Abstract.
Models for the mutual potential energy between two molecules proposed in the scientific literature often contain a sum of inverse-power interactions involving pairs of sites belonging to the two particles; in turn, these quantities are functions of a few scalar invariants involved in the problem at hand, and one is often interested in directly obtaining an explicit expression of the potential in terms of the latter; the extensively studied two-centre multipole expansion for the mutual electrostatic energy between two charge distributions is a well-known example of this procedure and of its restrictions. We consider here another, less widely known and possibly complementary, approach, proposed by Šebek some years ago [J. Šebek, Czech. J. Phys. B 38, 1185 (1988)]; the resulting formulae show that this procedure can become computationally favourable for sufficiently high molecular symmetry.
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References
G.C. Maitland, M. Rigby, E.B. Smith, W.A. Wakeham, Intermolecular Forces: Their Origin and Determination (Oxford University Press, Oxford, UK, 1981), Chap. 2, pp. 45–95; Chap. 9, pp. 485–530
M. Rigby, E.B. Smith, W.A. Wakeham, G.C. Maitland, The Forces between Molecules (Oxford University Press, Oxford, UK, 1986), Chap. 1, pp. 1–35; Chap. 8, pp. 165–213
C.G. Gray, K.E. Gubbins, Theory of Molecular Fluids, Volume 1: Fundamentals (Oxford University Press, Oxford, UK, 1984), Chap. 2, pp. 27–142
A.J. Stone, The Theory of Intermolecular Forces (Oxford University Press, Oxford, UK, 1997), Chap. 3, pp. 36–49; Chap. 4, pp. 50–63
P. Piecuch, J. Phys. A 18, L739 (1985)
J. Šebek, Czech. J. Phys. B 38, 1185 (1988)
J. Šebek, Czech. J. Phys. B 38, 1194 (1988)
J. Šebek, Czech. J. Phys. B 38, 1328 (1988)
J. Šebek, Czech. J. Phys. B 40, 1168 (1988)
R.A. Sack, J. Math. Phys. 5, 245 (1964)
R.A. Sack, J. Math. Phys. 5, 252 (1964)
R.A. Sack, J. Math. Phys. 5, 260 (1964)
Y.-N. Chiu, J. Math. Phys. 5, 283 (1964)
J. Downs, K.E. Gubbins, S. Murad, C.G. Gray, Mol. Phys. 37, 129 (1979)
S. Der Chao, J.D. Kress, A. Redondo, J. Chem. Phys. 120, 5558 (2004)
D. Sommacal, dissertation, Pavia University (1997); also available at http://jus.unipv.it/sommacal
P.R. Fontana, J. Math. Phys. 2, 825 (1961)
L. Blum, J.L. Torruella, J. Chem. Phys. 56, 303 (1972)
A.J. Stone, The Molecular Physics of Liquid Crystals, edited by G.R. Luckhurst, G.W. Gray (Academic Press, London, 1979), Chap. 2, pp. 31–50
A.J. Stone, Mol. Phys. 36, 241 (1978)
G.B. Arfken, H.J. Weber, Mathematical Methods for Physicists, 4th edn. (Academic Press, San Diego, USA, 1995), Chap. 7, pp. 410–455
L.A. Girifalco, J. Phys. Chem. 96, 858 (1992)
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Romano, S., Sommacal, D. Some remarks on generalised multipole expansions. Eur. Phys. J. D 32, 45–49 (2005). https://doi.org/10.1140/epjd/e2004-00174-3
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DOI: https://doi.org/10.1140/epjd/e2004-00174-3