REVEWS
3
tion of experiment with different styles
of quantum theory, and the impact of
this relationship on the development of
chemistry, are briefly considered. Speculations
are given on why Hiickel's work
exerted so little influence on organic
chemistry for decades before its importance
finally began to be recognized.
Keywords: aromaticity . history of
chemistry - Hiickel, Erich . pericyclic
reactions
Erich Huckel, Pioneer of Organic Quantum Chemistry:
Reflections on Theory and Experiment
Jerome A. Berson"
r
In the period between 1930 and 1937,
Erich Hiickel, a theoretical physicist,
made profound contributions to organic
chemistry in his quantum mechanical
descriptions of unsaturated and conjugated
compounds. A brief account of his
academic career is followed by simplified
expositions, from the point of view
of an organic chemist, of the highly approximate
theoretical methods he used.
Of special significance in the case of
cyclic molecules of the class C,H, is the
concept of filled shells when the number
of TC electrons is (4N +2) ( N =
0,1,2,. ..). Examinations of key applications
of Hiickel's ideas reveal how
they eventually motivated the exploration
of new fields in organic synthesis
and organic reaction mechanism. Another
significant (but until recently, virtually
ignored) contribution by Hiickel
was the recognition that atomic connectivity
is a strong determinant of spin
multiplicity in non-Kekule molecules.
This idea provides, in principle, a basis
for predicting violations of Hund's rule,
as recent computational and experimental
developments confirm. The interac-
1. Introduction
Erich Hiickel's position as one of the early leaders in the
development of quantum chemistry now is secure. Every modern
chemist uses ideas that sprang from his work. Yet certain
causes, undoubtedly connected but still not entirely clear,
marked his career with bitter frustration, delayed the recognition
that he deserved, and not incidentally, retarded the development
of organicchemistry by muffling the impact of his con-
tributions.
To trace the intellectual origins of his work is a challenge to
the historian of science. How did a man trained as a theoretical
physicist have the insight to choose problems of such significance
to organic chemistry? Where did he find the daring selfconfidence
to make the gross (but ultimately successful)approximations
of Hiickel molecular orbital theory? What circumstances
delayed the incorporation of his ideas into the everyday
working knowledge of organic chemists?
[*] Prof. J. A. Berson
Department of Chemistry, Yale University
225 Prospect Street. New Haven, CT 06520-8107 (USA)
Fax. Int. code +(203)432-6144
e-mail: berson %kekule(u biomed.med.yale.edu.
2. Biographical Sketch" -3l
This is the centennial year of Erich Hiickel, who was born on
August 9, 1896,the second of three sons of Marie and Armand
Hiickel. The intellectual development of the three boys was
strongly influenced by their father, a physician with an interest
in pure science.In the family line were several scientificnotables,
including the distinguished botanist Josef Gartner (1732-
1791). Erich Huckel enriched this heritage in 1921, when he
married Anne Zsigmondy, the daughter of Professor Richard
Zsigmondy of Gottingen, a renowned colloid chemist (Nobel
Prize in Chemistry, 1925). The marriage endured until Hiickel's
death in 1980. Erich Hiickel's brothers, Rudi (1899-2949) and
Walter (1 895- 1973), followed in the family tradition. Rudi becamea
physician, but died prematurely. Walter achieved prominence
as a professor of organic chemistry and a prolific author
of significant research contributions and influential text-
book~.[~]
Erich Hiickel was trained as a physicist. His thesis for the D.
Phil. at Gottingen (1921) under the supervision of Peter Debye
was an experimental study of the scattering of X-rays. Afterward,
he served briefly as an assistant to the mathematician
David Hilbert at Gottingen but then rejoined Debye, who had
moved to the Eidgenossische Technische Hochschule in Zurich.
Hiickel stayed in Zurich until 1927. Two years on a Rockefeller
Angew. Chem. In[.Ed. Engl. 1996. 35, 2750-2164 0 VCH VerlagsgesellschafimhH. D-694Si Weinheim.1996 OS7U-O833/96/3523-2751$ 15.UUi .25,0 2751
J. A. BersonREVIEWS
Foundation scholarship, which he spent with Donnan in London
and with Bohr in Copenhagen, were followed by two more
years on a Deutsche Notgemeinschaft scholarship in Leipzig
with Heisenberg and Hund. It was in Leipzig in 1930 that
Hiickel finished the first of his landmark papers on organic
quantum chemistry.
Note that nine years after the D. Phil, Hiickel still had no
permanent job. In effect, his situation was like that of all too
many of today’s postdoctoral researchers, who float in semi-employed
limbo. Through Debye’sintervention, a dozentur of sorts
was arranged for him at the TechnischeHochschule in Stuttgart
during the period 1930-1937. However, this was not a regularly
budgeted position, and even Hiickel’s salary was insecure. In his
book published in 1975,“l Hiickel relates that his wife often
referred to this time as “seven years of disgrace”.
Finally, in 1937 came a call to Marburg as Extraordinary
Professor (Associate Professor) of Theoretical Physics. Except
for a brief period immediately following the war, Hiickel held
this position until it was upgraded to that of Ordinary (Full)
Professor in 1961,a year before his formal retirement. It was a
mean career, blighted by marginalization and outright humiliation,
and in some ways incommensurate with the magnitude of
his contributions to science. As we shall see, some of his difficulties
in gaining recognition arguably were self-inflicted, but
others were not. More research would be needed to unravel all
the causes, but there is little doubt that that the personal frustrations
of Hiickel’s career mirrored the decades-long delay in general
acceptance of the significance of his work.
3. Hiickel’s Early Contributions to Fundamental
Physical Chemistry:The Debye-Hiickel Theory of
Electrolytic Solutions
As an assistant in Zurich, Hiickel collaborated on the famous
Debye-Hiickel theory of strong electrolytes (1923)J5]which is
described authoritatively elsewhere.[’. 6 , ‘I The details of the theory
need not detain us here, but even an amateur comes away
after reading these accounts with an appreciation of two major
characteristics of Hiickel’s later independent work, particularly
in the field of organic quantum chemistry: first the identification
of the significant questions for which no satisfactory answers
were yet available, and second the design of a theory based upon
bold simplifying assumptions, which although perhaps not rigorously
justifiable at the time, nevertheless showed the way to
plausible explanations of known facts and to testable predictions.
What is really operating here in this early phase of
Hiickel’s career is a particular style of theory in which the goal
is not a perfect, unshakable construct that will last for eternity,
but rather a more pragmatic procedure, which might be described
with the motto: let’s see ifthis works, and ifit does, let’s
keep using it until it shows deficiencies. Of course, this is the way
many theoreticians often operate, whether or not they admit as
much.
It is true, as has been said,r21that we don’t know for sure
whether Debye or Hiickel was the dominant partner in designing
the approach to their joint problem, but this issue is almost
beside the point here. One way or another, Hiickel learned (or
invented, or re-invented) this style in the work on the theory of
electrolytes. It was to be a hallmark of his later independent
research.
4. The Nature of the Double Bond
4.1. Originsof Hiickel’s Interest in Organic Chemistry
In searching for a pattern of influence on Hiickel’s famous
1930 papers[’’ “Zur Quantentheorie der Doppelbindung,” we
note that he acknowledges the stimulus given by Bohr, in whose
institute in Copenhagen he began the work in the summer of
1929. The first paper was finished in Leipzig at the end of the
year. Hiickel’s autobiography[’] implies that Bohr’s role consisted
largely of identifying chemistry as a field to which the new
quantum ideas might be fruitfully applied. There is no indication
that Bohr made specificsuggestionsas to the areas of chemistry
that might be interesting to examine.
Where then did Hiickel get the idea to work on unsaturated
and aromatic compounds? One might imagine that this much
insight into the details of so foreign a disciplinewould have been
unusual for a theoretical physicist of the time. It is conceivable
that as a student or subsequently in preparation for his theoretical
work, he may have acquired enough knowledge of chemistry,
especially of organic chemistry, to generate the required
motivation, but he makes no mention of special study. One can
hardly avoid the conjecture that Walter Hiickel’s encyclopedic
knowledge of the subject offered a far more accessible source.
According to Erich Hiickel’s acknowledgment in the 1930 paper,
Edward Tellerwas especially helpful on quantum mechanical
questions and Walter Hiickel on chemical matters. Our understanding
of the human factors that condition the interaction
of theory and experiment would be greatly enhanced if we knew
Jerome A. Berson was born in Sanford, Florida in 1924. He received the degree of B. S. in
chemistryfrom the City College of New York in 1944. After service in the Army of the United
States (1944-1946, China-Burma-India Theater), he returned to the study of chemistry at
Columbia University,where he received M A (1947) and PhD (1949) degrees, working with Pt!
von E. Doering. Following a postdoctoral year (1949- 1950) at Harvard University with R. B.
Woodward,Berson heldfaculty positions successively at the University of Southern California
(1950-1963) and the University of Wisconsin (1963-1969). Since 1969, he has been on the
faculty of Yale University, where he is now Sterling Professor Emeritus of Chemistry.
L J
AnZen. Chem. Int. Ed. Engl. 1996,3( 7750-21642752
REVIEWSErich Hiickel and Chemistry
more about Walter’s role. Although Erich’s autobiography and
other writings so far available to me are quite nonspecific about
just what Walter provided, it is my (as yet undocumented) working
hypothesis that Walter served as more than a mere source of
factual information. It seems likely that his professional immersion
in the culture of organic chemistry made it natural for him
to point out to Erich several profound unsolved problems of the
structure and reactions of organic compounds which one could
hope to illuminate with the new quantum theory. In other
words, Walter was in a position to perform a crucial service to
Erich: he could ask the right questions. Whether he did so remains
to be established.
4.2. Restricted Rotation of Double Bonds
In his first paper on organic quantum chemistry, Erich
Hiickel undertook to solve an intimidatingly deep problem,
which is concisely stated in his own words:[*]
“The chemist, especially the organic chemist, tends to link
more to the concept of valence than merely the valence of the
atoms. He would like to ascribe to the valence lines between
bonded atoms a definite real existence, in which, especiallyin
the chemistry of carbon, not only the number of valence
bonds, but also their direction in space should have significance..
. In this work the generality of this question will not
be treated; rather only a special case will be examined, which
makes a contribution to this question. This case concerns
what chemists call the ‘restricted rotation of double bonds’ ”.
The persistence of stereochemical configuration about C=C
and C=N bonds had long been known and had been rationalized
by the postulate of restricted rotation in such compounds.
J. H. van? Hoff‘” had provided a classical (that isa prequantum
theoretical) “explanation.” The carbon-carbon double bond
was imagined to be made up by contact of two tetrahedrally
disposed valences of each atom (Fig. 1).This would result in the
Fig. 1. Junction of two sets of tetrahedral carbon valences to produce a double
bond, in the manner of van’t Hoff [9].The bonds lie outside the C-C direction;the
remaining four valences lie pairwise above and below the plane of the paper.
stereochemistry shown, with the four remaining valences lying
in the same plane as the carbon atoms. The structure would be
resistant to rotation of the carbon atoms with respect to each
other about the line joining them, because such twisting would
diminish the contact of the valences. Of course, this proposal
begged the question that Hiickel was concerned with: what is
the physical nature of these valences?
Soon after the first“’ of Hiickel’s papers on the double bond
appeared, Paulingl’oaland Slater“ ‘I independently were to develop
a quantum mechanical description of ethylene which was
very close in spirit to van’t Hoff s representation. They visualized
the two carbon-carbon bonds as equivalent entities made
up by overlap of sp3hybrid orbitalswhose axes lay on either side
of the actual C-C internuclear line. As part of a general theory
of directed valence, these same sp3 hybrid orbitals had been
postulated to account for the tetrahedral orientation of the
bonds of tetravalent carbon atom.
Several textbook authors have wrongly ascribed to Pauling
the concept of trigonal (sp2)hybridization of the doubly bonded
carbon atoms in ethylene (see below). Pauling’s example of this
hybridization was graphite, not ethylene. In fact, he remained
strongly opposed to the concept that the two ethylene C-C
bonds were different, an unavoidable consequence of trigonal
hybridization. The H-C=C angle in a trigonally hybridized
alkene is predicted to be 120”,but Pauling’s The Nature of the
Chemical Bond (1961 which cites a number of experimental
determinations near 125’ 17’,stoutly defends the tetrahedral
model, which predicts the latter value (half the difference
between 360” and the tetrahedral angle H-C-H angle
109’26‘). It is probably fair to say that in the current era of ab
initio theory, a decision between these two approaches, which
are after all only models, has become moot.[‘Obl
Curiously, one often sees, in implied or direct form, similar
misattributions of the trigonal hybridization concept to Hiickel.
It is true that the essenceof Hiickel’smodel is that the two C-C
bonds are nonequivalent, one CT and one TC bond, a basic distinction
from the tetrahedral model favored by Pauling. However,
Hiickel’sethylene model in the first instance did not arise from
hybridization considerations and did not require trigonal hybridization.
In fact, the G - X ethylene model originated in the
quantum theoretical treatment of a seemingly very different
molecule, molecular oxygen, 0,. How Hiickel’s new plant
sprang from such unlikely soil makes a long story, but the lessons
to be learned about the genesis of ideas justify an abbreviated
version. The hybridization question is discussed in more
detail in Section 4.4.
4.3. From Dioxygen to Formaldehyde to Ethylene
In 1929 the year just preceding the appearance of Hiickel’s
paper, Lennard-Jones“ had made a molecular orbital analysis
of the electronic structure of dioxygen in its ground state,
which he represented as having the following occupation pattern:
(1~ ) ~ ( l s ) ~(2s)’ (2~)*(2p+)~(2p-)z (2pcr)’ (2pn+,2pn-) As
Hiickel points out,‘’] this notation differs from the “united
atom” MO formalism of Hund and Mulliken, which is more
familiar now, and which had been developed for diatomic molecules.
Lennard-Jones’s notation is more suitable for showing
the electronic states that are being generated during dissociation
of the “united atom.”
The results are shown in Figure 2.“31Note that the interaction
of the two filled 2s atomic orbitals gives rise to no net
bonding in this approximation, which (with apologies) limits the
discussion to the molecular orbitals (MOs) derived from the
atomic 2p orbitals and alters Lennard-Jones’s presentation to a
“united atom” form. An oxygen atom in its ground state has
four electrons in the three mutually perpendicular p atomic
orbitals (AOs).When two such atoms are brought into bonding
distance, the six AOs give rise to six MOs. Two of the MOs, a
strongly bonding (02p) and a strongly antibonding ( ~ * 2 p )pair,
Anem Chein. In[. Ed. Engl. 1996, 3s. 2150-2164 2753
REVIEWS J. A. Berson
TE
0 0 2 0
Fig. 2. Formation of 0, molecular orbitals from oxygenatomicorbitals. The occupation
pattern and spin state are derived by application of Hund’s highest multiplicity
rule. The energies are shown schematically (adapted ref. [13]with permission of
Oxford University Press).
result from mixing of the two original p orbitals that lie along
the internuclear line. The remaining four atomic p orbitals mix
to form two degeneratex MOs and two degenerate A* MOs. The
nodal planes of the x MOs are a mutually perpendicular (arbitrarily
chosen) pair containing the two atomicnuclei, and the A*
MOs each have the same pair of nodal planes in addition to a
perpendicular nodal plane bisecting the internuclear 0-0 line.
The total of eight electrons (originally from p orbitals) now
must be fed into this set of MOs. Two each, with opposed spins,
go into the bonding CT and the two bonding x MOs. Although
formally the remaining two electrons can go into the pair of n*
orbitals in any of several occupancy and spin configurations,
Lennard-Jones assumed that, in energy, “that state is held to be
lowest which has the greatest multiplicity, as is the case in
atoms”. Here, this would be a triplet state, in which the last two
electrons each occupy one of the degenerate A: and n: orbitals
and their spin vectors are parallel. The nominal overall bond
order is two, since although there are three bonds, one of them
can be considered to be formally cancelled by an antibond.
By this explanation of the experimentally known fact that
dioxygen is paramagnetic in its ground state, Lennard-Jones’s
analysis provided a brilliant early triumph for the quantum
theory. Apparently, Hund’s first rule,[’4,’ which originally
had been promulgated for atoms, also applies to certain molecules.
Dioxygen is a case in which the rule might be expected to
apply strictly, because of the symmetry-enforced degeneracy of
the z* orbitals (see below).
Nevertheless, this insight was not the major focus of Hiickel’s
interest in Lennard-Jones’s paper. In fact, the triplet nature of
dioxygen might well have bemused a lesser intellect, and a connection
between the intriguing special case of dioxygen and
the less spectacular but far more general problem of ethylene
might never have become clear. What attracted Hiickel was
the idea that there can be two kinds of oxygen-oxygen bonds,
o and 7 ~ .
The next step toward the description of doubly bonded carbon
was an ingenious gedunken experiment. Huckel imagined
the conversion of one of the oxygen nuclei of dioxygen to carbon
by the extraction of two protons, which then were bound to the
resulting carbon nucleus to give formaldehyde. If we today were
following this protocol, we probably would make formaldehyde
analogously to the construction of dioxygen shown in Figure 2,
with the exception that one of the oxygen atoms would be replaced
by an sp’-hybridized fragment CH,, and the units would
be brought together so that all four atoms were in a common
plane. Again, one of the carbon 2p orbitals could form a o bond
by overlapping a 2p orbital of the oxygen, and the other carbon
2p orbital would form a z bond with the oxygen p orbital.
However, Hiickel declined to make the assumption of coplanarity
at the start, and argued his way through alternative geometries
before rejecting them in favor of the planar one. Also,
in 1930, it was not obvious what should be the ordering of the
energies of the MOs resulting from the procedure. Hiickel again
presented arguments that favored the ordering we accept today.
The details, though interesting, are too lengthy to give here,
but one major point is worth emphasizing. In both arguments,
Hiickel resorted to experimental data to make his decisions.
With regard to the multiplicity question, it was clear that because
of the need to bind the substituent hydrogens to the carbon
atom in formaldehyde, the TI* MOs would not be each
singly occupied, and the degeneracy that causes a triplet ground
statein dioxygen would not exist in formaldehyde. Nevertheless,
it was (then) a difficult computational problem to decidewhether
the multiplicity of the ground state of formaldehyde should be a
singlet x or a triplet n-x*.Hiickel’sbasis for rejecting the triplet
was analogical: although no experimental information on the
magnetic properties of formaldehyde was available, it was
known that acetaldehyde was diamagnetic and hence a singlet.
Similarly, with regard to the molecular geometry, Hiickel
pointed out that a nonplanar monosubstituted formaldehyde,
for example, acetaldehyde, would be pyramidal, with three
nonequivalent substituents, and hence one would predict the
existence of optical isomers. No such isomers were known. It is
heartening to realizethat Hiickel, a pioneer of theory, was in the
latter case not too proud to use the organic chemist’s traditional
(but nonrigorous) argument of isomer numbers! We have no
evidence that Walter Hiickel provided this insight to his brother,
but it is easy to imagine his doing so.
Formaldehyde-to-ethylene then required only a repetition of
the oxygen-to-CH, gedanken step. Again, the presence of the
substituent hydrogens is the key structural feature that favors a
singlet ground state. Hiickel had now achieved his first objective,
a quantum mechanical description of the double bond that
would explain restricted rotation. In his model, the C=C double
bond is made up of a G and a n bond. The o bond is axially
symmetric about the internuclear C-C line, but the n bond is
not. Rotation of one of the CH, groups out of the plane of the
other is resisted because to continue this process to 90”would
require breaking a n bond. Hiickel did not provide a quantitative
estimate of the strength of this bond, but it must be substantial
to account for the thermal stability of olefinic cis-trans
isomers. He emphasized the deep structural difference between
this model and that of van’t Hoff, in which both of the C-C
bonds are equivalent.
2754 Anpen.. Chem. In[. Ed. E n d 1996. 35,2750-2764
Erich Hiickel and Chemistry
4.4. Hybridization in Double Bonds
It will be clear that a bit of mystery still lingers over Hiickel’s
picture of ethylene at this point: What is the nature of the C-H
bonds? Hiickel never clarified this but left it to others. In 1931
and 1932, the years immediately following Hiickel’s first paper
on ethylene, the concept of quantum mechanical hybridization
was introduced as the basis of a theory of directed bonding. As
we have seen, this idea played an important role in the development
of the Pauling-Slater equivalent-bond model of ethylene.
In 1933 Mulliken[“] suggested trigonal hybridization of the
carbon valences in ethylene, and in 1934 Penney[17]made a
more extensivecomparison of this model with two alternatives,
the so-called “right angle” model and the van? Hoff-like Pauling-Slater
tetrahedral model.
In the right angle model (Fig. 3), Penney imagined the C-H
bonds to be pure 2p0 bonds, and the double bond joining the
two carbons to be made up of one (s,s) and one ( 0 , ~ )bond.
Y
i
Ch
Fig. 3. Penney’s right angle model (ultimately rejected iii favor of the G-K model)
for ethylene.
The vicinal hydrogen interactions are neglected, and the C-C
bonds, although not equivalent, are both axially symmetrical
about the C-C direction, so that the energy of the configuration
does not depend on the the angle 4 through which one carbon
is rotated with respect to the other. As Penney recognized, this
model predicts freerotation about the C=C bond, and therefore
cannot account for one of the characteristic properties of alke-
nes.
Penney compared the tetrahedral model and the trigonal
model by means of a valence bond calculation and concluded
that the trigonal model was energetically preferred. Although
the sp3hybrid orbitals of the tetrahedral model have more extension
along the orbital axis than the sp2orbitals of the trigonal
model, the sp3orbitals are necessarily canted outward from the
internuclear C-C line and hence overlap poorly. He subsequently
proposed trigonally hybridized carbon as the building
block of the 0 framework of the benzene ring.
Eventually these suggestions became widely adopted for discussions
of doubly bonded carbon. In part, this acceptance must
have been furthered by later group theoretical arguments by
Kimball,“81but one may speculate that it also was based on the
simple conceptual continuity of the hybridization picture (sp3
for methane, sp2for ethylene, sp for acetylene), which made the
idea pedagogically attractive. Actually a more hard-eyed evaluation
of the quantitative merits of Penney’s calculations might
have been appropriate. One certainly should have been concerned
about Penney’s conclusion that the energy needed to
rotate one CH, plane in sp2 hybridized ethylene by 90” with
respect to the other was “quite small, probably about l/2 volt,”
(about 11.5kcalmol-I). If a similar value were required in substituted
ethylenes, stable cis-trans isomerism could not have
been observed at room temperature. In other words, were one to
take the calculation at face value, the same argument used to
reject the right angle model logically would have required rejection
of the trigonal model.
5. The Benzene Problem
It might be surmised that Hiickel proceeded from ethylene to
conjugated chain compounds such as allyl, butadiene, pentadienyl,
hexatriene, etc., and then to benzene, and other cyclopolyenes,
in the systematic manner that we teach Hiickel molecular
orbital (HMO) theory to students today. Actually, this is
not the sequence that occurred. Hiickel eventually considered
unsaturated chains as a class,[’g]but in the breakthrough paper
in 193
The paper was Hiickel’s Hubi/itation.~.~chr~tfor attaining the
veniu /egedi (right to teach) in theoretical physics at the Technische
Hochschule Stuttgart. A massive document of 84 printed
pages, it gave two descriptions of benzene and other conjugated
cyclopolyenes: the “first method,” which eventually came to be
the valence bond (VB) theory, and the “second method,” now
called the molecular orbital (MO) theory. Huckel gave reasons
for preferring the MO procedure, and although some of these
might not be very convincing today, he persisted in this choice
thereafter. Both the first method and the second method assumed
that the unique properties of cyclic conjugated systems
could be attributed approximately to the 7c electrons without
explicit consideration of their interaction with the G electrons.
his target was benzene itself.
5.1. Huckel’s First Method and
Classical Valence Bond Theory
The valence bond method, which Huckel had rejected, was
taken up soon after by Pauling and others,[”, ’l 251 who simplified
the mathematical procedures and gave reasons for preferring
the VB to the MO method. Again, with regard to the problem
of cyclic conjugated molecules, their reasons seem
insufficient today, but these workers held unwaveringly to their
choice in later years. This “classical” VB method, and Pauling’s
pedagogical packaging of its major results in the form of the
“theory of resonance,” dominated theoretical chemistry for 25
years after 1930. The reasons for this, further examined below,
were not necessarily that the theory was “correct” in any absolute
sense,but rather that Pauling, with consummate knowledge
of the whole field of chemistry, convincingly showed how a
broad range of chemical phenomena, especially in small molecules,
could be explained by some kind of quantum ideas“’”]
and thereby established a faithful and largely uncritical following.
As it happened, however, the classical VB method, in the
truncated form of it he used, was to prove theoretically inadequate
when applied to the problem of aromaticity.
Anpew Chem. Int. Ed. Engl. 1996,33. 273-2164 2155
J. A. Berson
REVIEWS
It is true that with the emergence of high-speed digital computers,
as is described elsewhere,[’4*26*”I the MO method, in
increasingly sophisticated manifestations, gradually became the
major basis for the explosive computational development of
electronic structure theory. However, one should not conclude
that VB theory is without adherents today. On the contrary,
many investigators have contributed developments of advanced
VB methods and successfulapplications to significantproblems,
including as we shall see, the reconciliation of the VB and MO
theories of aromaticity.[283291
The most characteristic feature of the valence bond method is
that it considers the combining atoms as a whole.[301The formation
of a molecule is thought of as arising from the bringing
together of complete atoms, which are then allowed to interact.
In this it differs from the MO method, in which only the nuclei
(or nuclei +electron inner shells) are first brought into position,
and afterwards the valence electrons are allotted to polycentric
molecular orbitals. Clearly the VB method corresponds more
closely with the conventional chemical picture, which probably
accounts for its widespread acceptance in the form presented by
Pauling.
Huckel’s first method, the early form of VB theory, was
derived from Heitler-Lond~n[~’Itheory for the formation of
molecular hydrogen from two hydrogen atoms. It starts with
each atom in a specified quantum state and then introduces
exchange. The exchange procedure, which takes into account
the indistinguishability of the two electrons 1 and 2 in the form
of the exchange integral (YA(1)YB(2)l%lYB(l)YA(2)),has major
significance in the VB method. For example, the binding
energy of hydrogen calculated without exchange is only
5.5 kcalmol-’ but when exchange is included in the wave function,
the binding energy rises to 69 kcalmol-’, a substantial
fraction of the experimental value of 104kcalm01-~.[~~]
By application of group theoretical procedures, Heisenberg[3z]used
this exchange method to explain ferromagnetism.
slate^-[^'] then developed a useful determinantal method which
made possible the treatment of interaction among a large number
of atoms without group theory and applied it to electrons in
metallic lattices. This method was further applied by B l o ~ h [ ~ ~ ]
in place of the Heisenberg group theoretical method for the
theory of ferromagnetism. Hiickel used the Bloch formalism
directly in his first method.
As described by Hii~kel,[~~]the treatment of a conjugated
molecule (such as benzene) by the classical VB method begins
by assigning to each carbon atom a n: electron which is in a
given state with the positional eigenfunction ba(rin),where the
suffixes indicate the ith electron in the atom a. The total positional
eigenfunction, taking coupling of the n: electrons into
account, is written as a linear combination of the products
41(ril)...b6(ri6).Starting from this, the Heitler-London perturbation
method is worked out to the first approximation. Spin
is taken into account, and only the linear combinations that
conform to the Pauli principle are considered.
In the Pauling modification of VB theory,[”] one selectsfrom
these linear combinations those which correspond to the
smallest value of the total spin (in this case S = 0), and chooses
from these the ones that are linearly independent. These functions
which belong to the value S = 0 can be associated with
models of the valency pattern of the n: electrons in which the
atoms arejoined in pairs by singlebonds, one and only one bond
radiating from each atom in such a way that the bonds do not
cross one another. Pauling called the schemesof valenciescorresponding
to the functions “canonical structures.” One then formulates
and solves the secular perturbations corresponding to
these functions, restricting the coupling to that between adjacent
atoms.
Wheland[’’] gives a simple example of the application of
this method to the case of cyclobutadiene. The canonical structures
are A and B. One designates
the 2p function on the ith carbon
atom as Yt,the coulomb integral
the eigenvalue of the energy as W, 1 2 1 2
El4 3
Dl4 3
(yi Y,Y ~ Y Y ,I2IyiYzY3y4) as
Q, and the single exchange integral A B
between adjacent carbons, for example,
( Y l Y 2 Y 3 Y 4 ~ ~ ~ Y y 1 2 Y l Y 3 Y / l )as a‘. All single interchange
integrals of the energy between nonadjacent atoms, all
multiple interchange integrals, and all interchange integrals of
unity are neglected. The Slater valence-bond eigenfunction may
be expressed as secular equation (a).
= 0 (a)
Q + a ‘ - W
1(1/2)Q +2a‘- (1/2)W
(1/2)Q+2 ~ ’- (1/2)W
Q + d - W
This has the solutions W = Q +2a’ and W = Q -2a’, of
which the former represents the ground state since the exchange
integral a’ is presumably negative. The resonance energy is obtained
by subtracting from this a quantity Q +a’, the energy of
one of the two canonical structures: Q +2a‘ -(Q +a’) = a’.
In the case of benzene, there are fivecanonical structures with
corresponding canonical functions : C and D correspond to the
Kekule forms, E,F, and G to the Dewar forms. Other structures,
C D
E F G
H
such as for example H, that of Claus, can be expressed as linear
combinations of the canonical functions [Eq. (b)].
Following a procedure silhflar to that used for cyclobutadiene,
the coupling energy for benzene is 6Q +2.6055a‘, and the
molecular eigenfunction is given by Equation (c).
2756 Angew. Chem. Int. Ed. End.1996.35.2150-2764
REVIEWSErich Hiickel and Chemistry
In the sense of the approximation. the ground state thus may
be considered to result from the superposition of the two Kekule
and the three Dewar forms.
One might be concerned about the approximation which limits
the exchanges to pairwise nearest neighbors. Clearly there are
many more permutations that could be included. Wheland[221
himself states:
“This assumption is an extremely drastic one and no rigorous
justification for it can be given. The integrals we ignore are
probably, to be sure, rather smaller in magnitude than the
other ones which we retain. There are, however, an enormous
number of the former integrals, and, even though some of
them are positive and some are negative, we can have no
assurance that their net effect is negligible. We shall, nevertheless.
make the assumption because, without it, our calculation
would become impracticably complicated, and because, with
it, surprisingly satisfactory results can be obtained.”
As we shall see, the neglect of some of these other permutations
has serious consequences for the description of cyclic conjugated
systems.
Although the classical VB procedure came to be called[221the
Heitler -London -Slater-Pauling (HLSP) method, Slater in
fact preferred to put some distance between himself and Pauling
in applications of the method. Thus, in a discussion[3s1at the
International Conference of Physics in 1934, Slater remarked
that he was in “entire agreement” with Huckel and Hund that
the MO method is superior to the Heitler-London method for
computing interatomic forces, and that “the calculations of
Pauling, for instance, seem to make quite unwarranted use of
the theory.” Slater gave no furtherdetails, but it seems a reasonable
conjecture that he was expressing misgivings over the trun-
cation.
5.2. Huckel’s Second Method and
Molecular Orbital Theory
This procedure, subsequently called1z21the Hund-MullikenHiickel
(HMH) method, had as an immediate intellectual precursor
another by Bloch on the quantum mechanics of
electrons in crystal lattices. Bloch. at that time in Leipzig, was
actively developing the theory of metals in order to understand
such phenomena as conduction and magnetism. Subsequently,
of course. he became famous for providing some of the theoretical
foundations for the field of nuclear magnetic resonance.
Bloch approached the problem of the electronic interactions
in a many-electron system by considering the properties of a
single electron in a spatial force field perturbed by the atomic
nuclei and the statistical charge distribution of the remaining
electrons. The idea is very similar to the Hartree-Fock method
for treating many-electron atoms. In Bloch’s sinewy words, “the
force field has the same periodicity as the crystal lattice itself,’’
and “we are thus dealing with plain de Broglie waves which are
modulated in rhythm with the lattice.”
The procedure Hiickel usedC2’]was to set up such a lattice for
benzene, calculate the MOs (wave functions) and energy levels
in terms of the parameters aand ,B(defined below) by solvingthe
Schrodinger equation, and construct the electronic configuration
by ngfhau. in accord with the Pauli principle and in analogy
to the practice of Hund, Mulliken, and Lennard-Jones for diatomic
molecules. Huckel’s benzene lattice was a regular hexagonal
array of carbon 2p, orbitals. As every chemistry student
now knows, the results can be expressed as shown in Figure 4,
- a-2/3
Fig. 4. Energy levels of benzene and occupation pattern in the ground state as
calculated by Hiickel’s second method. The parameters a and fc are defined in the
text.
where tl is the energy of an electron in an unperturbed carbon 2p
orbital, and fi is the stabilization energy (relative to a)experienced
by an electron when two such units interact at a defined
distance.
Hiickel generalized this result to other conjugated systems
with n centers, both to rings of other sizes and to
20.34*371 The energy levels can be expressed in the
famous Hiickel Equations (d), j=1,2,3,. . .n, and (e),
k = 0, 5 1, +2,. ..m, where rn = (n -1)/2 for n odd and m = n/
2 for n even.
Chains CnHn+Z:E = a +2,Bcosb?r/(n +I)] ( 4
Rings C,H,: E = a +2fi cos[2kn/n]
Among the messages that these equations convey are that the
energy levels for the chains are unique, whereas some of those
for the rings are doubly degenerate, that is, the eigenvalues
sometimes occur in pairs of equivalent energy. As Hiickel pointed
these degeneracies are a direct consequence of the
cyclic nature of the electron circulation in the ring compounds.
The physical reason is that in the energy states that have a finite
angular momentum associated with the electronic motion, the
circulation is directional in either a clockwise or a counterclockwise
sense. The eigenfunctions corresponding to these states are
not identical, even though the energies are, so two MOs must
exist at that energy. An equally important point is that for n
even or odd the lowest eigenvalues of the ring compounds are
unique, and for n even, the highest also are unique. These are
nonintuitive results that come out of the solution of the
Schrodinger equation and that mark this approach as fundamentally
different from the old (Bohr) quantum theory. Whereas
in the old theory, for example, the lowest atomic s states still
had angular momentum h/2x, in the new theory the s states now
have zero angular momentum. Similarly, in the unique states of
benzene, the angular momentum is zero, and consequently, the
“sense” of the electronic circulation becomes meaningless.
This difference between rings and chains will be familiar to
students of elementary quantum mechanic^,[^^-^'] where a favorite
pedagogical exercise is the calculation of the eigenvalues
of the “one-dimensional” Schrodinger equation. An electron is
Angcw. Chm In!. 611 Engi. 1996. 35,2750-2764 2757
J. A. BersonREVIEWS
imagined to be constrained to move along a line or in a circle
under zero potential. The solutions for the linear case are
unique; those for the circular case have the lowest energy level
unique but all the rest painvise degenerate.
H i i ~ k e l [ ’ ~ . ~ ~ *34, 371 emphasized that the MO method, in producing
such energy level patterns, led to the idea of closed electron
shells analogous to those of the noble gas closed shells in
atoms. Particularly significant for the n even conjugated rings
was the case of six electrons in benzene, which had been recognized
for some time as a feature leading to aromatic properties.
Since the Pauli principle allows each orbital to accommodate
two electrons of opposite spin, fillingthe first three orbitals (first
two energy levels)of the benzene set 1, 2, 2, 1 in this way would
give a stable configuration. On the other hand, four electrons in
cyclobutadiene would not give a closed shell, since only the
lowest level of the 1,2, 1 set could be filled.The next higher level
could accommodate four electrons but only would have two
available. Moreover, in the case of ions derived from oddmembered
rings, where all levels above the lowest are degenerate,
a closed shell configuration again is reached with six electrons,
as in the cyclopentadienide ion, but not with eight, as in
the cycloheptatrienide ion or with four as in the cyclopentadienylium
ion.
This rule, subsequently stated by others in the abbreviated
form (4N +2) (N = 0,1,2. ..), namely that aromaticity should
be associated with monocyclic 7c electron systems containing
2,6,10. .. electrons, was in accord with the known facts of organic
chemistry at the time. In addition, predictions now could
be made about the existence and properties of unknown but
easily imaginable new structures. Although the rule does not
apply strictly to polycyclic compounds such as naphthalene or
biphenyl, Hiickel showed by explicit MO calculations[371that
these systemstoo should be considered aromatic, as might have
been expected. There are limitations to the rule, but much computational
research in recent years confirms the essential fact
that Hiickel’s broad classification of aromatic and antiaromatic
character survives at higher levels of MO theory and is not just
an artifact of the approximations used in the early treatment.c4’]
Significantly, the classical VB method did not produce these
results. For example, it predicted that cyclobutadiene should
have the highest resonanceenergyper electron of any of the even
cyclicpolyenes, and it gave no reason to expect that cyclopentadiene
should be a much stronger acid than cycloheptatriene.
These failures of classical VB theory were among the reasons
that Hiickel in 1931 turned away from it as a basis for understanding
aromaticity. More than half a century later, the opinion
persists[43]that classical VB theory is “decisively unsuccessf
~ l ” ‘ ~ ~ ]for this purpose.
Nevertheless, one feels intuitively that a higher level of VB
theory should be capable of reproducing the Hiickel rule. After
all, both the MO and the VB approaches are approximations of
the complete solution of the Schrodinger equation. At successively
higher degrees of approximation, the two methods should
converge to give equivalent results. In fact, such convergence
can be shown analytically for a simple molecule such as H, and
is expected generally, however complicated the molecule may
be.[451It comes as no real surprise, therefore, that eventually
methods for deriving the Huckel rule by VB theory should
emerge.[44.46, 471 The key insight in solving this problem is the
crucial necessityto include cyclicpermutations of the 7c electrons
in the exchange procedure. Just such exchange integrals were
amongthose omitted in the classical VB method. An experimentalist
senses a gratifying propriety in this result.
6. A Chilly Reception from the Experimentalists
Huckel’s pioneering papers on the molecular orbital theory of
unsaturated and aromatic compounds appeared in the period
1930-1931, but they seemed to make little impact on the community
of chemists for many years after. In their biographical
memoir on Hiickel, Hartmann and Longuet-Higgin~[~]ascribe
the general neglect of his results to the national culture of German
science:
“ _..physicists in that country in any case were not ready to
accept investigations about more complicated chemical bond
phenomena as a typical contribution of a physicist. Still more
difficult was his (Huckel’s) relationship to the chemists. Before
World War 11, especially in the Anglo-Saxon countries,
chemical physics and within that field quantum chemistry
also was accepted by both physicists and chemists as an interestingnew
field of science.Chemists in Germany, on the other
hand maintained that chemistry is what chemistsdo. They did
not do quantum chemistry and therefore this kind of science
did not belong to chemistry.”
It may well be true that German chemists of that period or
even later resisted quantum ideas. Although Rolf Huisgen rep
o r t ~ ‘ ~ ~ ]that he was teaching Huckel’s results (but not the details
of how the calculations were done) as early as 1949, this
undoubtedly was exceptional. Even Walter Huckel makes only
cursory reference in his to the contribution his
brother had made to the problem of the aromatic sextet.
However, I regret to say that crediting a more receptive attitude
to “Anglo-Saxon” chemists, especially the experimental
organic chemists, pays them a higher compliment than most of
them deserve. Again, there were scattered exceptions. For example,
Ingoldrso]in Britain and Hammett[5’1 in the United
States clearly were aware of the importance of Hiickel’s work.
Elsewherein thesecountries, however, even though the problem
of aromaticity was prominent in the minds of chemists, and
much experimental effort was devoted to it, whatever theoretical
reasoning experimentalists brought to bear on such issues in
their research or teaching depended almost entirely on resonance
theory!”] Noller’s review of 1950,’531ostensibly an exposition
of molecular orbital theory prepared for the edification of
organic chemistry teachers, does not cite a single reference to
Hiickel. Most elementary and even advanced textbooks of those
years make no mention whatever of Hiickel’s ideas. One of the
most influential books in the field, the second edition (1943) of
the multi-authored Organic Chemistry - An Advanced Treatise,
edited by Gilman, contains a substantial chapter by Fieser on
aromatic compounds.r541The question of aromaticity is presented
only from a historical perspective,and for a theoretical rationale.
Fieser defersentirely to Pauling, who contributes a chapter
on theory in the same using the already well-known
resonance method. Although Pauling mentions the Hiickel theory
there, he declinesto discussit further on the grounds that the
2758 Angeu. Chem. In!. Ed. Engf. I996, 35,273-2764
REVIEWSErich Hiickel and Chemistry
resonance approach ”is the more closely related to the usual
concepts of chemistry”. Not surprisingly,Pauling’s omissions of
scholarly exposition and comparison here and elsewhere infuriated
Hiickel.[‘]
It is true that there was a flurry of theoretical activity, especially
in Britain. following up further implications of some of
Hiickel’s ideas. This included by, among others, Coulson
on mobile bond orders, Coulson and Rushbrooke on alternant
n-conjugated systems, Longuet-Higgins on non-Kekulemolecules,
and Dewar on a range of chemical properties deducible
from perturbational MO considerations. These papers,
written in the elegant lapidary style familiar to mathematicians,
and often published outside the conventional chemicaljournals,
were important, but they were either unknown or largely unintelligible
to many organic chemists.
by Mulliken and an important
early textbook by the Pullmans,’56b1both in French,
influenced a few young theoretically able workers such as
Simonetta. and through him, Heilbronner,[”] but their immediate
impact on the thinking of most organic chemists was not
great
Having lived through that period, I can attest that the attitude
of many American organic chemists toward MO theory was
uninformed and indifferent, if not hostile. Few of them would
have taken the trouble to slog through Hiickel’s highly technical
papers, which bristled with equations and matrices, and which,
with one obscurely placed exception,[341were not available in
English. The charismatic Pauling had provided them with a
theory which at some level required no mathematics and could
be applied by using familiar bond structures. Most of them were
content with that.
Similarly, a key two-part
7. Experimental Tests of the MO Description of
Conjugated Cyclic Compounds
If organic chemists were to a large extent unaware of the
Hiickel rule, how could there have been deliberate tests to explore
its scope? In fact, a number of molecules synthesized or
discovered in nature after Hiickel’s papers in the early 1930s
eventually turned out to be relevant test species, even though the
authors originally had some other motivation for studying
them. In this inadvertent process, we see again the familiar paradoxical
sequence encountered so frequently in science: “Here’s
the answer. what’s the question?’
Early examples of this come from the chemistry of the azulenes
(Scheme 1). a fascinating group of blue or violet substances,
several of which, including the parent compound, are found in
nature as such or are formed by chemical transformation of
hydroazulenic sesquiterpenoid precursors.158- 601
Scheme 1. Structural formulae of azulene (left) and its derivatwes guaiene (center)
and guaiazulene (right).
The substantial variety of natural and synthetic azulenes
available from the work of PlattnerlssI and others[591was augmented
by the powerful new Ziegler -Hafner synthesisJ6
which made azulenes accessible in a small number of steps without
the difficult final dehydrogenation previously employed.
A rich store of facts embodying the chemical and physical properties
of these substances now called for theoretical rationalization,
which, as has been instructively summarized by Heilbronner,1601Hiickel
MO theory ultimately provided.
This theme of answers anticipating questions lies at the heart
of one of the inspiring stories of organic chemistry, the discovery
of the troponoids.l6’] Space does not permit a full recounting
here, but a brief outline may suffice to make the relevant point.
In 1926 the Japanese chemist Tetsuo Nozoe settled in Formosa
(now Taiwan), where he was to live and work for the next 22
years. During the period between 1944 and 1947, he and his
co-workers had deduced the structure of hinokitiol (Scheme 21,
0 0 0
Scheme 2. StrUCtUrdl formulae of hinokitiol (p-thujapllcin, left), tropolone (center),
tropone (right)
an isopropyltropolone, but because of disruptions caused by the
war and the remoteness of his location, he was not aware of
related activity elsewhere,[621nor did others know of his work
on this subject, most of which was not published in readily
accessible journals until 1950.
Nozoef6’I recounts his attempts to explain by the theory of
resonance the peculiar aromatic properties of hinokitiol and of
tropolone itself, which he subsequently synthesized. His first
exposure to this form of quantum theory came in 1942/43,when
copies of the 1940 edition of Pauling’s Nature of the Chemical
Bond became available in Formosa. However, although one
could write resonance structures, this gave no real enlightenment
on the aromaticity of tropolone, and the matter remained
somewhat mysterious to him until 1951. In that year, simultaneously
published papers by Dauben and Ring~ld[‘~”~and by
Doering and Detert[63b1described the first syntheses of tropone.
Both papers called attention to the electronic structure of this
ketone and emphasized the presence of a potential aromatic
sextet. The Doering paper, giving an explicit reference to
Hiickel’s 1937 summary[371of n electron theory. pointed out
that the sextet was but one of a general class of stable configurations
characterized by having (4N +2) n electrons. (To my
knowledge, this was the first time that Hiickel’s rule was stated
in this succinct form). Nozoe reportsr621that at that time, he
had not heard of such a rule, but it was immediately obvious to
him that tropolone’s aromaticity must be derived from the same
source.
Forerunners of numerous contributions by many authors
that followed,‘641the two tropone papers[631clearly were examples
of directed rather than serendipitous tests of IC electron
Anger. Chem. In[.Ed. Ennl. 1996. 35. 2750--2764 2759
J. A. Berson
REVINYS
theory. Nevertheless, the most persuasive pieces of evidence
leading to the acceptance of Huckel’s ideas seem to have been
the subsequent syntheses of t r o p y l i ~ m ~ ~ ~ ’and cyclopropenyliions,
which were specifically mentioned in the citation to
Huckel’s Otto Hahn Prize in 1965 (see below).
8. Orbital Symmetry-The Extension of
Cyclic a-Electron MO Theory to
Transition States of Pericyclic Reactionsr6’-691
Pericyclic reactions, as the name implies, are those “in which
all first-order changes in bonding relationships take place in
concert on a closed It would be natural to conjecture
that Hiickel MO methods, which had been successful in rationalizing
the behavior of ground state conjugated cyclic molecules,
also might give a fruitful account of the transition states
of pericyclic reactions. The idea of applying x-electron theory to
reactions with cyclic transition states probably was first put
forth by M. G. Evans in 1939.r701He treated the six-electron
transition state of the Diels-Alder reaction as an analog of
benzene (Scheme 3) and actually wrote down a secular determi-
1
Scheme 3. The transition state of the Diels-Alder reaction between
butadiene (centers 1-4) and ethylene (centers 5 and 6) as5
4 benzene analogs.
nant for it differing from that of benzene only in the 1,6and 4,5
bond integrals. In his words:
“very qualitatively we may say that whereas in the initial state
the mobile electrons are those characteristic of an ethylene
and a butadiene structure in the transition state they simulate
the behaviour in a benzene structure.”
This is a definite insight, quite remarkable for its time. However,
it is questionable to maintain, as some have, that Evans
was thus formulating a “rule” of aromatic transition states.
Such a rule requires not only that one assert that aromatic
transition states are more favorable, but also that one have a
procedure for recognizing which transition states are aromatic.
Without such a procedure, a “rule” of aromatic transition states
verges on a tautology. Evans undoubtedly recognized this,
and in fact, he attempted to provide a procedure. Unfortunately,
his suggestions did not solve the problem. Apparently as a
result of an improper conflation of MO and classical VB resonance
ideas, Evans had only an uncertain grasp of the concept
of aromaticity and especially of antiaromaticity. In this way, he
was led to a formulation that stressed the total number of reactive
electrons:
“. ..there are qualitative rules which follow. The energy levels
of the mobile electrons lie lower in cyclical structures than in
straight chain compounds with the same number of centres
available. The energy levels of the mobile electrons are lower
the greater the number of available centres. These rules imply
that the lowering of the activation energy due to the resonance
effect will be greater in cyclisation reactions than in
chain formation and that the resonance energy in the transition
state will increase with the increasing degree of conjugation
of the reacting molecules.”
These rules must be carefully distinguished from the orbital
symmetry rules. The overarching lesson taught by orbital symmetry
and related theories is that favorable (“allowed”) pericyclic
transition states in a given geometry can be recognized
according to whether the number of reactive electrons is 4N or
4N + 2. In disrotatory electrocyclic reactions and supra-supra
cycloadditions, for example, this number is 4N +2, whereas in
conrotatory electrocyclic reactions and supra-antara cycloadditions
it is 4N. The predictions thus alternate accordingly.
Violation of these requirements results in a “forbidden” reac-
tion.
A literal application of the Evans rule favoring more highly
conjugated reactants would predict, forexample, that resonance
stabilization in the cyclooctatetraene-like transition state of the
hypothetical supra-supra 14+41 dimerization of butadiene
should be greater than that in the benzene-like transition state
of the supra-supra [4+2] association of butadiene and
ethylene. But we now recognize the supra-supra [4+4] transition
state as antiaromatic and therefore orbital symmetry for-
bidden.
Moreover, stereochemistry and electron count are inseparably
entwined in orbital symmetry theory. Because Evans had no
experimental examples of reactions whose stereochemistry
would be favorable with 4N electrons, he could not have incorporated
them into his thinking except by imagining them, which
he did not do. Nothing in his paper gives any indication that he
anticipated the idea that is central to orbital symmetry, that of
allowed versus forbidden (aromatic vs. antiaromatic) transition
states dependent on orbital phasing. To the contrary, continuation
along the direction he started would have ended in a theoretical
cul-de-sac. Therefore, Evans’s contribution was at most
a collateral, rather than a lineal, antecedent in the development
of orbital symmetry theory.
On the other hand, the intimate relationship of orbital symmetry
and the Hiickel “magic numbers” is obvious. Quite
analogously to our previous discussion of ground state molecules,
it is precisely because of the cyclic nature of pericyclic
reactions that one expects them to be more properly described
by Hiickel MO methods than by classical VB theory. The major
extension needed for the application of Hiickel theory to transition
states was the expansion of the original Hiickel (4N + 2)
magic numbers, derived for conventional cyclic conjugated xelectron
systems with no forced orbital phase inversions, to
another arrangement with a forced phase inversion, for which
the magic number is 4N.
9. Violations of Hund’s Rule in Biradicals
As we have seen, Lennard-Jones” applied to molecules (for
example, O,, B,) the generalization that later came to be known
as Hund’s first rule. This governs the prediction of the spin
multiplicity in cases where two electrons occupy degenerate orbitals:
“that state is held to be lowest which has the greatest
2760 Angew. Chem. Inr. Ed. Engl. 1996. 35,2750-2764
REVIEWSErich Hiickel and Chemistry
multiplicity."[' 2 - 15] Some theoreticians choose to interpret
Hund's rule as applicable only when the orbitals in question are
exactly degenerate, which except for rare accidental cases,
would limit the rule to molecules like O,, in which the degeneracy
is symmetry-enforced. Other theoreticians apply the rule
even when the degeneracy is only approximate.
L~nguet-Higgins[~~~invoked the approximate form (without
so identifying it) in a seminal 1950 paper, which is perhaps the
most influential theoretical writing on rr-conjugated biradicals
in the period between 1930 and 1970. He showed that, at
the Huckel MO theoretical level, non-Kekule molecules
such as trimethylenemethane (TMM), meta-quinodimethane
(MQDM). and tetramethyleneethane (TME), each have a den*XITMM
MQDM TME
generate pair of nonbonding (NB) MOs occupied by only two
electrons, and predicted for each of these molecules a triplet
ground state. The symmetry point group of TMM (D3h)contains
E representations, but those of MQDM (C2")and TME
(Dzh)do not. Thus, in the latter two cases, the NBMO degeneracies
are not symmetry-enforced, and the energies are expected to
split apart at higher levels of theory.
Longuet-Higgins cited no precedent for his predictions of
spin multiplicities in organic biradicals, and apparently there
had been only one prior such case in the literature: In 1936,
Hund had predicted a triplet ground state for one of
the Schlenk - Brauns hydrocarbons studied by Muller et al.
(Scheme 4).17'] This molecule too has degenerate NBMOs at the
Huckel level of theory and would have fit easily into the
Longuet-Higgins scheme.
Ph I
I-".
Ph Ph
Ph
Scheme 4. Formal rynthesis of the m.in'-Schlenk- Brauns hydrocarbon
However, Hund's prediction was immediately challenged by
Hii~keI,['~~who pointed out reasons why the rule of highest
multiplicity was of dubious validity in the case of the SchlenkBrauns
compound. Hiickel's argument developed from his
recognition that the Schlenk-Brauns structure could be derived
(conceptually) by a union of two triphenylmethyl radicals at the
rn and m' positions. In the NBMO of triphenylmethyl, the m
positions of the phenyl rings are nodes, that is, they have x-electron
coefficients of zero at this level of approximation. In these
circumstances, the exchange energy between the two halves of
the Schlenk-Brauns molecule is close to zero. Since it is essentially
just the exchange energy that accounts for the separation
between the triplet and the lowest singlet,[I4,' these two states
will be almost degenerate. Note that the argument has nothing
directly to do with the fact that the NBMO degeneracy in the
Schlenk-Brauns hydrocarbon is accidental and will be lifted at
higher levels of theory. Instead, in MO terminology, it really is
a recognition of the spatial separability of the NBMOs, a property
later to be called "disjoint" by Borden and D a v i d ~ o n [ ~ ~ " ~
(see below). Hiickel's main conclusion was that the ground state
is not predictable at this level of theory, contrary to the previous
assumption of Hund's rule.
The Schlenk- Brauns hydrocarbon, one of the few biradicals
known in 1936, after all was an esoteric species. One might then
think of Huckel's argument as pertaining to a highly specialized
compound of little interest to those outside the small field of
biradicals. Indeed the paper stimulated little or no interest. In
my view, however, it had significance far beyond the specific
compound, because it showed that the magnetic properties of
molecules cannot be treated by imagining that the exchange
interaction of two electrons in the field of the nuclei and the
remaining electrons will always favor the triplet. On the contrary,
such a problem must take into account the c.onnectivity of
the atoms. This is a profoundly chemical point of view, which
emphasizes something familiar to every chemist: molecular
structure determines molecular properties.
A simple extension of Hiickel's argument reveals that of the
three biradicals TMM, MQDM, and TME, the latter has the
same connectivity feature as the Schlenk- Brauns compound:
it can be made by a union of two radicals (ally1 in this case)
at NBMO nodal positions. Applying Ifiickel's argument, we
can see that TME should not have been classified by Hund's
rule.
Because of Longuet-Higgins' (deservedly) high reputation in
the field of theory, his unqualified use of Hunds rule in this case
had the effect of steering experimentalists along the same oversimplified
line of thinking. Also, the absence of a citation to
Hiickel's 1936work contributed to decades of obscurity for that
paper. One does not disparage the seminal significance of the
work of Borden and D a ~ i d s o n [ ~ ~ " ]and of O v c h i n n i k o ~ [ ~ ~ ~ Iby
noting that they rediscovered the essence of Hiickel's connectivity
argument after a lapse of forty years. As might be expected
after such a passage of time, these papers went far beyond
Huckel's original rather qualitative They brought
to bear the full power of modern electronic structure theory to
derive, by both MO (Borden and Davidson) and VB (Ovchinnikov)
methods, the idea that when the rr-electron system of a
biradical has the Hiickel type of NBMO node-to-node connectivity.
only a small energy gap separates the multiplet ~tates.1~~1
Ironically, at the time of their publications, these workers also
were unaware of Hiickel's paper!
Recent experimental and computational confirmations that
Hund's rule is violated in properly constituted disjoint n-conjugated
biradicals are reviewed elsewhere.[761
Angru. Cliciii. / i l l . Ed Engl. 1996, 35,2750- 2164 2761
REVIEWS J. A. Berson
10. Honors
Formal recognitions of Hiickel’s work were sparse until late
in his career. Three notable distinctions were: in 1965,the Otto
Hahn Prize, jointly awarded by the German Chemical Society
and the German Physical Society; in 1966,nearly 30 years after
his departure, an honorary degree from the Technische Hochschule
in Stuttgart; and in 1977, election as a Foreign Member
of the Royal Society.
11. Reflections on Huckel’s Career
Huckel’s entire contribution to organic quantum chemistry
amounted to 17 papers, a list that includes several summaries
and reviews. After 1937, when he was only 41 years old, his
original contributions to this field virtually stopped. (If Hiickel
were working now, subject to our dubious emphasis on “productivity”,
that publication record would put his grant applications
in grave jeopardy). As a member of the Marburg physics
department, he unsuccessfully tried to initiate work on the
theory of the nucleus, but apparently did not bestir himself to
seek professional contact with chemists such as, for example,
the talented and creative Hans Meerwein, then professor of
organic chemistry at Marburg. One cannot put all the blame
for the missed collaborative opportunities on Huckel, however.
For example, in the period around 1950, Meerwein tried to
persuade one of his graduate students to undertake the preparation
of the cycloheptatrienide ion,[”] apparently unaware that
a few yards away in the physics department lived a man who
twenty years before had predicted the properties of this very
species.
The history of the field of organic quantum chemistry after
1937 shows that there was much more to be done. What can
explain Huckel’s withdrawal? Some have the opinion that he
became discouraged when he failed to develop any further ideas
in the field comparable in significance to his early work. This
may be true, but, of course, it merely pushes the problem one
step deeper: Why did he run out of ideas?
Although there are shadowed aspects of Huckel’s life that
may hide some clues, I think we already know enough to make
a few plausible speculations. Hiickel“] blamed the experiences
of the war, the political atmosphere of the Third Reich, and a
succession of illnesses for the exhaustion of his energies. The
recollection of severalcolleagueswho knew him tend to confirm
this diagnosis, but there is also agreement that his was a difficult
and even paradoxical personality-shy yet sardonically witty,
hypochondriacal, petulant, pessimistic, depressed, ultimately
lethargic and withdrawn from academic contact with colleagues
and students. Reasons why these characteristics came to dominate
Hiickel’s psyche remain to be elucidated.
A glimpseof Hiickel’squirky character comes through in the
story of his absence from the Hahn Prize ceremony, which was
held in Bonn in September 1965,simultaneously with a symposium
celebrating the 100th anniversary of Kekule’s benzene
formula. In his letter[’*] to Richard Kuhn, president of the
German Chemical Society, Huckel pleads that, “the state of my
health does not permit me to receive this honor in person”, but
from his autobiography[’’ we get a significantly different excuse:
“I was on vacation and dreaded first the trip and then the
pompous style in which the Kekule symposium was planned. In
November the medal was presented to me in a small ceremony,
which went very harmoniously and was more to my taste than
a big display.”
Huckel’s personality traits surely contributed to his inability
to persuade others of the significance of his scientific
work.[’,7 7 3791 This would have required a level of showmanship
above his capacities. The duII, pedagogically ineffectiveIectures
for which Hiickel was for example, did little to enhance
his impact.
Particularly damaging was his confrontation with Pauling. As
we have seen, Pauling’sclassical VB theory, although successful
in other applications, really did not provide a good account of
conjugation and aromaticity, yet his ideas dominated the field
for decades. Here was a clear case of the power of persuasion.
Pauling’s personal magnetism, expository skill, and intellectual
breadth were dazzling. Few organic chemists really knew the
theoretical basis of Pauling’s ideas on aromatic molecules, but
he made it easy for them to apply his theory, such as it was. One
can only guesswhat the history of this field might have been had
Hiickeljust made an effort to reach his potential constituency in
chemistry, for example by casting his equations in the form of
the simplemnemonic diagram put forward twenty years later by
Frost and Musulin,’801or even by making use of the catchy
(4N +2) slogan. These steps would have gone far to popularize
his results and make them more intelligible.
12. Summary and Outlook
In the introduction to his landmark paper on partial valence,
Johannes ThieleI8 giveshis view of the role of theory in nurturing
a fruitful relationship with experiment:
“The opinions about unsaturated compounds that I shall
develop in the following may appear quite rash to many.
However, if one holds fast to the idea that a theory actually
is nothing other than a point of view which permits known
facts to be surveyed in a unified way and new facts to be
predicted, a point of view whose value and significancenaturally
can change with the progress of scientific knowledge,
then it seems to me that my opinions satisfy both of these
requirements.”
Certainly, the development of modern electronic structure
theory, from the early approaches by Hiickel and his followers
to the powerful methods of today, illustrates this view. Because
the original Hiickel MO method was a very approximate form
of a theory that others later took to a much higher level, one
senses now a certain amused condescension from some adepts,
who view it as a quaint relic. One must ask, however, whether
any other theoretical advance ultimately has done more to enlighten
the thinking of organic chemists than Hiickel’s brief,
bright flare of cognition, regrettably quenched too soon. Words
suitable to his legacy are found in Eliot’s terse homage to pio-
neers:c8’1
“Someone said: ’Thedead writers are remote from us because
we know so much more than they did.’ Precisely, and they are
that which we know.”
2762 Angen.. Chem. Int. Ed. Engl. 1996.35, 2150-2164
Erich Hiickel and Chemistry REVIEWS
Many colleagueshaveprovided relevant advice and documentation.
Several have submitted to recordedpersonal interviews. I am
greatly indebted to P. D. Bartlett, A. D. Buckingham, J. Fruton.
K. Hafner, M. Hanack, E. Heilbronner, P. C. Hiberty, E. I;:
Hilinski, R. Hofrmann, H. Hopf, R. Huisgen, I;: Hund, T Komm,
#! Liittke, 7: Noroe, A. Streitwieser, H. Tietz, H. A. Turner, E.
Vogel, #! Walcher, E. Wasserman, and K. B. Wiberg. B. Z .
Berson and staff members of the Yale University Library Department
o f Manuscripts and Archives provided bibliographic help.
Received: April 12, 1996 [A1631E]
German version. Angea. Chem. 1996, 108,2922-2937
[l] E. Huckel, Em Grlehrtenlehen. Ernst und Satire, Verlag Chemie, Weinheim,
[2] H. Hartmann. H. C. Longuet-Higgins, Biographical Memoirs ofFe1loif.softhe
[3] R. G.Parr, Int. J.Quantum Chem. Symp. 1977,25gives a theoretician’sview of
[4] A biographical sketch of Walter Hiickel is given by: R. Neidlein, M. Hanack.
[5] P. Debye. E. Hiickel. Ph.vs. Z. 1923, 24, 185, 305.
[6] H C. Longuet-Higgins, M. E. Fisher, Biogr. Mem. Natl. Acad. Sci.1991, 60,
183 (Memoir of Lars Onsager).
171 L. Onsager. Lcs Prj, Nobel en 1968. Stockholm. Norstedt and Soner, 1969.
p. 169; S i w m > .1969, 166, 1359.
[8] E. Huckel. Z. Phys. 1930.60,423;Z. Elektrochem. Angen. P11ys.Chem. 1930.
36. 641.
[9] 3. H. van7 Hoff, The Arrangement of Atoms in Space, 2nd ed. Longmans,
Green, London. 1898.
[lo] a) L. Pauling, J. Am. Chem. Soc. 1931, 53, 1367, 3225;Nature of the Chemical
Bond, Cornell University Press, Ithaca, NY, 2nd ed. 1940, Chapter 111; 3rd ed.
1961.b) For further discussionof this point, see K. B. Wiberg, Acc. Chem. Res.
1996.29. 229
1975.
Royal Society, 1982. 28, 153.
some of the topics covered here.
Chem. Ber. 1980, 113, I .
[ll] J. C. Slater. Phix. Rev. 1931, 37. 481; ihid. 1931, 38, 1109.
[12] J. E. Lenndrd-Jones, Trans. Faraduy Soc 1929, 25, 668.
[13] Adapted from C. A. Coulson, Valence.Oxford University Press, London, 1952.
1141 For a review, references, and conceptual discussion, see a) W. Kutzelnigg.
Angrn. (’hem. 1996. 108. 629; Angeu.. Chem. Int. Ed. Engl. 1996, 35,
573 - 586: b) W. Kutzelnigg, J. D. Morgan 111. Z. Phys. D Mol. Clusters 1996.
36. 197.
[15] See also J. A. Berson,in The Chemrstry ofQuinonoidCompounds, Vol.11,(Eds.:
S. Pdtai, Z. Rappoport), Wiley, New York, 1988, Chapter 10,and references
therein.
p. 100.
[16] R. S. Mulliken. Pliys. Rev. 1933, 43. 279.
[17] a)W. G. Penney, Proc. R. Soc. London A 1934,144.166;b)ibid. 1934,146,223.
For an account of Penney’slater career as a leader of Britain’s nuclear bomb
program. see Lord Sherfield, Biogr. Mem Fellows R. Soc. 1994,39,283. Penney
served on the target committee for the bombing of Hiroshima and Nagasaki:
R. Rhodes. The Making o/fheAtomic Bomb, Simon and Schuster, New
York. 1986, pp 522, 626, 628,677-678.
[lX] G. E Kimball. J. Chem. Phys. 1940, 8, 188.
[19] E. Hiickel, 2. Php. 1932, 76, 628.
[ZO] E. Hiickel, Z. P h w 1931, 70, 204.
1211 L. Pauling, J. Chem. Phys. 1933,1,280;L. Pauling, G. W. Wheland, ibid. 1933,
[22] G. W. Wheland. J. Chem. Phys. 1934,2,474.
[23] L. Pduling in Organic Chemistry - An Advanced Treatise Vol. II. (Ed.: H.
[24] G W. Wheland. The Theory of Resonance and Its Application to Organic Chem[25]
G W Wheland. Resonance in Organic Chemistry, Wiley, New York, 1955, p.
[26] R. S. Mulliken. Annu. Rev. Phys. Chem. 1978, 29, 1. and references therein.
[27] W J. Hehre, L. Radom, P. von R. Schleyer, J. A. Pople, Ah Initio Mofecltlar
Orbital Throrj, Wiley. New York, 1986.
[28] P. C. Hiberty. G. Ohanessian, S. Shaik. JLP. Flament, Pure Appl. Chem. 1993,
65.35;S. Shaik. P. C. Hiberty, Adv. Quant. Chem. 1995,26,99.and references
therein.
I, 362; L. Pauling. J. Sherman, ibid. 1933, I, 679.
Gilman) 2nd ed.. Wiley, New York, 1943, Chapter 26.
istr.v. Wiley. New York, 1944.
632.
[29] W Goddard. Ill. L. B. Harding. Annu. Res. Phys Chenz. 1978. 29, 363.
[30] C. A. Coulson. Valence.Oxford, 1952, p 109 ff.
[31] W Heitler, F. London, Z. Phys. 1927, 44,455.
[32] W. Heisenberg. 2. Phys. 1928,49,619;J. C. Slater. Phys. Rev. 1929.34, 1293:
cf. J. C. Slater. Introduction to Chemical Physics, McGraw-Hill, New York,
1939. p. 367 fl..
[33] F Bloch. Z. Phvs. 1930,61. 206.
E. Hiickel, Pap. and Discuss. Int. Con/: Phys. Vol. 11, The Physical Society,
London, 1935, p. 9.
J. C. Slater, Pap. and Discuss.Int. Con/: Phys. Vol. 11, The Physical Society,
London, 1935. p. 53.
F. Bloch, Z. Phys. 1928,52, 555.
E. Hiickel, Z. Elektrochem. Angen-.Physik. Chem. 1937,42.752,827.Reissued
as an off-print: “Grundziige der Theorie ungesiirtigfer und aromatischer
Verbindungen”,Verlag Chemie, Berlin, 1938.
E. Heilbronner in ref. [64c], p. 179.
A. Streitwieser,Jr. Molecular Orbital Theoryfor Organic Chemists, Wiley,New
York, 1961, p. 5.
K. B. Wiberg. Physical Organic Chemistry, Wiley, New York, 1964, p. 9.
J. P. Lowe, Quantum Chemistry.Academic Press, New York, 1978,
V. 1. Minkin,M. N. Glukhovtsev. B. Ya. SimkinAromaticit.vund Antiaromaticify,Wiley,
New York, 1994, p. 116 ff.
H. M. McConnell, Science, 1996, 271,603.
S. Kuwajima, J. Am. Chem. Soc. 1984. 106,6496.
C. A. Coulson, Valence,Oxford, 1952,p. 147 ff;H. C. Longuet-Higgins, Pror.
Phys. Soc.’ 1948,60, 270.
D. Maynau. J.-P. Malrieu, J Am. Chem. Soc. 1982, 104.3029.
J. J. C. Mulder, L. J. Oosterhoff, Chem. Commun. 1970, 305, 307.
R. Huisgen, tape-recorded interview with J. A. Berson, New Haven, October
29, 1995.
W. Hiickel, Theoretical Principles of Organic Chemistry, Vol. I, Elsevier, New
York, 1958, (English translation of Theoreti.sche Grundlagen der Organischen
Cliemie, Verlag Chemie, Weinheim, 7th ed.).
C. K. Ingold, Structure and Mechanism in Organic Chemistry. Cornell University
Press, Ithaca, NY, 1953, p. 185.
L. P. Hammett, Physicaf OrganicChemistry. McGraw-Hill, New York, 1940,
p. 16 ff.
Personal notes by J. A. Berson on lectures in Advanced Organic Chemistry, a
course given by W. von E. Doering, Columbia University, 1946-1947.
C. R. Noller, J. Chem. Educ. 1950.27, 504.
L. F. Fieser in Organic Chemistry - An Advanced Treatise Vol. 1, (Ed.: H.
Gilman), 2nd ed., Wiley, New York, 1943, Chapter 3; see also L. F. Fieser, M.
Fieser, Advanced Organic Chemistry, Reinhold, New York, 1961, p. 618.
a) C. A. Coulson, Proc. R. Soc. A 1939, f69, 414; b) C. A. Coulson, G. S.
Rushbrooke. Proc. Cambridge Philos. Soc. 1940, 36, 193; c ) H. C. LonguetHiggins,
J. Chem. Phys. 1950, 18, 265: d) M. J. S. Dewar, J Am. Chem. SOC.
1952, 74, 3345, 3357.
a) R. S. Mulliken, .IChim. Phys. Phys. Chim. Biol. 1949, 46, 497, 675; b) B.
Pullman, A. Pullman, Les Theories Elerrroniques de la Chimiv Organique,Masson
& Cie, Paris, 1952.
E. Heilbronner, tape-recorded interviewwith J. A. Berson. Herrliberg, Switzerland,
March 30,1996. Heilbronner reports that in a conversation in 1950-51,
Pauling remarked that only two people had ever read the Mulliken paper:
Mulliken and the poor guy who had to translate it into French.
A. S. Pfau, P. A. Plattner, Helv. Chim. Acta, 1936. f9,858; P. A. Plattner,
Angen. Chem. 1942, 55, 131, 154.
Review: W. Keller-Schierlein. E. Heilbronner in ref. [64c], Chapter VI.
E. Heilbronner in ref. [64c], Chapter V.
K. Hafner, Angen. Chem. 1958, 70, 419; K. Ziegler, K. Hafner, ibid. 1955,67,
301.
T. Nozoe, Seventy Years in Organrc Chemistry, American Chemical Society,
(Ed.: J. I. Seeman), Washington, DC. 1991; T. Nozoe, interview with .I.A.
Berson, Tokyo, May 18, 1995;T. Nozoe to J. A. Berson, personal letter, June
6, 1995. Review: T. Nozoe in ref. [64c]p. 339.
a) H. J. Dauben, H. Ringold. J. Am. Chem. Soc. 1951, 73, 876; b) W. von E.
Doering, F. L. Detert, ibid. 1951, 73, 876.
See among others: a) Theoretical Organic Chemistry. Proceedings and Discussions
of the Kekule Symposium, Butterworths ScientificPublications, London,
1959;b) Aromaticity, an International Symposium, The Chemical Society Special
Publication No. 21, London, 1967;c)Non-benzenoid Aromatic Compounds,
(Ed: D. Ginsburg), Interscience, New York, 1959;d) P. J. Garratt, Aromaticity.
Wiley, New York, 1986.
W. von E. Doering, L. H. Knox. J Am. Chem. SOC.1954, 76, 3203.
R. Breslow, H. Hover. H. W Chang, J. Am. Chem. Soc. 1962,84. 3168, and
references therein.
R. B. Woodward, R. Hoffmann, The Conservation of Orbilal Symmetry. Verlag
Chemie, Weinheim and Academic Press, New York, 1970, and references
therein.
K. Fukui, Acc. Chem. Res. 1971,4, 57; H. E. Zimmerman. ibid. 1972,5, 393;
M. J. S.Dewar, Angen. Chem. 1971,83,859;Angew. Chem.Int. Ed. Engl. 1971,
10,761;an important insight undergirding the latter two papers is given by E.
Heilbronner. Tetrahedron Lett. 1964, 1923.
Further references: ref. [67].p. 169.
M. G. Evans, Trans. Faraday Soc. 1939, 35, 824. For a much cIoser
early approach to modern orbital symmetry ideas, see Ya. K. Syrkin, Bull.
Acad. Sci. USSR, Div. Chem. Sci. 1959, 218: Izv. Akad. Nauk SSSR, Arm.
Khim. Nauki, 1959, 238; Ya. K. Syrkin, I. I. Moiseev, Uspekht Khim. 1958,
27, 1321.
Angea. Chrm. Int. ELI.Engl. 1996, 35, 2750-2764 2763
REVIEWS J. A. Berson
[71j F. Hund, personal communication to E. Muller, as cited by Miiller and Bunge
[72] E. Miiller, I. Miiller-Rudloff, Justus Liebigs Ann. Chem. 1936, 517. 134; E.
1731 E. Huckel, 2.Phys. Chem. Abt. E, 1936, 34, 339.
1741 a) W. T. Borden, E. R. Davidson, J: Am. Chem. Soc. 1977.99.4587; b) A. A.
Ovchinnikov, Theor. Chem. Acta, 1977, 47,497.
1751 Similar arguments led to the idea that square planar cyclobutadiene (not formally
a non-Kekulemolecule) also might violate Hund’s rule: W. T. Borden, .I
Am. Chem.SOC.1975,97, 5968. H. Kollmar, V. Staemmler, ibid. 1977,99,3586.
1761 J. H. Reynolds, J. A. Berson, K. K. Kumashiro, J. C. Duchamp. K. W. Zilm,
J. C. Scaiano, A. B. Berinstain, A. Rubello, P. Vogel,J. Am. Chem. Sac. 1993,
ff5.8073; W. T. Borden, H. Iwamura, J. A. Berson, Acc. Chem.Res., 1994.27,
109, and references therein; P. G. Wenthold, D. A. Hrovdt, W. T. Borden, W.
C. Lineberger, Science 1996. 272, 1456.
in ref.[72].
Miiller, W. Bunge, Eer. Dtsch. Chem. Ges. 1936, 69, 2168.
[77] K. Hafner, tape-recorded interview with J. A. Berson, Darmstadt, April 3,
1996.
[78f Undated letter of E. Huckel to R. Kuhn, reproauced in the Program of’the
Kekuli Celebration, Bonn, 1965.
1791 H. Tietz, “Einige personliche Worte zu Erich Hiickel.” unpublished text of a
celebratory colloquium, presented in Marburg, November 14, 1980; W.
Walcher, letter to J. A. Berson, March 6, 1996.
[SO] A. A. Frost, B. Musulm, J. Chem. Phys. 1953, 2/, 572.
[81] J. Thiele, Justus Liebigs Ann. Chem, 1899, 306, 87. I thank Prof. R. Huisgen
for this citation, which appears epigraphically in his own doctoral disserta-
tion.
1821 “Tradition and the Individual Talent”, T. S . Eliot in The Sacred Wood,
Methuen, London, p. 52.
2764 Angew. Chem. Int. Ed. Engl. 1996,35,2750-2764