This volume illustrates magnificently how important these Faraday journals have been to the development of physical chemistry. May the next 100 years prove equally fruitful.

100 Years of Physical Chemistry

By The Royal Society of Chemistry

The Royal Society of Chemistry

Copyright © 2003 The Royal Society of Chemistry
All rights reserved.
ISBN: 978-0-85404-987-5

Contents

Intermolecular Forces, 1,
Clusters, 23,
Molecular Spectroscopy, 35,
Magnetic Resonance, 47,
Quantum Chemistry, 57,
Photochemical Dynamics, 67,
Gas-Phase Kinetics, 85,
Ultrafast Processes, 105,
Molecular Reaction Dynamics, 123,
Atmospheric Chemistry, 141,
Astrophysical Chemistry, 159,
Theoretical Dynamics, 169,
Statistical Thermodynamics, 185,
Polymer Science, 197,
Colloids, 207,
Liquid Crystals, 225,
Liquid-Solid Interfaces, 237,
Liquid-Liquid Interfaces, 283,
Electrochemistry, 295,
Gas-Solid Surface Science, 307,
Biophysical Chemistry, 321,
Solid State Chemistry, 339,
Catalysis, 351,

CHAPTER 1

Intermolecular Forces

A. D. Buckingham

Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge, UK CB2 1EW

Commentary on: The general theory of molecular forces, F. London, Trans. 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 Wang showed that there is a long-range attractive energy between two hydrogen atoms that varies as R-6 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 effect. 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 dipole-dipole dispersion energy is not a simple product of properties of the separate atoms. A partial separation was achieved in 1948 by Casimir and Polder who expressed the R-6 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]IT [right arrow] ∞.

Casimir and Polder 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 10-7 m. The retarded dispersion energy varies as R-7 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 measurable. 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 has been presented by Lifshitz. 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.

If one or both of the molecules in an interacting pair lacks a centre of symmetry, e.g. CH4 ... CH4, Ar ... CH4, or Ar ... cyclopropane, there is, in addition to the dispersion energy terms in R-6, R-8, R-10, ..., an orientation-dependent contribution that varies as R-7. 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 R-3 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.

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...