Abstract
The history of van der Waals or dispersion forces dates a long way back [1, 2]. The recent book Van der Waals and Molecular Sciences [1] gives a detailed account of van der Waals’s own contributions and life-long interest in the field. It is interesting to note that this truly quantum-mechanical problem [3, 4, 5] has been addressed by theorists long before the birth of quantum mechanics. The force between atoms, molecules, clusters, complexes, surfaces, and other fragments of matter is dominated by the weak but long-ranged van der Waals interactions at large separations. This is the region that has been primarily addressed. Calculations of the interaction potential between neutral species were first done for molecules [6, 7], leading to the well known asymptotic R −6 form of London [5]. The asymptotic z −3 form of the interaction potential between a neutral atom and a surface was first identified by Lennard-Jones [8], with subsequent refined treatments of the atom and surface polarizabilities [9, 10]. For the interaction between solid bodies, general formulas have been derived [11], which for flat surfaces a long distance d apart give an interaction energy that varies as d −2 [12]. For very large distances, where the limited magnitude of the velocity of light matters, retardation effects are important [13]. Such relativistic effects are physically interesting but beyond the scope of the present work.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
A. Y. Kipnis, B. E. Yavelov, and J. S. Rowlinson, Van der Waals and Molecular Sciences (Oxford, New York, 1996).
H. Margenau and N. R. Kestner, Theory of Intermolecular Forces (Pergamon Press, Oxford, 1969).
D. Langbein, Theory of Van der Waals Attraction (Springer Verlag, Berlin, 1974).
R. Eisenshitz and F. London, Z. Phys. 60, 491 (1930).
F. London, Z. Phys. 63, 245 (1930).
M. Reinganum, Ann. Phys. (Paris) 38, 649 (1912).
S. C. Wang, Z. Phys. 28, 663 (1927).
J. E. Lennard-Jones, Trans. Faraday. Soc. 28, 333 (1932).
J. H. de Boer, Trans. Faraday Soc. 32, 21 (1936).
H. C. Hamaker, Physica 4, 1058 (1937).
E. M. Lifshitz, Sov. Phys. 2, 73 (1956).
I. E. Dzyaloshinskii, E. M. Lifshitz, and L. P. Pitaevskii, Adv. Phys. 10, 73 (1961).
H. B. G. Casimir and D. Polder, Phys. Rev. 73, 360 (1948).
J. Israelachvilii, Intermolecular and Surface Forces (Academic, London, 1991).
A. Buckingham, P. Fowler, and J. Hutson, Chem. Rev. 88, 963 (1988).
G. Chalasinski and M. M. Szczesinak, Chem. Rev. 94, 1723 (1994).
See, e.g., U. Hartmann, in Scanning Tunneling Microscopy III, edited by R. Wiesendanger and H.-J. Guentherodt (Springer, Berlin-Heidelberg, 1993), p. 293.
M. Spackman, J. Chem. Phys. 94, 1295 (1991).
A. Landragin, J. Y. Courtois, G. Labeyrie, N. Vansteenkiste, C. I. Westbrook, and A. Aspect, Phys. Rev. Lett. 77, 1464 (1996).
J. Israelachvilii and H. Wennerström, Nature 379, 219 (1996).
S. Andersson, L. Wilzen, and M. Persson, Phys. Rev. B 38, 2967 (1988).
S. Andersson, M. Persson, and J. Harris, Surf. Sci. 360, L499 (1996).
R. O. Jones and O. Gunnarsson, Rev. Mod. Phys. 61, 689 (1989).
K. Burke, J. Perdew, and Y. Wang, “Derivation of a generalized gradient approximation: the PW91 density functional”, in this volume.
D. C. Langreth and J. P. Perdew, Solid State Commun. 17, 1425 (1975).
O. Gunnarsson and B. I. Lundqvist, Phys. Rev. B 13, 4274 (1976).
D. C. Langreth and J. P. Perdew, Phys. Rev. B 15, 2884 (1977).
J. Harris, Phys. Rev. B 31, 1770 (1985).
J. F. Dobson, in Topics in Condensed Matter Physics, edited by M. P. Das (Nova, N. Y., 1994), p. 121.
B. I. Lundqvist, Y. Andersson, H. Shao, S. Chan, and D. C. Langreth, Int. J. Quantum. Chem. 56, 247 (1995).
E. Zaremba and W. Kohn, Phys. Rev. B 13, 2270 (1976).
W. Kohn and W. Hanke, Short-and long-wavelength contributions to the exchange-correlation energy of a metal surface, unpublished.
K. Rapcewicz and N. W. Ashcroft, Phys. Rev. B 44, 4032 (1991).
Y. Andersson, D. C. Langreth, and B. I. Lundqvist, Phys. Rev. Lett. 76, 102 (1996).
E. Hult, Y. Andersson, B. I. Lundqvist, and D. C. Langreth, Phys. Rev. Lett. 77, 2029 (1996).
J. F. Dobson and B. P. Dinte, Phys. Rev. Lett. 76, 1780 (1996).
J. F. Dobson, B. P. Dinte, and J. Wang, “Van der Waals functionals via local approximations for susceptibilities”, in this volume.
P. Hohenberg and W. Kohn, Phys. Rev. 136, B864 (1964).
W. Kohn and L. J. Sham, Phys. Rev. 140, A1133 (1965).
D. C. Langreth and S. H. Vosko, in Advances in Quantum Chemistry, edited by S. B. Trickey (Academic Press, New York, 1990), Vol. 21, p. 175.
D. C. Langreth and S. H. Vosko, Phys. Rev. Lett. 59, 497 (1987).
S. Lundqvist, Ark. Phys. 28, 399 (1965).
A. Zangwill and A. H. Levine, Am. J. Phys. 53, 1177 (1985).
A. Bagchi, N. Kar, and R. G. Barrera, Phys. Rev. Lett. 40, 803 (1978).
K. L. Kliewer, Surf. Sci. 101, 57 (1980).
P. Apell, Physica Scripta 25, 57 (1982).
P. Ahlqvist and P. Apell, Physica Scripta 25, 587 (1982).
P. J. Feibelman, Prog. in Surf. Sci. 12, 287 (1982).
D. C. Langreth and M. J. Mehl, Phys. Rev. Lett. 47, 446 (1981).
D. C. Langreth and M. J. Mehl, Phys. Rev. B 28, 18090 (1983).
C. Mavroyannis and M. J. Stephen, Mol. Phys. 5, 629 (1962).
K. T. Tang, J. M. Norbeck, and P. R. Certain, J. Chem. Phys. 64, 3063 (1976).
G. Mahan, J. Chem. Phys. 76, 493 (1982).
A. Dalgarno and W. Davison, in Advanced Atomic and Molecular Physics 2, edited by D. Bates and I. Esterman (Academic, Orlando, 1966).
F. Maeder and W. Kutzelnigg, Chem. Phys 42, 95 (1979).
M. Marinescu, H. Sadeghpour, and A. Dalgarno, Phys. Rev. 49, 982 (1994).
E. Clementi and C. Roetti, At. Data Nucl. Data Tables 14, 177 (1974).
Y. Andersson and H. Rydberg, J. Chem. Phys., in press.
In Biosym, a program package available from Molecular Simulations Inc.
W. Rijks, M. van Heeringen, and P. Wormer, J. Chem. Phys. 90, 6501 (1989).
S. van Gisbergen, J. Snijders, and E. Baerends, J. Chem. Phys. 103, 9347 (1995).
W. Rijks and P. Wormer, J. Chem. Phys. 90, 6507 (1989).
R. Amos, N. Handy, P. Knowles, J. Rice, and A. Stone, J. Phys. Chem. 89, 2186 (1985).
A. Kumar and W. Meath, Mol. Phys. 75, 311 (1992).
B. Jhanwar and W. Meath, Chem. Phys 67, 186 (1982).
A. Dalgarno, Adv. Chem. Phys 12, 143 (1967).
A. Liebsch, Phys. Rev. B 33, 7249 (1986).
Y. Andersson, E. Hult, D. C. Langreth, and B. I. Lundqvist, in Proceedings of the 18th Taniguchi Symposium: Elementary Processes in Excitations and Reactions on Solid Surfaces, edited by A. Okiji, H. Kasai, and K. Makoshi (Springer, Berlin, 1996), p. 52.
C. Holmberg, P. Apell, and J. Giraldo, Physica Scripta 33, 173 (1986).
B. N. J. Persson and P. Apell, Phys. Rev. B 27, 6058 (1983).
B. N. J. Persson and E. Zaremba, Phys. Rev. B 30, 5669 (1984).
D. M. Bishop and J. Pipin, J. Chem. Phys. 97, 3375 (1992).
H. Gollisch, J. Phys. B 17, 1463 (1984).
M. Persson, private communication, 1996.
J. P. Perdew, H. Q. Tran, and E. D. Smith, Phys. Rev. B 42, 11627 (1990).
A. Kiejna, Phys. Rev. B 47, 7361 (1993).
E. Huit and A. Kiejna, Surf. Sci. 383, 88 (1997).
Y. Andersson, E. Huit, P. Apell, D. C. Langreth, and B. I. Lundqvist, submitted to Solid State Commun.
W. Kohn and A. Yaniv, Phys. Rev. B 20, 4948 (1979).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1998 Springer Science+Business Media New York
About this chapter
Cite this chapter
Andersson, Y., Hult, E., Rydberg, H., Apell, P., Lundqvist, B.I., Langreth, D.C. (1998). Van der Waals Interactions in Density Functional Theory. In: Dobson, J.F., Vignale, G., Das, M.P. (eds) Electronic Density Functional Theory. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-0316-7_17
Download citation
DOI: https://doi.org/10.1007/978-1-4899-0316-7_17
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4899-0318-1
Online ISBN: 978-1-4899-0316-7
eBook Packages: Springer Book Archive