The Development of the Idea of a
Chemical Bond
BRIAN T. SUTCLIFFE
Department of Chemistry, University of York, York YO2 5DD, United Kingdom
Received July 27, 2994; revised manuscript received August 9, 1994; accepted May 6, 1995
ABSTRACT D
The development of the idea of a chemicalbond is traced from Frankland to Heitler and
London and beyond with emphasis on how electrons came to be considered essentialto
explaining the bond. 0 1996 JohnWiley & Sons, Inc.
Introduction
ost historians of chemistry now agree that
MFrankland was responsible for inventing the
chemical bond. According to Russell 111, the first
formal statement of the idea of a bond appeared in
Frankland’s article in J.Ckem SOC.19,377(1866). In
that article, Frankland said:
By the term bond, I intend merely to give a
more concrete expression to what has received
various names from differentchemists,
such as an atomicity, an atomic power, and
an equivalence. A monad is represented as
an element having one bond, a dyad as an
element having two bonds, etc. It is scarcely
necessary to remark by this term I do not
intend to convey the idea of any material
connection between the elements of a compound,
the bonds actually holding the atoms
of a chemical compound being, as regards
their nature much more like those which connect
the members of our solar system.
The idea of representing a bond by means of a
straight line joining the atomic symbols we probably
owe to Alexander Crum Brown. (He was very
long-lived, from 1832 until 1922, and as a young
man, the author met someone who had actually
been taught by him at the University of Edinburgh.)
Frankland, with due acknowledgment,
adopted Crum Brown’s representation (which put
circles round the atom symbols), but by 1867, the
circles had been dropped and more or less modern
chemical notation became widespread. This was,
in some measure, almost certainly because of the
ease with which isomers of hydrocarbons could be
represented and enumerated within this approach,
as shown especially in the work of Cayley 121.
What is notable here is Frankland’s extreme
caution ”to avoid any speculation as to the nature
of the tie which enables an element thus to attach
itself to one or more atoms of other elements” [l].
The historical reasons for this caution are not hard
to fathom, but what is rather harder to understand
InternationalJournal of Quantum Chemistry,Vol. 58, 645-655 (1996)
0 1996 John Wiley 8, Sons, Inc. CCC 0020-7608 I96 1060645-11
SUTCLIFFE
is why, within 40 years of it being made, chemists
(with some notable exceptions) were happy to
throw caution to the winds and espouse the electron
as the originator of the chemical bond. In this
article, I consider how this came about and to
what it led after the advent of modern quantum
mechanics.
In describing what went on, I rely chiefly on
secondary sources and it is in these that the references
to the primary material may be located.
Among the secondary sources consulted were
Russell [l],Lagowski [3], and Stranges [4]. Brock,
in his History of Chemistry [5], devoted a chapter to
the bond in the context of a general history (published
in the US.by Norton and in Europe by
Fontana). A work which provides a context within
which the development of the idea can be seen in a
most helpful way is the book From Chemical Philosophy
to Theoretical Chemistry by Nye [61.
The Bond and the Electron Until the
Beginning of the Twentieth Century
The idea of a chemical combination as being
due to electrical forces has, of course, a long history
in chemistry. It is probably not unfair to
attribute to Berzelius the early development of the
important ideas here, but the rise of organic chemistry,
in which the combination was not obviously
of an electrical kind, led to the eclipse of his
approach. The theory of types and the theory of
radicals both bid to replace it. It was not until the
1850’s that the idea of atoms having autonomous
valencies developed, and through this idea (which
he played an important part in developing; see,
e.g., [l, 31, Frankland arrived at the idea of a
chemical bond. His caution about saying precisely
what a bond was was probably due to his desire
not to give hostages to fortune in a way that could
give support to those adherents of either of the
older theories of chemical combination. It could
also have had something to do with the philosophical
controversiesabout the real existence of unobservable
entities, such as atoms and molecules,
which was then a lively part of the discussions
current in scientific and learned circles. It is interesting
to remember that the distinguished
Anglo-American mathematician Sylvester wrote
an article in 1878[7] whose aim was to show how
graphical formulas for molecules could be realized
in purely algebraic terms. (Sylvester called his
algebra “the algebra of binary quantics,” but we
should today call it the theory of binary or bilinear
forms.) The reasons that he chose to do this can, at
least in part, be inferred from the following quota-
tions:
Chemical graphs, at all events, for the present
are to be regarded as translations into
geometrical forms of trains of priorities and
sequences having their proper habitat in the
sphere of order and existing quite outside the
world of space. Were it otherwise, we might
indulge in some speculation as to the directions
of the lines of emission or influence or
radiation or whatever else the bonds might
then be supposed to represent as dependent
on the ‘manner of the atoms entering into
combination to form chemical substances.
Such not being the case. ...
The perhaps unworthy suspicion does enter
one’s mind that Sylvester founded and was first
editor-in-chief of the American Journalof Mathematics,
in which his article appeared, to get things like
this off his chest. This suspicion is supported
somewhat by the following, in which some rather
sententious thoughts are expressed:
In regard of atomicity theory (read ”valency
theory”), all these modes of colligation are
identical, and the supposition that there is
any real difference between them, or that
figures in space are distinguishable from figures
in a plane (as I heard suggested might
be the case by a high authority at a meeting
of the British Association for the Advancement
of Science, where I happened to be
present), is a departure from the cautious
philosophical views embodied in the theory
as it came from the hands of its illustrious
authors and continued to be maintained by
their sober-minded successors and coadjutors,
and affords an instructive instance of
the tendency of the human mind to worship,
as if of self-subsistent realities, of the symbols
of its own creation.
The idea of directed valence was, of course, 4 or
so years old by the time Sylvester wrote this and
he was not the only one who opposed van’t Hoff
and le Bel. Kolbe (with whom Frankland actually
published an article on valence in 1857),in particular,
remained vociferous in his opposition to the
idea until his death in 1884.(An account of Kolbe’s
646 VOL. 58, NO. 6
DEVELOPMENT OF THE IDEA OF A CHEMICAL BOND
extreme reaction to the article of van’t Hoff on the
tetrahedrally directed bonds in carboncanbe found
in the entertaining book by Klotz [8] and Kolbe’s
position is examined, in context, in Russell’sbook.)
There was also an extremely radical suggestion
made in 1866 by Sir Benjamin Brodie [91, Waynflete
professor of chemistry in the University of
Oxford, that not only bonds should be treated as
imaginative constructions but that so also should
atoms. His Calculus of Chemical Operations, he asserted,
was based on no theories about anything
but simply on observations. Again, some feeling
for how these ideas were received can be gained
from Russell’s book and also from an article by
Farrar [lo]. (It is clear from his article that Farrar
regards Brodie as just about fit for the funny farm,
which I think rather unfair, but it is difficult to
regard him as other than pretty eccentric by the
time of his second article in 1877[lll.)
In his article, Sylvester actually first attributed
the idea of a bond to Kekul6 and corrected himself
only in a footnote toward the end of the first
appendix. Frankland, however, clearly kept an eye
open for his priority and wrote a letter to Sylvester,
which Sylvester published, just to keep things
straight. At the end of this letter [12], Frankland
said:
I trust that you will go on with the consideration
of chemical phenomena from a mathematical
point of view, for I am convincedthat
the future progress of chemistry, as an extact
science, depends very much indeed upon the
alliance of mathematics.. ..
I cannot make up my mind as to whether or not
Frankland had his tongue in his cheek when he
wrote that. If he had really felt that, I feel that he
would perhaps of been more supportive of Sir
Benjamin Brodie during the atomic debates that
followed Brodie’s first article (see [13]). But perhaps
Frankland’s pragmatic attitude prevented
this. Sylvester, too, must have known of Brodie’s
work (he had an article that appeared immediately
before Brodie’s first article in Philos. Trans.) but he
never mentions him at all. As far as chemists were
concerned, Brodie was undoubtedly an embarrassment
and they do not seem to have thought much
of Sylvester’s ideas either. But it is interesting to
note that Sylvester’s approach did seem to influence
Matsen [14] in the 20th century, in the development
of his spin-free quantum chemistry.
The graphical notation and the ideas of Frankland
were further developed by Werner in the
1890sin his coordination theory for inorganiccomplexes,
but it was during this period that the first
tentative steps were made toward an electronic
theory of the chemical bond following J. J.
Thomson’s discovery of the electron in 1897.
Atomic structure seems first to have been related
to valency when both Mendeleef and Lothar
Meyer had observed, independently, in the late
1860show valency was correlated with position in
the periodic table. It was also, perhaps in the air,
for in his 1881 Faraday lecture that Helmholtz
revived and expanded the electrical theory of
chemical combination.The connection between the
electron and bonding originates with Thomson’s
association of the electron with the structure of the
atom. By 1902, Oliver Lodge in his Romanes Lecture
discussion of chemical union could say (as
quoted in Stranges [4]) that:
It becomes a reasonable hypothesis to surmise
that the whole of the atom may be built
up of positive and negative electrons interleaved
together, and of nothing else; an active
or charged ion having one negative electron
in excess or defect, but the neutral atom
having an exact number of pairs.
He then goes on to say that chemical combination
must be the result of the pairing of oppositely
charged ions. Lodge was, of course, developing the
ideas of J. J. Thomson in the context of Helmhotz’s
ideas. At this time, no positive electrons had been
observed and, after Rutherford’s construction of
the nuclear atom in 1911, the positive electron
became irrelevant in discussions of bonding.
Ideas very similar to those of Lodge were forming
in the mind of G. N. Lewis at about this time
(1902) but they were not published until 1916,
after the Bohr atom ideas had become prominent
in physics.
It is difficult to avoid presenting too ”triumphalist”
a view of the history of the development
of the idea of a bond from now on. How
things actually developed is now known and seems
as if it were foreordained.The history of the period
after the discovery of the electron and up to the
coming of wave mechanics is surveyed in some
detail in the book by Strangesand in outline in the
book by Russell and in the book by Lagowski [3].
But since it was Lewis’s ideas that were influential,
it is on Lewis that I shall concentrate. It was
INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY 647
SUTCLIFFE
Lewis’ skillful combinationof electronic ideas with
traditional ideas of the bond that proved so persuasive
to chemists.
The Bond from Lewis to Pauling
In his 1923book, Lewis [151 said the following
about the development of his theory:
In the year 1902...,I formed an idea of the
inner structure of the atom which, although it
contained certain crudities, I have ever since
regarded as representing essentially the arrangement
of electrons in the atom.. ..
The main features of this theory of atomic
structure are as follows:
1.
2.
3.
4.
The electrons in an atom are arranged in
concentric cubes.
A neutral atom of each element contains
one more electron than a neutral atom of
the element next preceding.
The cube of eight electrons is reached in
the atoms of the rare gases, and this cube
becomes in some sense the kernel about
which the larger cube of electrons of the
next period is built.
The electrons of an outer incomplete cube
may be given to another atom, as in Mg++,
or enough electrons may be taken from
other atoms to complete the cube, as in
C1-, thus accounting for “positive and
negative valence.”
Although it is proper to accord Lewis’the intellectual
priority here, the priority in publication of
the ”octet rule” is actually by Abegg in 1904 [161.
Lewis did not publish until 1916 [17], and he was
nearly pipped at the post by Kossel [MI, who had
arrived at very similar conclusions by this time.
However, in his article, Lewis introduced a new
idea and a new means of representation, and these
new things are quite unambiguously Lewis’ contributions
alone. The new idea was the ”rule of
two” in which he asserted that the occurrence of
electrons in molecules in even numbers was pretty
much universal. The new means of representation
was the method of symbolizing electrons by dots,
which is now so familiar to us. The ability to make
the correspondence of a pair of dots between two
atom symbols and the bond in this representation
made it extremely attractive to working chemists.
Lewis’ ’ approach carried the day and this was
in no small measure due to the effectiveness of
Langmuir as his fugleman (though this relationship
was not without its strains as evidenced in
Stranges’book).
The interesting things to notice, I think, are that
the ideas here owe absolutely nothing to quantum
mechanics and certainly nothing to Bohr, and, also,
that the model of the atom that is presupposed is a
static one. It would be wrong to believe that this
was because those involved in the developments
here did not know what was going on in physics.
They knew very well and were, on the whole,
pretty sceptical about them. At a meeting of the
AAAS in New York in December 1916, Lewis
devoted his address to the idea of a static atom
[19], and he actually said:
Unless we are willing, under the onslaught of
quantum theories, to throw over all the basic
principles of physical science, we must conclude
that the electron in the Bohr atom not
only ceases to obey Coulomb’s law, but exerts
no influence whatsoever upon another
charged particle at any distance.
This absence of the effect, Lewis considered logically
and scientifically objectionable, for, he said
[17]:“that state of motion which produces no
physical effect whatsoever may better be called a
state of rest.”
And he was not alone in his scepticism. J. J.
Thomson was trying to work a static atom theory
as late as 1923 as were Langmuir, Davey, Born,
Land6, and Parson. All involved were trying to
modify Coulomb’s force law to get a theory in
which the electrons in an atom remained still and
were distributed at the cornersof a cube. But in his
Nobel lecture in 1922, Bohr delivered an attack on
static atom theories, pointing out that Earnshaw’s
theorem showed that a static distribution of
charges must be unstable if Coulomb’slaw applies
and extending the argument to cover the proposed
modified potentials.
This clearly was, at least, a very uncomfortable
situation for chemists and some undoubtedly
thought it intolerable. Among those who did was
Sidgwick who attempted to avoid the difficulty by
shifting the argument away from atomic structure
as such, to the idea of molecular structure in
which pairs of electrons had common orbits of the
Bohr-Sommerfeld type involving the molecular
648 VOL. 58,NO. 6
DEVELOPMENT OF THE IDEA OF A CHEMICAL BOND
nuclei. He seems to be the first person to point out
that it was possible to imagine a dynamical situation
in which a pair of electrons could hold a pair
of nuclei together. This suggestion was made at a
meeting of the Faraday Society in Cambridge in
1923 [20], and at that meeting, Lewis in his introductory
address signaled his accession to a similar
point of view and his mature views are expounded
in his book [151 as those of Sidgwick are in his
1927book [21]. Lewis is clearly still unhappy with
quantum theory, for in the closing pages of his
book, he cannot resist referring to it as ”the entering
wedge of scientific bolshevism,” but Sidgwick
had decided to bite the bullet. The preface to his
book begins:
This book aims at giving a general account
of the principles of valency and molecular
constitution founded on the Rutherford-Bohr
atom.
In developing the theory of valency there
are two courses open to the chemist. He may
use symbols with no definite physical connotation
...or he may adopt the concepts of
atomic physics,. ..and try to explain chemical
facts in terms of these. But if he takes the
latter course, as is done in this book, he must
accept the physical conclusions in full.. ..
But, then, it is clear that he sensed the “cloud
no bigger than a man’s hand” on the horizon when
he acknowledged the newly published work of
Schrodinger and said:
It has yet given no proof that the physical
concepts which led (him) to his fundamental
differential equation should be taken so literally
as to be incompatible with the concep
tions of the nature of electrons and nuclei to
which the work of the last thirty years has
led.
In fact, Sidgwick‘s book was a threnody for
the old way of looking at things, for Heitler and
London’s article appeared in that year and it fell to
Pauling to make what reconciliation was possible
between the Lewis theory and the approach made
by Heitler and London. This he did in a series of
articles published between 1928 and 1933 and
whose conclusionsare brought together in his book
[221, dedicated to G. N. Lewis and published in
1939. In this enormously influential book, Pauling
had a clear program. He said:
I formed the opinion that, even though much
of the recent progress in structural chemistry
has been due to quantum mechanics, it
should be possible to describe the new developments
in a thorough-going and satisfactory
manner without the use of advanced mathematics.
A small part only of the body of
contributions of quantum mechanics to
chemistry has been purely quantum mechanical
in character.. ..The advances which have
been made have been in the main the result
of essentially chemical arguments.. .. The
principal contribution of quantum mechanics
to chemistry has been the suggestion of new
ideas, such as resonance.. ..
Pauling starts his exposition from the idea of
the electron pair bond as envisaged by Lewis and
shows how this can be understood in the context
of the Heitler-London calculation as being due to
strong orbital overlap. After introducing the idea
of orbital hybridization, he then uses the idea of
maximum overlap in discussing bonding generally.
It is an amazing tour deforce with just enough
mathematics to provide ”corroborative detail, intended
to give artistic verisimilitude to an otherwise
bald and unconvincing narrative” (to misappropriate
Pooh-Bah’s lines from The Mikado) and
not too much to be daunting. I feel sure that every
practicing latter-day quantum chemist must envy
Pauling his facility and wish that they had written
the book. (Though perhaps some might have
wished, on similar grounds, to have written
Coulson’s Valence.) It brought quantum mechanical
ideas into chemistry in an unthreatening way
by realizing the electron pair bond in terms of
hybrid orbitals, maximally overlapping. It dealt
with the problems that arose when equivalent
pairings were possible, by a judicious use of resonance.Thus,
once the book’s ideas had been assimilated,
chemists could carry on in much the same
way as had been the case formerly but with resonance
and hybrids added to their armory. And
they did so with the comforting feeling that the
most sophisticated theory in modern mathematical
physics supported their actions.
It should not be thought, however, that all were
convinced as was Pauling in the correspondence
between perfect pairing and the bond. Mulliken
arrived at very different conclusions from the
standpoint of molecular orbital theory. He devoted
INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY 649
SUTCLIFFE
his 1931 review [231 to a description of molecular
structure in terms of molecular orbitals, and at the
end of the last section, felt constrained to say:
The fact that valence electrons almost always
occur in pairs in saturated molecules
appears to have after all no fundamental connection
with the existence of chemical binding..
..
A clearer understanding of molecular
structure.. .can often be obtained by dropping
all together the idea of atoms or ions
held together by valence forces, and adopting
the molecular point of view, which regards
each molecule as a distinct individual built
up of nuclei and electrons.
For Mulliken at least, it was clearly somewhat
doubtful even then that the bond was either necessary
for or explicable in terms of the quantum
mechanics required to account for molecular
structure.
A very interesting and balanced account of the
field at about this time can be found in the 1935
review “The Quantum Theory of Valence” by Van
Vleck and Sherman [24]. On the whole, the review
seems to regard the molecular orbital viewpoint as
being the more satisfactory one and maintains
Mulliken‘s scepticism about the importance of
electron pairs.
The Bond from Pauling to the
Supercomputer
In all the schemes proposed at this time for
doing molecular calculations, the nuclei were
treated as providing a molecular geometry, in
terms of which a molecular electronic structure
calculation was parameterized, i.e., the nuclei were
considered as essentially classical particles, which
could be clamped at will to construct a molecule
with a chosen geometry. This was the approach
used by Heitler and London in their pioneering
calculation and it became usual to say that
it was justified “within the Born-Oppenheimer
approximation.”
The fascinating thing about the actual computational
developments in this period, however, was
that almost none used the approach, the so-called
valence bond (VB) approach, that Pauling had proposed
as the foundation of the theory of the bond.
The technical .reasons for this are well enough
known. The nonorthogonality between the hybrid
orbitals, a feature essential for the justification of
the Pauling approach, made formulating the equations
for calculation just too complicated and difficult,
and even if approximations were made, but
made in a consistent fashion, any consequent calculations
were impossible to perform. It was thus
not possible to provide a means of tying Pauling‘s
ideas to the detailed equations in any unambiguous
way.
In fact, almost all went the way that Mulliken
proposed using a molecular orbital approach. In
this approach, it was possible to formulate the
equations in a manner suitable for calculation and
to develop consistent approximation schemes that
allowed at least semiempirical calculations to be
made. A number of semiempirical schemes were
developed, particularly for aromatic and conjugated
systems, which can be regarded as inspired
by the initial efforts of Huckel in 1931 to use
molecular orbitals in this area. For such systems,
the idea of a delocalized electron distribution came
immediately out of the calculations, so that there
was no need to invoke the bond or the idea of
resonance. However, the parameterization schemes
within these semiempirical approaches were cast
in terms of integrals between hybrid orbitals, so
that aspect of Pauling’s ideas remained alive both
in chemistry and in quantum chemistry.
The principal computational approaches to
molecular electronicstructure that developed from
about 1950onward had molecular orbitals (MOS) as
their basis. Since the MOS were realized in terms of
linear combinationsof atomic orbitals (LCAOS), the
orbital remained a feature of the quantum mechanical
account of molecular structure. Initially at least,
it was not possible to realize fully the LCAO MO
approach because, except in diatomic systems, the
integrals over the orbitals,which were exponential
in their radial parts (Slater orbitals), proved too
difficult to evaluate quickly enough to make
nonempirical calculation feasible. But even given
these limitations, it was already clear that the role
of the bond in the emerging discipline of computational
quantum chemistry was going to be
problematic.
The state of affairs at this stage was well
summed up by Coulson in his 1951Tilden Lecture
[25], ”The Contributions of Wave Mechanics to
Chemistry.” In his lecture, he dwelt on three topics:
the simple chemical bond, .Ir-electron chemistry,
and chemical reactivity and it is the first of
650 VOL. 58,NO. 6
DEVELOPMENT OF THE IDEA OF A CHEMICAL BOND
those topics that is of interest here. Coulson used
the idea of hybrid orbitals in discussing bonds and
molecular shape, as might have been expected, but
the ground is shifting a little. He takes the electronic
charge density as the origin of binding:
We might say that the description of a bond
is essentially the description of the pattern of
the charge cloud.. ..Indeed in the very last
resort, we cannot entirely separate the charge
cloud for one bond from that for another
bond. But, subject to reasonable
limitations.. .they can be found in terms of
suitable patterns.. .for the isolated atoms.
And, of course, this position presages much
work done on in attempts to picture the bond as
related to the electronic charge density between
the nuclei. The first quantitative attempt here is
probably by Berlin [26], who in 1951 tried to use
the Hellmann-Feynman theorem to account for
the bond in terms of electrostatic forces engendered
by the charge cloud. The bond analysis of
charge densities has been extensively developed
by Bader and his co-workers; see, e.g., [27]. This
viewpoint has encouraged some experimental
work to try to ”see” the bond by looking for
localized charge densities in molecules and some
of this work was reviewed in [281.
Yet, in the closing section of his lecture, Coulson
seemed not quite sure that he was on the right
track. In fact, he adopted a really rather positivistic
attitude, reminiscent if not of Brodie then perhaps
of Sylvester at least. He said:
I described a bond, a normal chemical bond;
and I gave many details of its character (and
could have given many more). Sometimes it
seems to me that a bond between two atoms
has become so real, so tangible, so friendly,
that I can almost see it. And then I awake
with a little shock: for a chemical bond is not
a real thing: it does not exist: no-one has ever
seen it, no-one ever can. It is a figment of our
own imagination.
A certain scepticism, perhaps not quite as
marked as in the quote above, also found its place
in Coulson’s after-dinner speech entitled ”The
Present State of Molecular Structure Calculations”
1291, made at the Boulder Conference in 1959. He
said there:
The concepts of classical chemistry were
never completely precise.. ..Thus when we
carry these concepts over into quantum
chemistry we must be prepared to discover
just the same mathematical unsatisfactoryness
[sic].
In the nearly 10 years since Coulson’s Tilden
Lecture, enormous developments had been made
in electronic computers and schemes for the calculation
of molecular electronic structure were already
far advanced, though not to be completely
realized for another 10 years, with the further
developments in integral schemes. It was against
this background that Coulson introduced the celebrated
idea of the two groups of quantum chemists.
Group I were those who wanted to do as accurate
calculations as possible and who believed that the
role of wave mechanics was to obtain numbers.
Group I1 were those who believed that its role was
to account for the ”quite elementary” concepts of
ordinary chemistry. For those in group I, Coulson
maintained:
Mathematically. .., a bond is an impossible
concept.. .. It is not surprising.. .therefore
that it is practically never used by them. Yet
the existence of bond properties is basic to all
chemistry.
In these circumstances,it is perhaps not surprising
that Coulson was pessimistic about whether
for much longer the two groups would continue to
speak to one another. He opined that ”there is
now little point in bringing them together. This is
probably the last conference of the old kind.”
But with his customary perspicuity, Coulson
had touched the nerve of the problem and what he
said about computational quantum chemists and
the bond needs no modification even to this day.
Those who compute structure can often find ways
of getting bonds and the like out of their results. In
constructing trial wave functions, they are often
guided by classical chemical structure considerations.
But it is perhaps not too much to say that in
these contexts the perceived role of the bond is
that either of decorative embellishment in the first
instance or of intellectual scaffolding in the second.
For the computational quantum chemist, the legitimacy
of a molecular structure is decided by the
calculation. Though such a person appreciates the
INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY 651
SUTCLIFFE
aid of scaffolding and the appeal of decoration,
both, in the last analysis, can be done without.
One of the ways in which a wave function can
be analyzed in a manner suggestive of a particular
pattern of bonds is if important elements of the
wave function can be seen as consistingof strongly
overlapping orbitals. It is in this context that there
has been much discussion in the chemical education
literature over the past 10 or so years about
what should be taught about the bond in the light
of present knowledge. The sequence of articles,
between which and from which there are many
cross references, begins with some fairly radical
thoughts by Bent in two articles [30, 311 on atoms.
But things began to warm up in an article by
Ogilivie entitled, ”There Are No Such Things As
Orbitals” [32] in 1990. This generated a flurry of
responses [33-37] and, eventually, a thunderous
response from Pauling [38]. Pauling clearly felt
that he had dealt effectively with the whole controversy,
for he ends a magisterial last section,
entitled ”The Consequent Implications for Chemical
Education,” with the observation that the information
that has recently become available
has not decreased the value of the concept of
the chemicalbond. I am pleased and gratified
that in 1992 the chemical bond is alive and
well.
All these articles appeared in The Journal of
Chemical Education, and in the fashion of editors
everywhere in exchanges of this kind, the editor
declined to print any more contributions to the
debate after Pauling’s response. However, Ogilivie
provided a summary of and a commentary on the
whole exchange in his article [39]. The commentary
does not pretend to be impartial.
As noted earlier, all the discussion so far has
been in the clamped nucleus approximation for
electronic structure calculations. The wave function
of interest, in terms of which all the above
discussion has taken place, is the electronic wave
function for the molecule at its equilibrium nuclear
geometry. The equilibrium geometry is supposed
to be that nuclear geometry which minimizes the
sum of the electronicenergy and the nuclear repulsion
energy, this last calculated classically. As a
matter of fact, this process actually breaks the
permutational symmetry of the quantum mechanical
problem by identifying the nuclei. This seems
first to have been mentioned in print by Berry in
1960 [40], and this early article attempted to deal
with what Weininger so perceptively recognized,
somewhat later, as much more radical objections
to the idea of molecular structure and bonds [41].
These are about whether you could actually get
the bond and molecular structure out of quantum
mechanics without making assumptions about the
way the nuclei moved.
Deconstructlngthe Bond
For many involved in thinking about the problem
of molecular structure, and, hence, of the
chemical bond at this level, it seems as if it is the
old philosophical problem of reductionism that is
at the center of their anxieties. In general, it is
those quantum chemists who discount the value of
a reductionist perspective, who tend to be most
sceptical about the possibility of accounting for
molecular structure in terms of quantum mechanics.
It is odd, too, that their opponents in argument,
generally, are also opposed to reductionism,
in the sense that they would certainly resist
attempts to account for chemistry as a branch of
physics or even to account for organicchemistry as
a branch of physical chemistry.
Perhaps the widest-ranging account of the problem
of molecular structure is in the book by
Primas [42]. This book is very radical in its attempts
to undercut any reduction through quantum
mechanics to chemical ideas. In the precise
area of bonding and molecular structure, the important
radical work is that of Woolley [43-511
and that of Claverie 152, 531.
In general terms, the arguments are that if one
knew only the isolated molecule Schrodinger
equation and knew nothing of classical molecular
structure theory then there is nothing that would
lead one to expect molecule-like solutions among
its eigenstates. Indeed, there is actually much that
would make one hesitant about even looking for
such solutions. Thus, as Woolley pointed out, a
natural element of classical molecular structure
theory is to assign static dipoles to particular
molecules. Such assignments are often made in
terms of vector sums of bond dipole moments, so
that bonds are deemed to play an important role in
static molecular dipoles. But the Schrodinger
Hamiltonian commutes with the inversion operator,
so its eigenstates must be parity eigenstates
and, hence, must have zero expectation values for
the static dipole operator. But if an eigenstate
652 VOL.58, NO. 6
DEVELOPMENT OF THE IDEA OF A CHEMICAL BOND
INTERNATIONALJOURNAL OF QUANTUM CHEMISTRY 653
corresponds to a molecule with structure, then, it
follows, that the molecule cannot have a static
dipole moment. The result cannot be doubted, but
it has a very paradoxical flavor. A similar argument,
as again Woolley showed, leads to the conclusion
that the existence of stereoisomers cannot
be accounted for in terms of solutions of the
Schrodinger equation. Similarly, it is perfectly
well known that an electric dipole transition in a
rotating-vibrating molecule cannot occur without
a change in the principal rotational quantum number
1. The argument here is again one based entirely
on symmetry and the invariances of the
Schrodinger Hamiltonian. Thus, on the face of it, a
pure vibrational spectrum is not explicablein terms
of Schrodinger wave functions.
Woolley also made the point 'most eloquently in
his discussion of the isomers of polyatomic
molecules, [48, 511 that what one might think of,
e.g., as the molecular Hamiltonian for cubane,
C,H,, is also the molecular Hamiltonian for
cyclooctatetrene, vinylbenzene, and many other
systems, too. Indeed, it is even the Hamiltonian
for a system with optical isomers, 3-vinyl hexa-
1,4-diyne, which has the molecular formula
H
I
CH,=CH-~-C=CH
I
CSC-CH,
and in which the central carbon is clearly chiral by
the conventional rules.
Thus, the idea of a molecule with a particular
structure is, at best, only implicit in any molecular
Hamiltonian and criteria other than purely quantum
mechanical ones are therefore logically necessary
to identify a particular solution as the chemical
molecule. A similar point can be made in terms
of chemical reaction schemes, for there the Hamiltonian
for the products must be identical with the
Hamiltonian for the reactants.
Examples of these apparently paradoxical results
could easily be multiplied and, for some
radical thinkers, indicate that the Schrodinger
equation for the isolated molecule cannot be the
appropriate equation with which to describe
molecular structure. Thus, it is sometimes maintained
that molecular structure appears only when
the molecule is considered as surrounded by other
molecules or in its interaction with the vacuum
field and so on. Certainly, these ideas are in tune
with more modern thinking about the holistic
nature of quantum mechanics that has developed
since the work of Bell on the EinsteinPodolsky-Rosen
paradox. (For a cheerful account
of the work of Bell, see the articles collected in the
book by Mermin [541.)
However, it is actually possible to rescue particular
aspects of molecular structure even from full
solutions to the equation by adopting tactics much
like those used in getting bonds out of clamped
nucleus calculations. For example, it is perfectly
easy to show that given certain detailed assumptions
about the form of the wave function that
describes the molecule undergoing the dipole transition
spoken of above then the idea of a pure
vibrational transition can be rescued from mathematics.
The assumptions that have to be made are
essentially those made by Eckart in designing his
body-mixed frame [551, which enables the wave
function to be written as a product of a vibrational
part with an independent rotational part. A detailed
study of this with some numerical results
for triatomic systems can be found in le Sueur et
al. [56]. Of course, such approximations will not
always work but it is arguable that they fail just
where it is unreasonable to persist with the classical
idea of molecular structure. Rather general
discussions of what might be involved in
constructing and processing solutions of the
Schrodinger equation with a view to extracting
molecular structure from them can be found in
two articles by Sutcliffe [57, 581. There are also
articles on models of chemical bonding in the
collection edited by Maksi; [59].
It is thus arguable that if you know what you
want to get out of the full wave function then you
can usually get it by the use of suitable approximations.
In this view, the position in the full wave
function case is not too different from that described
earlier when talking about results obtained
in the fixed nucleus approximation. The idea of
molecular structure and the consequent idea of a
bond can then be accounted for in an approximate
and not entirely coherent way whenever it seems
important to do so. However, accounting for
molecular structure, and, hence, the bond, in terms
of straightforward recognition in the wave function
is still an open problem here. In this view, if
you want it out, you have to put it in.
Naturally, this position cannot be taken without
some feelings of anxiety, for it is perfectly conceivable
that the explanation that is offered of chemical
behavior in terms of molecular structure and
bonding could be somehow misleading. It could,
SUTCLIFFE
perhaps, prevent us seeing more deeply into the
nature of things. If we were to clear our minds of
our classical preconceptions and pay more attention
to the quantum mechanics, then we might see
more.
Conclusions
There are, of course, no firm conclusions to be
offered on a topic like this at this stage of its
development and it is perhaps hazardous even to
offer an opinion. But I think that most chemists
would agree that any theory is a work of the
imagination. They would thus agree with Coulson
in recognizing the bond as a figment of our imagination.
However, I think that few would seriously
doubt the utility of the idea of a bond in the
standard explicatory scheme. Few would say that
there is no such thing as a chemical bond. Most
would agree that the bond has a perfectly satisfactory
existence as a logical construct in a highly
developed and extremely effective theory of
molecular structure. However, I am sure that
many, if not most, quantum chemists performing
calculations in the clamped nucleus approach
would agree that the role that it plays in that
theory cannot be reduced in any invariant way to
an aspect of quantum mechanics. So, it is at least
arguable that, from the point of view of quantum
chemistry as usually practized, the supercomputer
has dissolved the bond.
In the context of solutions to the full
Schrodinger problem, personal inclination is to
agree with Charles Coulson’s Tilden Lecture position
even here and to think that, subject to reasonable
limitations, molecular structure can still be
found if you know what you are looking for. I
acknowledge that the radicals could be right but,
again with Coulson, I think that it is worthwhile to
adopt pragmatic schemes for getting molecular
structure out of wave functions whenever possible.
I think that such pictures seldom mislead seriously
whenever it is possible to draw them. However, I
think that it will be unrewarding to search for a
perfectly mathematicallysatisfactoryinvariant way
of accounting for the bond by analyzing a wave
function.
If I were to guess the future, I should guess that
the idea of the bond and of molecular structure
will prove rather slippery when it comes to interpreting
the results of really high-precisionspectroscopic
experiments. I think that it will also prove
unhelpful in the study of highly excited states. But
in most other areas, particularly organic chemistry
and biochemistry, I feel that I should have to
follow Pauling and predict, that there, the bond
will remain alive and well.
This article is offered to Jens-PederDahl on the
occasion of his 60th birthday. It is offered in grateful
acknowledgement of my trust in the thoughtfulness
and honesty of his opinions in all intellectual
matters and the consequent confidence that
I have always placed in them. It is offered, too,
with thanks for friendship over many years. Rara
temporum felicitas ...quae senfias dicere licet.
ACKNOWLEDGMENTS
This article was completedwhile the author was
on leave of absence at the Chemistry Department
of New York University. He would like to express
his grateful thanks to his colleagues there for their
help, interest, and forbearance, particularly Yorke
Rhodes for sharing his knowledge of chirality. He
would also like to thank Roald Hoffmann and Guy
Woolley for looking at and commenting on drafts
of this article.
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