Supporting Information for:
Asymmetric Choreography in Pairs of Orthogonal Rotors
Antonio Rodríguez-Fortea,† Jírí Kaleta,‡ Cécile Mézière,¶ Magali Allain,¶ Enric Canadell,*,#
Pawel Wzietek,*,§ Josef Michl,*,||,‡ and Patrick Batail*,¶
Table of Contents
Synthesis of Bu4N+[1–]•H2O ……….………..……….S2 Crystal structure of Bu4N+[1–]•H2O...S2 Table S1. Crystal data and structure refinement for Bu4N+[1–]•H2O……….S2 VT 1H spin–lattice relaxation time (T1)……….……….….…...S4 Computational details.………..……….……….….………..…….S4 Figure S1. Structural reorganization along the rotational motion associated with the ma-ma I path of Figure 3……….…S5 References……….…….………...S5
Synthesis of Bu4N+[1–]•H2O
2.30 mL of Bu4NOH 1M in methanol (2.30 mmol) are added to a solution of 1,4- bis(carboxyethynyl)bicyclo[1.1.1]pentane2c 1 (469 mg, 2.30 mmol) in suspension in 20 mL of HPLC-grade MeOH. The mixture is stirred during 30 minutes, then the solvent is evaporated to dryness under vacuum to yield a white crystalline solid. The hygroscopic white crystals are kept under vacuum in presence of P2O5. The yield is quantitative for Bu4N+[1-].H2O. Anal. found for C27H45NO5 (calc.) C 69.72 (69.94), H 9.43 (9.78), N 3.01 (3.02).
Crystal structure of Bu4N+[1–]•H2O
A single crystal was selected out of the white crystalline solid. X-ray single-crystal diffraction data for Bu4N+[1–]•H2O were collected at 180 K and 100 K on an Agilent Technologies SuperNova diffractometer equipped with Atlas CCD detector and mirror monochromated micro-focus Cu-Kα radiation (λ = 1.54184 Å). The structure was solved by direct methods, expanded and refined on F2 by full matrix least-squares techniques using SHELX97.8 All non-H atoms were refined anisotropically. All the H atoms were included in the calculation without refinement except for the hydrogen atoms on the carboxylic group and water molecule, which were found by Fourier difference synthesis.
Multiscan empirical absorption was corrected using CrysAlisPro program (CrysAlisPro, Agilent Technologies, V1.171.37.35g, 2014). The carbon atoms of the rotor are statistically disordered and two groups of three carbons were refined on two positions with final occupation ratios of 0.71/0.29 at 180 K and 0.83/0.17 at 100 K. CCDC- 1580416 and 1812873 contains the supplementary crystallographic data for this paper.
Table S1. Crystal data and structure refinement for Bu4N+[1–]•H2O 180 K
Empirical formula C54 H88 N2 O9; 2(C11 H7 O4), 2(C16 H36 N), H2 O
Formula weight 909.26
Temperature 180.0(1) K
Wavelength 1.54184 Å
Crystal system, space group Monoclinic, C 2/c
Unit cell dimensions a = 22.3412(5) Å alpha = 90 deg b = 15.9121(3) Å beta = 93.240(2) deg
c = 15.4268(4) Å gamma = 90 deg
Volume 5475.4(2) Å3
Z, Calculated density 4, 1.103 mg/m3
Absorption coefficient 0.584 mm-1
F(000) 1992
Crystal size 0.204 x 0.148 x 0.102 mm
Theta range (data collection) 3.41 to 72.90 deg
Limiting indices -26<=h<=27, -19<=k<=19, -18<=l<=19 Reflections collected / unique 21972 / 5390 [R(int) = 0.0274]
Completeness to theta = 72.90 98.6 %
Absorption correction Semi-empirical from equivalents Max. and min. transmission 1.00000 and 0.87302 Refinement method Full-matrix least-squares on F^2 Data / restraints / parameters 5390 / 1 / 332
Goodness-of-fit on F2 1.022
Final R indices [I>2sigma(I)] R1 = 0.0695, wR2 = 0.1954 [4624 Fo]
R indices (all data) R1 = 0.0777, wR2 = 0.2050
Largest diff. peak and hole 0.648 and -0.451 e. Å-3 100 K
Crystal system, space group Monoclinic, C 2/c
Unit cell dimensions a = 22.2703(6) Å alpha = 90 deg b = 15.8902(5) Å beta = 93.297(3) deg
c = 15.2838(5) Å gamma = 90 deg
Volume 5399.7(3) Å3
Z, Calculated density 4, 1.118 mg/m3
Absorption coefficient 0.592 mm-1
F(000) 1992
Theta range (data collection) 3.42 to 76.31 deg
Limiting indices -27<=h<=27, -19<=k<=19, -14<=l<=19 Reflections collected / unique 12140 / 5538 [R(int) = 0.0138]
Completeness to theta = 72.90 99.0 %
Absorption correction Semi-empirical from equivalents
Max. and min. transmission 1.00000 and 0.614
Refinement method Full-matrix least-squares on F2 Data / restraints / parameters 5538 / 0 / 329
Goodness-of-fit on F2 1.061
R indices (all data) R1 = 0.0784, wR2 = 0.1974 Largest diff. peak and hole 0.818 and -0.505 e. Å-3
VT 1H spin–lattice relaxation time (T1)
Experiments were carried out as described previously1,4-7 on a static polycrystalline sample at two 1H Larmor frequencies (55 and 209 MHz) and over a wide range of temperatures using a NMR spectrometer and probe built at Orsay. The probe is designed so as to reduce spurious proton signals. The polycrystalline sample was loaded into a small glass tube (typically 1.2 mm in diameter) on which the NMR coil was wound.
1H signals were recorded using the FID following a π/2 pulse (typically 0.8-1.5 μs) and spin-lattice relaxation was measured using the standard saturation recovery sequence.
For each T1 measurement we recorded signals for 20 values of the relaxation delay between the saturating comb and the measuring pulse.
A few comments on spin-lattice measurements. As far as the rotator dynamics is concerned there is no relevant information one can get from the broad and rather featureless proton spectra dominated by strong dipolar H-H interactions, as typically found in solid-state 1H NMR of organic materials. On the other hand, the dipolar coupling is responsible of fast spin diffusion ensuring that the measured relaxation is well described by a single exponential (that is, all the spins reach equilibrium at the same spin temperature) which makes T1 measurements easier and more precise. However, we have to resort to modeling of the whole T1 curve vs temperature in order to de- convolute contributions coming from different processes.
The dynamics of molecular rotators can be characterized by their rotational correlation frequencies, τc-1, that are usually described by the Arrhenius equation (Eq. 1) in terms of characteristic activation energies (Ea) and pre-exponential factors (τ0-1). The temperature dependence of the relaxation rates T1-1 is obtained by substituting τc -1 (Eq.
1) in the Kubo-Tomita (KT) equation (Eq. 2) :
τc-1 = τ0-1exp(-Ea/RT) (Eq. 1)
T1-1 = C[ωc(1 + ω02τc2)-1+4τc(1 + 4ω02τc2)-1] (Eq. 2)
where the constant C depends the nature of the moving parts (strength of the dipolar interactions) and their relative number.
Here we consider two processes (synchronous and asynchronous events) governed by different energy barriers, therefore we fit the relaxation rate with a weighted sum of two KT expressions (a similar procedure was used in ref. 5) . Note that this approach is not a strict application of the Kubo-Tomita theory (which, strictly speaking, only applies to a single spherically isotropic diffusive process). Rather, it is a simple heuristic approximation for a system of coupled rotors where jumps may be correlated or not.
Computational details
Calculations were performed as described previously1,4-7 using the hybrid M06- 2X functional9 and the 6-31G(d,p) basis set10 as implemented in the Gaussian09 package.11
Figure S1. Structural reorganization along the rotational motion associated with the ma-ma I path of Figure 3.
References
8 Sheldrick, G. M. Acta Crystallogr. Sect. A: Found. Crystallogr. 2008, 64, 112.
9 Zhao, Y.; Truhlar, D. G. Theor. Chem. Acc. 2008, 120, 215.
10 Hariharan, P. C.; Pople, J. A. Theoret. Chimica Acta 1973, 28, 213.
11 Gaussian 09, Revision B1, Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.;
Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, G.
A.; Nakatsuji, H.; Caricato, M.; Li, X.; Hratchian, H. P.; Izmaylov, A. F.; Bloino, J.;
Zheng, G.; Sonnenberg, J. L.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Vreven, T.; Montgomery Jr.; J. A., Peralta, J. E.; Ogliaro, F.; Bearpark, M.; Heyd, J. J.; Brothers, E.; Kudin, K. N.;
Staroverov, V. N.; Kobayashi, R.; Normand, J.; Raghavachari, K.; Rendell, A.;
Burant, J. C.; Iyengar, S. S.; Tomasi, J.; Cossi, M.; Rega, N.; Millam, J. M.; Klene, M.;
Knox, J. E.; Cross, J. B.; Bakken, V.; Adamo, C.; Jaramillo, J.; Gomperts, R.;
Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.;
Martin, R. L.; Morokuma, K.; Zakrzewski, V. G.; Voth, G. A.; Salvador, P.;
Dannenberg, J. J.; Dapprich, S.; Daniels, A. D.; Farkas, Ö.; Foresman, J. B.; Ortiz, J. V.;
Cioslowski, J.; Fox, D. J. Gaussian, Inc., Wallingford CT, 2009.
