Theoretical studies on a carbonaceous molecular bearing: Association thermodynamics and dual-mode rolling dynamics

Chemical Science

Volumn 6, Issue 5, 2015, Pages 2746-2753

  Isobe, Hiroyuki ^a   Nakamura, Kosuke ^a   Hitosugi, Shunpei ^a   Sato, Sota ^a   Tokoyama, Hiroaki ^b   Yamakado, Hideo ^b   Ohno, Koichi ^a,c   Kono, Hirohiko ^a  

^a TOHOKU UNIVERSITY   (Japan)

^b WAKAYAMA UNIVERSITY   (Japan)

^c Institute for Quantum Chemical Exploration   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

DYNAMICS; FULLERENES; MOLECULES; THERMODYNAMICS; VAN DER WAALS FORCES;

ASSOCIATION ENERGIES; DUAL MODES; DYNAMIC MOTIONS; FULLERENE MOLECULES; MOLECULAR BEARINGS; ROLLING MOTION; THEORETICAL STUDY; VAN DER WAALS INTERACTIONS;

DENSITY FUNCTIONAL THEORY;

EID: 84928138258     PISSN: 20416520     EISSN: 20416539     Source Type: Journal    
DOI: 10.1039/c5sc00335k     Document Type: Article

References (85)

1. B. W. Smith M. Monthioux D. E. Luzzi Nature 1998 396 323 324
2. I. V. Krive R. I. Shekhter M. Jonson Low Temp. Phys. 2006 32 1171 1194
3. M. Monthioux Carbon 2002 40 1809 1823
4. S. Iijima Phys. B 2002 323 1 5
5. Adopting a technological term used by bearing engineers (cf. ref. 50), we describe the dynamic motions of fullerene journals as "rolling". This description also helps to avoid the confusion with the other dynamics of arylene units or alkyl substituents that have freedom of "rotations".
6. J. Cumings A. Zettl Science 2000 289 602 604
7. N. Solin M. Koshino T. Tanaka S. Takenaga H. Kataura H. Isobe E. Nakamura Chem. Lett. 2007 36 1208 1209
8. M. Koshino N. Solin T. Tanaka H. Isobe E. Nakamura Nat. Nanotechnol. 2008 3 595 597
9. H. Isobe S. Hitosugi T. Yamasaki R. Iizuka Chem. Sci. 2013 4 1293 1297
10. S. Hitosugi R. Iizuka T. Yamasaki R. Zhang Y. Murata H. Isobe Org. Lett. 2013 15 3199 3201
11. S. Sato T. Yamasaki H. Isobe Proc. Natl. Acad. Sci. U. S. A. 2014 111 8374 8379
12. S. Hitosugi K. Ohkubo R. Iizuka Y. Kawashima K. Nakamura S. Sato H. Kono S. Fukuzumi H. Isobe Org. Lett. 2014 16 3352 3355
13. T. Matsuno S. Sato R. Iizuka H. Isobe Chem. Sci. 2015 6 909 916
14. T. Matsuno H. Naito S. Hitosugi S. Sato M. Kotani H. Isobe Pure Appl. Chem. 2014 86 489 495
15. http://www.orgchem2.chem.tohoku.ac.jp/finite/
16. T. Matsuno S. Kamata S. Hitosugi H. Isobe Chem. Sci. 2013 4 3179 3183
17. S. Hitosugi T. Yamasaki H. Isobe J. Am. Chem. Soc. 2012 134 12442 12445
18. S. Hitosugi W. Nakanishi H. Isobe Chem.-Asian J. 2012 7 1550 1552
19. T. Kawase H. Kurata Chem. Rev. 2006 106 5250 5273
20. T. Iwamoto Y. Watanabe T. Sadahiro T. Haino S. Yamago Angew. Chem., Int. Ed. 2011 50 8342 8344
21. T. Iwamoto Y. Watanabe H. Takaya T. Haino N. Yasuda S. Yamago Chem.-Eur. J. 2013 46 6777 6785
22. T. Iwamoto Z. Slanina N. Mizorogi J. Guo T. Akasaka S. Nagase H. Takaya N. Yasuda T. Kato S. Yamago Chem.-Eur. J. 2014 47 14403 14409
23. J. Xia J. W. Bacon R. Jasti Chem. Sci. 2012 3 3018 3021
24. Y. Nakanishi H. Omachi S. Matsuura Y. Miyata R. Kitaura Y. Segawa K. Itami H. Shinohara Angew. Chem., Int. Ed. 2014 53 3102 3106
25. E. R. Kay D. A. Leigh F. Zerbetto Angew. Chem., Int. Ed. 2006 46 72 191
26. D. Canevet E. M. Pérez N. Martín Angew. Chem., Int. Ed. 2011 50 9248 9259
27. Structure-thermodynamics studies indicated that the contribution of alkyl chains on the thermodynamics is not large for [4]CC. See ref. 6b.
28. S. Kigure S. Okada J. Phys. Soc. Jpn. 2013 82 094717
29. L. A. Girifalco M. Hodak R. S. Lee Phys. Rev. B: Condens. Matter Mater. Phys. 2000 62 13104
30. A. D. McLean G. S. Chandler J. Chem. Phys. 1980 72 5639 5648
31. K. Raghavachari J. S. Binkley R. Seeger J. A. Pople J. Chem. Phys. 1980 72 650 654
32. S. Simon M. Duran J. J. Dannenberg J. Chem. Phys. 1996 105 11024 11031
33. S. F. Boys F. Bernardi Mol. Phys. 1970 19 553 566
34. J. Tomasi B. Mennucci R. Cammi Chem. Rev. 2005 105 2999 3093
35. T. Yanai D. Tew N. Handy Chem. Phys. Lett. 2004 393 51 57
36. J.-W. Song T. Hirosawa T. Tsuneda K. Hirao J. Chem. Phys. 2007 126 154105
37. O. A. Vydrov G. E. Scuseria J. Chem. Phys. 2006 125 234109
38. H. Iikura T. Tsuneda T. Yanai K. Hirao J. Chem. Phys. 2001 115 3540 3544
39. A. Dreuw J. L. Weisman M. Head-Gordon J. Chem. Phys. 2003 119 2943 2946
40. Y. Tawada T. Tsuneda S. Yanagisawa T. Yanai K. Hirao J. Chem. Phys. 2004 120 8425 8433
41. J.-D. Chai M. Head-Gordon J. Chem. Phys. 2008 128 084106
42. S. Grimme J. Comput. Chem. 2006 27 1787 1799
43. J.-D. Chai M. Head-Gordon Phys. Chem. Chem. Phys. 2008 10 6615 6620
44. A. D. Boese J. M. L. Martin J. Chem. Phys. 2004 121 3405 3416
45. F. Weigend R. Ahlrichs Phys. Chem. Chem. Phys. 2005 7 3297 3305
46. In solution, the pyrrolidine ring on the fullerene molecule acts as a shaft for the single-axis rolling motion of the journal, and, in the time-averaged structure, this five-membered ring stands aligned along the C4 symmetry axis of the outer [4]CC bearing.
47. E. F. Pettersen T. D. Goddard C. C. Huang G. S. Couch D. M. Greenblatt E. C. Meng T. E. Ferrin J. Comput. Chem. 2004 25 1605 1612
48. F. P. Schmidtchen, in Supramolecular Chemistry: From Molecules to Nanomaterials, ed., J. W. Steed, and, P. A. Gale, Wiley, Chichester, 2012, vol. 2, pp. 275-296
49. Note that ITC analysis directly provides an experimental enthalpy for the association, which enables straightforward comparisons with theoretical energetics without nuisance considerations of entropic terms (see also ref. 48 and 49).
50. The association enthalpy of unsubstituted C60 in dichloromethane is -11.6 ± 0.4 kcal mol-1 (ref. 5 and 6d), which shows that introduction of substituents does not hinder but rather enforces the association of the journal by ca. -1 kcal mol-1
51. The dispersion force is undoubtedly playing a key role for the peapod formation with close van der Waals contacts (ref. 6b), and the present results indicate its premature treatment in the present DFT methods (see also ref. 34). Effects on the lengthening of the tubular structure is thus of great interest for in the near future. (See also ref. 6d).
52. The geometries from LC-BLYP/PCM and BMK/PCM methods matched with RMSD of 0.090 Å. See Fig. S1
53. R. Peverati K. K. Baldridge J. Chem. Theory Comput. 2008 4 2030 2048
54. R. Peverati K. K. Baldridge J. Chem. Theory Comput. 2010 6 1924
55. Yamago and coworkers also reported a tendency of overestimate of association energies with M06-2X. See ref. 8.
56. One reviewer expressed his/her interest in further extensions of polarization functions over hydrogen atoms as well as in other DFT methods with more recent dispersion treatments. Albeit preliminary within a framework of the Gaussian program, these comparisons were made by single-point calculations, and the results were summarized in Table S1. In short, the extension of polarization functions to (d,p) setting did not affect the results considerably. The inclusion of dispersion effects with modern D3 methods did not improve the results by showing overestimations of the association energy over 35 kcal mol-1. The results may indicate that further improvements in the theoretical models of dispersion forces are necessary especially for the curved π-systems. The present results also show that our carbonaceous molecular bearing provides an interesting and challenging test case for theoretical evaluations (ref. 48d), and the evaluation of other recent dispersion models, such as many-body dispersion models implemented in the Amsterdam Density Functional program, may be of interest for the further theoretical studies in the future. See ref. 48 for representative examples.
57. Z.-Q. You Y.-C. Hung C.-P. Hsu J. Phys. Chem. B 10.1021/jp511216c
58. The rolling energetics also shows that the starting geometry is the global minimum for the single-axis rolling motions by showing the minimum at 0° in Fig. 3.
59. D. Casarini L. Lunazzi A. Mazzanti Eur. J. Org. Chem. 2010 2035 2056
60. The two carbon atoms on the equator are located in the middle of biaryl linkages. A similar anomalous location of carbon atoms on the biaryl linkages is also experimentally observed in the solid state. See ref. 6b.
61. D. Porezag T. Frauenheim T. Köhler G. Seifert R. Kaschner Phys. Rev. B: Condens. Matter Mater. Phys. 1995 51 12947 12957
62. G. Seifert D. Porezag T. Frauenheim Int. J. Quantum Chem. 1996 58 185 192
63. M. Elstner D. Porezag G. Jungnickel J. Elsner M. Haugk T. Frauenheim S. Suhai G. Seifert Phys. Rev. B: Condens. Matter Mater. Phys. 1998 58 7260 7268
64. The association energy of (P)-(12,8)-[4]CC⊃ 1+ was estimated as -78.9 kcal mol-1 by the DFTB method. This value was larger than that of ωB97X-D method (-69.8 kcal mol-1, cf. Table 1).
65. PCM implementation in the DFTB method is not accessible with our resource using DFTB+ program (cf. ref. 52).
66. Although the relative stabilities of two minima were switched from the LC-BLYP calculations, the energy differences of minima were as small as <0.2 kcal mol-1 for SCC-DFTB calculations and <0.6 kcal mol-1 for LC-BLYP calculations. The switching of two minima may be the origin of minimum-switching of realistic motions (Fig. S5): stabilities of 1/4 precession and bp structures were switched between SCC-DFTB and LC-BLYP calculations.
67. Because of minute differences in the chemical shifts of resonances, we could not study the experimental dynamics of this system
68. N. Niitsu M. Kikuchi H. Ikeda K. Yamazaki M. Kanno H. Kono K. Mitsuke M. Toda K. Nakai J. Chem. Phys. 2012 136 164304
69. A. B. Marahatta M. Kanno K. Hoki W. Setaka S. Irle H. Kono J. Phys. Chem. C 2012 116 24845 24854
70. K. Ohno S. Maeda Chem. Phys. Lett. 2004 384 277 282
71. S. Maeda K. Ohno J. Phys. Chem. A 2005 109 5742 5753
72. K. Ohno S. Maeda J. Phys. Chem. A 2006 110 8933 8941
73. The energy barriers from MD and TS analysis are comparable to the one estimated with LC-BLYP/PCM for the idealized rolling motions (Fig. S4, +4.3 kcal mol-1).
74. M. H. Levitt, Spin Dynamics: Basics of Nuclear Magnetic Resonance, Wiley, Chichester, United Kingdom, 2001, ch 15.5
75. A. Tkatchenko D. Alfé K. S. Kim J. Chem. Theory Comput. 2012 8 4317 4322
76. A. Ambrosetti D. Alfé R. A. DiStasio Jr A. Tkatchenko J. Phys. Chem. Lett. 2014 5 849 855
77. L. Kronik A. Tkatchenko Acc. Chem. Res. 2014 47 3208 3216
78. S. Grimme Chem.-Eur. J. 2012 18 9955 9964
79. T. Risthaus S. Grimme J. Chem. Theory Comput. 2013 9 1580 1591
80. J. Antony R. Sure S. Grimme Chem. Commun. 2015 51 1764 1774
81. Delicate care must be taken in the comparison of experimental and theoretical data especially for large supramolecular systems. As we experimentally demonstrated in our systems (ref. 6), entropy terms in the association should be very complicated by the involvement of conformations and solvent molecules. Such entropy effects cannot be readily reproduced by any simple theoretical models (ref. 48).
82. A. Harnoy, Bearing Design in Machinery: Engineering Tribology and Lubrication, Dekker, New York, USA, 2003, ch. 1
83. M. J. Frisch, G. W. Trucks, H. B. Schlegel, G. E. Scuseria, M. A. Robb, J. R. Cheeseman, G. Scalmani, V. Barone, B. Mennucci, G. A. Petersson, H. Nakatsuji, M. Caricato, X. Li, H. P. Hratchian, A. F. Izmaylov, J. Bloino, G. Zheng, J. L. Sonnenberg, M. Hada, M. Ehara, K. Toyota, R. Fukuda, J. Hasegawa, M. Ishida, T. Nakajima, Y. Honda, O. Kitao, H. Nakai, T. Vreven, J. A. Montgomery Jr, J. E. Peralta, F. Ogliaro, M. Bearpark, J. J. Heyd, E. Brothers, K. N. Kudin, V. N. Staroverov, R. Kobayashi, J. Normand, K. Raghavachari, A. Rendell, J. C. Burant, S. S. Iyengar, J. Tomasi, M. Cossi, N. Rega, J. M. Millam, M. Klene, J. E. Knox, J. B. Cross, V. Bakken, C. Adamo, J. Jaramillo, R. Gomperts, R. E. Stratmann, O. Yazyev, A. J. Austin, R. Cammi, C. Pomelli, J. W. Ochterski, R. L. Martin, K. Morokuma, V. G. Zakrzewski, G. A. Voth, P. Salvador, J. J. Dannenberg, S. Dapprich, A. D. Daniels, Ö. Farkas, J. B. Foresman, J. V. Ortiz, J. Cioslowski and D. J. Fox, Gaussian 09, Gaussian, Inc., Wallingford, CT, 2009
84. Bremen Center for Computational Materials Science, University of Bremen. See also http://www.dftb-plus.info
85. G. Zheng S. Irle K. Morokuma Chem. Phys. Lett. 2005 412 210 216