J . Phys. Chew. 1989, 93, 2927-2931 give a reasonable representation of the experimental spectrum of the isolated hydrazine molecule and provide a reference point for judging the effect of intermolecular interactions, such as dimer formation and complex formation, upon these parameters and hence upon the vibrational spectra and upon the structure of the molecule. It is hoped that these results will aid an ongoing study of the behavior of hydrazine in clays.33
2927
Acknowledgment. ‘K.H.K.B., W.B.P., and T.T. are grateful for partial support of this work by Tyndall AFB (Contract No. F08636-83-(2-0136, Task order 86-4), and for support of computing costs by the National Institute of Health Research Grant No. G M 32988. We also thank Dr. M. Szczesniak and Dr. Lester Andrews for helpful discussions and for providing the information quoted in ref 24 prior to publication. Registry No. N2H4, 302-01-2; D2,7782-39-0; N2, 7727-37-9; Ar,
(33) Johnston, C. T., private communication.
7440-37-1.
Empirical Energy Parameters for Structural Modeling of Alkali Halide Crystals in Standard Formalisms G . Brink, L. Glasser,* and R. C. Mboweni Department of Chemistry, University of the Witwatersrand, Johannesburg 2001, South Africa (Received: April 27, 1988; In Final Form: September 19, 1988)
Potential energy parameters, describing Coulombic, van der Waals, and repulsion energies, have been established for each of the nine common alkali halide ions in two forms of the exp-6 potential, with use of the standard, ambient-stable alkali halide crystal structures for reference. The derived potential parameters fit the lattice energies of the stable NaC1-type structures to better than 1 kcal/mol and predict the lattice energies of the stable CsC1-type structures to better than 3 kcal/mol. For the unstable alkali halide structures, lattice constants are predicted to better than 0.2 A, in general, while the lattice energies obtained are more positive than for the corresponding stable structures and agree well with published values where available.
A number of comprehensive schemes exist for the calculation of intermolecular attractive and repulsive interactions by the summation of pairwise terms that correspond to Coulombic, van der Waals, and repulsion energies. Examples of these schemes are AMBER,’ CHARMM? WEN? EPEN/~: OPLS? and ECEPP.6 These algorithms for potential energy have proved suitable for the calculation of conformations of flexible molecules,’ as well as for the calculation of the packing of molecules in crystal structures.8 Such modeling has generally been developed for neutral molecules, but virtually identical schemes are also in use for simple ionic systems9 (though often in the past with specific parameters for each ion pair rather than for independent ions such as we will use below). Modeling of systems with complex ions has also been reported.I0 Since we intend to apply the EPEN/2 scheme (of the form Coulomb plus exp-6), which was developed for neutral molecules, to calculations of lattice energies of crystal structures containing complex ions, it is first necessary for us to develop an appropriate set of empirical constants for the interactions of simple (1) Weiner, P. K.; Kollman, P. A. J . Comput. Chem. 1981, 2, 287. (2) Brooks, B. R.; Bruccoleri, R. E.; Olafson, B. D.; States, D. J.; Swaminathan, S.; Karplus, M. J. Comput. Chem. 1983, 4 , 187. (3) Shipman, L. L.; Burgess, A. W.; Scheraga, H. A. Proc. Natl. Acad. Sci. U.S.A. 1975. 72. 543. Burgess. A. W.: Shioman. L. L.: Scheraaa. H. A. Ibid. 1975, 72, 854. Burgess,-A. W.; Shipman, L. L.; Nemenofi, R. A.; Scheraga, H. A. Ibid. 1976, 98, 23. (4) Snir, J.; Nemenoff, R. A.; Scheraga, H. A. J. Phys. Chem. 1978,82, 2497. Nemenoff, R. A.; Snir, J.; Scheraga, H. A. Ibid. 1978, 82, 2504. Nemenoff. R. A,: Snir. J.: Scheraaa. H. A. Ibid. 1978.82.2513. Nemenoff. R. A.; Snir, J.; Scheraga, H. A: Ibid. 1978, 82, 2521. Kincaid, R. H.; Scheraga, H. A. Ibid. 1982,86, 833. Kincaid, R. H.; Scheraga, H. A. Ibid. 1982, 86, 838. (5) Jorgensen, W. L.; Madura, J. D.; Swenson, C. J. J. Am. Chem. SOC. 1984, 106, 6638, and references therein. (6) Momany, F. A,; Carruthers, L. M.; McGuire, R. F.; Scheraga, H. A. J . Phys. Chem. 1975, 79, 2361. Nemethy, G.; Pottle, M. S.; Scheraga, H. A. Ibid. 1983, 87, 1883. Sippl, M. J.; Nemethy, G.; Scheraga, H. A. Ibid. 1984,88, 623 1. (7) Li, Z.; Scheraga, H. A. Proc. Natl. Acad. Sci. U.S.A.1987,84, 6611. Purisima, E. 0.;Scheraga, H. A. J. Mol. Biol. 1987, 196, 697. (8) Glasser, L.; Scheraga, H. A. J . Mol. Biol. 1988, 199, 513. (9) Shanker, J.; Agrawal, G. G. Phys. Status Solidi B 1984, 123, 11. Shanker, J.; Kumar, M. Ibid. 1987, 142, 325. (10) Catlow, C. R. A,; Cormack, A. N.; Theobald, F. Acta Crystallogr., Secr. B Struct. Sci. 1984, E40, 195. Catlow, C. R. A,; Cormack, A. N. Int. Rev. Phys. Chem. 1987,6, 227.
0022-365418912093-2927$01.50/0
charged species within the exp-6 formalism in order to provide reference values of the parameters for more complex cases. In this paper, we report on the first stage of the development, viz., the establishment of a small set of parameters for alkali metal and halogen ions within alkali halide crystals. Although our aim is to obtain parameters for EPEN/2, it has proved convenient to begin by establishing parameters for the Gilbert potential” (Coulomb plus exponential only) since good starting values for this potential have already been determined. With the present results as our basis, we intend later to develop consistent exp-6 sets of empirical energy parameters for complex ions, such as NH4+ and NO3-. The structures’* and lattice energiesI3 of the alkali halides are well-known, and many accurate and elaborate schemes have been developed for the calculation of the energies and other thermodynamic and dynamic properties of these m a t e r i a l ~ . ~ JWhile ~ these schemes are appropriate to the modeling of alkali halide and of mixed alkali halide crystals,15their extent of elaboration is a computational hindrance and may even be inappropriate for modeling of the less well-determined structures of more complex materials. Thus, our present limited objective is to seek the fewest possible parameters, within the exp-6 formalism, consistent with a reasonable representation of the structures of the alkali halide crystals. These parameters must also be transferable to be useful to us; that is, the parameters must be usable in quite different crystal structures and must thus be crystal-independent though they will be specific to each ion considered. The E P E N / ~formalism4 places positive charges on the atoms of a rigid molecule and negative charges (“electrons”) in pairs both within bonds and at suitably placed lone-pair positions. The (1 1) Gilbert, T. L. J. Chem. Phys. 1968, 49, 2640. See also: Gilbert, T. L.; Simpson, 0. C.; Williamson, M. A. Ibid. 1975, 63, 4061. (1 2) Hellwege, K.-H. Landolt-Bornstein Tables (New Series); Springer: Berlin, 1973; Vol. III/7a. (13) Tosi, M. P. Solid State Phys. 1964, 16, 1. (14) Ree, F. H.; Holt, A. C. Phys. Rev. E: Solid State 1973, 8, 826. Catlow, C. R. A,; Diller, K. M.; Norgett, M. J. J . Phys. C 1977, IO, 1395. Fitzsimons, P. B.; Corish, J.; Jacobs, P. W. M. Cryst. Lattice Defects Amorphous Mater. 1987, 15, 7 . ( 1 5) Shanker, J.; Sharman, S. C.; Kumar, M. Phys. Status Solidi E 1987, 141, 409.
0 1989 American Chemical Society
2928 The Journal of Physical Chemistry, Vol. 93, No. 8, 1989 rigid molecular structure is taken from experiment while the positions assigned to the electrons are part of the assignable parameters of the model, determined by reference to the symmetry, energy, and other properties of molecular groupings and crystals of the relevant species. The total energy, E , of a grouping in EPEN/2 is the sum of a Coulomb interaction between all charges, q, and a nonbonded Buckingham interaction between electrons only, as follows where charges
Ecoul(kcal mol-') = 332.0719 i
