J . Phys. Chem. 1990, 94, 981-984
98 1
Studies in Hydrogen Bonding: Modeling of Water in Crystalline Hydrates George Brink* and Leslie Glasser Department of Chemistry, University of the Witwatersrand, 2050 Wits, South Africa (Received: April 1 1 , 1989; In Final Form: July 6, 1989)
The orientations and symmetries of the water molecules in the crystalline hydrates NaCI-2H20, NaBr.2H20, NaI.2H20 and Lil.3H20 have been investigated by use of computer modeling of the hydrates. The interatomic pair potential function EPEN/2 (involving exp(-6) plus Coulombic terms) was applied using previously determined parameters for the alkali-metal and halide ions and the water molecule. Rotational orientations, 0-H bond lengths, and H-0-H bond angles of the water molecules were adjusted subject to symmetry constraints, using the computer program WMIN, to give structures with minimum energy. The hydrogen bonding in the modeled structures is compared with experimental evidence on the nature of the hydrogen bonding, particularly that given by infrared spectroscopy of the partially deuterated hydrates. Satisfactory agreement is found between experimental and calculated lattice energies, which provides justification for transferring the EPEN/2 parameters among the various ionic and molecular structure types. The enthalpy of formation of NaCI.2H20 is calculated from this result to be -255.9 kcal/mol (&5%); this value has not heretofore been reported.
Introduction Water has been modeled by computer in all of its states: gas, liquid, and solid. On the other hand, although the nature of water in crystalline hydrates has been the subject of extensive experimental studies,' little if any computer modeling of such hydrates has been performed. Crystalline hydrates are of inherent interest because they provide a rich variety of systems on which to study the interactions of water molecules. From a practical point of view, computer studies of water in such systems will complement X-ray crystallographic studies where the positions of hydrogen atoms may not be accurately placed. Fundamentally, such computer studies should give insight into the ways in which water molecules interact with one another and with their surroundings. Many potential functions have been developed for modeling interactions between atoms, molecules, and ions. Thus the MCY potential functionZis considered to give good results in representing ice geometries and some other water-water interaction^.^ Unfortunately, most potential functions are applicable only to the systems for which they were specifically developed. For example, the MCY potential is only applicable to pure water; there are no parameters for ions or other substances. On the other hand, transferable potentials, such as TIPS4 and EPEN/2,5 can be applied to a variety of mixed-species systems when parameters for the individual species are available. In this work we have used the more general EPEN/2 potential, where parameters are available for a wide variety of molecules (mostly constructed from small molecular fragment^)^ and for some simple ions,6 and we here extend the model to flexible water molecules. EPEN/2 is of the e x p ( d ) type of potential, plus Coulombic terms, and provides easily computed models of hydrogen-bonded oligomers, consistent in geometry with ab initio results; the absolute values of the energies that it provides are of the correct magnitude, although the actual values may not always be reliable. We have earlier determined EPEN/2 parameters for 5 alkali-metal ions and 4 halogen ions which are consistent with the structural parameters and lattice energies of 20 alkali-metal halides6 in both their stable and unstable crystalline structures. In this work we examine four alkali-metal halide hydrates: NaCI.2H20, NaBr.2H20, NaI.2H20, and LiI.3H20. These four ( I ) Falk, M.; and Knop, 0. In Water: A Comprehensive Treatise; Franks, F., Ed.; Plenum Press: New York, 1973; pp 55-112. (2) Matsuoka, 0.;Clementi, E.; Yoshimine, Y. J. Chem. Phys. 1982,86, 873. (3) Ywn, B. J.; Morokuma, K.; Davidson, E. R. J. Chem. Phys. 1983.83, 1223. (4) Jorgensen, W. L. J . Am. Chem. SOC.1981, 103, 335. ( 5 ) Snir, J.; Nemenoff, R. A,; Scheraga, H. A. J . Phys. Chem. 1978.82, 2497, 2504, 2513, 2521, 2527. Marchese, F. T.; Mehrota, P. K.;Beveridge, D. L. J. Phys. Chem. 1981, 85, I . (6) Brink, G.; Glasser, L.; Mboweni, R. C. J. Phys. Chem. 1989, 93, 2928.
0022-3654/90/2094-098 1$02.50/0
were chosen from the many known alkali-metal halide hydrates because the elegant infrared experiments of Falk and others' on isotopically dilute HDO in these crystalline hydrates have provided reliable information on the symmetries of the water molecules and qualitative information on the strengths of the hydrogen bonds. The results of a neutron diffraction structure determination on NaBr.2Hz0 are also available for comparison with the results obtained here. The lattice energy calculations provide us with the opportunity to estimate the enthalpy of formation of NaC1.2H20 (not previously reported) by means of a Born-Haber cycle calculation.
Calculations The FORTRAN computer program WMIN by W. R. Busing' was used to calculate the lattice energies of the crystalline solids, using the EPEN/2 potential functions with earlier determined potential energy parameters. The parameters that describe the structure include crystal lattice constants, together with the translations and orientations from their initial positions of the rigid units that make up the molecules or ions. The program is used to minimize the energy of the crystal by adjusting the structural parameters with reference to the fixed potential energy parameters. The crystals under consideration were built up with charged ionic species and either rigid or flexible water molecules. The computer program allows entities to both rotate and translate, but in this work, all heavy atoms were not permitted to translate and were confined to their X-ray determined positions. The water molecules were allowed to rotate about the fixed oxygen positions, and when flexible molecules were used, the hydrogen atoms were allowed to move, subject to symmetry constraints, relative to the oxygen atoms. The EPEN/2 potential is described by Scheraga and coworkers,5 and it, and the original version EPEN, have previously been lrsed by It consists of a Coulombic term between all point charges and an exp(-6) term involving interactions between electrons only; the electrons are placed in bonds and at lone-pair positions. The Coulombic and van der Waals energy calculations are built into WMIN;the other interactions were programmed by us in a user subroutine. We have extended the framework of EPEN/2 to take account of electron-ion and ion-ion interactionsS6 (7) Busing, W. R. WMIN: A computer program to model molecules and crystals in terms of potential energy functions; Oak Ridge National Laboratory, Oak Ridge, TN; ORNL-5747, 1981. (8) Brink, G.; Glasser, L. J. Comput. Chem. 1981, 2, 14. (9) Brink, G.; Glasser, L. J . Comput. Chem. 1981, 2, 177. (10) Brink, G.; Glasser, L. J . Mol. Struct. 1981, 85, 317. (11) Brink, G.; Glasser, L. S. Afr. J . Chem. 1981, 34, 18. (12) Brink, G.; Glasser, L. J . Compur. Chem. 1982, 3, 47.
0 1990 American Chemical Society
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Direct lattice-sum limits were typically set at spherical shell radii about each atom of 6-8 A, such that the difference in lattice energy contributions between shells 1 8, different was about 0.1 kcal/mol. To accelerate convergence of the Coulombic and van der Waals lattice sums, WMIN incorporates the Ewald-BertautWilliams method13 of reciprocal lattice summation. Reciprocal lattice summations were performed to spherical shell limits of 0.5 and 0.6 8,-*,which converged to better than 0.001 kcal/mol. Iterations for structural optimizations were continued until the difference in lattice energy between cycles was less than 0.01 kcal/mol; six cycles were usually sufficient.
EPEN/2 Parameters for Water Molecules, Alkali-Metal Ions, and Halide Ions The water molecule used in a modeling has equilibrium 0 - H bond lengths of 0.9572 8, and an equilibrium H-0-H angle of 104.52'. Other parameters used in the EPEN/2 model are given in the original reference^.^ The standard EPEN/2 formulation assumes a rigid water molecule (no stretching or bending), but in this work, we have added simple quadratic stretching and bending force constants in the hope of getting more realisitc hydrogen-bonding behavior of the water molecules in the hydrates. (Flexible water molecules have occasionally been used in computer simulations of water. For example, in a molecular dynamics study of the dielectric properties of water14 the "flexible SPC" model was used, but this uses a somewhat different modeling approach to EPEN/2). In the absence of other information, we have used the free water molecule parameter of 8.45 mdyn k'(1216 kcal mol-') for the 0 - H stretching ~ 0 n s t a n t . I The ~ actual value chosen does of course affect the energy and bond lengths of the hydrogen bonds, but the qualitative nature of the hydrogen bond seems not to be very sensitive to changes of up to about 20%. In this simple model, the EPEN/2 bonding electron pairs are kept at a constant distance from the oxygen atom on the 0-H bond. We have also, on occasion, used a lower value for the stretching force constant to get better agreement with the vibrational frequencies predicted by WMIN. H-O-H bending was also permitted. Here the H atoms were constrained to lie on the (oxygen bonding electron pair) axes, so that it was effectively the (bonding pairoxygen bonding pair) that was bending. Furthermore, the angles on either side of the H-O-H bisector were constrained to be equal, and the bisector maintained its original orientation to the lone pairs. The gas-phase value of 0.697 mdyn 8, rad-* (0.0306 kcal mol-' deg-2) was initially used for the bending force constant, but this gave H-0-H bond angles of typically greater than 1 lo', which are probably too large. A value of 0.2 kcal mol-' d e g 2 was used instead, which gives angles closer to the equilibrium value. The EPEN/2 parameters for Li', Na+, K+, Rb+. and Cs', and for F.CI-, Br-, and I-, have been earlier determined6 and fit the experimental lattice energies of the stable NaC1-type structures to better than 1 kcal/mol and those of the stable CsCI-type structures to better than 3 kcal/mol. These values are within the experimental precision of the lattice energies. The energy parameters also correctly predict the energies of the unstable structures, as far as they are known. The alkali-metal ion and halide ion parameters used for the alkali-metal hydrates discussed below were taken from this set of parametersS6 An implicit assumption in this modeling of the hydrates is that the parameters are transferable, and this assumption is tested in this paper. The assumption is, in fact, quite firmly based; the potential is pairwise additive (with a very small energy contribution from molecular distortions, when this is permitted in the modeling), it is constructed to be of the same form in both the ionic and molecular cases, and each set of parameters has been directly calibrated (13) Ewald, P. P . Ann. Phys. (Leiprig) 1921,64, 253. Bertaut, F. J . Phys. Radium 1952, 13, 499. Williams, D. E. Acta Crystallogr. 1971, A27, 452. Williams, D. E. Ibid. 1972, A28, 629. Williams, D. E. Top. Curr. Phys. 1981, 26. 3. (14) Anderson, J.; Ullo, J. J.; Yip, S. J . Chem. Phys. 1987, 87, 1726. ( 1 5 ) Fuhrer, H.; Kartha, V. B.; Kidd, K. G.; Krueger, P. J.; Mantsch, H. H. Computer Programs f o r Infrared Spectroscopy; National Research Council of Canada; NRCC Bulletin No. 15, 1976: p 173.
Brink and Glasser against experimental structures and energies.
Experimental Lattice Energies The WMIN modeling of the hydrates yields lattice energies that need to be compared with the experimental values. The experimental values have been calculated by a Born-Haber cycle calculation from thermodynamic quantites reported in the litera t ~ r e . ' ~ . ' 'The negative lattice enthalpy of an n-hydrate is obtained from the summation of the standard enthalpies at 25 'C of the following values: negative of the enthalpy of formation of the alkali-metal n-hydrate, less the enthalpy of formation of the n water molecules from their elements; vaporization of n water molecules; atomization of the alkali metal; ionization of the alkali-metal atom; atomization of the dihalogen; and electron addition to the halogen atom (the electron affinity). The calculated lattice enthalpy is converted to an approximate lattice energy by subtraction of the ideal work of condensation of the ionic and molecular gaseous species (RT per mole = 0.59 kcal/mol). The experimental lattice energies are then NaBr.2H20, -207.6 kcal/mol; NaI-2H20, -197.0 kcal/mol; and LiI.3H20, -232.2 kcal/mol. We have no value for NaC1.2H20 since no enthalpy of formation has been reported.
NaCI.2H20 Sodium chloride and water form a stable compound NaCI. 2H20, which melts under its own vapor pressure at -0.1 'C.'* Before an X-ray structure determination had been done, the hydrogen bonding in the substance had been studied by infrared spectroscopy using HDO in low isotopic concentrations in NaC1.2H20 and NaC1-2D20.19 It was shown that three of the four O H groups in the formula unit form hydrogen bonds of very similar strengths and the fourth OH group is much more weakly hydrogen bonded. The subsequent X-ray crystal structure determination20 confirmed the infrared results, giving three 0 - H bonds of similar length and one shorter. The actual H positions seem not to have been very accurately determined, and there has been no neutron diffraction study on the substance. However, one has been done on the isomorphic NaBr.2H20, which is discussed in the next section; this clearly shows the presence of three similar and one much weaker hydrogen bonds. NaCI.2H 0 has the space group P2,/c with II = 6.3313 A, b = 10.1178 and c = 6.5029 8,;p = 114.407'; and Z = 4.20 These parameters were fixed in the present EPEN/2 modeling of the hydrate. The cation-cation distances in the hydrate are much shorter than in the dehydrated salt, with the shortest Na-Na distances being 3.523 and 5.640 A, respectively, while the Na-CI distances are almost the same at 2.79 and 2.80 A, respectively. In this structure, and the others considered in this paper, the hydrogen bonds point toward the halide ions; the lengths and linearity of the hydrogen bonds are given in Table I. The X-ray crystal structure determination of NaC1.2H20 gives the four OH bond lengths as 0.79, 0.83, 0.85, and 0.87 Clearly, these are too short to be realistic; bonds involving hydrogen atoms usually appear shorter by about 0.1 A in X-ray determinations than in neutron diffraction.2' The H O H angles were found to be 112.3' and 98.0'. In our modeling of the hydrates, the heavy-atom positions were fixed in the positions given by the X-ray structure determination. The water molecules were allowed to rotate and, later, stretch and bend about the fixed oxygen positions. It is possible to allow all the entities in the asymmetric unit to move freely, but this results in a structure different from the experimental one. We have taken
A,
(!6) Landolt-Bornstein, Funktionen und Zahlenwerte, 6th ed.; Springer: Berlin, 1961; Vol. 11, Part 4. ( 1 7) Selected Values of Chemical Thermodynamic Properties; NBS Circular 500; US.Dept. of Commerce: Washington, DC, 1952. (18) Gmelin Handbuch der Anorganischen Chemie, System no. 21 (sodium); Verlag Chemie: Berlin, 1967; No. 7 , p 2. (19) Ford, T. A,; Falk, M. J . Mol. Srrucr. 1969, 3, 445. (20) Klewe, B.; Pedersen, B. Acta Crystallogr. 1974, B30, 2363. (21) Glusker, J.; Trueblood, K. N. Crystal Srructure Analysis; Oxford University Press: London, 1972; p 131
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Modeling of Water in Crystalline Hydrates TABLE I: Geometries of the Flexible Water Molecules in the Crystalline Hydrates NaCI-2H20, NaBr-2H20, NaI.2H20, and LiI.3H20, As Modeled by WMIN" water
H
angles/deg distances/ A H-0-H O-H...X0-H H-..X- O...XNaC1.2H20 (Calc -228.4 kcal/mol)
I I
147.5
0.9937
2.484
3.365
167.7 177.8
1.0029 1.0035
2.236 2.195
3.223 3.198
172.8
1.0045
2.197
3.196
105.5 2 1
2
106.0 2
NaBr.2H20 (Calc -21 8.5; Expt -207.6 kcal/mol) I 1
138.7
0.9902
2.772
3.576
169.8 176.3
1.0011 1.0005
2.376 2.371
3.366 3.370
170.4
1.0038
2.325
3.319
105.5
2 1 2
105.9 2
NaI.2H20 (Calc -208.8; Expt -197.0 kcal/mol) 1 1
149.9
0.948
2.720
3.615
177.5 176.1
0.9980 0.9988
2.644 2.654
3.641 3.651
170.4
1.0010
2.598
3.589
105.6 2 1 106.6 2
Lil.3H20 (Calc -233.4; Expt -232.2 kcal/mol) 1
1,2,3
120.6
0.9846
3.080
3.680
142.1
0.9896
2.8485
3.680
106.6 2
"The lattice energies of the modeled hydrate, using flexible water molecules, are given in parentheses, as are the experimental values. the approach that the computer modeling at the present stage is most useful if it successfully predicts the hydrogen atom positions on the basis of known heavy-atom positions, since this is the information that is most often not available in X-ray structure determinations. The lattice energy calculated by WMIN when a rigid water molecule is used is -227.7 kcal/mol, and when a stretching and bending water molecule is used, a lattice energy of -228.4 kcal/mol is obtained; see Table I. Ideally, we would have liked to use force constants that gave the known vibrational frequencies, but this proved unrealistic when using such a simple force field, and also because we have no a priori way of knowing which O H frequency corresponds to which 0 - H bond. Nevertheless, a slightly smaller stretching force constant of 1100 kcal A-2 mol-l gave stretching frequencies in the general region of the experimental stretching frequencies. The lattice energy then obtained was barely altered at -229.4 kcal/mol. No experimental lattice energy is available for this substance but, based on the results of the other three hydrates which we have studied, this value is probably correct to within 5%. The geometries of the water molecules found for this hydrate are given in Table I for the stretching-bending model. The experimental 0 - H frequencies of isotopically dilute HDO in the hydrate at -195 'C are 3530, 3434, 3426, and 3416 cm-l (and the 0-D stretching frequencies are 2607, 2536, 2531, and 2523 c ~ n - ~ )There . ' ~ is an excellent linear least-squares correlation between the calculated 0 - H bond lengths in Table I and the observed 0-H or 0-D stretching frequencies given above. The correlation would allow prediction of an 0-H bond length to about 0.0001 A from an 0 - H or 0-D frequency-had the correlation parameters been known in advance! No particular significance can be attached to this, however, since the grouping of the 0 - H bond lengths into three similar values and one isolated value makes a linear correlation almost inevitable. Further, we have ordered the 0 - H bond lengths with the frequencies without having direct experimental evidence for doing so. On the other hand, this behavior does coincide with the common belief that strong hydrogen bonds occur in conjunction with long 0 - H bonds and weaker hydrogen bonds occur with shorter 0-H bonds. From Table I we see that the three stronger hydrogen bonds have fairly
linear O-H-CI- angles, while the weak hydrogen bond is significantly bent at 147.5'. The quality of these results suggests that it is appropriate to estimate the unknown enthalpy of formation of NaC1.2H20 from the calculated lattice energy. Reversing the Born-Haber procedure described earlier, we obtain APf(NaCI-2H20,298K, 1 atm) = -255.9 kcal/mol (f5%). This fits well into the sequence of standard enthalpies of formation of the set of sodium halide dihydrates, viz., NaC1.2H20, -255.9 kcal/mol; NaBr.2H20, -227.3 kcal/mol; and NaI.2H20, -21 1.1 kcal/mol. NaBr.ZH20 NaBr.2H20 is isomorphic with NaCb2H 0. It has the space group P2,/c with a = 6.575 A, b = 10.456 and c = 6.776 A; /3 = 113.38'; and 2 = 4,22323which parameters were used in the present EPEN/2 modeling. Again, the cation-cation distances in the hydrate are much shorter than in the dehydrated salt: the shortest Na-Na distances are 3.595 and 5.978 A, respectively. The lattice energies obtained with a rigid and a flexible water molecule were -218.3 and -218.5 kcal/mol, respectively; the experimental value is -207.6 kcal/mol, i.e., an agreement to within 5%. The calculated geometries of the water molecules are given in Table I. There is a fair correlation of the calculated 0 - H bond lengths with the experimental 0 - D stretching frequencies of isotopically dilute HDO in the hydrate: 2608, 2544, 2532, and 2522 cm-I. The least-squares and WMIN-calculated 0-H bond lengths agree to within 0.0004 A, but the correlation with the infrared frequencies has a different slope from that for sodium chloride dihydrate. The H-0-H bond angles found are about the same as in NaC1.2H20. The 0-H bond lengths given by the neutron diffraction study of the hydrate24 are 0.938, 0.957 and 0.955, 0.958 A, but the hydrogen positions are actually uncertain "because of the inadequate treatment of the vibrations in the analysis of the diffraction data" and because "a discussion of the internal geometry of the water molecule will have to be postponed until a more realistic description of the vibrational motions has been obtained". However, the presence of a weak hydrogen bond and three similar stronger ones was confirmed and agrees well with the infrared results and the present computer modeling.
1,
NaI.2H20 NaI.2H20 is not isomorphic with the two previous hydrates. It has the triclinic space group P1 with a = 7.161 A, b = 6.035 A, and c = 7.282 A; a = 81.2'; /3 = 118.7'; y = 115.3'; and Z = 4,25 which parameters were used in the present EPEN/2 modeling. The lattice energies obtained with a rigid and a flexible water molecule were -208.5 and -208.8 kcal/mol, respectively; the experimental value is -197.0 kcal/mol, Le., an agreement to within 6%. The geometries of the water molecules are given in Table I. Again, there are three hydrogen bonds of comparable strength, with nearly linear 0-He-I- angles, and one weaker hydrogen bond with a nonlinear 0-H.-I- angle of 149.9'. The OD stretching frequencies of the isotopically dilute HDO in the hydrate at -195 OC are 2579 cm-l 2546 cm-I, and an unresolved doublet at 2541 cm-'. Again, there is a fair correlation between the calculated 0-H bond lengths and the infrared frequencies; the least-squares and wMrN-calculated 0-H bond lengths agree to better than 0,001 A, but this is strongly influenced by the unresolved doublet, the single value of which was taken for two frequencies. No neutron diffraction study has been reported and the X-ray study does not give the hydrogen positions. A single-crystal NMR study26gives the H-0-H bond angles as 112' and 115O, but these (22) Culot, J. P.; Piret, P.; Van Meerssche, M. Bull. Sor. Fr. Mineral. Crisfallogr. 1962, 85, 282. (23) Haaf, W. R.; Carpenter, G. B. Acta Crystallogr. 1964, 17, 730. (24) Tegenfeldt, J.; Tellgren, R.; Pedersen, B.; Olovsson, I. Acta Crystallogr. 1979, B35, 1679. (25) Verbist, J.; Piret, P.; Van Meerssche, M. Bull. SOC.Fr. Mineral. Crisfallogr. 1970, 93, 509. (26) Ladd, M. F. C. Z . Kristallogr. 1968, 126, 147.
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values are based on assumed 0-H bond lengths of 0.96 A.
LiI.3H20 The crystal structure of LiI.3H20 was examined in 1928 by H e n d r i ~ k swho , ~ ~ reported an hexagonal unit cell with a = 7.45 A, c = 5.45 A, Z = 2, space group P63mc. Westz8 reexamined the structure in 1934 and confirmed the space group and derived the approximate atomic coordinates for iodide, oxygen, and lithium. In this structure, the water molecules lie within mirror planes of symmetry and are coordinated to two lithium cations and, through hydrogen bonds, to two iodide anions. An infrared study of the 0-D stretching frequencies of isotopically dilute HDO in the hydrate29showed nonequivalence of the two hydrogen atoms of each water molecule, so that it was proposed that the space group, including the hydrogens, was one of lower symmetry, P63. This space group was used in the present modeling. The splitting of the fundamentals of isotopically dilute HDO also indicates that the water molecules are distorted such that each forms one strong (and presumably nearly linear) 0-H-I- hydrogen bond and one weak (presumably nonlinear) hydrogen bond. The lattice energies obtained with rigid and with flexible water molecules were -229.1 and -233.4 kcal/mol, respectively; the experimental value is -232.2 kcal/mol, in remarkable agreement. The geometries of the water molecules are given in Table I. We see that the 0-H bonds are not of the same length, which agrees with the infrared result which, at -175 OC, gave only two 0-D absorption^,^^ 2642 and 2529 cm-I, showing that the three water molecules are each asymmetric but equivalent by symmetry. The 2642-cm-' peaks corresponds to an extremely weak hydrogen bond. The WMIN calculations reveal that stronger of the two hydrogens bonds is rather nonlinear at 142O, while the weaker is extremely nonlinear at 120°, which conforms with the infrared results.
Discussion Computer modeling of chemical structures is now an established procedure, giving information and insight that cannot easily be obtained by experimental means. However, although a great deal of modeling has been done on simple ionic crystals, little or none has been done on their hydrates or solvates. Recently, modeling of the simple alkali-metal halides6 showed how effective the simple exp(-6) plus Coulombic potential can be in reproducing lattice constants and lattice energies in stable and unstable structures. The extension to the crystalline hydrates of these alkali-metal halides is a natural one, since the EPEN/2 parameters for water (27) Hendricks, S. Am. J . Sci. 1928, 15, 403. (28) West, C. D.Z.Kristallogr. 1934, 88, 198. (29) Brink, G.; Falk, M . Can. J . Chem. 1971, 49, 347.
Brink and Glasser are of the same form and well established, but the assumption of transferability of the parameters needed confirmation. The present computer modeling of four alkali-metal hydrates, for which the structures (of all four) and lattice energies (of three) are known and infrared results on the isotopically dilute HDO systems are available, have shown that the EPEN/2 potential yields realistic and informative results. It should be stressed that the parameters for the EPEN/2 potential for the alkali-metal and halogen ions were established quite indepndently of those for the water molecules and that the transferability properties among the alien systems of water molecules and alkali-metal and halide ions have here been demonstrated by the satisfactory values of the calculated lattice energies. Obviously, better potentials could be established for water within this specific environment, but this would require the generally absent data on the geometries of the water molecules in these systems; further refinement of the potentials might then allow modeling of the complete structure. However, even the situation explored in this work, where the heavy atoms were fixed in their X-ray established positions, should still be of interest to crystallographers trying to establish hydrogen atom positions. It might also be of interest to those needing lattice energies and other thermodynamic quantities for which information is not otherwise available, as has been the case for NaC1.2Hz0. The reduction in lattice energy when the alkali-metal halide forms its hydrate (for the four hydrates studied here) is calculated to be 18-20 kcal/mol water (or 16-18 kcal/mol water, if the three available experimental lattice energies are used). This incorporation energy is larger than the 1 1.1 kcal/mol for the condensation of water (vapor to ice). As indicated earlier, the effect of incorporating the water in the salt is to cause the ionic structure to become more compact, with the cations significantly closer together than in the dehydrate. Modeling is now possible of water molecules in all those alkali-metal halide hydrates whose crystal structures are known. Additional refinements to the potential function for water in a strong ionic environment should improve the reliability and detail of the structural and thermodynamic information obtained from such modeling. It should also be possible to extend these methods to examination of the alkali-metal halide solvates in general. Acknowledgment. We thank the Foundation for Research Development for financial assistance. We acknowledge with gratitude the use in this work of the computer program WMIN written by W. R. Busing, Oak Ridge National Laboratory, Oak Ridge, TN. Registry No. NaCI.2H20, 23724-87-0; NaBr.ZH,O, 13466-08-5; NaI.2H20, 1351 7-06-1; LiI.3H20, 7790-22-9.
