Merck molecular force field. I. Basis, form, scope, parameterization, and performance of MMFF94

Journal of Computational ChemistryVolume 17, Issue 5-6 p. 490-519 Merck molecular force field. I. Basis, form, scope, parameterization, and performance of MMFF94 Thomas A. Halgren, Corresponding Author Thomas A. Halgren Department of Molecular Design and Diversity, Merck Research Laboratories, Rahway, New Jersey 07065Department of Molecular Design and Diversity, Merck Research Laboratories, Rahway, New Jersey 07065Search for more papers by this author Thomas A. Halgren, Corresponding Author Thomas A. Halgren Department of Molecular Design and Diversity, Merck Research Laboratories, Rahway, New Jersey 07065Department of Molecular Design and Diversity, Merck Research Laboratories, Rahway, New Jersey 07065Search for more papers by this author First published: April 1996 https://doi.org/10.1002/(SICI)1096-987X(199604)17:5/6<490::AID-JCC1>3.0.CO;2-PCitations: 1,396AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onEmailFacebookTwitterLinkedInRedditWechat Abstract This article introduces MMFF94, the initial published version of the Merck molecular force field (MMFF). It describes the objectives set for MMFF, the form it takes, and the range of systems to which it applies. This study also outlines the methodology employed in parameterizing MMFF94 and summarizes its performance in reproducing computational and experimental data. Though similar to MM3 in some respects, MMFF94 differs in ways intended to facilitate application to condensed-phase processes in molecular-dynamics simulations. Indeed, MMFF94 seeks to achieve MM3-like accuracy for small molecules in a combined “organic/protein” force field that is equally applicable to proteins and other systems of biological significance. A second distinguishing feature is that the core portion of MMFF94 has primarily been derived from high-quality computational data—ca. 500 molecular structures optimized at the HF/6-31G* level, 475 structures optimized at the MP2/6-31G* level, 380 MP2/6-31G* structures evaluated at a defined approximation to the MP4SDQ/TZP level, and 1450 structures partly derived from MP2/6-31G* geometries and evaluated at the MP2/TZP level. A third distinguishing feature is that MMFF94 has been parameterized for a wide variety of chemical systems of interest to organic and medicial chemists, including many that feature frequently occurring combinations of functional groups for which little, if any, useful experimental data are available. The methodology used in parameterizing MMFF94 represents a fourth distinguishing feature. Rather than using the common “functional group” approach, nearly all MMFF parameters have been determined in a mutually consistent fashion from the full set of available computational data. MMFF94 reproduces the computational data used in its parameterization very well. In addition, MMFF94 reproduces experimental bond lengths (0.014 Å root mean square [rms]), bond angles (1.2° rms), vibrational frequencies (61 cm−1 rms), conformational energies (0.38 kcal/mol/rms), and rotational barriers (0.39 kcal/mol rms) very nearly as well as does MM3 for comparable systems. MMFF94 also describes intermolecular interactions in hydrogen-bonded systems in a way that closely parallels that given by the highly regarded OPLS force field. © 1996 John Wiley & Sons, Inc. Supporting Information This article includes Supplementary Material available from the authors upon request or via the Internet at ftp.wiley.com/public/journals/jcc/suppmat/17/490 Please note: The publisher is not responsible for the content or functionality of any supporting information supplied by the authors. Any queries (other than missing content) should be directed to the corresponding author for the article. References 1 J. B. Hendrickson, J. Am. Chem. Soc., 83, 4537–4547 (1961). For an even earlier reference, see: F. H. Westheimer, in Steric Effect in Organic Chemistry, M. S. Newman, Ed., Wiley, New York, 1956, Chapter 12. 2 D. H. Wertz and N. L. Allinger, Tetrahedron, 30, 1579 (1974). 3(a) N. L. Allinger, J. Am. Chem. Soc., 89, 8127 (1977); (b) U. Burkert and N. L. Allinger, Molecular Mechanics; American Chemical Society, Washington, DC, 1982; (c) N. L. Allinger and Y. Yuh, QCPE, 12, 395 (1980). 4 N. L. Allinger, Y. H. Yuh, and J-H. Lii, J. Am. Chem. 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Boyd, Eds., VCH Publishers, New York, 1991, Vol. 2, pp. 99–163. See also: J. Palca, Nature, 322, 586 (1986). 16(a) 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). 17 N. L. Allinger, K. Chen, and J.-H. Lii, J. Comput. Chem. (this issue). 18(a) W. J. Hehre, L. Radom, P. v. R. Schleyer, and J. A. Pople, Ab Initio Molecular Orbital Theory, Wiley, New York, 1986, Chapter 6; (b) D. J. DeFrees, B. A. Levi, S. K. Pollack, W. J. Hehre, J. S. Binkley, and J. A. Pople, J. Am. Chem. Soc., 101, 4085–4089 (1979). 19 For a recent example of a significant experimental error which was corrected on the basis of information from ab initio calculations, including calculations at the MP2/6-31G* level used in the present work, see: B. J. Smith and L. Radom, J. Am. Chem. Soc., 112, 7525–7528 (1990). 20(a) See, for example: U. Dinur and A. T. Hagler, J. Chem. Phys., 91, 2949–2958 (1989); (b) U. Dinur and A. T. Hagler, J. Chem. Phys., 91, 2959–2970 (1989); (c) U. Dinur, J. Comput. Chem., 12, 91–105 (1991); (d) U. Dinur, J. Comput. Chem., 12, 469–486 (1991); (e) U. Dinur, J. Phys. Chem., 94, 5669–5671 (1990). 21(a) See, for example: 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); (g) For an early implementation of induced-dipole effects, see also L. Dosen-Micovic, D. Jeremic, and N. L. Allinger, J. Am. Chem. Soc., 105, 1716, 1723 (1983). 22 S. Dasgupta and W. A. Goddard III, J. Chem. Phys., 90, 7207–7215 (1989). 23 The MMFF94 parameters (Appendix B, Supplementary Material) are available in computer-readable form (see footnote * on first page of this article). 24 Part II: T. A. Halgren, J. Comput. Chem. (this issue). 25 Part III: T. A. Halgren, J. Comput. Chem. (this issue). 26 Part IV: T. A. Halgren and R. B. Nachbar, J. Comput. Chem. (this issue). 27 Part V: T. A. Halgren, J. Comput. Chem. (this issue). 28 This collaboration involved Prof. Martin Karplus (Harvard University) and Dr. Ryszard Czerminski and others of Molecular Simulations, Inc. (San Diego, CA). Currently, a version of CHARMm that supports the earlier and less widely parameterized MMFF93 force field (which lacks, e.g., the ability to recognize a number of the ionic species parameterized in ref. 27; see also refs. 25 and 26) is available from MSI. However, while the local Merck code for CHARMm employs MMFF94, arrangements for including MMFF94 in the distributed MSI version have not yet been concluded. 29 P. S. Shenkin and T. A. Halgren (work in progress). The MacroModel program suite and its BatchMin module, developed in the laboratories of Professor Clark Still, are available from Columbia University (New York, NY). 30 OPTIMOL has been developed and maintained by the author, but is based in part on computer code adapted from a public domain version of MM2 or written by Drs. R. B. Nachbar, B. L. Bush, G. M. Smith, E. F. Fluder Jr., and J. D. Andose of the Merck Research Laboratories. 31 Distribution of OPTIMOL by the Quantum Chemistry Program Exchange (Indiana University) would permit free usage of the program but would prohibit its commercialization. 32 T. A. Halgren and R. B. Nachbar (work in progress). 33 The Merck Index, 11th ed., S. Budavari, Ed., Merck & Co., Rahway, NJ, 1989. 34 Fine Chemicals Directory Handbook, Fraser Williams (Scientific Systems), London, 1983–1985. Connection tables distributed by Molecular Design Ltd., Hayward, CA. 35 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. (now Molecular Simulations, Inc.); cf. refs 15 and 16a. The derivation of MMFF94 used a 1991 version of PROBE. 36 See, for example, G. C. Lie and E. Clementi, Phys. Rev., 33A, 2679 (1986). 37 H. J. C. Berendsen, J. P. M. Postma, W. F. van Gunsteren, and J. Hermans, In Intermolecular Forces, B. Pullman, Ed., Reidel, Dordrecht, Holland, 1981, pp. 331–342. 38 B. M. Pettit, in Computer Simulation of Biomolecular Systems, W. F. van Gunsteren and P. K. Weiner, Eds., ESCOM, Leiden, 1989, pp. 94–100. 39 T. A. Halgren, J. Am. Chem. Soc., 114, 7827–7843 (1992). 40 W. J. Hehre, L. Radom, P. v. R. Schleyer, and J. A. Pople, Ab Initio Molecular Orbital Theory, Wiley, New York, 1986, Chapter 4. The 6-31G* basis sets also known as 6-31G(d). 41 A. D. MacKerell Jr. and M. Karplus, J. Phys. Chem., 95, 10559–10560 (1991); A. D. MacKerell Jr., J. Wiórkiewicz-Kuczera, and M. Karplus, J. Am. Chem. Soc. (in press). 42 M. J. Frisch, J. E. Del Bene, J. S. Binkley, and H. F. Schaeffer III, J. Chem. Phys., 84, 2279–2289 (1986). 43 T. A. Halgren, J. Am. Chem. Soc., 112, 4710–4723 (1990). 44 M. Orozco and F. J. Luque, J. Comput. Chem., 14, 881–894 (1993). 45 E. B. Wilson Jr., J. C. Decius, and P. C. Cross, Molecular Vibrations, Dover, New York, 1955, Chapter 4. 46 M. K. Holloway, J. M. Wai, T. A. Halgren, P. M. D. Fitzgerald, J. P. Vacca, B. D. Dorsey, R. B. Levin, W. J. Thompson, L. J. Chen, S. J. deSolms, N. Gaffin, A. K. Ghosh, E. A. Giuliani, S. L. Graham, J. P. Guare, R. W. Hungate, T. A. Lyle, W. M. Sanders, T. J. Tucker, M. Wiggins, C. M. Wiscount, O. W. Woltersdorf, S. D. Young, P. L. Darke, and J. A. Zugay, J. Med. Chem., 38, 305–317 (1995). 47 Note that this truncation does not lead to a “cubic-bend” catastrophe because the range of the angle is limited to 180° and the cubic-bend constant is relatively small. 48 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). 49 M. Waldman and A. T. Hagler, J. Comput. Chem., 14, 1077–1084 (1993). 50 Most of the ab initio calculations used in parameterizing MMFF were performed on the Merck Research Laboratories Cray YPM8i/4-128 supercomputer. 51 M. J. Frisch, M. Head-Gordon, H. B. Schlegel, K. Raghavachari, J. S. Binkley, C. Gonzalez, D. J. Defrees, D. J. Fox, R. A. Whiteside, R. Seeger, C. F. Melius, J. Baker, R. L. Martin, L. R. Kahn, J. J. P. Stewart, E. M. Fluder, S. Topiol, and J. A. Pople, Gaussian 88, Gaussian, Inc., Pittsburgh, PA, 1988, as modified at Merck for improved I/O performance by E. M. Fluder. 52 M. J. Frisch, M. Head-Gordon, G. W. Trucks, J. B. Foresman, H. B. Schlegel, K. Raghavachari, M. Robb, J. S. Binkley, C. Gonzalez, D. J. Defrees, D. J. Fox, R. A. Whiteside, R. Seeger, C. F. Melius, J. Baker, R. L. Martin, L. R. Kahn, J. J. P. Stewart, S. Topiol, and J. A. Pople, GAUSSIAN 90 (Revision J), Gaussian, Inc., Pittsburgh, PA, 1990. 53 M. L. Frisch, G. W. Trucks, M. Head-Gordon, P. M. W. Gill, M. W. Wong, J. B. Foresman, B. G. Johnson, H. B. Schlegel, M. A. Robb, E. S. Replogle, R. Gomperts, J. L. Andres, K. Raghavachari, J. S. Binkley, C. Gonzalez, R. L. Martin, D. J. Fox, D. J. Defrees, J. Baker, J. J. P. Stewart, and J. A. Pople, GAUSSIAN 92 (Revision C), Gaussian, Inc., Pittsburgh, PA, 1992. 54 Calculations at the MP2/6-31G* /MP2/6-31G* level are used as the basis of structure determination in the high-level composite G1 and G2 methods developed by Pople and coworkers; cf. L. A. Curtiss, K. Raghavachari, G. W. Trucks, and J. A. Pople, J. Chem. Phys., 94, 7221–7230 (1991), and references therein. Comparisons to experiment for a number of the molecules employed in the derivation of MMFF94 are summarized in A. St.-Amant, W. D. Cornell, T. A. Halgren, and P. A. Kollman, J. Comput. Chem., 16, 1483–1506 (1995). 55 See, for example, G. Chalasinski, M. M. Szczesniak, P. Cieplak, and S. Scheiner, J. Chem. Phys., 94, 2873–2883 (1991), and references therein. 56 The ESP-fit calculations were carried out with a version of Gaussian 88 to which Dr. M. D. Miller (Merck Research Laboratories) had interfaced PDM88 (D. E. Williams, QCPE, Program No. 568, 1988). 57 In these MMFF optimizations, weak penalty-function restraints were applied to the torsion angles to insure that comparable MMFF and ab initio conformations were being compared (cf. ref. 26). 58 TORFIT is a versatile program developed at the Merck Research Laboratories which derives torsional parameters via least-squares fits to relative conformational energies (cf. ref. 26). 59 The procedure used is not strictly “mathematically” self-consistent, however, because formal couplings between parameters belonging to different classes (e.g., between reference values and force constants for angles at trigonal centers) have not been addressed. Further iterations would probably cause a slow drift away from the parameter values reported in this work. We view the parameters as being “physically” self-consistent, however, in the sense that such further iterations would not materially improve the fit to the computational data. 60 The cited rms deviations in dipole directions are weighted rms deviations constructed to avoid overemphasizing large errors in directions for dipole moments of small magnitude (cf. ref. 24). 61 We should note that MM2X actually uses the Allinger (MM2/MM3) definition for out-of-plane angles. To clarify the comparison to MMFF, however, we have used the Wilson definition in analyzing the MM2X-optimized geometries. The Allinger angles typically are about three times smaller in magnitude. 62 See, for example: M. W. Wong and K. B. Wiberg, J. Phys. Chem., 96, 668–671 (1992). 63 The first rms value is much lower for MM2X because some high-energy structures in the transition state region for CN amide bond rotation in N-methylformamine were poorly treated by MM2X and had to be removed from the test set (cf. ref. 26). 64 For structures, see T. Head-Gordon, M. Head-Gordon, M. J. Frisch, C. L. Brooks III, and J. A. Pople, J. Am. Chem. Soc., 113, 5989–5997 (1991). 65 W. L. Jorgensen, J. Chandrasekhar and J. D. Madura, J. Chem. Phys., 79, 926–935 (1983). 66(a) B. L. Bush, J. L. Banks, R. Czerminski, and T. A. Halgren (work in progress), using a local version of CHARMm into which MMFF94 has been integrated; (b) T. A. Halgren, S.-S. So, and M. Karplus (work in progress). 67 As an example, we might at some point wish to define different bond-charge increments for CO groups in amides, esters, ketones, etc., for which differing symbolic atom types but common numeric atom types currently are assigned. The equivalence procedure provides a convenient way to do so without requiring that atom types and parameters describing common bond, angle, torsion, and other interactions simultaneously be modified. 68 For bending of the i–j–k angle, a five-stage process based in the level combinations 1–1–1, 2–2–2, 3–2–3, 4–2–4, and 5–2–5 is used. For i–j–k–l torsion interactions, a five-stage process based on level combinations 1–1–1–1, 2–2–2–2, 3–2–2–5, 5–2–2–3, and 5–2–2–5 is used, where stages 3 and 4 correspond to “half-default” or “half-wild-card” entries. For out-of-plane bending ijk; l, where j is the central atom [cf. eq. (5)], the five-stage protocol 1–1–1; 1, 2–2–2; 2, 3–2–3; 3, 4–2–4; 4, 5–2–5; 5 is used. The final stage provides wild-card defaults for all except the central atom. 69 N. L. Allinger and M. J. Hickey, Tetrahedron, 28, 2157–2161 (1972). Although not specifically referenced, the results of this work were used in developing a force field for carbonyl compounds: N. L. Allinger, M. T. Trible, and M. A. Miller, Tetrahedron, 28, 1173–1190 (1972) (N. L. Allinger, private communication). 70 W. F. van Gunsteren, In Computer Simulation of Biomolecular Systems, W. F. van Gunsteren and P. K. Weiner, Eds., ESCOM, Leiden, 1989, pp. 27–59. 71 M. Mezei and J. J. Dannenberg, J. Phys. Chem., 92, 5860–5861 (1988). 72 Appendix A is available in Supplementary Material (see footnote * on the first page of this article). Citing Literature Volume17, Issue5-6April 1996Pages 490-519 ReferencesRelatedInformation