Merck molecular force field. II. MMFF94 van der Waals and electrostatic parameters for intermolecular interactions

Journal of Computational Chemistry

Volumn 17, Issue 5-6, 1996, Pages 520-552

  Halgren, Thomas A ^a  

^a MERCK RESEARCH LABORATORIES   (United States)

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EID: 0011134241     PISSN: 01928651     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1096-987X(199604)17:5/6<520::AID-JCC2>3.0.CO;2-W     Document Type: Article

References (126)

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36. 2, but this fractional foreshortening is the same as is used for C - H bonds: cf. J.-H. Lu and N. L. Allinger, J. Am. Chem. Soc., 111, 8576-8582 (1989). The MM3 calculations were performed using a modified version of OPTIMOL/MM2X (ref. 18).
37. Like the MM3 calculations, the CHARMm calculations were performed using OPTIMOL. While these calculations were performed with the vdW parameters distributed with QUANTA Version 3.2, we note that the QUANTA 3.3, QUANTA 3.4, and QUANTA 4.0 values for these parameters are unchanged.
38. W. J. Hehre, L. Random, P. v. R Schleyer, and J. A. Pople, Ab Initio Molecular Orbital Theory, Wiley, New York, 1986, Chapter 4. The 6-31G* and 6-31 + G** basis sets are also known as 6-31G(d) and 6-31 + G(p,d), respectively.
39. For the most part, these systems correspond to those listed in Table I of ref. 1.
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48. PROBE is a computer program used to derive molecular-mechanics parameters in least-squares fits to data obtained from ab initio calculations. PROBE was created for the Biosym Consortium on Potential Energy Functions by Biosym Technologies, Inc. (San Diego, CA) (cf. ref. 79).
49. K. B. Wiberg, R. F. W. Bader, and C. D. H. Lau, J. Am. Chem. Soc., 109, 1001-1012 (1987).
50. Cf. G. Karlström, P. Linse, A. Wallqvist, and B. Jönsson, J. Am. Chem. Soc., 105, 3777-3782 (1983). A similar value of ca. 0.143 on hydrogen in benzene can be inferred from the structure of benzene and from the data and analysis in M. R. Battaglia, A. D. Buckingham, and J. H. Williams, Chem. Phys. Lett., 78, 421-423 (1981).
51. Cf. G. Karlström, P. Linse, A. Wallqvist, and B. Jönsson, J. Am. Chem. Soc., 105, 3777-3782 (1983). A similar value of ca. 0.143 on hydrogen in benzene can be inferred from the structure of benzene and from the data and analysis in M. R. Battaglia, A. D. Buckingham, and J. H. Williams, Chem. Phys. Lett., 78, 421-423 (1981).
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55. That is, a force field like MMFF which does not displace the vdW center along the bond away from the hydrogen nucleus would have to use a compensatingly smaller vdW radius to obtain a similar interaction between vdW centers in roughly head-on contacts.
56. W. L. Jorgensen and J. Tirado-Rives, J. Am. Chem. Soc., 110, 1657-1666 (1988).
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60. These calculations used Gaussian 88 (ref. 24) and employed the MP2 model for electron correlation in conjunction with 6-31G basis sets supplemented by single diffuse Gaussian p functions on H and He (exponents 0.20, 0.30) and d functions on F (exponent 0.35).
61. The nonbonded and other MMFF94 parameter files are included in Appendix B in the Supplementary Material for paper I (ref. 1).
62. The MM2X parameters are provided as supplementary material in ref. 18.
63. The supplementary material for this article (Appendix A), can be accessed on the Internet (see footnote * on the first page of this article).
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71. These results are for dimers between "MMFF water" and acetamide constructed in the same manner as those reported in ref. 35. Specifically, we, too, had to restrict the water molecule in the anti conformer to lie in the plane of the carbonyl group to prevent collapse to the syn form, in which the oxygen of the water molecule interacts with a hydrogen on the amide nitrogen to form a second hydrogen bond (cf. Fig. 4 of ref. 35).
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77. (a) J. Mullay, J. Comput. Chem., 12, 369-375 (1991);
78. (b) J. Mullay, J. Comput. Chem., 9, 399-405 (1988).
79. A. K. Rappé and W. A. Goddard III, J. Phys. Chem., 95, 3358-3363 (1991).
80. The Gasteiger charges, which do not depend on the geometry, were obtained using the implementation of this method in SYBYL, Version 5.5 (Tripos Associates, Inc., St. Louis, MO).
81. The QEq charges were obtained for MP2/6-31G*-optimized geometries using the QEq implementation in CERIUS (Molecular Simulations, Inc., Burlington, MA) for MP2/6-31G* optimized geometries.
82. This objection applies particularly strongly to an iterative approach like that employed by Mortier (ref. 61). Rappé and Goddard (ref. 63) suggest in their manuscript title that their approach is applicable for molecular-dynamics simulations, but present no algorithm for computing charge derivatives analytically. Moreover, their method as described employs a matrix inversion which has a higher power dependence on system size than does the calculation of the molecular-mechanics energy function itself.
83. W. L. Jorgensen and J. Gao, J. A. Chem. Soc., 110, 4212-4216 (1988).
84. G. Del Re, J. Chem. Soc., 4031 (1958); G. Del Re, B. Pullman, and T. Yonezawa, Biochim. Biophys. Acta, 75, 153 (1963).
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86. (a) R. J. Abraham, G. H. Grant, I. S. Haworth, and P. E. Smith, J. Computer-Aided Mol. Design, 5, 21-39 (1991);
87. (b) R. J. Abraham and P. E. Smith, J. Computer-Aided Mol. Design, 3, 175-187 (1989).
88. This judgment is supported by the preliminary results of attempting to apply a charge equilibration scheme to heteroaromatic compounds: M. D. Miller and T. A. Halgren (unpublished research).
89. ref|. By weighting the squared deviations in direction by the product of the force-field calculated and (scaled) reference HF/6-31G* dipole moments and by computing the angle between the dipole moments in a manner which yields a finite value even when one or both dipole moments vanish, this formula ensures that the weighted rms deviation mainly reflects differences in direction in cases in which the dipole moment is relatively large in magnitude. In particular, it keeps large differences in direction from dominating the comparison when either of the dipole moments is small in magnitude.
90. Using unscaled HF/6-31G* dipole moments, MM2X gives an rms error of 0.58 D in the dipole magnitudes. The rms deviation for dipole directions is of course unaffected.
91. M. J. Frisch, J. A. Pople, and J. E. Del Bene, J. Phys. Chem., 89, 3664-3669 (1985).
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93. Double-zeta plus polarization (DZP) basis sets: T. H. Dunning Jr., J. Chem. Phys., 53, 2823-2833 (1970); T. H. Dunning Jr. and P. J. Hay, In Methods of Electronic Structure Theory, H. F. Schaefer III, Ed., Plenum Press, New York, 1977, Vol. 2, pp. 1-27. The polarization exponents were those defined in ref. 3, i.e., 0.80 for hydrogen, 0.60, 0.85, 1.20, and 1.65 for C, N, O, and F, and 0.50, 0.65 and 0.80 for P, S, and Cl.
94. Double-zeta plus polarization (DZP) basis sets: T. H. Dunning Jr., J. Chem. Phys., 53, 2823-2833 (1970); T. H. Dunning Jr. and P. J. Hay, In Methods of Electronic Structure Theory, H. F. Schaefer III, Ed., Plenum Press, New York, 1977, Vol. 2, pp. 1-27. The polarization exponents were those defined in ref. 3, i.e., 0.80 for hydrogen, 0.60, 0.85, 1.20, and 1.65 for C, N, O, and F, and 0.50, 0.65 and 0.80 for P, S, and Cl.
95. These calculations used the Lennard-Jones 9-6 potential for intermolecular vdW interactions, and used partial charges computed for use in intermolecular interactions (cf. ref. 18).
96. W. L. Jorgensen and J. Gao, J. Phys. Chem., 90, 2174-2182 (1986).
97. J. R. Maple, M.-J. Hwang, T. P. Stockfish, U. Dinur, M. Waldman, C. S. Ewig, and A. T. Hagler, J. Comput. Chem., 15, 161-182 1994; M.-J. Hwang, T. P. Stockfish, and A. T. Hagler, J. Am. Chem. Soc., 116, 2515-2525 (1994).
98. J. R. Maple, M.-J. Hwang, T. P. Stockfish, U. Dinur, M. Waldman, C. S. Ewig, and A. T. Hagler, J. Comput. Chem., 15, 161-182 1994; M.-J. Hwang, T. P. Stockfish, and A. T. Hagler, J. Am. Chem. Soc., 116, 2515-2525 (1994).
99. E. D. Stevens and P. Coppens, Acta Cryst., B36, 1864-1876 (1980).
100. R. G. Delaplane and J. A. Ibers, Acta Cryst., B25, 2423-2437 (1969).
101. For a pertinent comparison of OPLS and earlier Lifson et al. (ref. 8a) force-field results for liquid-phase simulations, see: W. L. Jorgensen and C. J. Swenson, J. Am. Chem. Soc., 107, 569-578 (1985). Consistent with the present arguments, the Hagler-Lifson force field, which was derived using a similar energy-minimization methodology, gave longer energy-minimized hydrogen bond lengths for gas-phase dimers than Jorgensen and Swenson found would allow OPLS to correctly reproduce liquid-phase properties of simple amides.
102. U. Dinur and A. T. Hagler, J. Am. Chem. Soc., 111, 5149-5151 (1989).
103. H. S. Sun, S. J. Mumbry, J. R. Maple, and A. T. Hagler, J. Am. Chem. Soc., 116, 2978-2987 (1994).
104. See, for example, the "vdW and hydrogen bonding" parameters listed in Table I of: J.-H. Lii and N. L. Allinger, J. Comput. Chem., 12, 186-199 (1991).
105. J.-H. Lii and N. L. Allinger, J. Comput. Chem., 12, 186-199 (1991).
106. L. A. Curtiss, D. J. Frurip, and M. Blander, J. Chem. Phys., 71, 2703 (1979).
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108. W. D. Cornell, P. Cieplak, C. I. Bayly, I. R. Could, K. M. Merz Jr., D. M. Ferguson, D. C. Spellmeyer, T. Fox, J. W. Caldwell, and P. A. Kollman, J. Am. Chem. Soc., 117, 5179-5197 (1995).
109. MM2 and MM3 allow contributions from induced dipoles to be included in the calculation (N. L. Allinger, personal communication). This feature does not, however, appear to be used in routine work.
110. (a) U. Dinur and A. T. Hagler, J. Comput. Chem., 16, 154-170 (1994);
111. (b) U. Dinur and A. T. Hagler, J. Chem. Phys., 91, 2949-2958 (1989);
112. (c) U. Dinur and A. T. Hagler, J. Chem. Phys., 91, 2959-2970 (1989).
113. See, for example: (a) U. Dinur, J. Comput. Chem., 12, 91-105 (1991); (b) U. Dinur, J. Comput. Chem., 12, 469-486 (1991); (c) U. Dinur, J. Phys. Chem., 94, 5669-5671 (1990).
114. See, for example: (a) U. Dinur, J. Comput. Chem., 12, 91-105 (1991); (b) U. Dinur, J. Comput. Chem., 12, 469-486 (1991); (c) U. Dinur, J. Phys. Chem., 94, 5669-5671 (1990).
115. See, for example: (a) U. Dinur, J. Comput. Chem., 12, 91-105 (1991); (b) U. Dinur, J. Comput. Chem., 12, 469-486 (1991); (c) U. Dinur, J. Phys. Chem., 94, 5669-5671 (1990).
116. H. Umeyama and K. Morokuma, J. Am. Chem. Soc., 99, 1316-1332 (1977), and references therein. This article indicates that charge transfer contributes ̃ 2 kcal/mol to the interaction energy for the water dimer, a quantity smaller than the electrostatic stabilization of ̃ 8 kcal;mol but by no means negligible. The authors also note that charge transfer appears to play a larger role in weaker hydrogen-bonding complexes, and we think it possible that this may particularly be true for hydrogen bonds to such higher row atoms as sulfur.
117. See, for example: (a) G. Corongiu, M. Migliore, and E. Clementi, J. Chem. Phys., 90, 4629 (1989); (b) L. X. Dang, J. E. Rice, J. Caldwell, and P. A. Kollman, J. Am. Chem. Soc., 113, 2481-2486 (1991), and references therein; (c) M. Sprik, J. Phys. Chem., 95, 2283-2291 (1991), and references therein; (d) S.-B. Zhu, S. Yao, J.-B. Zhu, S. Singh, and G. W. Robinson, J. Phys. Chem., 95, 6211-6217 (1991); (e) S. W. Rick, S. J. Stuart, and B. J. Berne, J. Chem. Phys., 101, 6141-6156 (1994); (f) D. N. Bernardo, Y. Ding, K. Krough-Jespersen, and R. M. Levy, J. Phys. Chem., 98, 4180-4187 (1994).
118. See, for example: (a) G. Corongiu, M. Migliore, and E. Clementi, J. Chem. Phys., 90, 4629 (1989); (b) L. X. Dang, J. E. Rice, J. Caldwell, and P. A. Kollman, J. Am. Chem. Soc., 113, 2481-2486 (1991), and references therein; (c) M. Sprik, J. Phys. Chem., 95, 2283-2291 (1991), and references therein; (d) S.-B. Zhu, S. Yao, J.-B. Zhu, S. Singh, and G. W. Robinson, J. Phys. Chem., 95, 6211-6217 (1991); (e) S. W. Rick, S. J. Stuart, and B. J. Berne, J. Chem. Phys., 101, 6141-6156 (1994); (f) D. N. Bernardo, Y. Ding, K. Krough-Jespersen, and R. M. Levy, J. Phys. Chem., 98, 4180-4187 (1994).
119. See, for example: (a) G. Corongiu, M. Migliore, and E. Clementi, J. Chem. Phys., 90, 4629 (1989); (b) L. X. Dang, J. E. Rice, J. Caldwell, and P. A. Kollman, J. Am. Chem. Soc., 113, 2481-2486 (1991), and references therein; (c) M. Sprik, J. Phys. Chem., 95, 2283-2291 (1991), and references therein; (d) S.-B. Zhu, S. Yao, J.-B. Zhu, S. Singh, and G. W. Robinson, J. Phys. Chem., 95, 6211-6217 (1991); (e) S. W. Rick, S. J. Stuart, and B. J. Berne, J. Chem. Phys., 101, 6141-6156 (1994); (f) D. N. Bernardo, Y. Ding, K. Krough-Jespersen, and R. M. Levy, J. Phys. Chem., 98, 4180-4187 (1994).
120. See, for example: (a) G. Corongiu, M. Migliore, and E. Clementi, J. Chem. Phys., 90, 4629 (1989); (b) L. X. Dang, J. E. Rice, J. Caldwell, and P. A. Kollman, J. Am. Chem. Soc., 113, 2481-2486 (1991), and references therein; (c) M. Sprik, J. Phys. Chem., 95, 2283-2291 (1991), and references therein; (d) S.-B. Zhu, S. Yao, J.-B. Zhu, S. Singh, and G. W. Robinson, J. Phys. Chem., 95, 6211-6217 (1991); (e) S. W. Rick, S. J. Stuart, and B. J. Berne, J. Chem. Phys., 101, 6141-6156 (1994); (f) D. N. Bernardo, Y. Ding, K. Krough-Jespersen, and R. M. Levy, J. Phys. Chem., 98, 4180-4187 (1994).
121. See, for example: (a) G. Corongiu, M. Migliore, and E. Clementi, J. Chem. Phys., 90, 4629 (1989); (b) L. X. Dang, J. E. Rice, J. Caldwell, and P. A. Kollman, J. Am. Chem. Soc., 113, 2481-2486 (1991), and references therein; (c) M. Sprik, J. Phys. Chem., 95, 2283-2291 (1991), and references therein; (d) S.-B. Zhu, S. Yao, J.-B. Zhu, S. Singh, and G. W. Robinson, J. Phys. Chem., 95, 6211-6217 (1991); (e) S. W. Rick, S. J. Stuart, and B. J. Berne, J. Chem. Phys., 101, 6141-6156 (1994); (f) D. N. Bernardo, Y. Ding, K. Krough-Jespersen, and R. M. Levy, J. Phys. Chem., 98, 4180-4187 (1994).
122. See, for example: (a) G. Corongiu, M. Migliore, and E. Clementi, J. Chem. Phys., 90, 4629 (1989); (b) L. X. Dang, J. E. Rice, J. Caldwell, and P. A. Kollman, J. Am. Chem. Soc., 113, 2481-2486 (1991), and references therein; (c) M. Sprik, J. Phys. Chem., 95, 2283-2291 (1991), and references therein; (d) S.-B. Zhu, S. Yao, J.-B. Zhu, S. Singh, and G. W. Robinson, J. Phys. Chem., 95, 6211-6217 (1991); (e) S. W. Rick, S. J. Stuart, and B. J. Berne, J. Chem. Phys., 101, 6141-6156 (1994); (f) D. N. Bernardo, Y. Ding, K. Krough-Jespersen, and R. M. Levy, J. Phys. Chem., 98, 4180-4187 (1994).
123. R. Czerminski, J. L. Banks, and T. A. Halgren (unpublished research). Currently, a version of CHARMm that supports the earlier and less widely parameterized MMFF93 force field (refs. 2-4) is available from Molecular Simulations, Inc. (San Diego, CA). However, while the local Merck code employs MMFF94, arrangements for including MMFF94 in the distributed MSI version have not yet been concluded.
124. P. S. Shenkin and T. A. Halgren (work in progress). The MacroModel program suite and its BatchMin module, developed in the laboratories of Prof. Clark Still, are available from Columbia University (New York, NY).
125. (a) J. L. Banks, R. Czerminski, and T. A. Halgren (work in progress);
126. (b) B. L. Bush, J. L. Banks, and T. A. Halgren (work in progress).