Abstract
Calculations of minimum energy configurations for aggregates of up to forty atoms, commonly referred to as clusters, are presented. In contrast to previous studies, random initial configurations have been optimised to find the lowest energy structure for a given number of atoms. Three different two-body, bireciprocal potential functions were used in these calculations and in the case of the Lennard-Jones potential, previously calculated results have been confirmed. New structures obtained using softer potentials are also presented. Minimum energy structures of small clusters containing two different types of atoms have also been calculated, and the relationship between the geometry of a cluster and the relative sizes of its constituent atoms examined.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
C.A. Rodgers, Proc. London Math. Soc. (3) 8 (1958)609.
A.H. Boerdijk, Philips Res. Rep. 7 (1952)303.
A.L. Mackay, Acta Cryst. 15 (1962)916.
J.G. Allpress and J.V. Sanders, Surface Sci. 7 (1967)1.
Y. Fukano and C.M. Wayman, J. Appl. Phys. 40 (1969)1656.
J.G. Allpress and J.V. Sanders, Aust. J. Phys. 23 (1970)23.
J.J. Burton, Nature 229 (1971)335.
J.D. Bernal, Nature 185 (1959)141.
G. Mason and W. Clark, Nature 207 (1965)512.
G. Mason and W. Clark, Nature 211 (1966)957.
J.D. Bernal and S.V. King, Faraday Disc. Chem. Soc. 43 (1967)60.
J.D. Bernal and J.L. Finney, Faraday Disc. Chem. Soc. 43 (1967)62.
M.R. Hoare and P. Pal, Adv. Phys. 20 (1971)161.
M.R. Hoare and P. Pal, Nature 230 (1971)5.
M.R. Hoare and J. McInnes, Faraday Disc. Chem. Soc. 61 (1976)12.
M.R. Hoare, Adv. Chem. Phys. 40 (1979)49.
L.T. Wille, Chem. Phys. Lett. (1987) 133; 405.
J. Uppenbrink and D.J. Wales, J. Chem. Soc. Faraday Trans. 87 (1991)215.
J.A. Northby, J. Chem. Phys. 87 (1987)6166.
W.C. Davidson, Math. Prog. 9 (1975)1.
B.W. Clare, M.C. Favas, D.L. Kepert and A.S. May, Adv. Dyn. Stereochem. 1 (1985)1.
M.C. Favas,The MINIM Subroutine (University of Western Australia, 1985).
B.W. Clare and D.L. Kepert, Proc. Roy. Soc. London A405 (1986)329.
N.R. Taylor, Ph.D. Thesis, University of Western Australia (1990).
D.J. Fuller and D.L. Kepert, Inorg. Chem. 21 (1982)163.
B.W. Clare and D.L. Kepert, Inorg. Chem. 23 (1984)1521.
B.W. Clare and D.L. Kepert, Polyhedron 6 (1987)619.
H.M. Cundy and A.P. Rollet,Mathematical Models, 2nd ed. (Oxford University Press, Oxford, 1974).
J.D. Bernal, Proc. Roy. Soc. A280 (1964)299.
B.K. Teo, M.C. Hong, H. Zhang and D.B. Huang, Angew. Chem. Int. Ed. Engl. 26 (1987)897.
D.M. Washecheck, E.J. Wucherer, L.F. Dahl, A. Ceriotti, G. Longoni, M. Mamassero, M. Sansoni and P. Chini, J. Amer. Chem. Soc. 101 (1979)6110.
B.K. Teo, H. Zhang and X. Shi, J. Amer. Chem. Soc. 112 (1990)8552.
B.K. Teo and K. Keating, J. Amer. Chem. Soc. 106 (1984)2224.
M.S. Stave, D.E. Sanders, T.J. Raeker and A.E. DePristo, J. Chem. Phys. 93 (1990)4413.
J. Farges, M.F. de Feraudy, B. Raoult and G. Torchet, J. Chem. Phys. 78 (1983)5067.
J. Donohue,The Structures of the Elements (Wiley-Interscience, New York, 1974).
D.J. Wales, J. Amer. Chem. Soc. 112 (1990)7908.
Wen Yu and R.B. Freas, J. Amer. Chem. Soc. 112 (1990)7126.
J. Caldwell, L.X. Dang and P.A. Kollman, J. Amer. Chem. Soc. 112 (1990)9144.
A.T. Amos, T.F. Palmer, A. Walters and B.L. Burrows, Chem. Phys. Lett. 172 (1990)503.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Bytheway, I., Kepert, D.L. The mathematical modelling of cluster geometry. J Math Chem 9, 161–180 (1992). https://doi.org/10.1007/BF01164842
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01164842