Does it contain any genuinely novel features which take
it so far beyond conventional procedures as to make it worth
mastering?
2) If so, is it simple enough to learn and sufficiently easy
to apply that it can hope to gain acceptance as a practical
substitute for the conventional procedures, whenever the latter
fail to yield unambiguous conclusions?
This report is an attempt to answer these two questions
in the afirmative as regards Orbital Correspondence Analysis
in Maximum Symmetry (OCAMS)[3.41.Like the WoodwardHoffmann approach and unlike methods that adopt a valence
bond formalismr5s6l or take configuration interaction into
account[’], and even though it can be used as a basis for
state-correlation studies which include electron interaction[’],
OCAMS is essentially a one-electron, Hiickel molecular orbital
procedure. Moreover, although orbital symmetry and molecular topology are evidently related, explicit consideration of
top0Iogy1~~
’‘1 or aromaticity“ 12,6al is
’
avoided. Finally, no
special weight is placed on the frontier orbitals[’3*14], all
of the occupied orbitals of reactant and product being afforded
equal a priori status.
OCAMS is related to several aspects of Bader’s pioneering
work[”], which has more recently been revived and
extended[I6*‘’I, and also has certain features in common with
the method newly proposed by Mcluer[’81.However, its closest
relative is Woodward and H o f f a n n ’ s orbital correlation procedure[I9],which was formally justified by Longuet-Higgins and
Abrahamson in terms of configuration correlation[20?Accord-
’.
[*] Prof. Dr. E. A. Halevi
Department of Chemistry
Technion-Israel Institute of Technology
Haifa (Israel)
[**I This paper was written while the author was enjoying the hospitality
of the Department of Chemistry, University of California, Irvine.
Angew. Chem. Int. Ed. Engl. 1 Val. 15 (1976) No. 10
ingly, the procedure and findings of OCAMS will be repeatedly
compared in the ensuing discussion with those of the WHLHA
analysis which, in addition to being similar to it in outlook,
is by far the best known of the earlier methods. For the
latter reason too, the commonly used “S,A notation will
be adopted in this report instead of group-theoretical notation,
which-although it is both more compact and less ambiguous-is unfamiliar to many organic chemists.
2. Orbital Correspondence Analysis: Polyene Cyclization
In their first communication~’31,Woodward and H o f f a n n
discussed the cyclization of polyenes solely in terms of the
symmetry properties of their highest occupied and lowest
unoccupied molecular orbitals (HOMOS and LUMOs). In
their second communication[’91, they returned to the same
reaction, which Longuet-Higgins and Abrahamson also used
as a central
but now considered correlations
between all the molecular orbitals of the reactant and product
that might be involved in the reaction. The present discussion
will therefore begin with a brief review of the familiar WHLHA
analysis of the cyclization of s-cis-butadiene to cyclobutene,
which will facilitate the exposition of OCAMS that is to
follow.
2.1. WHLHA Correlation Procedure
It is seen at the top of Figure 1 that the reactant (I)
and product (2) have two symmetry elements in common:
A twofold rotational axis Cz and a mirror plane m which
bisects the molecule. (I) and ( 2 ) , which belong to the symmetry point group C2”, each also has reflection symmetry in
the molecular plane, but this third symmetry element, which
we might denote by m’, is discarded as “useless”, since it
does not bisect bonds made or broken in the reaction12!
In the order to convert (1) into ( 2 ) , the two methylene
groups must each be rotated by 90°, but if they are twisted
separately, all molecular symmetry is destroyed along the
reaction path. By carrying out the two rotations in a concerted
manner, either C2 or m-but not both-can be retained
as a symmetry element; which one is retained depends on
whether the two methylene groups are rotated in the same
(conrotation) or the opposite sense (disrotation). Two correlation diagrams are then set up, one for each mode. In each,
the symmetry properties of the molecular orbitals are specified
with respect to that symmetry element which is retained along
the reaction path, i.e. C2 in the conrotation (Fig. 1 a) and
593
o*A
n* A
a) Conrotation
b) Disrotation
IA136.11
Fig. 1. WHLHA correlation diagrams for cyclization of s-cis-butadiene.
m in the disrotation (Fig. 1 b). The stacking of the molecular
orbitals in order of increasing energy, which is of course
the same in both diagrams, is self-evident, as is their characterization as S (symmetric) or A (antisymmetric) in each of the
two modes. Correlation lines are drawn between orbitals of
similar symmetry, care being taken not to violate the quantum
mechanical rule that prevents two lines correlating pairs of
orbitals with the same symmetry from crossing. (Non-crossing
rule.)
Figure l a shows that the two orbitals which are doubly
occupied in the ground state of the diene correlate with the
two occupied orbitals of the product along a conrotatory
pathway. In terms of configuration correlation, the groundstate configurations of reactant and product correlate with
each other: $1(A)’$z(S)2~~(S)’n(A)z.From the viewpoint
of either orbital or configuration correlation, the thermal,
ground-state, reaction can be characterized as conrotatorily
“allowed”. In contrast, Figure 1 b shows thermal cyclization
along the disrotatory pathway to be “forbidden”, whether
one invokes the orbital cross-correlation between occupied
and unoccupied orbitals, familiarly referred to as a “HOMOLUMO crossing”, or the failure of the ground-state configurations to intercorrelate: $l(S)2$2(A)2#xs(S)2n(S)z.
Before going on to the excited state reaction, we must
recognize that no one-electron analysis can distinguish
between singlet and triplet states having the same orbital
occupancy. In anticipation of our discussion of open shell
reactions (Section 5) the arrows in Figure 1 representing spin
have been drawn so as to suggest a triplet state reaction.
At this stage, however, the excited state reaction is discussed
as if it were the same for both multiplicities.
Returning to Figure l a , we focus our attention on the
excitation from $’ (HOMO) to $7 (LUMO), which causes
each to be singly-occupied.Since singly-occupied +z correlates
with doubly-occupied o rather than with singly-occupied n
594
or a*, the conrotatory excited state reaction is “forbidden”,
a conclusion borne out by the lack of configuration
correlation
between
the
lowest
excited
states:
l(A)’+ 2(s)1+xA)1%m 2 W 1 n * ( s ) ’ .
From Figure 1 b we see that, thanks to the cross-correlation
between the singly-occupied HOMOS and LUMOs and the
fact that the doubly-occupied $1 and o are both S, or
-equivalently
and
more
compactly-because:
~l(S)z$~(A)1$7(S)1~(3(S)2~(S)1n*(A)1,
the photochemical
reaction is “allowed” along a disrotatory pathway.
For the purpose of comparison with OCAMS, we note
two important features of WHLHA:
1) Not all the symmetry elements common to reactant
and product are used in the analysis. Specifically, reflection
in the molecular plane m’ has been dismissed as “unimportant”.
2) Reaction paths corresponding to different ways of reducing symmetry are analyzed separately. The symmetry-breaking
motion (here a conrotation or a disrotation) is not considered
explicitly; rather, its consequences are explored by characterizing each orbital with respect to the symmetry elements that
are retained after the distortion has been applied, in our
example either Cz or m but not both.
It will now be shown how OCAMS elicits the same information about polyene cyclization in a rather different way, i.e.
by investigating the symmetry properties not only of the
molecular orbitals but also of the symmetry-breaking
motions, and by ensuring that their symmetry is specified
with respect to all, not just an arbitrarily selected few, of the
symmetry elements common to the reactant and product.
+
2.2. Direct Correspondence
We first examine the symmetry of the MOs with respect
to both of the “important” symmetry elements. Figure 2 which
Angew. Chem. Int. Ed. Engl. 1 Vol. 15 (1976) No. 10
is essentially a superposition of Figures 1 a and 1 b, shows
that, in the original geometry, the MOs fall into four types:
(I) SS-symmetric with respect to both C 2 and m; ( 2 ) AAantisymmetric with respect to both; (3) SA-symmetric with
respect to C2 but antisymmetric with respect to m; and (4)
AS-vice versa. Orbitals of the first two types evidently lie
in the molecular plane and are symmetric to reflection in
it m', whereas those of the third and fourth type have a
node in the molecular plane and are thus antisymmetric to
m'. Clearly, types (1) and ( 2 ) are o-orbitals whereas types
(3) and (4)are n-orbitals. If we wished to make the n or
o nature of each orbital explicit, we might add a third A
or S, referring to the symmetry with respect to m', to those
for C2 and m. Then, AS would become ASA, SA would
be SAA and the two of o type would be SSS and AAS.
In Czy symmetry, this overspecification is unnecessary, the
x or o character of each orbital being evident without it.
The symmetry properties with respect to C2,m and m' are
fully determined in terms of any two of
so with respect to which ever one of them is retained along
the pathway.
Note, however, that rt corresponds with both q1 and $7
while n* corresponds with both $ 2 and $3, whereas, along
any reaction path, each orbital of the product can correlate
with only one reactant orbital. Therefore, a correspondence
line between orbitals of the same overall symmetry, i. e., one
that denotes a direct correspondence, merely indicates that
the two orbitals can correlate whether or not the symmetry
of the reacting system is reduced, but not whether they will
correlate. The eventual orbital correlations, which differ for
different reaction paths, can hardly be ascertained before the
nature of the pathway has been
Since the
two o-orbitals, notably o(SS) which is doubly-occupied in
both the ground and first excited state, are left out of all
thedirect correspondences, it is obvious that cyclization cannot
take place unless symmetry is reduced, and the onus is placed
firmly on the requirement that two electrons be taken from
a x-orbital of butadiene and delivered to a o-orbital of cyclobutene.
23. Induced Correspondence
B
\
/.
,/
n*S A
'
Hn
A S
a s s
Fig. 2. Correspondence diagram for cyclization of s-cis-butadiene.
Induced corresvondence
Two of the four x-orbitals of butadiene can be brought
into direct correspondence (SAt+SA; AS-AS) with those
of cyclobutene,ensuring that two reactant orbitals could correlate with two of the product without any reduction of symmetry
at all. Moreover, if the symmetry does happen to be reduced
by a conrotation or a disrotation, these pairs of orbitals could
still correlate with each other, since their symmetry properties
are identical with respect to both C 2 and m and would remain
Angew. Chem Int. Ed. Engl. f Vol. 15 (1976) No. 10
We must therefore find a way of inducing a correspondence
between one of the doubly occupied n-orbitals of butadiene
and the bonding o-orbital of cyclobutene. For this purpose
a procedure is borrowed from the way spectroscopic selection
rules are deduced, and reformulated as follows: Correspondence between two orbitals, both of which are either symmetric
or antisymmetric with respect to a given symmetry element,
can only be induced by a displacement which is symmetric
with respect to that element. I f one orbital is symmetric and
the other is antisymmetric with respect to a given element,
they can be brought into correspondewe only by a disphcement
that is antisymmetric with respect to that element.
For example, in order to induce a correspondence of the
type AS-SS, the system must be distorted along a coordinate
that is antisymmetric with respect to C 2 but symmetric with
respect to m, i.e. one that can be represented as AS. Alternatively to induce the correspondence SA-SS (and/or
AS-AA) a motion of type SA is called for.
The specification of the symmetry properties of displacements, which is common practice in vibrational spectroscopy,
is less familiar to organic chemists than the similar characterization of molecular orbitals, but it is no more difficult. Figure
3 shows a number of symmetry coordinates, i. e. coordinates
that are either symmetric or antisymmetric with respect to
all the symmetry elements of the system, by means of arrows
depicting the motion of the individual atoms. If, on application
of a given symmetry coordinate-say m-to the molecule,
all the arrows go into themselves or into arrows identical
with them in length and direction, the coordinate is S with
respect to m. If m takes all the arrows into arrows of the
same length pointing in the opposite directions, it is A. If
it does neither, the displacement depicted is not a symmetry
The correspondence diagram in Figure 2 can now be completed by adding the required induced correspondences
(denoted by two-headed arrows labeled according to the symmetry of the inducing coordinate)to the direct correspondences
between occupied orbitals. For the ground-state reaction,
$z(SA)c*o(SS) clearly calls for an SA distortion, which Figure
595
cussed in subsequent sections, it can be put to good diagnostic
use, whether or not it bisects bonds made or broken[24!
c) By characterizing the orbitals fully before symmetry is
reduced, OCAMS eliminates the necessity for choosing the
pathway by intuition or by trial and error. This feature can
be particularly important in reactions for which the possible
pathways are less intuitively obvious than they are in our
example, and where a possible reaction path might therefore
conceivably be overlooked.
3. Maximum Symmetry: Reactions of Cyclobutadiene
c2
S y m m e t r i c distortion
S
A
9-p
4
b
4f
4t
Conrotation
In-plane a n t i s y m m e t r i c
distortion
Fig. 3. Some symmetry coordinates of s-cis-butadiene.
Chapman et al., having produced cyclobutadiene photochemically at very low temperatures in an argon matrix,
found it to react as summarized in Scheme
These
reactions will be used to demonstrate the advantages of two
aspects of maximum symmetry:
a) Allowing a preferred reaction path to emerge from a
correspondence diagram, rather than choosing several possible
pathways by intuition and analyzing them individually for
“allowedness”.
b) Retaining all the symmetry elements that are necessary
to characterize the system fully, rather than arbitrarily selecting
several of them as more important than others.
Scheme 1
Photochemical fragmentation
F
3 identifies to be a conrotation. Similarly, in the excited state
reaction, a disrotation, which Figure 3 characterized as AS,
is suitable for inducing the required correspondence:
+l(AS)-o(SS). The agreement with the WHLHA predictions
becomes all the more evident when it is noted that the set
of correspondences, direct and induced, selected by a conrotation (full lines in Fig. 2) reproduce the correlation lines of
Figure 1 a, whereas the disrotatory correspondences (dashed
lines in Fig. 2) similarly reproduce Figure 1 b.
18 K)
Caged
fragments
“Thermal”
Dlrfurlo”
dirnerization
(35 K)
(35 K)
H-C
C-H
f
syn -Dimer
2.4. Has Anything Been Gained?
Since the predictions of OCAMS are identical with those
of WHLHA for polyene cyclization, we shall have to go on
to less simple reactions in order to illustrate the greater predictive power of the former. Several marginal advantages are,
however, already perceptible.
a)The driving force for the reaction, and the factor governing
its stereochemistry in both the thermal and photochemical
reactions, is clearly identified to be formation of a 0 bond
from a pair of electrons originating in a rr-orbital. This point
is obscured in the conventional analysis, in which rr and
CF orbitals, each of which can be either S or A with respect
to C2 or m, are not formally distinguished from each other.
b) The justification for regarding certain symmetry elements
as more important than others becomes clear. Cz is the essential symmetry element for a conrotation, as m is for a disrotation, because it is the one diagnostic symmetry element that
is not destroyed along the reaction coordinate. The lesser
importance of m’ in this reaction, does not depend on its
failure to bisect bonds made or broken in the reaction, but
rather on the fact that it is not retained along either pathway
leading to polyene cyclization. In other reactions, to be dis596
3.1. Fragmentation of Cyclobutadiene
The ground state of cyclobutadiene is almost certainly a
planar singlet, but whether it is rectangular as required by
Huckel theory or whether electron correlation is strong enough
to preferentially stabilize it in the square geometry, is less
~ l e a r ~ ~In~ either
~ ~ ’ !case, fragmentation to two acetylene
molecules necessarily distinguishes between the bonds that
are to be ruptured and those that will remain intact in the
product. The “reactant” can thus be regarded either as one
of the two equivalent isomers of cyclobutadiene, or-if the
lowest singlet is indeed square-planar-as having been distorted slightly in the direction of eventual fragmentation.
We begin once more with the WHLHA approach, and
characterize the molecular orbitals in Figure 4 on the basis
of the two “important” mirror planes, m, and mz, that bisect
the rr-bonds being formed and the o-bonds being broken
respectively. The four occupied orbitals and the lowest unoccupied orbital (which is the only one shown in the figure) on
either side are ordered on the basis of the usual considerations:
0-interactions are stronger than n-interactions, the energy
Angew. Chem. Int. Ed. Engl. J Vol. 15 (1976) No. 10
serve as a reasonable reaction coordinate. In the ground state
reaction this is: o-(AS)*s’+(SA), which can be induced by
distortion along an AA symmetry coordinate. In the excited
state reaction, the singly-occupied HOMOSand LUMOs correspond directly with one another, so the required correspondence is: o-(AS)-nr(SA), which also requires a distortion
of type AA. The observed photochemical fragmentation can
thus be rationalized on the basis of a reaction coordinate
that is antisymmetric to both m, and m2;but then, why
is thermal fragmentation, which seems to require the same
type of reaction coordinate, not observed
The reason for the apparent discrepancy is that two coordinates-or two orbitals for that matter-can both be characterized as AA and still not be symmetrically equivalent, because
their characterization on the basis of ml and m2, alone is
inadequate in the higher symmetry adopted for the
A So-
n-y
S
z+y
s
Displacement
n n
Fig. 4. Preliminary analysis offragmentation of cyclobutadiene(higher unoccupied orbitals not shown).
Full lines: WHLHA correlations. Two-headed arrows: Induced correspondences (full -thermal; dashed-photochemical).
increases with the number ofnodal surfaces, etc.. .. Two specific
points should be noted:
1) JI, and
which would have the same energy in a
square-planar molecule, are split as shown to become the
HOMO and LUMO, respectively.
2) As must often be done when the “product” is made
up from two separate molecules, it is thought of as representing
a point along the reaction coordinate at which they are still
close enough to interact. Otherwise, all four combinations
of the bonding s-orbitals would be degenerate, and there
would be no justification for characterizing s5’, the most
bonding combination of the s* orbitals, as the LUMO and
ignoring the other three.
When the usual WHLHA correlation lines are drawn into
Figure 4, the reaction is found to be both thermally and
photochemically forbidden, because the strongly bonding doubly-occupied orbital a-(AS) correlates with the LUMO, which
is unoccupied in the ground-state and only singly-occupied
in the lowest excited state.
Adopting those features of OCAMS which have already
been introduced, we can regard the WHLHA correlation lines
as direct correspondences and investigate whether the missing
correspondence can be induced by a distortion that might
+*+,
Angew. Chem. Int. Ed. Engl. 1 Val. 15 (1976) No. 10
ki
c
ml m2
m3
A
A
A
A
A
S
1
+
-1
Fig. 5. AA coordinates of cyclobutadiene.
Of the two AA coordinates in Figure 5, one is an “out-ofplane twist” that is antisymmetric with respect to the discarded
symmetry element m3 and the other is an “in-plane glide”,
symmetric to m3. The former, which is fully characterized
as AAA, might serve as a reasonable reaction coordinate
for concerted rupture of both a bonds to yield two acetylene
molecules, as in Scheme 2; the latter, AAS, coordinate would
not, since weakening of the bonds initially on the sides of
the rectangle would presumably be accompanied by bonding
across the diagonal to form a transoid four-carbon chain.
Scheme 2 .
597
m3
ml
A
S
A
A
‘k-
r+’ S
A
S
S
S
A
$+
r-y S
A
A
A
S
s
6-
r+’ S
S
A
Fig. 6. Correspondencediagram for fragmentation of cyclobutadiene (higher unoccupied orbitals not
shown).
In order to determine which of these two coordinates to
associate with the thermal and which with the photochemical
fragmentation, Figure 4 is redrawn as Figure 6, in which
the orbitals are characterized with respect to ml, m2, and
m3.
The direct correspondences between the three pairs of bonding orbitals remain as before. The correspondence that has
to be induced in order to allow thermal fragmentation is
now seen to be of the unsuitable AAS type, and-since a
reaction that is formally “allowed by a coordinate that is
geometrically unsuited to serve as a reaction coordinate is
as surely prevented from taking place as one that is formally
“forbidden’-failure to observe it is understandable. The
o -(ASS)c*&(SAA) correspondence needed to allow photochemical fragmentation is just the type shown in Scheme
2 to be appropriate. The same AAA coordinate is also capable
of inducing a cross-correspondence between HOMO and
LUMO, which are no longer in direct correspondence, as
Figure 4 erroneously had them. The observed fragmentation
behavior has thus been rationalized, but only after carrying
out the analysis in maximum symmetry.
598
3.2. Dimerization of Cyclobutadiene: Alternative Product
Stereochemistry
The choice of the geometry in which the analysis is carried
out is not crucial; a poor choice is corrected by OCAMS
by suggesting a reorientation to another geometry. The axial,
noncoplanar, orientation at the top of Figure 7 was chosen
for the analysis of cyclobutadiene dimerization in order to
illustrate three points:
a) Maximum symmetry does not imply the imposition on
the system of as many symmetry elements as possible. In
the geometry adopted, the system is evidently less symmetrical
than in the plane-rectangular orientation (cf. Fig. 8 a) whichin addition to the three rotational axes-also has three mirror
planes and a center of inversion. Figure 8 a implies a product
with a planar cyclobutane ring whereas Figure 7 suggests
that the central ring is puckered. The two are interconvertible
by means of a slight, energetically inexpensive, twist about
the longitudinal axis1301,so it is fully to be expected that
analyses in both geometries would yield the same result-as
indeed they do. The T-orientation shown in Figure 8 b has
Angew. Chem. Int. Ed. Engl.
Vol. I S (1976) No. 10
lA136.71
Fig. 7 Correspondence diagram for dimerimtion of cyclohutadiene (higher unoccupied orbitals
not shown).
as many symmetry elements as the axial orientation, but it
is inherently less symmetrical in that the upper molecule can
use either of its two rc-bonds for a-bonding to the lower
molecule, whereas the latter is constrained to bond via the
two carbon atoms nearest to its partner. Such orientations
can lead to erroneous conclusions and are avoided.
b) Rotational axes alone suffice to characterize orbitals
and coordinates, mirror planes offering no particular advantages over them.
c) The analysis can be carried out in an assumed geometry
which cannot possibly be that of a stable product. The axially
symmetric dimer shown at the upper right of Figure 7 is
too strained to be a real molecule, nor does it stand for
one. What it does represent is a point along the reaction
pathway at which the reactants have come close enough for
(T bonding between them to begin, but beyond which increasing
steric strain forces the system into either the syn or anti
Angew Chem. Int.
Ed. Engl. J Vol 15 (1976) No. I0
[A136.81
Fig. 8, Alternative initial orientations: a) Plane rectangular (acceptable);
b) T-orientation (unacceptable-see text).
599
conformation. Which of the two stereoisomeric products will
be preferred is ascertained with the aid of the correspondence
diagram.
Like the products of fragmentation in Figure 6, the reactant
molecules are brought close enough to interact. Provided
that the twist of the two reactants about the z-axis is not
too great, the ordering of the orbitals-which allows us to
ignore all of the antibonding orbitals above the LUMO-is
~elf-evidentr~~!
As in Czv,two of the three diagnostic symmetry
elements suffice to characterize the molecular orbitals fully.
The choice of Cl, and CX,, rather than of either one of them
and C3,is arbitrary.
The three uppermost pairs of doubly-occupied orbitals are
in direct correspondence, so the ground-state reaction is
allowed by motion along an AA coordinate (i. e. antisymmetric
to CX, and Cl, and thus necessarily symmetric to Cy), which
induces the remaining correspondence JI,(AA)* o ( S S ) . The
folding motion leading to the syn-dimer, shown in Scheme
3, evidently has the proper symmetry; the alternative folding
motion towards the anti conformation is easily seen to have
unsuitable AS symmetry. We might also note that the stereochemical requirements of the thermal and photochemical reactions are the same, and that photochemical fragmentation
of the syn-dimer to cyclobutadiene would be expected to
occur whereas that of the anti-dimer would not.
Scheme 3 .
r - --1
AA
d
Woodward and Hoffiann[2' characterize the formation of
either dimer as thermally allowed by virtue of the reaction
IAI3s.j
Fig. 9. Possible pathways for [n4+K2] cycloadditibn.
600
Angew. Chem. l n t . Ed. Engl. 1 Val. 15 (1976) No. 10
being a Cn4,+ .&I cycloaddition, but favor the syn-isomer
on the basis of secondary orbital interactions. To OCAMS,
the reaction cannot uniquely be characterized as [As .2,]
any more than [&,+,4,] or [n2s+n2,], and the preference
for the observed syn-isomer emerges from it as unambiguously
primary.
+
4. Symmetry, Geometry, and Energy: [Ip+x2] Cycloaddition
Although the predictions of OCAMS with regard to the
prototype Diels-Alder reaction, cycloaddition of ethylene to
butadiene, do not differ essentially from those of WHLHA,
this familiar reaction serves as a good vehicle for conveying
several additional features of the method:
a) How the choice of an orientation of reactants and products
in which to carry out the analysis affects the results of that
analysis.
b) How the method can be applied to systems in which
the product is inherently less symmetrical than the reactant,
because it may be formed as one of several chemically identical
isomers, differing only in the bonding sequence of indistinguishable atoms.
c) How a possible reaction path that is not a symmetry
coordinate can be investigated.
d) How far symmetry alone can take us, and when considerations of energy-always implicit in orbital symmetry arguments-must be made explicit.
Woodward and Hoffmanntzl characterize ground-state cycloaddition as “allowed” when both reactants react suprafacially r.4, + *2,] or antarafacially [n4s =2.] and the excited
+
state reaction as allowed when either-but not both-of the
reaction partners reacts antarafacially, i. e. [As .2,] or
+
[A +
JS].
The coplanar orientation of the reactants, shown in Figure
9a, emphasizes the analogy with a six-membered aromatic
ring, and seems to be a good starting point for the allowed
[As+ n2s] reaction, but it is certainly not the only one. For
example, in Figure 9 b, the ethylene molecule has been rotated
about its axis so that each of its methylene groups is bisected
by the plane containing the butadiene skeleton; this is an
equally good initial orientation for CR4, x2s] cycloaddition
proceeding along an AS coordinate. Beginning with the orientation in 9c, a geometry suitable for [,4,+.2,] cycloaddition
is obtained by motion along the SA coordinate pictured.
The initial mutual disposition of reactants shown in 9d would
seem to be an eminently suitable one from which to begin
along the SA pathway leading to [lp, .2,] cycloaddition.
The fourth mode of cycloaddition, [=4, ,2,], does not suggest
an initial geometry from which the reaction can proceed along
a single symmetry coordinate. A suitable reaction coordinate
can, however, be put together out of a sequence of two:
Beginning from the same initial orientation as in 9b, 9e proceeds via a conrotatory twist of the ethylenic CHI groups
by 90“ and generates a coplanar orientation which differs
from that of 9a only in that the H-atoms-say 1 and 3-that
were initially cis to one other have become trans. When this
is followed by the same AS coordinate as in 9a, cis-geometry
is obtained once more, but the ethylene has reacted antarafacially.
Clearly,whereas someinitial orientations appear to be partio
ularly well suited to a single pathway, others can serve as
good starting points for more than one, and some pathways-
+
+
+
C2m
a?A A
b
:
s s
n”S A
S A $;
A S
s sx
a- A A
A S
a+ S S
IA136.101
Fig. 10. Correspondence diagram for [.4+,2]
Angew. Chem. Int. Ed. Engl.
/ Vol. 15 (1976) No. 10
cycloaddition (initial geometry of Fig. 9b).
60 1
+
C2 is that shown in Figure 9b, which is-except
for the
disrotation at the terminal carbons of the diene-merely a
reorientation that costs no energy. The [.4* n2s] reaction
is thus judged to be eminently allowed. The [,4. + ,2,] reaction,
in contrast, does not emerge from the analysis at all.
Going on to the photochemical reaction, we see that the
HOMO-LUMO cross-correspondence is direct and thus
imposes no stereochemical requirements. Of the two-electron
correspondences, x(SS)-o+(SS) remains, but now +l(AS)
must be brought into correspondence with o-(AA) by means
of an SA displacement very similar to that in Figure 9c
and also leading to [n4a+n25] cycloaddition. Now it is
[BS+ z2aJ cycloaddition, which has the advantage of leading
to a more stable cis-joined product that does not appear.
We try again, starting with the coplanar arrangement of
Figure 9 a and construct the new correspondence diagram
shown in Figure 11. The two x-systems interact and, as a
result, the “reactant’s” x-orbitals now display marked similarity to those of a distorted benzene ring, but the orbital order
is unchanged. The correspondences look different from those
of Figure 10, but the conclusions are not; they are merely
more complete. In the thermal reaction, there is only one
direct correspondence: x(AS)- x(AS). The two remaining correspondences can be induced in one of two ways: 1) An
AS coordinate, such as that of Figure 9 a leading to [n4r
+.2,]
notably that for [,4, .2,] cycloaddition-do not seem to
have a good starting point at all. A good method of analyzing
reaction pathways by symmetry should not be dependent
on the way the problem has been set up. We will find that
OCAMS is substantially independent of the geometrical model
employed, but not entirely: A. poor choice of an assumed
initial orientation of reactants may obscure a possible pathway; it will not, however, let a “forbidden” pathway appear
to be “allowed”.
+
4.1. The Choice of an Initial Geometry
Rather than begin with the too-familiar orientation a of
Figure 9 with its intimations of aromaticity, we base the
correspondence diagram, Figure 10, on that of b. The “product” is also drawn as if it had Czv geometry, although it
will certainly be forced out of planarity and go into either
a cis- or a truns-conformation. As in cyclobutadiene dimerization (Section 3.2), it represents a point along the reaction
coordinate just before the way in which symmetry is to be
broken has been chosen by the reacting system.
In the thermal reaction there are two direct correspondences: +I(AS)ux(AS) and x ( S S ) u o + ( S S ) , whereas the third
+,(SA)uo-(AA) is induced by an AS motion. A coordinate
that is appropriately symmetric to m and antisymmetric to
Y
IA136.111
Fig. 1 I , Correspondence diagram for [n4+r2] cycloaddition (initial geometry
602
Of
Fig. 9a).
Angew. Chem. Int. Ed. Engl. J Vol. 15 (1976) No. 10
cycloaddition, induces +l(AS)*o+(SS) and $z(SA)o-(AA); 2) Motion along an SA coordinate induces: $l(AS)t*
o-(AA) and $z(SA)t*o+(SS). We now note that a rotation
of the ethylene molecule about the Cz axis, which is SA in
character, generates the initial orientation of Figure 9d and
thus leads to C.4, .2,] cycloaddition. The reorientation costs
no energy; the conrotatory distortion in 9d is no more severe
than that in 9c. Thus, apart from the inherent instability
of the trans-joined product, [.4,+ .2.] cycloaddition is
allowed.
Why then does this mode of reaction not emerge from
Figure lo? It is not the “aromaticity” of the coplanar orientation assumed in Figure 11 that makes it a better choice;
the x-interaction does not change the orbital sequence and
so-for qualitative purposes-it is irrelevant. The advantage
of the coplanar orientation is simply that it can be brought
into a suitable geometry for either [,4,+.2,]
or [,4,+.2,]
cycloaddition by motion along a single symmetry coordinate,
AS or SA respectively. The initial disposition of reactants
in Figure 9 b is ideal for [,4, + .2,] but it is too remote from
that required for [,4.+.2,].
In order to convert the initial
geometry of Figure 9 b to that of Figure 9d, motion must
occur along two symmetry coordinates in which only the
ethylene molecule is rotated: (1) About its longitudinal axis
+
the initial orientation of Figure 9a is converted by rotation
of ethylene about its axis (AS) to that of Figure 9b, from
which-as confirmed by Figure 10-a rotation about the
C Z axis (SA) leads to C4.. + .2,] cycloaddition, the paradox
is resolved.
We have seen some of the limitations of symmetry arguments
when these are divorced from consideration of energy, particularly when either the reactant or product is a pair of molecules
that can be arbitrarily oriented relative to one another. Characterizing motions in terms of their symmetry properties alone
cannot distinguish reorientations, which cost no energy, from
molecular distortions, which do. Thus the sequence just described, in which an AS reorientation followed by an SA reaction coordinate that includes a rather mild distortion, is equivalent-purely in terms of symmetry-to the composite motion
of Figure 9e. It is obvious from the dissection of these two
composite motions in Scheme 4 that they are energetically
very different: It is the fact that two of the symmetry coordinates in (a) are reorientations whereas two of (b) are distortions-one
quite severe-that
makes photochemical
C.4, .2,] cycloaddition different from the C.4, + .2,] mode.
Therefore, though the former leads to a less stable product,
it can be regarded as genuinely “allowed”, whereas the latter
cannot c3 ’1.
+
Scheme 4 .
AS-Reorientation
SA-Distortion
(C onrotation)
SA-Reorientation
AS-Distortion
(Disrotation)
SA-Distortion
$,
.
AS- Reorientation
(AS) to the initial orientation of a; (2) about the Cz axis
(SA). Another possible sequence is: (1’) about the Cz axis
to the orientation in c; (2’) about its “new” longitudinal axis
(AA).Neither of these reorientation sequencescosts any energy,
but both formally destroy the symmetry of the system completely before restoring it, so the prediction of Figure 11,
that thermal [A,+ n2a] cycloaddition is allowed, is not made
by Figure 10.
Another paradox concerns the photochemical C.4, .2,]
reaction, that does not appear in Figure 11, even though
it is allowed by Figure 10. In both, the HOMO-LUMO correspondences are direct, but in Figure 11 the two lowest reactant
orbitals are AS orbitals whereas in the product one is AA
and the other is SS. As a result, a proper reaction coordinate
for photochemical cycloaddition would involve motion along
both an AS and a SA coordinate. When it is realized that
+
Angew. Chon. Int. Ed. Engl.
1 Vol. 15 (1976) No. 10
4.2. Alternate Bonding Patterns
+
An important property of C4..
.2,] and C4.. + .2,] cycloadditions, which they share with many other reactions, is illustrated in Figure 12. At the top left and right of the figure
are the respective initial orientations of Figure 9c and 9d,
which are interconvertible by means of a rotation of ethylene
about its longitudinal axis (AA). The reactant pair has Czv
symmetry in both orientations and the molecular orbitals
are characterized accordingly.
The product, as represented at the top center of Figure
12, is less symmetric, since it can be formed in either of
two bonding sequences: [lu14] or [llu4], depending on
whether the upper carbon atom of ethylene bonds to C1
and the lower to C4,.or vice versa. As in previous examples,
we can define the “product” to represent a point along the
603
CZ
A S*I*
n*(SA)
S AS2
s sx
x A A
A S$i
H
h
A s
+
Fig. 12. Correspondence diagrams for [E4a n2,] and [n4. + .2.] cycloaddition (higher unoccupied orbitals
not shown).
reaction coordinate just before symmetry is reduced below
that of the reactants. Now, however, the fact that two bonding
schemes-not just two possible geometries-can be generated,
must be reflected in the symmetry properties of the product's
molecular orbitals.
The HOMO, x, and the LUMO, n*, pose no problem;
they are the same in both enantiomers. Neither do the two
lowest orbitals ofeither product. In [lu14], they are the symmetric and antisymmetric combinations of the 1-u and 4-1
o bonds; in [llu4] they are the analogous linear combinations
of 1-1 and 4-u. In order to restore Czv symmetry to the
product, it is generalized to include both alternatives, so that
the lowest orbital is represented by a suitable superposition
of the two symmetric combinations and the second by a
superposition of the antisymmetric ones. The question that
arises is how to specify correctly the phase of each superposition. Specifically, should the lowest orbital be SS as in the
figure, or should it be the a priori equally valid SA orbital,
in which 4-1 and 1-u are of opposite phase to 1-1 and
4-u? The decision is dictated by the requirement that the
generalized orbital be consistent with an equal probability
of forming either enantiomer. Since C1, for example, must
be equally bonding with C, and CI a moment before the
course of the reaction has been chosen, I-u and 1-1 must
have the same phase. This condition suffices to fix o+(SS)
and (r-(AA) as the two o-orbitals of the generalized product.
The correspondence lines are drawn in the usual way. Thermal [,+la
+ .2,] cycloaddition formally requires that the
JI,(SA)-o-(AA)
correspondence be induced by an AS displacement, but geometry requires an SA motion, as is evident
from Figure 9c. The latter does have the proper symmetry
to induce the JIl(AS)-o-(AA) correspondence required for
photochemical [*4. + n2s] cycloaddition, which is therefore
allowed. Conversely it is the thermal Cn4. E2a]cycloaddition
+
604
which is'allowed under the geometrically appropriate SA displacement shown in Figure 9d, whereas the photochemical
reaction calls for an unsuitable AS motion. Our previous
conclusions have thus been reinforced. The correspondence
diagrams in Figure 12 are different from those of Figures
10 and 11, but the conclusions from them are all mutually
consistent and the additional bits of insight supplied by
each of them complement one another.
5. Open Shell Reactions
The three topics taken up in this section are related by
the fact that unpaired electrons enter into all of them:
1) Odd-electron systems lend themselves as easily to
OCAMS as do those with an even number of electrons, though
their photochemical reactions introduce a new ambiguity.
2) The distinction between the photochemical reactions of
singlet and triplet excited states goes beyond any qualitative
molecular orbital theory, which necessarily neglects electron
correlation, but does call for some comment in the present
context.
3) Several reactions in which the product has a different
spin-multiplicityfrom that of the reactant have been reported,
and will presumably become more common. An orbital
method like OCAMS cannot deal with such reactions without
modification, but a suggestion can be made as to the direction
which a possibly fruitful extension of the present approach
might take.
5.1. Odd Electron Reactions: Cyclization of Butadiene Anion
When an electron is added to s-cis-butadiene, it occupies
the LUMO, (IT,of Figure 2, which becomes a correspondence
diagram for the thermal cyclization of the radical anion, proAngew. Chem. Int. Ed. Engl. J Vol. 15 (1976)
No. 10
vided the five arrows are taken to represent five electrons,
rather than four in two alternative configurations.
As in the thermal cyclization of the neutral diene, correspondence between $l(AS) and K(AS)is direct, and the remaining
two-electron correspondence, $2(SA)-o(SS) calls for a conrotation. The one-electron correspondence $?(AS)-n*(SA)
requires an AA displacement, which can be seen in Figure
3 to describe neither a conrotation nor a disrotation, but
an in-plane distortion. It is, however, shown in Scheme 5
that a 45” disrotation following a 45” conrotation generates
a 90” twist of a single methylene group to a geometry that-if
only momentarily-is symmetric to m’ but not to Cz or
m. Scheme 5 expresses schematically the fact that-in a limited
way-a superposition of an AS and an SA motion is the
equivalent of an AA motion[331.
In the preceding example it was noted that, in contrast
to thermal reactions, where it is sufficient to know which
orbitals are occupied and which are vacant, a reliable OCAMS
treatment of a photochemical reaction requires-at the very
least-identification of the HOMO and LUMO of the reactant. When the reactant has only one unpaired electron, this
is also a sufficient condition, but in photochemical reactions
of even-electron systems it is not. Van der Lugt and Oosterhoff
early raised the question whether a reactant excited by a
two-electron excitation to a state in which both were in the
LUMO would not “funnel through” to the ground-state, in
much the same way as has been postulated above for odd-electron systems, so rapidly that the first excited singlet (HOMO’
LUMO’) is bypassed entirely[36! Even when the first excited
singlet is formed, internal-conversion to a vibrationally excited
Scheme 5.
yields
and
Disrotation
M A )
Unsymmetric
twist
“AA(S)”Geometry
C onrotation
SA (A )
Consequently, our prediction from Figure 2 would be that
the two-electron correspondences require thermal cyclization
of the butadiene radical anion to be fundamentally conrotatory, but that, in order to induce the one-electron correspondence as well, some disrotation must be admixed into the
conrotation, i. e. the two methylene groups would be expected
to rotate at somewhat different ratesr34!
Figure 2 can also be used to discuss the photochemical
reaction. The identity of the first excited state of the product
is irrelevant, since there is no apparent reason for the excited
reactant not to correlate smoothly with the ground state of
the product. In the excited state of the diene anion $rf(SA),
rather than $?(AS), is singly occupied, and its correspondence
to rc*(SA) is direct, so the conrotatory excited state reaction
is allowed. The reverse photochemical reaction is also allowed
under aconrotation, if we assume the excitation in the cyclobutene anion to be n*-m*, because the o*(AA)-$?(AS) correspondence, like that between o(SS) and q2(SA)requires a conrotation. If the lowest excited state were formed by a x+x*
excitation instead, the n*(SA)-q2(SA) and n(AS)-$f(AS)
correspondences would be direct, but that between o ( S S ) and
$l(AS) would call for a disrotatory, AS-type, displacement.
Thus, as will always be the case in photochemical reactions,
a reliable prediction cannot be made unless the reactive excited
stateis known, though-as has been noted-a firm characterization of the lowest excited state of the product can be dispensed with when there is only one unpaired electron in
the system.
ground-state molecule must be considered. The product will
then be formed in its ground-state whenever, before the reactant is vibrationally deactivated, vibrational energy can find
its way into a coordinate of proper symmetry-and geometry-to induce the necessary correspondence to the ground
state of the product. Internal conversion is ordinarily such
a facile process-except perhaps for very small molecules
in the dilute gas phase-that is seems reasonable to doubt
whether configuration correlation between the lowest excited
singlet states of reactant and product can be a reliable qualitative criterion for the prediction of photochemical pathways.
It is with this reservation in mind that all of the correspondence diagrams in this report have been drawn so as to
suggest that the photochemical reaction occurs between the
lowest triplets of the reactant and product. These are sufliciently long-lived with respect to intersystem crossing to the
reactant ground-state for an “allowed” open-shell reaction
to be considered a generally accessible pathway connecting
them. To be sure, a reaction in which the lowest triplet of
the reactant crosses over smoothly to the ground-state singlet
of the product can be envisaged. Such a process would be
analogous to the thermal singlet-triplet reactions to be discussed briefly in the following subsection, and would similarly
occur only in special circumstances. Ordinarily, the triplet
state of the reactant would presumably either decay to its
own singlet ground-state, in which case the reaction would
not occur, or maintain its multiplicity until the triplet product
has been produced, and can decay at leisure to its own groundstate.
5.2. Comments on Photochemical Reactions
5.3. Singlet-Triplet Reactions:Isomerization of Dewar-Benzene
The applicability of orbital symmetry arguments to photochemical reactions, a question which has generated extensive
discussion[35J,will only be touched upon briefly here.
Angew. Chem. I n t . Ed. Engl.
/
161. I5 (1976) No. 10
Several reactions have recently been described in which
a relatively unstable reactant in its singlet ground-state either
605
A S
/
IA1 3 6.131
Fig, 13. Correspondence diagram for Dewar-benzene-benzene
unoccupied orbitals of reactant not shown).
isomerization (higher
decomposes to a singlet and a triplet fragment or isomerizes
to the triplet of its more stable isomer[37'.
The correspondence diagram for the interconversion of
Dewar-benzene and benzene shown in Figure 13 includes
only the three occupied orbitals of the reactant. The familiar
six molecular orbitals of benzene, which include two degenerate pairs, are shown at the extreme right. The simplest way
of bringing reactant and product to a common symmetry,
in this example C2,, is to work backwards and distort the
product slightly in the direction of the reactant, i. e. to bend
two para-disposed carbon atoms out of the molecular plane
towards one another. As a result, the two degeneracies are
split as shown, jr3(AS) going up in energy and $T(SS) going
down.
In the thermal reaction, the one correspondence that is
not direct is O(SS)++$~(AS),which requires distortion of the
Dewar-benzene molecule along a coordinate that is antisymmetric with respect to C1 but symmetric with respect to m.
If one of the o-bonded carbon atoms were pulled outward
along an AS coordinate, such as that shown at the top of
Figure 14, the other atom would move in the same direction
and the long bond would not be ruptured. Such a motion
is clearly inappropriate for generating ground-state benzene,
so thermal isomerization is forbidden.
606
The total energy of Dewar-benzene is not only higher than
that of ground-state benzene, but is above that of its lowest
triplet as well. Its conversion to the latter can occur if two
conditions are fulfilled simultaneously:
1) A mechanism is provided for uncoupling the antiparallel
spins of an electron pair in one doubly-occupied orbital, prefer-
C, m
m'
A
S
A
S
A
A
A
S
A
A
A
S
pTi3Kiq
Fig. 14. Geometrically inappropriate AS-coordinate and the three rotational
coordinates of Dewar-benzene.
Angew. Chem. Int. Ed. Eng1.j Vol. 15 (1976) No. 10
entially that in o(SS), which is not in direct correspondence
with a doubly-occupied orbital of the product;
2) one of these electrons can thep pass directly over to
+T(SS), but an AS perturbation must still be found that will
allow the other electron to pass from o(SS) to $3(AS).
A mechanism with the correct propertiesto fulfil both require
ments at once is spin-orbit coupling. The three components
of spin of a triplet have the symmetry properties of rotations
about three perpendicular axes. In Figure 14 we see that
rotation in the xz-plane, that including m, is of the proper
symmetry to induce a correspondence between an SS and
AS orbital. It must be stressed that we are not speaking
of a molecular rotation, which-though it has the proper
symmetry-does not affect the potential energy of the reacting
system and is therefore ineffective. The perturbation is spinorbit coupling which, as it uncouples the opposing spins of
a pair of electrons, produces a net spin about just the right
axis-y in our example-to generate the lowest triplet of
benzene.
Although a spin-orbit coupling mechanism of this type
has been shown to be theoreticallysound, and to be of reasonable magnitude in at least one
there is as yet neither
experimental nor theoreticalevidencethat it is in fact operative.
Moreover, since it represents at best a future modification
designed to broaden the scope of OCAMS beyond its present
limits, it provides an appropriate point at which to conclude
this report.
Received: May 4, 1976 [A 136 I€]
German version: Angew Chem. 88, 664 (1976)
E . Wigner and E . E. Wittmer, 2. Phys. 51, 859 (1928).
R . B . Woodward and R . Hofmann, Angew. Chem. 81,797 (1969); Angew.
Chem. Int. Ed. Engl. 8,789 (1969); The Conservation of Orbital Symmetry. Verlag Chemie, Weinheim 1970, and Academic Press, New York
1970.
E. A. Halevi, Helv. Chim. Acta 58, 2136 (1975).
J . Katriel and E. A. Halevi, Theor. Chim. Acta 40, 1 (1975).
W! A. Goodard Ill, J. Am. Chem. SOC.94, 793 (1972).
a) J . J . C . Mulder and L. J . Oosterhofl, Chem. Commun. 1970, 305,
307; b) W 7: van der Hart, J . J . C . Mulder, and L . J . Oosterhoff,
J . Am. Chem. SOC.94, 5724 (1972).
N . D. Epiolis, Angew. Chem. 86, 825 (1974); Angew. Chem. Int. Ed.
Engl. 13, 751 (1974).
E . A. Halevi, J . Katriel, R . Pauncz, F. A . Matsen, and 7: L. Welsher,
to be published.
E. Heilbronner, Tetrahedron Lett. 1964, 1923.
H . E. Zimmerman. Acc. Chem. Res. 4, 272 (1971), and papers cited
therein.
M. G . Evans and E. Warhurst, Trans. Faraday SOC. 34, 614 (1938).
M . J . S. Dewar, Angew. Chem. 83, 859 (1971); Angew. Chem. Int.
Ed. Engl. 10, 761 (1971), and papers cited therein.
R. B. Woodward and R. Hoffmann, J. Am. Chem. SOC.87, 395 (1965).
H . Fukui, Acc. Chem. Res. 4, 57 (1971), and papers cited therein.
R. F. W! Bader, Can. J. Chem. 40, 1164 (1962).
L . Salem and J . S . W i g h t , J. Am. Chem. SOC.91, 5947 (1969).
R. G . Pearson, Acc. Chem. Res. 4, 152 (1971).
Angew. Chem. Int. Ed. Engl. / Vol. 15 (1976) No. 10
[293
[30]
[3i]
[32]
[33]
[34]
[35]
[36]
[37]
[38]
J . W Mclver, Jr., Acc. Chem. Res. 7, 72 (1974), and papers cited
therein.
R. B. Woodward and R . Hoflmann, J. Am. Chem. SOC.87, 2406 (1965).
H . C . Longuet-Higgins and E . W Abrahamson, J. Am. Chem. SOC.
87, 2045 (1 965).
If the molecule lies in the xr-plane, with its C2 axis along z, then:
SS=A l ; SA=A2; AA=Bt; AS=B2. Each of these denotes a different
one of the four irreducible representations of C2,, so the symmetry
of each orbital has been fully characterized.
We distinguish between correlation and correspondence by denoting
the former by 9 and the latter by -.
OCAMS avoids degenerate coordinates, to which these criteria do
not apply, just as it avoids degenerate orbitals. See Sections 3.1, 3.2,
and 5.3 for examples.
See also: W. G . Dauben, L. Salem, and N . J . Turro, Acc. Chem. Res.
8, 41 (1975). These authors point out that the “plane containing the
pertinent reaction centers” is, for many photochemical reactions, “the
discriminating symmetry element”.
0. L. Chapman, C . L . Mclntosh, and J . Pacansky, J . Am. Chem. SOC.
95, 614 (1973).
W J . Hehre and J . A . Pople, J. Am. Chem. SOC. 97, 6941 (1975),
and references therein.
An OCAMS analysis and a Hiickel-Hubbard state-correlation study
both show that the two equivalent plane-rectangular isomers could
rapidly be interconverted via a rhomboid transition state. ( E . A . Halevi,
F. A. Matsen, and 7:L. Welsher, to be published).
R. J. Buenker and S. D . Peyerimhoff, J. Chem. Phys. 48, 354 (1968),
calculated cyclobutadiene to be less stable than two acetylene molecules,
but the difference is not large. One might therefore argue that, since
this finding is inconclusive, thermal fragmentation, though “allowed”
by symmetry, may be prevented by its endothermicity. Whatever the
energetics, the symmetry analysis so far has been too superficial t o
permit characterization of either the thermal or the photochemical
reaction as allowed.
A plane-rectangular system has the eight symmetry elements of D2h.
but m,, ml, and m3 can easily be shown to exhaust its eight irreducible
representations, just as Cz and m sufTice.to span the four of CZv(see
ref. [21]).
J. M . Stone and I . M . Mills, Mol. Phys. 18, 631 (1970).
If the two rings are twisted until their planes are perpendicular, jl,
and j12 become indistinguishable, as do Jla and J14. Likewise, the bonding
pattern of the product becomes indeterminate. A slight twist back
towards coplanarity removes all these ambiguities.
A “photochemical Diels-Alder reaction” which is formally [=4. +,2J
doesseem to occur in the cyclization of hexatriene. In this case, however,
the reaction is allowed by OCAMS because the “diene” and “dienophile”
are part of the same conjugated polyene. This reaction, and also contraventionofthe Woodward-Hoffmann rule concerning thermal [,2, +=2.]
cycloaddition, are discussed at length in ref. [3].
As explained in ref. [4], the composite coordinate (AS and SA) is
equivalent in second order to an AA symmetry coordinate. Formally,
the reducible representation [A2 + B2] introduces second order terms
of the irreducible representation: A2 x B2 = B, into the potential energy.
M. J . S. Dewar and S. Kirschner, J. Am. Chem. SOC.96, 6809 (1974)
have shown that the “forhiddenness” of the disrotatory thermal cyclohutene-butadiene interconversion, is greatly relieved when the rotation
at the two ends of the bond being ruptured is not constrained to
be synchronous.
For a critical discussion, with references, see J . Michl, Top. Curr.
Chem. 46, 1 (1974).
W! Th. A. M. oan der Lugt and L. J. Oosterhofl, J. Am. Chem. SOC.
91. 6042 (1 969).
N . J . Turro and P . Lechtken, J. Amer. Chem. SOC.95, 264 (1973);
P. Letchtken, R . Bredow, A. H . Schmidt, and N . J . Turro, J. Am. Chem.
SOC.95, 3025 (1 973).
E. A. Haleui, R. Pauncz, I . Schek, and H . Weinstein, Jerusalem Symposia
on Quantum Chemistry and Biochemistry 6, 167 (1974).
607
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