Van der Waals Forces

Van der Waals forces are interactions between atoms, molecules, or nonbonded groups within a molecule that arise without forming a conventional chemical bond. In the broad chemical definition, they include permanent dipole–dipole interactions, dipole-induced dipole interactions, and London dispersion forces, together with short-range repulsion. They exclude electrostatic interactions involving ions as such. The term is also used more narrowly, particularly in materials physics, for dispersion-dominated attractions. Its meaning therefore depends partly on context. (goldbook.iupac.org)

Historical development and terminology

The forces are named after Johannes Diderik van der Waals, who in 1873 introduced an equation of state incorporating molecular attraction and finite molecular size. This helped explain departures from ideal-gas behavior and the continuity between gaseous and liquid states. He received the Nobel Prize in Physics in 1910 for his work on the equation of state of gases and liquids. His macroscopic model preceded the quantum explanation of dispersion. (nobelprize.org)

“Van der Waals forces” is not synonymous with “London dispersion forces”: dispersion is one component of the broader category. Likewise, a hydrogen bond should not simply be identified with generic van der Waals attraction; hydrogen bonding has specific donor–acceptor arrangements and can involve orbital interactions as well as electrostatics. Accurate descriptions distinguish the interaction mechanism rather than treating all noncovalent forces as interchangeable. (goldbook.iupac.org)

Physical origins

The conventional attractive contributions are classified into three types:

• Orientation, or Keesom, interactions occur between permanent electric dipoles. Their energy depends on molecular orientation. Thermal motion competes with favorable alignment, so the averaged attraction between freely rotating dipoles weakens as temperature increases.
• Induction, or Debye, interactions arise when the electric field of a permanent dipole distorts another molecule’s charge distribution, inducing a dipole.
• London dispersion forces arise from correlated fluctuations in electronic charge distributions. They occur even between particles with no permanent dipole and also contribute to interactions between polar molecules. (goldbook.iupac.org)

A central property is polarizability, the ease with which an electronic cloud responds to an electric field. In a simple isotropic description, the induced dipole is proportional to the applied field. Polarizability can differ along different molecular directions, making some interactions anisotropic. (goldbook.iupac.org)

Dispersion requires quantum mechanics for its microscopic explanation. The familiar picture of an instantaneous dipole inducing a neighboring dipole is a useful simplification; more precisely, correlated electron fluctuations lower the combined system’s energy. Fritz London developed the foundational quantum treatment in 1930. Dispersion strength depends on electronic response and excitation energies, not merely on whether a molecule is polar. (journals.aps.org)

Distance dependence and interaction potentials

For two well-separated, neutral ground-state particles in the nonretarded regime, the leading dispersion interaction commonly takes the form

where $r$ is separation and $C_6$ is a positive coefficient determined by the particles’ electronic properties. This expression describes potential energy, not force. Differentiation gives the radial force,

with the negative sign indicating attraction. Higher-order contributions and collective effects may be needed beyond this approximation. (arxiv.org)

At very short separations, electronic-cloud overlap produces strong repulsion. Molecular simulations often represent attraction and repulsion together using the Lennard–Jones potential:

Here $\varepsilon$ is the well depth and $\sigma$ is the separation where the potential crosses zero. The minimum lies at $r=2^{1/6}\sigma$. The inverse-twelfth-power repulsion is a convenient model rather than a universal microscopic law. A simple pair potential cannot capture every molecular shape, orientation, or many-body contribution. (arxiv.org)

At larger distances, the finite propagation speed of electromagnetic interactions introduces retardation. For isolated ground-state atoms in vacuum, the asymptotic dispersion energy can cross over from an inverse-sixth-power dependence to an inverse-seventh-power dependence. Interactions between extended bodies follow different distance laws because geometry, material response, and the intervening medium matter. (arxiv.org)

Roles in molecular and material behavior

Van der Waals interactions contribute to cohesion in liquids and molecular solids. Their collective effects help explain condensation and departures of real gases from ideal behavior. They can be important even when each individual contact is weak, because many contacts act together. (nobelprize.org)

At surfaces, they underpin physisorption, a form of adsorption that does not substantially reorganize the electronic orbital patterns of the adsorbate and substrate. Dispersion also contributes to biomolecular structure and molecular-crystal packing, although it acts alongside electrostatics, hydrogen bonding, and other interactions rather than providing a complete explanation by itself. (old.goldbook.iupac.org)

An experimentally studied example is gecko adhesion. Research published in 2002 demonstrated adhesion of individual toe hairs on both hydrophobic and hydrophilic polarizable surfaces, supporting a van der Waals contribution to dry attachment. The fine contact structures allow molecular-scale attractions to generate measurable attachment forces. (pubmed.ncbi.nlm.nih.gov)

Collective interactions and computational treatment

Adding independent atom-pair attractions is useful but not always sufficient. In condensed materials, neighboring particles alter one another’s polarizability; screening and collective fluctuations can substantially change cohesion. Lifshitz theory treats interactions between macroscopic bodies through their electromagnetic response and includes the properties of the intervening medium. (arxiv.org)

In electronic-structure calculations, many common local and semilocal density functional theory approximations do not adequately describe long-range dispersion. Treatments include pairwise dispersion corrections, nonlocal correlation functionals, and many-body dispersion models. Their accuracy depends on the material, geometry, and importance of collective electronic response. (arxiv.org)