Abstract
The realism of a computer simulation is usually limited by the accuracy of the fundamental scientific input into the calculation: the model intermolecular potential. We examine the problems in establishing accurate model potentials, by considering the physical origins of intermolecular forces, highlighting the approximations which are usually made in the potentials used in simulations, and discussing the problems in quantifying intermolecular potentials by ab initio methods and by fitting to experimental data. This emphasises the importance of choosing a realistic functional form for the potential. The isotropic atom-atom model potential, which is usually used for modelling polyatomic molecules, is contrasted with the recently developed anisotropic site-site approach to designing model potentials. The electrostatic interaction can be represented very accurately within the anisotropic site-site formalism, by the use of an ab initio based distributed multipole model. We show how empirical anisotropic site-site potentials have been used to great effect in a Molecular Dynamics simulation of liquid chlorine and Monte Carlo simulations of three condensed phases of benzene. Thus we can expect that the use of such model potentials will lead to more realistic simulations in the future.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
G. C. Maitland, M. Rigby, E. B. Smith, and W. A. Wakeham, Intermolecular Forces, Clarendon press, Oxford., 1981.
B. M. Axilrod and E. Teller,‘Interaction of van der Waals type between three atoms’, J. Chem. Phys., 11, 299 (1943).
P. A. Monson and M. Rigby,‘Non-additive three body contribution to the lattice energies of nitrogen and carbon dioxide’, Molec. Phys., 39, 1163 (1980).
A. D. Buckingham,‘Permanent and induced molecular moments and long range intermolecular forces’, Adv. Chem. Phys., 12, 107 (1967).
A. J. Stone and R. J. A. Tough,‘Spherical tensor theory of long range intermolecular forces’, Chem. Phys. Letts., 110, 123 (1984).
A.J. Stone, ‘Intermolecular Forces’ in Molecular Liquids Dynamics and Interactions, A.J. Barnes, W.J. Orville-Thomas and J. Yarwood, eds., NATO ASI Series C 135, 1984.
A. J. Stone and S. L. Price,‘Some new ideas in the theory of intermolecular forces: anisotropic atom-atom potentials’, J. Phys. Chem, 92, 3325 (1988).
S. L. Price, A. J. Stone and M. Alderton,‘Explicit formulae for the electrostatic energy, forces and torques between a pair of molecules of arbitrary symmetry’, Molec. Phys., 52, 987 (1984).
Gray C.G. and Gubbins K.E., Theory of Molecular Fluids Vol. 1, Oxford, 1984.
A. J. Stone,‘Distributed polarizabilities’, Molec. Phys., 56, 1065 (1985).
C.S. Tong, ‘Anisotropy in repulsion and dispersion forces between atoms in molecules’, Ph.D. Thesis, University of Cambridge (1988).
E.A. Mason and L. Monchick,‘Methods for the determination of intermolecular forces’, Adv. Chem. Phys., 12, 329 (1967).
H. J. Böhm and R. Ahlrichs,‘The N2—N2 interaction A theoretical investigation’, Molec. Phys., 55, 1159 (1985).
K. T. Tang and J. P. Toennies,‘An improved model for the van der Waals potential based on universal damping functions for the dispersion coefficients’, J. Chem. Phys., 80, 3726 (1984).
P. J. Knowles and W. J. Meath,‘A separable method for the calculation of dispersion and induction energy damping functions with applications to the dimers arising from He, Ne and HF’, Molec. Phys., 60, 1143 (1987).
M. S. H. Ling and M. Rigby,‘Towards an intermolecular potential for nitrogen’, Molec. Phys., 51, 855 (1984).
M. Rigby, E.B. Smith, W.A. Wakeham and G.C. Maitland, The forces between molecules, Clarendon press, Oxford., 1986.
J.A. Barker, R.A. Fisher and R.O. Watts,‘Liquid argon: Monte-Carlo and Molecular Dynamics calculations’, Molec. Phys., 21, 657 (1971).
P. M. Rodger, A. J. Stone and D. J. Tildesley,‘The intermolecular potential of chlorine: a three phase study’, Molec. Phys., 63, 173 (1988).
D. J. Tildesley and P. A. Madden,‘Time correlation functions for a model of liquid carbon disulphide’, Molec. Phys., 48, 129 (1983).
P. J. Grout and Leech J. W.,‘Lattice dynamics of crystalline carbon disulphide revisited’, Molec. Phys., 45, 51 (1982).
P. J. Grout and Leech J. W.,‘Intermolecular modes of solid carbon disulfide’, J. Phys. C, 15, L1083 (1982).
R. W. Impey and M. L. Klein,‘Intermolecular force models and the crystal structure of carbon disulphide’, Chem. Phys. Letts., 103, 143 (1983).
S. Nose and M. L. Klein,‘Constant pressure molecular dynamics for molecular systems’, Molec. Phys., 50, 1055 (1983).
E. Burgos and R. Righini,‘The effects of anisotropic atom-atom interactions on the crystal structure and lattice dynamics of solid CS2’, Chem. Phys. Letts., 96, 584 (1983).
U. Burkert and N.L. Allinger, Molecular Mechanics, ACS Monograph 177, 1982.
S. J. Harris, S. E. Novick, J. S. Winn and W. Klemperer,‘(Cl2)2: A polar molecule’, J. Chem. Phys., 61, 3866 (1974).
A. J. Pertsin and A. I. Kitaigorodsky, The Atom-Atom Potential Method, Springer Series in Chemical Physics, vol 43, 1987.
E. D. Stevens,‘Experimental electron density distribution of molecular chlorine’, Molec. Phys., 37, 27 (1979).
G. Moss and D. Feil,‘Electrostatic molecular interactions from X-ray diffraction data. I Development of method: test on pyrazine’, Acta Cryst. A, 37, 414 (1981).
S. L. Price and A. J. Stone,‘The electrostatic interactions in van der Waals complexes involving aromatic molecules’, J. Chem. Phys., 86, 2859 (1987).
M. J. Alderton,‘Distributed Multipole Analysis’, Ph.D. Thesis, University of Cambridge, (1983).
A. J. Stone and M. Alderton,‘Distributed multipole analysis Methods and applications’, Molec. Phys., 56, 1047 (1985).
W.A. Sokalski and A. Sawaryn,‘Correlated molecular and cumulative atomic multipole moments’, J. Chem. Phys., 87, 526 (1987).
F. Vigné-Maeder and P. Claverie,‘The exact multicenter multipolar part of a charge distribution and its simplified representation’, J. Chem. Phys., 88, 4934 (1988).
J.F. Rico, J.R. Alvárez-Collado and M. Paniagua,‘1.1.1. electrostatic description of molecular systems’, Molec. Phys., 56, 1145 (1985).
A. Pullman and D. Perahia,‘Hydration scheme of uracil and cytosine’, Theor. Chim. Acta, 48, 29 (1978).
D. L. Cooper and N. C. J. Stutchbury,‘Distributed multipole analysis from charge partitioning by zero-flux surfaces: the structure of HF complexes’, Chem. Phys. Letts., 120, 167 (1985).
Z. Berkovitch-Yellin and L. Leiserowitz,‘The role of Coulomb forces in the crystal packing of amides. A study based on experimental electron densities’, J. Amer. Chem. Soc., 102, 7677 (1980).
R. D. Amos, CADPAC: The Cambridge Analytical Derivatives Package, publication CCP1/84/4, S.E.R.C. Daresbury Laboratory, Daresbury, Warrington WA4 4AD, England, 1984.
S. L. Price,‘A distributed multipole analysis of the charge densities of some aromatic hydrocarbons’, Chem. Phys. Letts., 114, 359 (1985).
S. L. Price and A. J. Stone,‘A distributed multipole analysis of the charge densities of the azabenzene molecules’, Chem. Phys. Letts., 98, 419 (1983).
S. L. Price, R. J. Harrison and M. F. Guest, ‘An ab initio distributed multipole study of the electrostatic potential around a undecapeptide cyclosporin derivative and a comparison with point charge electrostatic models’, J. Comput. Chem., in press.
C. H. Faerman and S. L. Price, manuscript in preparation.
A. D. Buckingham and P. W. Fowler,‘A model for the geometries of van der Waals complexes’, Canad. J. Chem., 63, 2018 (1985).
G. J. B. Hurst, P. W. Fowler, A. J. Stone and A. D. Buckingham,‘Intermolecular forces in van der Waals dimers’, Int. J. Quant. Chem., 29, 1223 (1986).
A. C. Legon and D. J. Millen,‘Directional character, strength and nature of the hydrogen bond in gas-phase dimers’, Ace. Chem. Res., 20, 39 (1987).
U. C. Singh and P. A. Kollman,‘An approach to computing electrostatic charges for molecules’, J. Comput. Chem., 5, 129 (1984).
S. R. Cox and D. E. Williams,‘Representation of the molecular electrostatic potential by a net atomic charge model’, J. Comput. Chem., 2, 304 (1981).
D. E. Williams and R. R. Weiler,‘Lone-pair electronic effects on the calculated ab initio SCF-MO electric potential and the crystal structures of azabenzenes’, J. Amer. Chem. Soc., 105, 4143 (1983).
R. Bonaccorsi, E. Scrocco and J. Tomasi,‘An approximate expression for the electrostatic molecular potential in terms of completely transferable group contributions’, J. Amer. Chem. Soc., 99, 4546 (1977).
C. S. Murthy, S. F. O’Shea and I. R. McDonald,‘Electrostatic interactions in molecular crystals Lattice dynamics of solid nitrogen and carbon dioxide’, Molec Phys., 50, 531 (1983).
M. T. Dove and R. M. Lynden-Bell,‘A model of the paraelectric phase of thiourea’, Philosophical Mag. B, 54, 443 (1986).
S. C. Nyburg and C. H. Faerman,‘A revision of van der Waals atomic radii for molecular crystals: N, O, F, S, Cl, Se, Br and I bonded to carbon’, Acta Cryst. B, 41, 274 (1985).
S. L. Price,‘Is the isotropic atom-atom model potential adequate?’, Molec. Simulation, 1, 135 (1988).
S. L. Price,‘The limitations of isotropic site-site potentials to describe a N2—N2 intermolecular potential surface’, Molec. Phys., 58, 651 (1986).
J. T. Brobjer and J. N. Murrell,‘The intermolecular potential of HF’, Molec. Phys., 50, 885 (1983).
S. L. Price and A. J. Stone,‘The anisotropy of the Cl2—Cl2 pair potential as shown by the crystal structure Evidence for intermolecular bonding or lone pair effects?’, Molec. Phys., 47, 1457 (1982).
L.-Y. H. Hsu and D. E. Williams, ‘Potential energy models for nonbonding and bonding interactions in solid chlorine’, Inorganic Chem., 18, 79 (1979);
L.-Y. H. Hsu and D. E. Williams, ‘Potential energy models for nonbonding and bonding interactions in solid chlorine’, Inorganic Chem., 19, 2200 (1980).
S. C. Nyburg and W. Wong-Ng,‘Anisotropic atom-atom forces and the space group of solid chlorine’, Proc. Roy. Soc. A, 367, 29 (1979).
S. L. Price,‘The structure of the homonuclear diatomic solids revisited -a distorted atom approach to the intermolecular potential’, Molec. Phys., 62, 45 (1987).
F. P. Ricci, D. Rocca and R. Vallauri,‘A Monte Carlo simulation study of liquid chlorine’, Molec. Phys., 60, 1245 (1987).
A. J. Stone,‘The description of bimolecular potentials, forces and torques: the S and V function expansions’, Molec. Phys., 36, 241 (1978).
A. J. Stone, ‘Intermolecular forces’ in The molecular physics of liquid crystals, G. R. Luckhurst and G. W. Gray, eds., Academic press, 1979, ch. 2.
S. L. Price and A. J. Stone,‘A six-site intermolecular potential scheme for the azaben-zene molecules, derived by crystal structure analysis’, Molec. Phys., 51, 569 (1984).
Busing W.R., WMIN, a computer program to model molecules and crystals in terms of potential energy functions, Oak Ridge National Laboratory Report ORNL-5747, 1981.
S. Yashoneth, S.L. Price and I. R. McDonald,‘A six-site anisotropic atom-atom potential model for the condensed phases of benzene’, Molec. Phys., 64, 361 (1988).
D. E. Williams and S. R. Cox,‘Nonbonded potentials for azahydrocarbons: the importance of the Coulombic interaction’, Acta Cryst. B, 40, 404 (1984).
S. C. Nyburg, C. H. Faerman and L. Prasad,‘A revision of van der Waals atomic radii for molecular crystals II: hydrogen bonded to carbon’, Acta Cryst. B, 43, 106 (1987).
S. L. Price,‘Model anisotropic intermolecular potentials for saturated hydrocarbons’, Acta Cryst. B, 42, 388 (1986).
M. G. Munowitz, G. L. Wheeler and S. D. Colson,‘A critical evaluation of isotropic potential functions for chlorine Calculations on the three phases of p-dichlorobenzene at 100K’, Molec. Phys., 34, 1727 (1977).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1990 Kluwer Academic Publishers
About this chapter
Cite this chapter
Price, S.L. (1990). Towards Realistic Model Intermolecular Potentials. In: Catlow, C.R.A., Parker, S.C., Allen, M.P. (eds) Computer Modelling of Fluids Polymers and Solids. NATO ASI Series, vol 293. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-2484-0_2
Download citation
DOI: https://doi.org/10.1007/978-94-009-2484-0_2
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-7621-0
Online ISBN: 978-94-009-2484-0
eBook Packages: Springer Book Archive