J. Phys. Chem. B 2000, 104, 8089
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COMMENTS Comment on “Crystal Structure Prediction by Global Optimization as a Tool for Evaluating Potentials: Role of the Dipole Moment Correction Term in Successful Predictions” Bouke P. van Eijck* and Jan Kroon Department of Crystal and Structural Chemistry, BijVoet Center for Biomolecular Research, Utrecht UniVersity, Padualaan 8, 3584 CH Utrecht, The Netherlands ReceiVed: April 14, 2000 A few years ago, we tried to answer the question of how to calculate the Coulomb energy of polar crystals.1 In a recent paper,2 Pillardy et al. suggested that our recommendation might lead to erroneous crystal structure predictions. Briefly, the issue is as follows. The energy, U, of a polar crystal can be written as follows:
U ) UEwald + Uouter 0 2 where UEwald is the result of an Ewald summation (without the 0 is a term that depends on the shape of h ) 0 term3) and Uouter 2 the crystal, corresponding to the presence of a surface charge. For a crystal with spherical or cubic external form, the second term is equal to 2πp2/(3V), where p is the dipole moment of one unit cell and V is its volume. The question under discussion is whether such a term should be included in the energy calculation. Our point of view was and is that the best approach is to omit the surface term. Otherwise, no meaningful energy calculations would be possible without specifying the crystal form, and tabulation of thermodynamic data would be precluded for polar crystals. One would like to have very convincing arguments before accepting that situation. Furthermore, there are reasons to believe that, under most practical circumstances, external charges will accumulate on the crystal to annul the surface charge (“tin-foil boundary conditions”). In cases where such conditions might not exist, the crystal could acquire an external form with minimal energy for which the contribution of the surface term vanishes again. Pillardy et al. argue that the last argument is only valid for limiting shapes of the crystal, such as an extremely long and thin needle. This is true, but for less extreme forms, a considerable reduction in surface energy would still be attainable. Their argument against tin-foil boundary conditions is (p 911) that “... the crystal can therefore no longer be treated computationally in isolation from that medium”. It is, in fact, the other way around: these conditions are necessary to be able to perform energy calculations without information about the external shape of the crystal, which is surely influenced by the outside medium. The crystal predictions reported by Pillardy et al. were meant to provide support for their opinion, but they do nothing of that kind. The main argument appears to be given on pp 917 and 920: if the surface term is not included, many hypothetical structures with large cell dipoles become feasible. Some of these * Author to whom correspondence should be addressed. E-mail: vaneyck@chem. uu.nl.
structures have a lower energy than the experimental structure, from which it was concluded that the surface term cannot be omitted. It is our opinion that this conclusion would only be justified if at least one polar structure could be found with an energy appreciably lower than the best nonpolar structure, but that is not the case. Inspection of Tables 3-6 of ref 2 shows that the best polar structure is at most 0.22 kcal/mol below the best hypothetical nonpolar structure (maleic anhydride). In comparison with the experimental nonpolar structures, the best polar structure is at most 0.62 kcal/mol lower in energy (imidazole). However, for this substance, a hypothetical nonpolar structure was found with essentially the same low energy (-20.12 versus -20.13 kcal/mol). We fail to see why that structure should pose no problem, whereas “the existence of very low-energy structures with a high dipole moment ... suggests that calculating the electrostatic energy using the Ewald summation alone is incorrect” (p 920). Moreover, these lowenergy structures occur only in the DISCOVER force field, which the authors judge to be less successful. On the other hand, in the two cases where the experimental crystal structure is polar (Tables 7 and 8), the global minimum is up to 1.12 kcal/mol below the experimental structure if the surface term is included (formic acid, DISCOVER). Upon omission of the surface term, the largest energy difference drops to 0.64 kcal/mol (pyrimidine, AMBER). Thus, omission of the surface term now leads to an improvement in the crystal structure predictions. However, Pillardy et al. prefer to explain the situation by assuming that the force fields are not adequate for these two molecules (p 921). The main point is that energy differences of less than 1 kcal/ mol are outside the level of accuracy expected for the force fields that were used and that the crystal structure predictions discussed here simply do not allow the issue in question to be settled. That line of reasoning can only be convincing for large energy differences. In our previous paper,1 the case of glycine was mentioned, for which the γ polymorph would have a relative energy of over 30 kcal/mol with respect to the R and β forms if the surface term were included (or, equivalently, if the energy were calculated simply with a large cutoff radius). It is unlikely that such a high-energy form would be observable. Ewald calculation without the surface term brings the energies of the three polymorphs together within 1 kcal/mol.4 Except for such an extreme case, one should not take the fact that an experimental structure has the lowest energy in a certain force field as proof that “the predictions were successful” (p 920) or that “the potential is correct” (p 909). We have encountered several cases in which an arguably better force field led to results that were less satisfactory in that respect. Acknowledgment. We are grateful to Wijnand Mooij for numerous helpful discussions. References and Notes (1) van Eijck, B. P.; Kroon, J. J. Phys. Chem. B 1997, 101, 1096. (2) Pillardy, J.; Wawak, R. J.; Arnautova, Y. A.; Czaplewski, C.; Scheraga, H. A. J. Am. Chem. Soc. 2000, 122, 907. (3) Deem, M. W.; Newsam, J. M.; Sinha, S. K. J. Phys. Chem. 1990, 94, 8356. (4) Derissen, J. L.; Smit, P. H.; Voogd, J. J. Phys. Chem. 1977, 81, 1474.
10.1021/jp001434j CCC: $19.00 © 2000 American Chemical Society Published on Web 07/20/2000
