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

Journal of Computational Chemistry

Volumn 17, Issue 5-6, 1996, Pages 490-519

  Halgren, Thomas A ^a  

^a MERCK RESEARCH LABORATORIES   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0037571112     PISSN: 01928651     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1096-987X(199604)17:5/6<490::AID-JCC1>3.0.CO;2-P     Document Type: Article

References (99)

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23. J. R. Maple, U. Dinur, and A. T. Hagler, Proc. Null. Acad. Sci. USA, 85, 5350-5354 (1988). A. T. Hagler, J. R. Maple, T. S. Thacher, G. B. Fitzgerald, and U. Dinur, In Computer Simulation of Biomolecular Systems, W. F. van Gunsteren and P. K. Weiner, Eds., ESCOM, Leiden, 1989, pp. 149-167. U. Dinur and A. T. Hagler, in Reviews in Computational Chemistry, K. B. Lipkowitz and D. B. Boyd, Eds., VCH Publishers, New York, 1991, Vol. 2, pp. 99-163. See also: J. Palca, Nature, 322, 586 (1986).
24. J. R. Maple, U. Dinur, and A. T. Hagler, Proc. Null. Acad. Sci. USA, 85, 5350-5354 (1988). A. T. Hagler, J. R. Maple, T. S. Thacher, G. B. Fitzgerald, and U. Dinur, In Computer Simulation of Biomolecular Systems, W. F. van Gunsteren and P. K. Weiner, Eds., ESCOM, Leiden, 1989, pp. 149-167. U. Dinur and A. T. Hagler, in Reviews in Computational Chemistry, K. B. Lipkowitz and D. B. Boyd, Eds., VCH Publishers, New York, 1991, Vol. 2, pp. 99-163. See also: J. Palca, Nature, 322, 586 (1986).
25. J. R. Maple, U. Dinur, and A. T. Hagler, Proc. Null. Acad. Sci. USA, 85, 5350-5354 (1988). A. T. Hagler, J. R. Maple, T. S. Thacher, G. B. Fitzgerald, and U. Dinur, In Computer Simulation of Biomolecular Systems, W. F. van Gunsteren and P. K. Weiner, Eds., ESCOM, Leiden, 1989, pp. 149-167. U. Dinur and A. T. Hagler, in Reviews in Computational Chemistry, K. B. Lipkowitz and D. B. Boyd, Eds., VCH Publishers, New York, 1991, Vol. 2, pp. 99-163. See also: J. Palca, Nature, 322, 586 (1986).
26. (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).
27. (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).
28. N. L. Allinger, K. Chen, and J.-H. Lu, J. Comput. Chem. (this issue).
29. (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
30. (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).
31. 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).
32. See, for example: (a) 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).
33. See, for example: (a) 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).
34. See, for example: (a) 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).
35. See, for example: (a) 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).
36. See, for example: (a) 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).
37. See, for example: (a) G. Corongiu, M. Migliore, and E. dementi, 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).
38. See, for example: (a) G. Corongiu, M. Migliore, and E. dementi, 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).
39. See, for example: (a) G. Corongiu, M. Migliore, and E. dementi, 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).
40. See, for example: (a) G. Corongiu, M. Migliore, and E. dementi, 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).
41. See, for example: (a) G. Corongiu, M. Migliore, and E. dementi, 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).
42. See, for example: (a) G. Corongiu, M. Migliore, and E. dementi, 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).
43. See, for example: (a) G. Corongiu, M. Migliore, and E. dementi, 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).
44. S. Dasgupta and W. A. Goddard III, J. Chem. Phys., 90, 7207-7215 (1989).
45. The MMFF94 parameters (Appendix B, Supplementary Material) are available in computer-readable form (see footnote * on first page of this article).
46. Part II: T. A. Halgren, J. Comput. Chem. (this issue).
47. Part III: T. A. Halgren, J. Comput. Chem. (this issue).
48. Part IV: T. A. Halgren and R. B. Nachbar, J. Comput. Chem. (this issue).
49. Part V: T. A. Halgren, J. Comput. Chem. (this issue).
50. 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.
51. 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).
52. 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.
53. Distribution of OPTIMOL by the Quantum Chemistry Program Exchange (Indiana University) would permit free usage of the program but would prohibit its commercialization.
54. T. A. Halgren and R. B. Nachbar (work in progress).
55. The Merck Index, 11th ed., S. Budavari, Ed., Merck & Co., Rahway, NJ, 1989.
56. Fine Chemicals Directory Handbook, Fraser Williams (Scientific Systems), London, 1983-1985. Connection tables distributed by Molecular Design Ltd., Hayward, CA.
57. PROBE is a computer program used to derive molecularmechanics 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.
58. See, for example, G. C. Lie and E. Clementi, Phys. Rev., 33A, 2679 (1986).
59. 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.
60. B. M. Pettit, in Computer Simulation of Biomolecular Systems, W. F. van Gunsteren and P. K. Weiner, Eds., ESCOM, Leiden, 1989, pp. 94-100.
61. T. A. Halgren, J. Am. Chem. Soc., 114, 7827-7843 (1992).
62. 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).
63. A. D. MacKerell Jr. and M. Karplus, J. Phys. Chem., 95, 10559-10560 (1991); A. D. MacKerell Jr., J. WiórkiewiczKuczera, and M. Karplus, J. Am. Chem. Soc. (in press).
64. A. D. MacKerell Jr. and M. Karplus, J. Phys. Chem., 95, 10559-10560 (1991); A. D. MacKerell Jr., J. WiórkiewiczKuczera, and M. Karplus, J. Am. Chem. Soc. (in press).
65. M. J. Frisch. J. E. Del Bene, J. S. Binkley, and H. F. Schaeffer III, J. Chem. Phys., 84, 2279-2289 (1986).
66. T. A. Halgren, J. Am. Chem. Soc., 112, 4710-4723 (1990).
67. M. Orozco and F. J. Luque, J. Comput. Chem., 14, 881-894 (1993).
68. E. B. Wilson Jr., J. C. Decius, and P. C. Cross, Molecular Vibrations, Dover, New York, 1955, Chapter 4.
69. 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).
70. 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.
71. See, for example, the "vdW and hydrogen bonding" parameters listed in Table I of: J.-H. Lu and N. L. Allinger, J. Comput. Chem., 12, 186-199 (1991).
72. M. Waldman and A. T. Hagler, J. Comput. Chem., 14, 1077-1084 (1993).
73. Most of the ab initio calculations used in parameterizing MMFF were performed on the Merck Research Laboratories Cray YPMSi/4-128 supercomputer.
74. 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.
75. 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.
76. 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.
77. 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).
78. 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).
79. See, for example, G. Chalasinski, M. M. Szczesniak, P. Cieplak, and S. Scheiner, J. Chem. Phys., 94, 2873-2883 (1991), and references therein.
80. 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).
81. 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).
82. 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).
83. 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.
84. 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).
85. 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.
86. See, for example: M. W. Wong and K. B. Wiberg, J. Phys. Chem., 96, 668-671 (1992).
87. 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).
88. 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).
89. W. L. Jorgensen, J. Chandrasekhar and J. D. Madura, J. Chem. Phys., 79, 926-935 (1983).
90. (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
91. (b) T. A. Halgren, S.-S. So, and M. Karplus (work in progress).
92. 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.
93. 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.
94. N. L. Allinger and M. J. Mickey, 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).
95. N. L. Allinger and M. J. Mickey, 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).
96. N. L. Allinger and M. J. Mickey, 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).
97. W. F. van Gunsteren, In Computer Simulation of Biomolecutar Systems, W. F. van Gunsteren and P. K. Weiner, Eds., ESCOM, Leiden, 1989, pp. 27-59.
98. M. Mezei and J. J. Dannenberg, J. Phys. Chem., 92, 5860-5861 (1988).
99. Appendix A is available in Supplementary Material (see footnote * on the first page of this article).