100 Years of Physical Chemistry doc

100
Years
of
Physical Chemistry
RSeC
advancing the chemical sciences
ISBN 0-85404-9878
hardback
ISBN 0-85404-9827
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The
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2003
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111
Preface
This special volume is published to mark the Centenary of the founding of the Faraday Society in
1903. It consists of 23 papers re-printed from Faraday journals-the
Transactions, General

Discussions
and Symposia-that have been published over the past
100
years. Each article has been
selected by an expert in one of the many scientific fields,
bounded
by
chemistry, physics and biology,
which the Faraday Society and its successor the
RSC
Faraday Division seek to promote. Each paper is
accompanied by a short commentary written by the same expert. They were invited to describe how
the paper that they selected influenced the subsequent development
of
the field, including their own
work.
As
a whole the volume provides a fascinating insight into the wide range of topics that
physical
chemists
seek to study and understand, as well as demonstrating the wide range
of
techniques that they
deploy in this quest.
In
addition,
I
hope that this volume demonstrates the seminal part that the
activities
of

the Faraday Society/Division have played
in
the development of
so
many aspects of
physical chemistry.
Of course, the papers chosen are personal choices and the volume makes no claim to being
fully
comprehensive.
No doubt 23 different individuals would have selected 23 different papers, nor, by
any means, are the selected papers the only ones published in Faraday journals that have had a lasting
impact on physical chemistry. Nevertheless, we hope that they do leave an impression of how
important these journals have been in the development
of
the scientific fields central to the interests
of
the Faraday Society and its successor.
Not surprisingly, the origins of the Faraday Society are not clearly defined. Our founding fathers
were not concerned with giving their successors a particular date on which the Centenary could be
celebrated! The idea of such a society seems to have been conceived in 1902 and to have emphasised
the study
of
electrochemistry and electrometallurgy though these interests very soon started to broaden
out. It seemed to take about a year (maybe nine months?) for the seed planted in 1902 to gestate and
the first meeting of the fledgling society with a scientific content seems to have taken place in June
of
1903.
This early history
is
briefly sketched out

in
an Editorial
in
Physical Chemistry Chemical Physics
(the successor to the
Transactions
of
the Faraday Society)
written by Professor John Simons
(President of the
RSC
Faraday Division 1993-1995)' and more details can be found in the splendid
history of the Faraday Society written by Leslie Sutton and Manse1 Davies and published in 199fi2
The first volume of the Transactions appeared in 190.5, but this publication was apparently preceded
by several meetings at which papers were read and discussed.
The idea of larger scientific meetings, at which papers on a particular topic within physical
chemistry were read and discussed, and both were subsequently published, was born
in
1907. The first
General Discussion of the Faraday Society, on
Osmotic Pressure,
was held in London and published
in
the
Transactions
that same year. For many years, the proceedings of the General Discussions were
published as part of the
Transactions.
Only in 1947 was
it

decided to publish the General Discussions
separately and the present numbering of Discussions dates from then. One result is confusion as to
how many Faraday Discussions there have now been. By my count, the recent Discussion on
Nunoparticle Assemblies,
held at the University of Liverpool and numbered 125, is actually the 219th
Discussion!
The series of General Discussions
is
perhaps the aspect of its activities in which the Faraday
Division continues to take most pride-and not just for their longevity! The meetings are quite
unique, on a world-wide basis, in their emphasis on discussion which is recorded and forms part of the
1v
published volume. Each General Discussion continues to attract the international leaders in the field
under consideration. Each published volume provides
a
wonderful record of the state of that particular
branch of science
at
the time the meeting was held. For this reason, it is scarcely surprising that about
half of those invited to contribute to the present volume have selected to highlight a Discussion paper.
Despite its antiquity the Faraday Society has evolved and will continue to evolve. Of course, a very
important change came
in
the early 1970's when the Faraday Society, which to that point had been run
on
a
shoestring by essentially two dedicated individuals-the Honorary Secretary and the Secretary-
amalgamated with the Chemical Society and became part of the much larger Royal Society of
Chemistry. The Faraday Society became the Faraday Division of the Royal Society
of

Chemistry and
the General
Discussions
of
the
Faraday
Society
became the
Faraday
Discussions
of
the Chemical
Society.
The Transactions also underwent some modifications but the most important change came in
1998
when,
in
a very positive move, the Faraday Division played an important role in joining with its
sister societies in Europe to found the journal
Physical Chemistry Chemical Physics.
This special volume largely looks back-to give a glimpse of how our science has evolved over the
past hundred years. The titles of General Discussions give
a
good impression of how scientific
interests have altered over that time. (There is unlikely to be another Discussion on Osmotic
Pressure-at least in the foreseeable future!) The topics discussed at General Discussions
also
give
a
good idea of the range of scientific interests encompassed by the Faraday Society/Division. The

Society/Division has always emphasised
interdisciplinarity-even
before that word became
so
fashionable!
At the beginning of its second century, the Faraday Division
is
in
good health and believes that the
general areas of its interests remain
as
scientifically alive and important as ever. As a witness to our
faith
in
the future and as its second major event to celebrate this Centenary, the Faraday Division, in
conjunction with the Royal Institution, is to hold a special meeting on October 27th
2003.
It will
contain two demonstration lectures, by Professors Alex Pines (UC, Berkeley) and Tony Ryan
(Sheffield) designed to show post-1
6
students something of the excitement and relevance of physical
chemistry in the 21" century.
Finally,
I
should like to express my thanks. First, to those who have contributed to this volume, not
only for their magnificent contributions but also for co-operating
so
well that it has been
a

positive
pleasure to bring this volume together. Second, I must thank
Dr
Susan Appleyard and staff at the
Royal Society of Chemistry for their work in preparing the volume in short time and with great skill.
Special thanks go to Susan who first had the idea of a volume
of
this kind and volunteered to do much
of the work to make it a reality.
References
1
J.
P. Simons,
Phys. Chem. Chem. Phys.,
2003,5(13),
i.
2
L. Sutton and
M.
Davies,
The
History
of
the
Faraday
Society,
The Royal Society of Chemistry,
Cambridge,
1996.
Ian

W
M
Smith
President of the RSC Faraday Division
200
1-2003
The RSC Faraday Division is pleased to acknowledge Shell Global Solutions and ICI Group
Technology as sponsors
of
this publication.
Contents
Intermolecular Forces
A.
D.
Buckinghunz
comments on “The general theory
of
molecular forces
”
F.
London,
T~UFZS.
Furucluy
Soc.,
1937, 33,
8.
I
Clusters 23
A.
J.

Stace
comments on “Experimental study
of
the transition from van der Waals, over
covalent to metallic bonding in mercury clusters”
H.
Haberland,
H.
Kornmeier,
H.
Langosch, M. Oschwald and
G.
Tanner,
J.
Chem
Soc.,
Furuduy
Truns.,
1990,
86, 2473.
Molecular Spectroscopy
A.
Currington
comments on “The absorption spectroscopy of substances of short life”
G.
Porter,
Discuss.
Faruduy
So< ,
1950.

9,
60.
Magnetic Resonance
R.
Freeman
comments on “Fourier Transform Multiple Quantum Nuclear Magnetic
Resonance”
G.
Drobny,
A.
Pines,
S.
Sinton,
D.
P.
Weitekamp and
D.
Wemmer,
Furuduy
Sjmp.
Chenz.
Soc.,
1978, 13,49.
Quan tum Chemistry
N.
C.
Hundy
comments on “Independent assessments
of
the accuracy of correlated wave

functions for many-electron systems”
S.
F.
Boys,
Symp.
Furaduy
Soc.,
1968,2,95.
35
47
57
Photochemical Dynamics 67
R.
N.
Dixon
comments on “Excited fragments from excited molecules: energy partitioning in
the photodissociation of alkyl iodides”
S.
J.
Riley and
K.
R. Wilson,
Fumdq
Discuss.
Chem.
Soc., 1972, 53, 132.
Gas-Phase Kinetics
85
R.
Wulslz

comments on “Rates
of
pyrolysis and bond energies of substituted organic iodides”
E.
T. Butler and
M.
Polanyi,
Truns.
Furuduy
SOC.,
1943,39,
19.
Ultrafast Processes
D.
Phillips
comments on “Picosecond-jet spectroscopy and photochemistry”
A.
H.
ZewaiI,
Faruduy
Discuss.
Chem.
Soc ,
1983,
75,
315.
105
Molecular Reaction Dynamics 123
G.
H~FZCOC~

comments on “Crossed-beam reactions
of
barium with hydrogen halides”
H.
W. Cruse,
P.
J.
Dagdigian and
R.
N.
Zare,
Furuduy
Discuss. Chem.
SOC.,
1973,55,277.
Atmospheric Chemistry
141
M.
J.
Pilling
comments on “Rate measurements of reactions of
OH
by resonance
absorption”
C. Morley and
I.
W.
M.
Smith,
J.

Chem.
Soc.,
Faruduy
Trans.
2,
1972,
68,
1016.
Vi
Astrophysical Chemistry
P.
J.
Sarre
comments on “Infrared spectrum
of
H3+
as
an
astronomical probe”
T. Oka and M F. Jagod,
J.
Chem.
Soc.,
Faraday Trans.,
1993, 89, 2147.
Theoretical Dynamics
h4.
S.
Child
comments on “The transition state method”

E. Wigner,
Trans. Faraday
Soc.,
1938,34, 29.
Statistical Thermodynamics
J.
S.
Rowlinson
comments on “The statistical mechanics of systems with non-central force
fields”
J.
A.
Pople,
Discuss.
Faraday
Soc.,
1953, 15, 35.
Polymer Science
A.
J.
Ryan
comments on “Organization of macromolecules
in
the condensed phase: general
introduction”
F.
C. Frank,
Faraday
Discuss
R.

Soc.
Chem.,
1979,68,7.
Colloids
B.
Vincent
comments on “Classical coagulation: London-van der Waals attraction between
macroscopic objects’’
J.
Th.
G.
Overbeek and M.
J.
Sparnaay,
Discuss.
Faraday
Soc.,
1954,
18,
12.
Liquid Crystals
G.
R. Luckhurst
comments on “On the theory of liquid crystals”
F. C. Frank,
Discuss.
Faraday
Soc.,
1958,25, 19.
Liquid-S olid Interfaces

R.
K.
Thomas
comments on “Theory of self-assembly
of
hydrocarbon amphiphiles into
micelles and bilayers”
J.
N.
Israelachvili, D.
J.
Mitchell and
B.
W. Ninham,
J.
Chem.
Suc.
Faraday Trans.
2,
1976,
72,
1525.
Liquid-Liquid Interfaces
J.
G.
Frey
comments on “Ionic equilibria and phase-boundary potentials in oil-water
systems”
F.
M.

Karpfen and
J.
E.
B.
Randles,
Trans. Faruday
Soc.,
1953,49, 823.
Electrochemistry
P.
N.
Bartfett
comments on “Kinetics of rapid electrode reactions”
J.
E.
B.
Randles,
Discuss.
Faraday
SOC.,
1947,
1,
1
1.
Gas-Solid Surface Science
M.
W. Roberts
comments on “Catalysis: retrospect and prospect”
H.
S.

Taylor,
Discuss.
Faraday
Soc.,
1950, 8,9.
Biophysical Chemistry
R.
H.
Templer
comments on “Energy landscapes
of
biomolecular adhesion and receptor
anchoring at interfaces explored with dynamic force spectroscopy”
E. Evans,
Faraday
Discuss.,
1998,111,
1.
159
169
185
197
207
225
237
283
295
307
321
Solid State Chemistry

C.
R.
A.
Catlow
comments on “Intracrystalline channels
in
levynite and some related
zeolites”
R.
M.
Barrer and
I.
S.
Kerr, Truns. Faraday
Soc.,
1959,55, 1915.
vii
339
Catalysis
J.
M.
Thomas
comments
on
“Studies of cations in zeolites: adsorption
of
carbon monoxide;
formation
of
Ni

ions and
Na,”’
centres”
J.
A.
Rabo, C.
L.
Angell,
P.
H.
Kasai and
V.
Schomaker,
Discuss.
Farday
Soc.,
1966,41,
328.
35
1

Intermolecular
Forces
A.
D.
Buckingham
Department
of
Chemistry, University
of

Cambridge, Lensfeld Road, Cambridge,
UK
CB2
1EW
Commentary
on:
The general theory of molecular forces,
F.
London,
Truns. Faraday
SOC.,
1937,33,
8-26.
The origin of the substantial attractive forces between nonpolar molecules was a serious problem in
the early 20th century. While much was known of the strength of these forces from the Van der Waals
equation of state for imperfect gases and from thermodynamic properties of liquids and solids, there
was little understanding. The difficulty can be illustrated by the fact that the binding energy of solid
argon is of the same order of magnitude as that of the highly polar isoelectronic species HCl. Debye’
suggested in 1921 that argon atoms, while known to be non-dipolar, may be quadrupolar; however,
after the advent of quantum mechanics
in
1926,
it
was clear that the charge distribution of an inert-gas
atom is spherically symmetric. In 1928 Wang2 showed that there is a long-range attractive energy
between two hydrogen atoms that varies as
Kh
where
R
is their separation. Soon afterwards, London

presented his ‘general theory of molecular forces’ and gave
us
approximate formulae relating the
interaction energy to the polarizability of the free molecules and their ‘internal zero-point energy’.
London showed that these forces arise from the quantum-mechanical fluctuations
in
the coordinates of
the electrons and called them the
dispersion
efect.
He demonstrated their additivity and estimated
their magnitude for many simple molecules. The paper points out the important role of the Pauli
principle
in
determining the overlap-repulsion force (on p. 21 it associates the Coulomb interaction of
overlapping spherical atomic charge clouds with an incomplete screening of the nuclei, causing a
repulsion; actually the enhanced electronic charge density
in
the overlap region between the nuclei
would lead to an attraction,
so
the strong repulsion at short range is due to the Pauli principle).
A feature of London’s paper is its emphasis on the zero-point motion of electrons: it is the
intermolecular correlation of this zero-point motion that is responsible for dispersion forces. London’s
Section 9 extends the idea of zero-point fluctuations to the interaction of dipolar molecules. If their
moment of inertia is small, as it is for hydrogen halide molecules, then even near the absolute zero of
temperature when the molecules are
in
their non-rotating ground states, there are large fluctuations in
the orientation of the molecules and these become correlated in the interacting pair.

London’s eqn.
(15)
for the dipoledipole dispersion energy is not a simple product of properties of
the separate atoms.
A
partial separation was achieved in 1948 by Casimir and Polder3 who expressed
the
R-‘
dispersion energy as the product of the polarizability of each molecule at the imaginary
frequency iu integrated over
u
from zero to infinity. The polarizability at imaginary frequencies may
be a bizarre property but it is a mathematically well behaved function that decreases monotonically
from the static polarizability at
u
=
0
to zero as
u-+
00.
Casimir and Polder3 also showed that retardation effects weaken the dispersion force at separations
of the order of the wavelength of the electronic absorption bands of the interacting molecules, which is
typically
lop7
m. The retarded dispersion energy varies as
K7
at large
R
and is determined by the
static polarizabilities

of
the interacting molecules. At very large separations the forces between
molecules are weak but for colloidal particles and macroscopic objects they may add and their effects
are meas~rable.~ Fluctuations in particle position occur more slowly for nuclei than for electrons,
so
the intermolecular forces that are due to nuclear motion are effectively unretarded. A general theory
of the interaction of macroscopic bodies
in
terms of the bulk static and dynamic dielectric properties
1
2
100
Years
of
Physical Chemistry
has been presented by Lifshitz.5 Proton movements in hydrogen-bonded solids and liquids may
contribute to the binding energy as well as to the dielectric constant, electrical conductivity and intense
continuous infrared absorption.6
If one or both of the molecules
in
an interacting pair lacks a centre of symmetry, e.g. CH4-CH4,
Ara.CH4, or
Arm.
xyclopropane, there is, in addition to the dispersion energy terms in
R4,
R-’,
R-lo,
.
.
.,

an orientation-dependent contribution that varies as
K’.
It
could be significant for coupling the
translation and rotation in gases and liquids and for the lattice energy of solids.*
London illuminated the origin of dispersion forces by considering the dipolar coupling of two three-
dimensional isotropic harmonic oscillators. He obtained the exact energy and showed that it varies as
R-6
for large
R.
Longuet-Higgins discussed the range
of
validity of London’s theory and used a
similar harmonic-oscillator model to show that at equilibrium at temperature
T
there is a lowering of
the free energy
A(R),
though not of the internal energy
E(R),
through the coupling
of
two
classical
harmonic oscillators,
so
their attraction is entropic in nature and vanishes at
T
=
0.

It is the
quantization of the energy of the oscillators that leads to a lowering of
E(R)
through the dispersion
force. If one of a pair of identical oscillators is in its first excited state the interaction lifts the
degeneracy and leads to a first-order dipolar interaction energy proportional to
K3;
this is an example
of a
resonance
energy which may be considered to arise from the exchange
of
a photon between
identical oscillators.
Since the dispersion energy arises from intermolecular correlation of charge fluctuations, it is not
accounted for by the usual computational techniques of density functional theory
(DFT)
which employ
the local density and its spatial derivatives. Special techniques are needed
if
DFT
is
to be used
for
investigating problems where intermolecular forces play a significant role.’
References
1 P. Debye,
Phys.
Z.,
1921,22,302.

2
S.
C.
Wang,
Phys.
Z.,
1928,28,663.
3
H.
B.
G.
Casimir and D. Polder,
Phys. Rev.,
1948,73,
360.
4
J.
N.
Israelachvili,
Intermolecular and SLi$uce Forces with Applications to Colloidal and Biological
Systems,
Academic Press, London, 1985.
5
E.
M.
Lifshitz,
Sov.
Phys.
JETP
(Engl. Transl.),

1956,
2,73.
6
G.
Zundel,
Adv.
Chem. Phys.,
2000,111, 1.
7
H. C. Longuet-Higgins,
Discuss. Faraday Soc.,
1965,40,7.
8
A.
D.
Buckingham,
Discuss. Faraday
Soc.,
1965,40,
232.
9
W. Kohn,
Y.
Meir and
D. E.
Makarov,
Phys. Rev. Lett.,
1998,
80,
4153.

Intermolecular
Forces
8
THE
GENERAL THEORY
OF
MOLECULAR FORCES
3
THE GENERAL
THEORY
OF
MOLECULAR
FORCES.
BY
F.
LONDON (Paris).
Received
31st
July,
1936.
Following Van der Waals, we have learnt
to
think
of
the molecules
as
centres of forces and to consider these so-called
Molecular
Forces
as

the common cause for various phenomena: The deviations
of
the
gas
equation from that of an ideal gas, which, as one knows, indicate the
identity
of
the molecular forces in the liquid with those in the gaseous
state
;
the phenomena of capillarity and of adsorption
;
the sublimation
heat of molecular lattices
;
certain effects
of
broadening
of
spectral lines,
etc.
It
has already been possible roughly to determine these forces in
a
fairly consistent quantitative way, using their measurable effects
its
basis.
In
these semi-empirical calculations, for reasons
of

simplicity,
one
imagined the molecular forces simply as rigid, additive central forces,
in general
cohesion,
like gravitation
;
this presumption actually implied
4
100
Years
of
Physical Chemistry
F.
LONDON
9
a
very suggestive and simple explanation
of
the parallelism observed in
the different effects of these forces. When, however, one began to
try
to
explain the molecular forces by the general conceptions
of
the electric
structure of the molecules it seemed hopeless to obtain such
a
simple
result.

8
1.
Orientation
Effect.1
Since molecules as a whole are usually uncharged the
dipole
moment
p
was regarded
as
the most important constant for the forces between
molecules. The interaction between two such dipoles
pI
and
pII
depends
upon their relative orientation. The interaction energy is well known
to
be given to
a
first approximation
by
U
=
-
's(2
cos
0,
cos
011

-
sin
4
sin
O,,
cos
(+I
-
dII))
(I)
R3
where
O,,
+I
;
011,
are polar co-ordinates giving the orientation of the
dipoles, the polar axis being represented by the line joining the two
centres,
R
=
their distance. We obtain attraction
as
well
as
repulsion,
corresponding to the different orientations.
If
all orientations were
equally often realised the average

of
p
would
be
zero.
But
according to Boltzmann statistics the orientations of lower
energy are statistically preferred, the more preferred the lower the
temperature. Keesom, averaging over all positions, found as
a
result
of
this preference
:
For
low temperatures or small distances
(KT
5
'*)
this expression
does not hold.
It
is obvious that the molecules cannot have
a
more
favourable orientation than parallel to each other along the line joining
the two molecules, in which case one would obtain as interaction energy
(see
(I))
:

-
u=
2prp11
R3
(valid for
'3
>
KT)
.
(3)
which gives in any case
a
lower limit
for
this energy.
(2)
and
(3)
represent
an
attractive force, the so-called
orientation
effect,
by which
Keesom tried to interpret the Van der Waals attraction.
5
2.
Induction Effect.a
Ac-
cording to

(2)
they give an attraction which vanishes with increasing
temperature. But experience shows that the empirical Van der Waals
corrections do not vanish equally rapidly with high temperatures, and
Debye therefore concluded that there
must
be,
in
addition,
an interaction
energy independent
of
temperature. In this respect it would not help to
consider the actual charge distribution
of
the molecules more in detail,
W.
H.
Keesom,
Leiden
Comm.
Suppl.,
1912, 248, 24b,
25,
26
;
1915,
39a,
39b.
Proc.

Amst.,
1913,
15,
240,
256,
417,
643
;
1916,
18,
636;
1922,
24,
162.
Physik.
Z.,
1921,
22,
129,
643
;
1922,
23,
225.
H.
Falckenhagen,
Physik.
Z.,
1922,
23,

87.
Debye remarked that these forces cannot be the only ones.
2P.
Debye,
Physik.
Z.,
1920,
21,
178;
1921,
22, 302.
I*
In
te
rmol
ec
u
la
r
Forces
10
THE GENERAL THEORY
OF
MOLECULAR
FORCES
5
e.g.
by introducing the quadrupole and higher moments. The average
of
these interactions also would vanish for high temperatures.

But by its charge distribution alone
a
molecule is, of course, still
very roughly characterised.
Actually, the charge distribution will
be
changed under the influence of another molecule. This property of
a
molecule can very simply be described by introducing
a
further constant,
the
polarisability
a.
In an external eIectric field of the strength
F
a
molecule of polarisability
a
shows an
induced
moment
M=a.F
.
*
(4)
Uz-
&a.F2
.
*

(5)
(in addition to
a
possible
permanent
dipole moment) and its energy in
the field
F
is given by
Now
the molecule
I
may produce near the molecule
I1
an electric
field
of
the strength
This field polarises the molecule
I1
and gives rise to an additional
interaction energy according to
(5)
which is always negative
(attraction)
and therefore its average, even for
infinitely high temperatures, is also negative. Since
cos2
6'
=

Q
we
obtain
:
A
corresponding amount would result for
DII-+I,
i.e.
for
the action
of
pII
upon
aI.
As
totai interaction
of
the two molecules we obtain
:
If
the two molecules are of the same kind
(pI
=
pII
=
p
and
uI
=
uII

=
a)
we
have
*
(8')
-
zap2
u=
R8
'
This is the so-called
induction
effect.
In
such
a
way Debye and Falckenhagen believed it possible to
explain the
Van
der
Waals
equation. But many molecules have
certainly no permanent dipole moment (rare gases,
H,,
N,,
CH,,
etc.).
There they assumed the existence
of

quadrupole moments
T,
whlch
would
of
course also give rise to a similar interaction
by
inducing
dipoles in each other.
Instead of
(8)
this would give
:
Since no other method of measuring these quadrupoles was known, the
Van der Waals corrections (second Virial coefficient) were used in order
to determine backwards
T,
which, after
p
and
a,
has been regarded as the
most
fundamental molecular constant.
6
F.
LONDON
100
Years
of

Physical Chemistry
I1
5
3.
Criticism
of
the Static
Models
for
Molecular Forces.
The most obvious objection to all these conceptions is that they
do not explain the above mentioned parallelism in the different mani-
festations of the molecular forces. One cannot understand why, for
example, in the liquid and in the solid state between all neighbours
simultaneously practically the same forces should act as between the
occasional pairs of molecules in the gaseous state. All these models are
very far from simply representing a general additive cohesion
:
Suppose that two molecules I and I1 have such orientations of their
permanent dipoles that they are attracted by a third one
;
then between
the two former molecules very different forces are usually operative,
mostly repulsive forces. Or,
if
the forces are due to polarisation, the
acting field will usually be greatly lowered, when many molecules from
different sides superimpose their polarising fields. One should expect,
therefore, that in the liquid and
in

the solid state the forces caused by
induced or permanent dipoles or multipoles should at least be greatly
diminished, if not by reasons of symmetry completely cancelled.
The situation seemed to be still worse when wave mechanics showed
that the rare gases are exactly spherically symmetrical, that they have
neither
a
permanent dipole nor quadrupole nor any other multipole.
They showed none
of
the mentioned interactions. It is true, that for
H,,
N,,
etc., wave mechanics, too, gives at least quadrupoles. But for
H,
we are now able to calculate the value
of
the quadrupole moment
numerically by wave mechanics.
One
gets only about
I/IOO
of the
Van der Waals forces that were attributed hitherto to suitably chosen
quadrupoles.
On
the other hand, wave mechanics has provided us with a completely
new aspect of the interaction between neutral atomic systems.
5
4.

Dispersion Effect; a Simplified Model.3
Let
us
take two spherically symmetrical systems, each with a polaris-
ability
a,
say two three-dimensional isotropic harmonic oscillators with
no permanent moment in their rest position.
If the charges
e
of these
oscillators are artificially displaced from their rest positions by the dis-
placements
+
3
r1
=
(XI,
Yr,
21)
and
TI1
=
(%I,
YII,
211)
respectively, we obtain for the potential energy
:
-
Elastic Energy. Dipole Interaction Energy

(cf.
(I)).
CZassicaZZy
the two systems
in
their equilibrium position
(XI
=
XI1
=
.
.
.
=
211
=
0)
would not act upon each other and, when brought into finite distance
(R
>
G),
remain in their rest position. They could not influence a
momentum in each other.
F.
London,
2.
physik.
Clzem.,
19x0.
€3,

I
I,
222.
Intermolecular Forces
12
THE
GENERAL
THEORY
OF
MOLECULAR
FORCES
7
However, in
quantum mechanics,
as is well known,
a
particle cannot
lie absolutely at rest on
a
certain point.
That would contradict the
uncertainty relation.
According
to
quantum mechanics our isotropic
oscillators, even in their lowest states, make a so-called
wo-point
moth
which one can only describe statistically, for example, by
a

probability function which defines the probability with which any con-
figuration occurs
;
whilst one cannot describe the way in which the
different configurations
follow
each other.
For the isotropic oscillators
these probability functions give a spherically symmetric distribution of
configurations round the rest position.
(The rare gases, too, have such
a
spherically symmetrical distribution for the electrons around the
nucleus.)
We need not know much quantum mechanics in order to discuss our
simple model. We only need to know that in quantum mechanics the
lowest state of a harmonic oscillator of the proper frequency
u
has the
energy
E,=
ihv
.
-
(11)
the so-called
zero-point energy.
If
we introduce the following co-
ordinates

("
normal "-co-ordinates)
:
the potential energy
(10)
can be written as
a
sum
of
squares like the
potential energy
of
six
independent oscillators (while the kinetic energy
would not change its form)
:
=
&[(I
za
+
$)(z+2
+
r+2)
+
(I
-
$)( p
+
y-2)
+

(I
-
2;).+p
+
(I
+
2$)e_']
(10')
The frequencies
of
these
six
oscillators are given by
a
a2
vZf=uy~=vO1/~
If:a/R*Z
V*(I
&s-mf.
.
.)
e
dTa
Here
u0
=
-
is the
pruper
frequency

of
the two elastic systems, if
isolated from each other
(R
+=
a),
and
m
is their reduced mass. Assum-
ing
or
R3,
we have deveIoped the square roots in
(12)
into powers
of
(
a]Ra).
The lowest state of this system of
six
oscillators will therefore be
given, according to
(11),
by
:
8
F.
LONDON
100
Years

of
Physical Chemistry
I3
h
E,
=
-
(Y,+
+
vy+
+
vz+
+
v,-
+
vy-
+
vz-)
2
hv
OC
U2
=
-++
2
(Q+
-
I
-
4

-
Q
+
I)@
-
(++
$)p+.
.
=
3hvo
-
-
-
huoaa
+
. .
.
.
4
R6
The first term
3hvo
is,
of
course, simply the internal zero-point energy
of
the two isolated elastic systems.
The second term, however,
depends upon the distance
R

and is to be considered as an interaction
energy which, being negative, characterises an attractive force. We
shall presume that this type of force,* which is not conditioned by the
existence
of
a
permanent dipole
or
any higher multipole, will be respons-
ible for the Van der Waals attraction of the rare gases and also
of
the
simple molecules
H,,
N,,
etc. For reasons which will be explained
presently these forces are called the
dispersion
effect.
§
5.
Dispersion
Effect
;
General
Formula.5
Though it is
of
course not possible to describe this interaction
mechanism in terms of our customary classical mechanics, we may still

illustrate it in a kind
of
semi-classical language.
If
one were to take an instantaneous photograph of a molecule
at
any time, one would find various configurations
of
nuclei and electrons,
showing in general dipole moments. In a spherically symmetrical rare
gas molecule, as well as in our isotropic oscillators, the average over very
many
of
such snapshots would of course give no preference for any
direction. These very quickly varying dipoles, represented by the zero-
point motion of
a
molecule, produce an electric field and act upon the
polarisability
of
the other molecule and produce there induced dipoles,
which are in phase and in interaction with the instantaneous dipoles
producing them. The zero-point motion is,
so
to speak, accompanied by
a
synchronised electric alternating field, but not by a radiation field
:
The energy of the zero-point motion cannot be dissipated by radiation.
This image can be used for interpreting the generalisation

of
our
formula
(13)
for the case of a general molecule, the exact development
of
which
would
of
course need some quantum mechanical calculations.
We
may imagine a molecule
in
a state
k
as represented by
an
orchestra
of
periodic dipoles
pkr
which correspond with the frequencies
El-
Ek
h
vkZ
=
of (not forbidden) transitions to the states
1.
These “oscillator

strengths,”
pkl,
are the same quantities which appear in the
“
dis-
persion formula
”
which gives the polarisability
ak(v)
of
the
molecule
in the state
k
when acted on by an akernating field
of
the frequency
Y.
4
This type
of
force
first
appeared in
a
calculation
of
S.
C.
Wang,

Physik.
2.
1927,
zB,
663.
R.
Eisenschitz
and
F.
London,
Z.
Physik,
1930,
60,
491.
Intermolecular Forces
14
THE GENERAL THEORY
OF
MOLECULAR
FORCES
9
If the acting field
of
the frequency
vo
has the amplitude
F,,
the induced
moment

M
is given by
and the interaction energy between field and molecule by
Now this acting field may be produced by another molecule by one
of its periodic dipoles
ppo
with the frequency
vpo
and inclination
ePo
to
the line joining the two molecules.
Near the first molecule
(we
call it
the “Latin” molecule, using Latin indices for its states, and Greek
indices to the other one) the dipole
ppo
produces an electric field of the
strength (compare
(6))
:
FPa
=
b41
Ra
+
3
cos
WPu.

-
(6’)
This field induces in the Latin molecule
a
periodic dipole of the amount
:
Mpok
=
ak(vpo)
Fpo,
and an interaction energy (compare
(5’))
:
If
we now consider the whole orchestra of the
“
Greek
”
molecule in the
state
p
we have to sum over
all
states
a
and to average over all direc-
tions
6ppcr
(cosp
6

=
1/3).
This would give us the action of the Greek
atom
upon
the polarised Latin atom
:
Adding the corresponding expression for the action
of
the Latin
molecule upon the Greek one, we obtain the total interaction due to the
“periodic” dipoles
of
a
molecule
in
the state
k
with another in the state
p
:
$6.
Additivity
of
the
Dispersion
Effect.
Of course this reasoning does not claim to be an exact proof of
(IS),
but it may perhaps illustrate the mechanism

of
these forces. It can be
shown that the formula
(IS)
has the peculiarity of
additivity;
this
means that
if
three molecules
act
simultaneously upon each other, the
three interaction potentials between the three pairs
of
the form
(15)
are
simply to be added, and that any influence
of
a
third molecule upon the
interaction between the first two is only
a
small perturbation effect of a
smaller order of magnitude than the interaction itself. These attractive
10
100 Years
of
Physical
Chemistry

I5
F.
LONDON
forces can therefore simply be superposed according to the parallelogram
of
forces, and they are consequently able to
represent the
fact
of
a
general
cohesion.
If several molecules interact simultaneously with each other, one has
to imagine that each molecule induces
in
each of the others
a
set of
co-ordinated periodic dipoles, which are in constant phase relation with
the corresponding inducing original dipoles. Every molecule
is
thus the
seat of very many incoherently superposed sets
of
induced periodic
dipoles caused by the different acting molecules. Each
of
these induced
dipoles has always such an orientation that it
is

attracted by its corres-
ponding generating dipole, whereas the other dipoles, which are not
correlated by any phase relation, give rise to a
periodic
interaction only
and,
on
an average over all possible phases, contribute
nothing
to the
interaction energy.
So
one may imagine that the simultaneous inter-
action of many molecules can simply be built up as an
additive
super-
position of single forces between pairs.
5
7.
Simplified Formula
;
Some
Numerical
Values.
For many simple gas molecules
(e.g.
the rare gases,
H,,
N,,
O,,

CH4),
the empirical dispersion curve has been found
to
be representable, in a
large frequency interval, by
a
dispersion formula
of
the
type
(14)
con-
sisting
of
one single term only. That means that for these molecules
the oscillator strength
pkz
for frequencies
of
a
small interval
so
far
exceed the others that the latter can entirely be neglected.
In this case,
and for the limiting case
v
+
o
(polarisability in a

static
field) the formula
(14)
can simply be written
:
(&
signifies the dipole-strength
of
the only main frequency
vk)
and
formula
(15)
for the interaction
of
the two systems goes over into
:
This formula is identical with
(13)
in the case of two molecules of the
same kind.
It can, of course, only be applied
if
one already knows that
the dispersion formula has the above-mentioned special form. But
in
any case,
if
the dispersion formulae
of

the molecules involved are empiric-
ally known, their data can be used and are sufficient to build up the
attractive force
(IS).
No
further details of the molecular structure need
be known.
We give, in Table
I.,
a
list
of
theoretical values for the attractive
constant
c
(i.e.
the factor
of
-
1/R6
in the above interaction law) for
rare gases and some other simple gases where the refractive index can
fairly well be represented by a dispersion formula of one term only.
The characteristic frequency
YO
multiplied by
h
is in all these cases very
nearly equal to the ionisation energy
hv1.

This may, to a first approxi-
mation, justify using the latter quantity in similar cases where a disper-
sion
formula
has
not yet been determined.
It
is seen that the values
of
Intermolecular Forces
16
THE
GENERAL
THEORY
OF
MOLECULAR
FORCES
"I
(6.
volts).

24'5
21.5
15'4
13'3
11.5
16-4
I7
I3
14'3

14'5
I
8.2
13'7
13'3
12.7
G
vary
in
a
ratio from
I
to
1000,
and this wide range
of
the order of
h*D
(8.
VOltS).
25'5
25-7
17'5
14'7
12-2
I
7-2
14'7
15.45
TABLE

I DISPERSION EFFECT BETWEEN
SIMPLE
MOLECULES.
7
He.
Ne
.
Ar
.
Kr
.
Xe
.
Ha
-
Na
0,
co
.
CH,
COa
c1,
.
HCl
HBr
HI.
Na
.
-
I

2'1
I
a.
xo*
[cm.*].
0'20
0.39
1.63
2.46
4-00
0.81
1-74
1-57
1
'99
2.58
2.86
4-60
2.63
5
'4
29'7
3'58
0'77
2-93
34'7
69
146
8.3
38.6

27'2
42'4
73
94'7
288
71
128
2
78
960
mag&ude makes even
a
very crude experi-
mental test
of
these
forces instructive (see
J.
E.
Mayer has
shown that, for the
negative rare
-
gas
-
like
ions, one
is
not justified
in simplifying the dis-

persion
of
the con-
tinuum by assuming one
single frequency only.
He used
a
simple ana-
lytical expression for
the empirical continu-
ous absorption and re-
placing the
sums
in
(15)
by integrals over these
continua he gets the
following list
of
c
values
for the
zg
possible pairs
of ions (Table
11.)
:
Starting from
a
dif-

ii
11).
ferent method (variation method) and using some sirnplifTing assump-
tions as to the wave functions of the atoms (products
of
single electronic
wave functions) Slater and Kirkwood
6a
have also calculated these forces.
They found the following formula
:
(N
=
number
of
electrons in the outer shell.)
This expression usually gives
a
somewhat greater value than
(13)
and
may
be applied in those
cases
in which the characteristic frequencies
in
(13)
are not obtainable. But
at
present it

is
difficult to say how far
one
may
rely
on
formula
(13'').
TABLE
II DISPERSION
EFFECT
BETWEEN IONS.
(c
.
104*
in
units
[e
.
volts
cm.*]).
1
F
Q
Br.
I
Li+
.
Na+
.

K+
.
Rh+
.
cs+ .
c-+
=
0.13
3'2
4'0 5'4
7-14 17-8
22-2
30'3
31.0 76.3
95'3
130
49'2
125
I57
214
82.5 205
259
356
C,,
"23-30 176-206 294-332
600-676
J.
E.
Mayer,
J.

Chem.
Physics.
1933.
I,
270.
J.
C.
Slater
and
J.
G.
Kirkwood,
Physic.
Rev.,
c++
=
0'11
2.68
38.6
94'3
247
11
12
100
Yenrs of Physical Chemistry
F.
LONDON
17
4
8.

Systematics
of
the
Long Range
Forces.'
The formula
(15)
applies quite generally for freely movable mole-
cules
so
long as the interaction energy can be considered as small com-
pared with the separation of the energy-levels
of
the molecules in
question
;
i.e.
so
long as
With this restriction, the formula
(IS)
holds for freely movable dipole
molecules,
as
well as for rare gas molecules. There is therefore always
a
minimum distance for
R
up to which we can rely on
(15).

The difference between a molecule with permanent dipole and a rare
gas
molecule consists in the following
:
A
rare gas molecuIe has such
a
high excitation energy (electronic jump) that for normal temperatures
we
can assume that all molecules are in the ground state
;
therefore we
have forces there independent
of
temperature. For a dipole molecule,
on the other hand, we have to consider a Boltzmann distribution over at
least the different rotation states, because the energy difference between
these states is usually small
Ir)-
comparison with
kT.
Let
us
at first consider an
absolutely
rigid dipole
(dumb-bell) molecule
(ie.
a
molecuIe without electronic or oscillation states). Then the pro-

bability
p,,
that the Greek molecule is in the pure rotation state
p
and
the Latin one
in
the pure rotation state
k
is given by
where
1
A-1
=
xe-jpifEP)*
kp
The mean interaction between two such molecules is accordingly
If
in
this expression we interchange the notation
of
the summation
indices
p
and
K
with
Q
and
I,

the value of the sum of course remains
unchanged. Therefore, taking the average of these two equivalent
expressions we
can
write (since
pkz
=
plk)
:
Ek
f
EP
El
+
Em
A
2e-T
-
e-
EIP
3R61pk'ZLLpo
El
+
E,
-
Ek
-
Ep
'
*

(17')
&=
01
pk
Developing the exponentials into powers
of
r/kT
we notice that the con-
stant terms cancel each other (no interaction for high temperature as
in
0
I).
The first and the only important term
of
the development of
(17')
yields
:
Here
we
designate by
pI
and
pII
the permanent moments
of
the
dipole
molecule, which
for

an
absolutely rigid molecule are
of
course independent
F.
London,
2.
PhysiR,
1930,
63,
245.
In
te
rmol
ecu
In
r
Fore
es
18
THE GENERAL THEORY
OF
MOLECULAR
FORCES
13
of
the state. We therefore obtain exactly the same result
as
Keesom
did from classical mechanics. One can, by the way, show that whilst

the validity
of
(15)
is bounded by the condition
(16)
the result
(IS)
is
only bounded by the weaker condition
which was also the limit for the validity
of
the classical calculation.
In reality a dipole molecule cannot,
of
course, be treated as a simple
rigid dumb-bell. It has
electronic
and
oscillation
transitions as well.
Let us, for sake of simplicity, assume that
kT
is big in comparison to the
energy differences for pure rotation jumps, but small for all the other
jumps.
In this general case we have again formula
(17),
but here it
is
sufficient

to extend the Boltzmann sum
C
only over those states which imply pure
rotation jumps from the ground state, since the thermo-dynamical prob-
ability
of
the other states being occupied is negligible. We now divide
the
sum
over
(I
and
1
in
(17)
into four parts
Pk
in the following way
:
(I)
In
U,,
both,
a
and
I,
shall
be restricted to those values which
differ from the ground-state only
by

a pure rotation transition. For
this sum (with certain uninteresting reservations) the above calculation
for the rigid dipoles remains valid.
Accordingly we get
(18)
3R6
kT
P12cLI12
u,,
=
-
-
-
i.e. Keesom’s
orientation
efiect.
(2)
In
U,,
the summation over
Q
as before shall be extended only
over those terms which differ from the ground state by a pure rotation
jump; but
I
shall designate
a
great (not a pure rotation-) jump. Then
we may neglect
E,

-
E,
in comparison with
El
-
Ek
in the denominators
of
(17)
and can write
Comparison with
(14)
shows that the terms
of
the second sum on the
right-hand side can be represented by the static polarisability
a,
=
a,
(0)
of the second molecule which will depend very little on the state
of
rotation
p
of
the molecule
so
that we may signify it simply by
aII;
whereas the first sum again gives the square of the permanent dipole

moment
of
the first molecule, of which we also may assume that it is
approximately independent of the state
of
rotation
We obtain
2
PI%,
3R6
.
p12
.
+aII(o)
=
-
-
R6
*
u,,
=
-
-
(3)
Correspondingly
u,,
=
cLII2GLI
Re
(2)

and
(3)
are exactly
Debye’s
induction
effect.
a
great (not a pure rotation-) jump.
(4)
In
U,,
finally both,
a
and
I,
shall differ from the ground state by
If
we assume that the transition
14
Induction
Effect
acre,.
1060
[erg
cm.3.
I00
Years
of
Physical
Chemistry

Dispersion
Effect
Qa'kv*
.
,060
[erg
cm.61.
F.
LONDON
I9
a.
1024.
probabilities
of
such a jump do not depend noticeably on the state
of
rotation, we can take simply the ground state for
p
and
k
and obtain
hvo
(Volts).
2.e.
the
dispersion
effect.
join the three effects in the form
If the conditions for
(13')

are fulfilled we may
1-99
5'4
3'58
2-63
1-48
2-21
We give, in Table
III.,
a short list for the three effects
of
some dipole
14'3
13'3
13'7
16
I8
I2
molecules
:
T.ARI,E
III THE
THREE
CONSTITUENTS
OF
THE
VAN
DER
WAALS'
FORCES.

co
.
HI
.
HBr
.
HCl
.
NH
H,O
.
I(
.
1018.
0.1
2
0.38
0.78
I
-03
1'5
1.84
I
1
Orientation
Effect
2l.Y
1060
3
k293"

'
[erg
cm.61.
-I
0'0034
0.35
6.2
I
8.6
84
1
90
0'057
I
-68
4-05
5'4
I0
I0
It
is
seen that the induction effect is in all cases practically negligible,
and that even in such
a
strong dipole molecule as HCl the permanent
dipole moments give no noticeable contribution to the Van der Waals'
attraction. Not earlier than with
NH,
does the orientation effect
become comparable with

the
dispersion effect, which latter seems in no
case
to
be negligible.
5
9.
Limits
of
Validity.
We have yet to discuss the physical meaning
of
the condition
(16).
In quantum mechanics, in characteristic contrast to classical
mechanics, a freely movable polyatomic molecule has a centrally sym-
metric and, particularly in its lowest state, a spherically symmetric
structure,
i.e.
a
spherically symmetric probability function. That
means that
on
the average, even in its lowest state, a free molecule does
not prefer any direction, it changes its orientation permanently owing
to
its zero-point motion.
If
another molecule tries to orientate the
molecule in question a compromise between the zero-point motion and

the directing power will be made, but only for
cL!!l
>
1
E,
-
E,
1
.
.
(zoa)
RS
the directive forces preponderate over the zero-point rotation. Accord-
ingly, in this case, the motion of the dipoles becomes more similar to
a
vibration near the equilibrium orientation
of
the dipoles (parallel to each
other along the line joining the two molecules) and the interaction will
then be
of
the nature
of
orientated dipoles,
i.e.
of
the order
of
magnitude
of

-~
2pIpT1
R3
'
Intermolecu lur Forces
20
THE
GENERAL
THEORY
OF
MOLECULAR
FORCES
15
In quantum mechanics, we learn, in contrast to
(3),
the condition
is
not sufficient for the molecules being orientated. The orientating
forces have not only to overcome the temperature motion but in addition
the zero-point motion also.
If
0
is the moment of inertia of the molecule
the right-hand side of
(zoa)
becomes equal to
-
;
and using this one
can easily show that, for example, for

HI
molecules,
at
the distances
they have in the solid state, the directive forces
of
the dipoles are still
too weak to overcome the zero-point rotation.
One has therefore to
imagine these molecules always rotating even
at
the absolute zero
in
the
solid state. But
HI
is certainly rather
an
exceptional case.
It
is
obvious that for larger molecules and for small molecuIar
distances in the solid and liquid state the directive forces are quite
insufficiently represented by the dipole action. For these one has
simply to replace the left-hand side of
(20)
by the classical orientation
energy in order to obtain
a
reasonable estimate for the limit of free

mot
ion.
As
long
as we are within the limits
of
(16)
our argument in
8
6
as to
the additivity holds quite generally for all the three effects collected in
formula
(19).
Only if, in consequence of
(20),
the free motion of the
molecules is hampered does the criticism of
8
3
apply, and this concerns
the non-additivity of the direction effect as well as
of
the induction effect.
The internal
electronic
motion of
a
molecule, however, will not ap-
preciably be influenced when the rotation

of
the molecule as
a
whole
is
stopped.
Thus
one is justified in applying the formula for the dispersion
effect for non-rotating molecules also.
It
is
obvious, however, that only the highly compact molecules, as
listed in Tables
I.
and
II.,
can
reasonably be treated simply as force
centres. For the long organic molecules it seems desirable to
try
to build
up the
Van
der Waals’ attraction as a sum of single actions
of
parts of the
molecules.
As
it is rather arbitrary to attribute the frequencies appear-
ingin

(IS)
or
(13)
to the single parts of a molecule,
it
has been attempted
to eliminate them by making use
of
the approximate additivity
of
the
atomic refraction
as
well as of the diamagnetic susceptibility.
If
there is one single “strong” oscillator
pk
only
(cf.
14’)
the dia-
magnetic smceptibility has simply the form
:
h2
4m9
2N
6mc2
Xk
=
-

p”
(<
0)
(NJ
Loschmidt’s number)
therefore, because of
[14’),
We
can
therefore write, instead of
(137,
UkP= aa-
Xk
xp

3
h
4mc2
ak
up
2
Rg
’hN&
Xklak
+
xpl%
-
I
6mc2
akap

Re
NL
uk/xk
+
%/XP
.
(13”’)
J.
G.
Kirkwood,
Physik.
Z.,
1932,
33,
57;
A.
Miiller.
Proc.
Roy.
SOC.
A,
1936,
154,
624-