# London dispersion force: Wikis

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# Encyclopedia

Interaction energy of argon dimer. The long-range part is due to London dispersion forces

London dispersion forces, named after the German-American physicist Fritz London, are weak intermolecular forces that arise from the interactive forces between temporary multipoles in molecules without permanent multipole moments. London dispersion forces are also known as dispersion forces (see dispersion), London forces, or induced dipole–dipole forces.

London forces can be exhibited by nonpolar molecules because electron density moves about a molecule probabilistically (see quantum mechanical theory of dispersion forces). There is a high chance that the electron density will not be evenly distributed throughout a nonpolar molecule. When electrons are unevenly distributed, a temporary multipole exists. This multipole will interact with other nearby multipoles and induce similar temporary polarity in nearby molecules. London forces are also present in polar molecules, but they are only a small part of the total interaction force.

Electron density in a molecule may be redistributed by proximity to another multipole. Electrons will gather on the side of a molecule that faces a positive charge and will retreat from a negative charge. Hence, a transient multipole can be produced by a nearby polar molecule, or even by a transient multipole in another nonpolar molecule.

In vacuum, London forces are weaker than other intermolecular forces such as ionic interactions, hydrogen bonding, or permanent dipole-dipole interactions.

This phenomenon is the only attractive intermolecular force at large distances present between neutral atoms (e.g., a noble gas), and is the major attractive force between non-polar molecules, (e.g., nitrogen or methane). Without London forces, there would be no attractive force between noble gas atoms, and they wouldn't exist in liquid form.

London forces become stronger as the atom or molecule in question becomes larger. This is due to the increased polarizability of molecules with larger, more dispersed electron clouds. This trend is exemplified by the halogens (from smallest to largest: F2, Cl2, Br2, I2). Fluorine and chlorine are gases at room temperature, bromine is a liquid, and iodine is a solid. The London forces also become stronger with larger amounts of surface contact. Greater surface area means closer interaction between different molecules.

## Quantum mechanical theory of dispersion forces

The first explanation of the attraction between noble gas atoms was given by Fritz London in 1930.[1][2] He used a quantum mechanical theory based on second-order perturbation theory. The perturbation is the Coulomb interaction V between the electrons and nuclei of the two monomers (atoms or molecules) that constitute the dimer. The second-order perturbation expression of the interaction energy contains a sum over states. The states appearing in this sum are simple products of the excited electronic states of the monomers. Thus, no intermolecular antisymmetrization of the electronic states is included and the Pauli exclusion principle is only partially satisfied.

London developed the perturbation V in a Taylor series in $\frac{1}{R}$, where R is the distance between the nuclear centers of mass of the monomers.

This Taylor expansion is known as the multipole expansion of V because the terms in this series can be regarded as energies of two interacting multipoles, one on each monomer. Substitution of the multipole-expanded form of V into the second-order energy yields an expression that resembles somewhat an expression describing the interaction between instantaneous multipoles (see the qualitative description above). Additionally an approximation, named after Albrecht Unsöld, must be introduced in order to obtain a description of London dispersion in terms of dipole polarizabilities and ionization potentials.

In this manner the following approximation is obtained for the dispersion interaction $E_{AB}^{\rm disp}$ between two atoms A and B. Here αA and αB are the dipole polarizabilities of the respective atoms. The quantities IA and IB are the first ionization potentials of the atoms and R is the intermolecular distance.

$E_{AB}^{\rm disp} \approx -{3 \alpha^A \alpha^B I_A I_B\over 4(I_A + I_B)} R^{-6}$

Note that this final London equation does not contain instantaneous dipoles (see molecular dipoles). The "explanation" of the dispersion force as the interaction between two such dipoles was invented after London gave the proper quantum mechanical theory. See the authoritative work[3] for a criticism of the instantaneous dipole model and[4] for a modern and thorough exposition of the theory of intermolecular forces.

The London theory has much similarity to the quantum mechanical theory of light dispersion, which is why London coined the phrase "dispersion effect".

## References

1. ^ R. Eisenschitz and F. London, Z. Physik 60, 491 (1930)
2. ^ F. London, Z. Physik 63, 245 (1930) and Z. Physik. Chemie, B11, 222 (1930). English translations in H. Hettema, Quantum Chemistry, Classic Scientific Papers, World Scientific, Singapore (2000).
3. ^ J. O. Hirschfelder, C. F. Curtiss, and R. B. Bird, Molecular Theory of Gases and Liquids, Wiley, New York, 1954
4. ^ A. J. Stone, The Theory of Intermolecular Forces, 1996, (Clarendon Press, Oxford)