van der Waals radius

van der Waals radius The van der Waals radius is a conceptual atomic parameter used to describe the effective size of atoms in nonbonded contexts, originally arising from the work of Johannes Diderik van der Waals and later quantified in studies by Linus Pauling, Fritz London, Lothar Meyer, and experimentalists at institutions like University of Amsterdam and Cavendish Laboratory. It appears in models developed by researchers associated with Royal Society, American Chemical Society, Max Planck Society, Institut Pasteur, and in computational frameworks created by groups at Massachusetts Institute of Technology, California Institute of Technology, University of Oxford, Harvard University, and ETH Zurich. The parameter is widely tabulated by organizations such as International Union of Pure and Applied Chemistry and used in software from vendors like Schrödinger, Gaussian (software), Accelrys, and research centers including Lawrence Berkeley National Laboratory and Los Alamos National Laboratory.

Definition and concept

The term denotes the radius of an imaginary sphere representing an atom's effective size when it is not covalently bonded, invoked in descriptions used by J. D. van der Waals in equations of state, the van der Waals equation, and in conceptual frameworks developed by James Clerk Maxwell and Rudolf Clausius. In molecular modelling traditions traced to groups at University of Cambridge and Imperial College London, it appears alongside parameters from the Lennard-Jones potential, theories by Fritz Haber, and dispersion formulations by Hendrik Anthony Kramers and Sir Nevill Francis Mott. Work by Gilbert N. Lewis and Amedeo Avogadro influenced how the parameter is interpreted in contexts such as Avogadro (software) visualizations and datasets curated by NIST and Royal Society of Chemistry.

Measurement and determination methods

Values are inferred from experimental observables recorded at facilities like Brookhaven National Laboratory, CERN, Argonne National Laboratory, and synchrotrons such as Diamond Light Source and European Synchrotron Radiation Facility. Techniques include analysis of crystallographic contacts from studies at Rutherford Appleton Laboratory and diffraction data produced by teams at Stanford Synchrotron Radiation Lightsource, scattering methods developed by Ernest Rutherford-inspired groups, and surface force measurements pioneered in laboratories affiliated with Bell Labs and IBM Research. Computational approaches employ quantum chemistry algorithms advanced at Los Alamos National Laboratory and in packages from Gaussian (software), using ab initio methods popularized by John Pople and density functional theory formulations by Walter Kohn and Lu Jeu Sham. Empirical and semiempirical tabulations have been compiled by scientists associated with Cambridge University Press and Wiley, and parameter fitting often references datasets from NIST Chemistry WebBook and benchmark sets used in competitions sponsored by European Research Council.

Trends across the periodic table

Periodicity evident in tables first systematized by Dmitri Mendeleev and expanded by Henry Moseley informs general trends: values typically decrease across a period as seen in data discussed at University of Tokyo and increase down a group as documented in handbooks from Oxford University Press and Springer. Anomalies connected to electronic structure derive from concepts developed by Erwin Schrödinger, Wolfgang Pauli, Enrico Fermi, and relativistic effects formulated in work by Paul Dirac and investigated by researchers at Lawrence Livermore National Laboratory. Comparisons among metals studied at Max Planck Institute for Chemical Physics of Solids, noble gases explored at Royal Institution, and transition elements characterized by teams at Argonne National Laboratory reveal systematic behavior linked to shells described by Niels Bohr and subshell occupations analyzed in textbooks from Princeton University Press.

Applications and relevance in chemistry and biology

Van der Waals radii underpin molecular packing concepts used in structural biology by groups at European Molecular Biology Laboratory, Wellcome Trust Sanger Institute, National Institutes of Health, and labs studying protein folding at Scripps Research Institute and Max Planck Institute for Biophysical Chemistry. Crystallographers at Diamond Light Source and Brookhaven National Laboratory employ the parameter to interpret steric clashes in macromolecular models deposited in the Protein Data Bank. Medicinal chemistry teams at Pfizer, Roche, Novartis, and Merck & Co. use radii in ligand design workflows, while materials scientists at Toyota Central R&D Labs and BASF use them to model adsorption and surface interactions. In supramolecular chemistry, concepts from Jean-Marie Lehn and Donald J. Cram integrate van der Waals considerations with host–guest systems; in nanotechnology, groups at IBM Research and HP Labs use the parameter for van der Waals heterostructures studied alongside Andre Geim and Konstantin Novoselov research on two-dimensional materials.

Relationship to other atomic radii and intermolecular forces

The parameter is compared to covalent radii tabulated by researchers like Linus Pauling and ionic radii compiled by teams influenced by Fajans and Walter Gordy, while effective radii used in solid-state chemistry come from studies at Bell Labs and MIT. Its role in nonbonded interaction models complements theoretical formalisms such as the Lennard-Jones potential developed in contexts involving John Lennard-Jones and dispersion forces quantified by Fritz London. Work on hydrogen bonding by G. N. Lewis and Linus Pauling and electrostatic models advanced at Central European Institute tie into comparisons with Debye forces characterized by Peter Debye. Computational treatments integrating parameters from Perdew–Burke–Ernzerhof functionals and many-body dispersion corrections used in studies at University of California, Berkeley and University College London reconcile van der Waals radii with concepts from Kohn–Sham theory and force fields like CHARMM, AMBER, and OPLS.

Category:Atomic physics