Conformational Dynamics of Propane, Di-ieri-butylmethane, and Bis(9-triptycyl)methane. An Analysis of the Symmetry of Two 3-fold Rotors on a Rigid Frame in Terms of Nonrigid Molecular Structure and Energy Hypersurfaces

Journal of the American Chemical Society

Volumn 105, Issue 6, 1983, Pages 1427-1438

  Bikrgi, Hans Beat ^a   Hounshell, W Douglas ^b   Nachbar, Robert B ^c   Mislow, Kurt ^c  

^a UNIVERSITY OF BERN   (Switzerland)

^b Molecular Design Ltd ^*  (United States)

^c PRINCETON UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

PROPANE;

EID: 0020721012     PISSN: 00027863     EISSN: 15205126     Source Type: Journal    
DOI: 10.1021/ja00344a004     Document Type: Article

References (98)

1. (a) Universitat Bern, (b) Molecular Design, Ltd. (c) Princeton University.
2. Hounshell, W. D.; Iroff, L. D.; Iverson, D. J.; Wroczynski, R. J.; Mislow, K. Isr. J. Chem. 1980, 20, 65.
3. See also: Hounshell, W. D.; Iroff, L. D.; Wroczynski, R. J.; Mislow, K. J. Am. Chem. Soc. 1978, 100, 5212.
4. Iroff, L. D. J. Comput. Chem. 1980, 1, 76.
5. Schilling, B. E. R.; Hoffmann, R. J. Am. Chem. Soc. 1978, 100, 6274; 1979, 101, 3456.
6. Edidin, R. T.; Norton, J.R.; Mislow, K. Organometallics 1982, 1, 561.
7. For a preliminary report, see: Hounshell, W. D.; Johnson, C. A.; Guenzi, A.; Cozzi, F.; Mislow, K. Proc. Natl. Acad. Sci. U.S.A. 1980, 77, 6961.
8. Gear shafts may lie in the same plane (spur and bevel gears have parallel and intersecting axes, respectively) or in parallel planes with inclined axes. For a classification of the disposition of gear shafts, see: Watson, H. J. “Modern Gear Production”; Pergamon Press: Oxford, 1970.
9. On the topic of sterically crowded molecules, see: Tidwell, T. T. Tetrahedron 1978, 34, 1855.
10. Relevant citations to the literature are collected in ref 2.
11. Torsional frequencies in molecules with geminal or vicinal methyl groups have been analyzed in terms of Fourier series that include terms corresponding to coupled rotation of methyl rotors. See, for example: Lide, D. R., Jr.; Mann, D. E. J. Chem. Phys. 1958, 28, 572
12. J. Chem. Phys. 1958, 29, 914.
13. Swalen, J. D.; Costain, C. C. J. Chem. Phys. 1959, 31, 1562.
14. Rush, J. J. J. Chem. Phys. 1967, 47, 3936.
15. Dreizler, H.; Sutter, D. Z. Naturforsch. A 1969, 24 A, 2013.
16. Grant, D. M.; Pugmire, R. J.; Livingston, R. C.; Strong, K. A.; McMurray, H. L.; Brugger, R. M. J. Chem. Phys. 1970, 52, 4424.
17. Burnell, E. E.; Diehl, P. Mol. Phys. 1972, 24, 489.
18. Burnell, E. E.; Diehl, P. Org. Magn. Reson. 1973, 5, 137.
19. Livingston, R. C.; Grant, D. M.; Pugmire, R. J.; Strong, K. A.; Brugger, R. M. J. Chem. Phys. 1973, 58, 1438.
20. Durig, J. R.; Craven, S. M.; Mulligan, J. H.; Hawley, C. W.; Bragin, J. J. Chem. Phys. 1973, 58, 1281.
21. Rojhantalab, H.; Nibler, J. W.; Wilkins, C. J. Spectrochim. Acta, Part A 1976, 32 A, 519.
22. Durig, J. R.; Groner, P.; Griffin, M. G. J. Chem. Phys. 1911, 66, 3061.
23. Groner, P.; Durig, J. R. J. Chem. Phys. 1977, 66, 1856.
24. Durig, J. R.; Griffin, M. G.; Groner, P. J. Phys. Chem. 1977, 81, 554.
25. Durig, J. R.; Compton, D. A. C. J. Chem. Phys. 1978, 69, 4713.
26. Durig, J. R.; Compton, D. A. C. J. Phys. Chem. 1979, 83, 265.
27. Durig, J. R.; Compton, D. A. C.; Jalilian, M.-R. J. Phys. Chem. 1979, 83, 511.
28. Durig, J. R.; Compton, D. A. C. J. Phys. Chem. 1979, 83, 2873.
29. Radom, L.; Pople, J. A. J. Am. Chem. Soc. 1970, 92, 4786.
30. Tang, J.; Pines, A. J. Chem. Phys. 1980, 73, 2512.
31. Hirota, E.; Matsumura, C.; Morino, Y. Bull. Chem. Soc. Jpn. 1967, 40, 1124.
32. Hoyland, J. R. J. Chem. Phys. 1968, 49, 1908.
33. Durig, J. R.; Compton, D. A. C.; Rizzolo, J. J.; Jalilian, M. R.; Zozulin, A. J.; Odom, J. D. J. Mol. Struct. 1981, 77, 195.
34. As a notable example, we single out the study of Kwart and Alekman10 of internal rotations in the dimesitylcarbinyl system, which led to the postulation of a “cogwheel effect”. The correlated rotation of aryl rings in systems containing two such rings attached to a single atom (Ar2Z) have been described and classified.” The permutational consequences of the one-ring flip are satisfied by an internal motion in which the two aryl rings rotate in synchrony, so that when one ring is in the C-Z-C plane, the other is perpendicular to it. In crowded systems, i.e., in systems containing phenyl rings with ortho substituents, this cogwheeling motion corresponds to the lowest energy pathway, with ground and transition states assuming helical and perpendicular conformations,” respectively.
35. Kwart, H.; Alekman, S. J. Am. Chem. Soc. 1968, 90, 4482.
36. Gust, D.; Mislow, K. J. Am. Chem. Soc. 1973, 95, 1535.
37. Bartell, L. S.; Bradford, W. F. J. Mol. Struct. 1977, 37, 113.
38. X-ray structures of related compounds yield values close to the lower limit of this range: 126° (Bunn, C. W.; Holmes, D. R. Discuss. Faraday Soc. 1958, 25, 95).
39. 122.6° (Benedetti, E.; Pedone, C.; Allegra, G. Macromolecules 1970, 3, 16).
40. 123.8 and 124.1° (Adiwidjaja, G.; Voss, J. Chem. Ber. 1976, 109, 761).
41. 123.1 and 123.8° (McKinnon, B. J.; de Mayo, P.; Payne, N. C.; Ruge, B. Nouv. J. Chem. 1978, 2, 91).
42. 125.0° (Ermer, O.; Bödecker, C.-D. Chem. Ber. 1981, 114, 652).
43. Oki, M. Angew. Chem., Int. Ed. Engl. 1976, 15, 87 and referencess therein.
44. Yamamoto, G.; Oki, M. Chem. Lett. 1979, 1251, 1255
45. Bull. Chem. Soc. Jpn. 1981, 54, 473, 481.
46. Strictly speaking, the rotors in 2 are not directly comparable to those in 1 and 3, for whereas the methyl groups in 1 and the triptycyl groups in 3 may be considered as rigid entities, the tert-butyl groups in 2 are not rigid.
47. Ruch, E.; Hásselbarth, W.; Richter, B. Theor. Chim. Acta 1970, 19, 288.
48. Hásselbarth, W.; Ruch, E. Theor. Chim. Acta 1973, 29, 259.
49. Klemperer, W. G. J. Chem. Phys. 1972, 56, 5478
50. J. Am. Chem. Soc. 1972, 94, 6940; 1973, 95, 380.
51. Brocas, J.; Willem, R. Bull. Soc. Chim. Belg. 1973, 82, 469.
52. For work from this laboratory, see, for example: Mislow, K. Acc. Chem. Res. 1976, 9, 26.
53. Hutchings, M. G.; Nourse, J. G.; Mislow, K. Tetrahedron 1974, 30, 1535.
54. Nourse, J. G.; Mislow, K. J. Am. Chem. Soc. 1975, 97, 4571.
55. Finocchiaro, P.; Hounshell, W. D.; Mislow, K. J. Am. Chem. Soc. 1976, 98, 4952.
56. Skeleton A is a schematic projection of the propane framework, with the labeled ligands (1-6 and a-b are methyl and methylene hydrogens, respectively) in their respective reference sites.
57. Longuet-Higgins, H. C. Mol. Phys. 1963, 6, 445.
58. This group is isomorphic to the MSG of ethane, whose character table has been given.21
59. Woodman, C. M. Mol. Phys. 1970, 19, 753.
60. The elements of V are e, (14)(26)(35)(ab), (23)(56)(ab)., (14)-(25)(36)'.
61. Murray-Rust, P.; Bürgi, H.-B.; Dunitz, J. D. Acta Crystallogr., Sect. A 1979, A35, 703.
62. Dunitz, J.D. “X-ray Analysis and the Structure of Organic Molecules”; Cornell University Press: Ithaca, NY, 1979.
63. Bürgi, H.-B. MATCH 1980, 9, 13.
64. Inclusion of individual methyl group rotations would bring the problem to an unmanageable level: the MSG is given by ((C3)3 A C3)2 A V, a group of order 26 244. Similarly, for purposes of labeling and isomer enumeration (see below), we regard each methyl group as a single unit; that is, we distinguish among different methyl groups but not among the hydrogens within each group.
65. Two structures are isometric if they are properly or improperly congruent. Alternatively, nuclear configurations are isometric if their labeled graphs are the same, the labeling being by nuclear charge and mass for the vertices and by internuclear distances for the edges (Bauder, A.; Meyer, R.; Günthard, H. H. Mol. Phys. 1974, 28, 1305).
66. The group of transformations may be expressed as a group of matrices acting on the vector [x, y, 1]T. The generators of the group are
67. For the concept of groups by modulus, see: Shubnikov, A. V.; Koptsik, V. A. “Symmetry in Science and Art”; Plenum Press: New York, 1974; p. 246.
68. International Tables for X-ray Crystallography, Kynoch Press: Birmingham, England, 1969; Vol 1, p. 64.
69. Müller, K. Angew. Chem., Int. Ed. Engl. 1980, 19, 1.
70. Stanton, R. E.; Mclver, J. W., Jr. J. Am. Chem. Soc. 1975, 97, 3632.
71. Ermer, O. J. Am. Chem. Soc. 1976, 98, 3964.
72. Iverson, D. J.; Mislow, K. QCPE 1981, 13, 410.
73. Allinger, N. L. J. Am. Chem. Soc. 1977, 99, 8127.
74. The stationary structures of 1 and 2 were also determined by use of the Allinger 1971 38 and MM139 force fields, with results essentially identical with those obtained with the MM2 force field.
75. Allinger, N. L.; Tribble, M. T.; Miller, M. A.; Wertz, D. H. J. Am. Chem. Soc. 1971, 93, 1637.
76. Wertz, D. H.; Allinger, N. L. Tetrahedron 1974, 30, 1579.
77. Andose, J. D.; Mislow, K. J. Am. Chem. Soc. 1974, 96, 2168.
78. Mislow, K.; Dougherty, D. A.; Hounshell, W. D. Bull. Soc. Chim. Belg. 1978, 87, 555 and references therein.
79. The program bigstrn-3 is being prepared for submission to QCPE. A listing is available upon request. The program uses full matrix Newton-Raphson optimization. All atoms are moved simultaneously, and symmetry is thus conserved. For a critical discussion of symmetry conservation during geometry optimization, see Ermer4
80. Ermer, O. Tetrahedron 1975, 31, 1849.
81. Allinger, N. L.; Yuh, Y. H. QCPE 1981, 13, 395.
82. Osawa, E.; Onuki, Y.; Mislow, K. J. Am. Chem. Soc. 1981, 103, 7475.
83. Ermer, O. “Aspekte von Kraftfeldrechnungen”; Wolfgang Baur Verlag: Munich, 1981.
84. Pople, J. A. J. Am. Chem. Soc. 1980, 102, 4615.
85. See also: Flurry, R. L., Jr. J. Am. Chem. Soc. 1981, 103, 2901.
86. Johnson, C. A.; Guenzi, A.; Nachbar, R. B., Jr.; Blount, J. F.; Wennerstróm, O.; Mislow, K. J. Am. Chem. Soc. 1982, 104, 5163.
87. In terms of the mechanical gear analogy, this contribution can be visualized as a measure of the play between the gears.
88. Two modes generate the same group if one contains inverses of the elements in the other.
89. We exclude tunneling, rearrangements making use of excited state surfaces, etc.
90. A primitive rearrangement process connects an energy minimum across a single rate-determining transition state with the neighboring minimum.
91. Gust, D.; Finocchiaro, P.; Mislow, K. Proc. Natl. Acad. Sci. U.S.A. 1973, 70, 3445.
92. Nourse, J. G. Proc. Natl. Acad. Sci. U.S.A. 1975, 72, 2385.
93. A particular permutation only gives information relating to models of a given starting structure and the final structure that results from the rearrangement in question. It emphatically says nothing about the mechanism of the rearrangement it describes: no information pertaining to energetics or geometries of intermediate states traversed during a rearrangement is implied in, or may be inferred from, a permutation.
94. As used in the present and previous4 paper, the term “meso” refers to an isomer that is achiral by virtue of possession of an improper axis of rotation (S., including a (n = 1) and i (n = 2)) or because any chiral components, referred to as d and l isomers, undergo rapid interconversion under the operation of the given rearrangement mode. In contradistinction, a “dl” pair consists of two residual enantiomers that are not interconverted under the operation of the mode and thus retain their individual chirality; by implication, the chiral components (d or l) do not enantiomerize under the operation of the mode.
95. 1 is a normal subgroup of G consisting of all the permutations in G. The number of double cosets is given by
96. The term “maximally labeled”19a signifies that the identity is the only symmetry element in the MSG of the unlabeled structure capable of generating an isometric structure from a maximally labeled one. That is, the MSG of a maximally labeled structure consists only of the identity. The isomer count assumss its maximum value for such a structure (cf. L1 in Table X), though the converse does not always follow (e.g., cf. L2b and L1 under G12, Table X). The substitution pattern listed for L1 in Table X (AAAABABCj is thus a valid representation of a maximally labeled structure, even though there is a redundancy of ligands (i.e., of A and B).
97. Nachbar, R. B., Jr.; Johnson, C. A.; Mislow, K. J. Org. Chem. 1982, 47, 4829.
98. Guenzi, A.; Johnson, C. A.; Cozzi, F.; Mislow, K. J. Am. Chem. Soc., following paper in this issue.