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J. Am. Chem. Soc. 2000, 122, 2346-2354
Structure, Vibrational Absorption and Circular Dichroism Spectra, and Absolute Configuration of Tro¨ger’s Base A. Aamouche, F. J. Devlin, and P. J. Stephens* Contribution from the Department of Chemistry, UniVersity of Southern California, Los Angeles, California 90089-0482 ReceiVed October 13, 1999
Abstract: The structure of Tro¨ger’s Base, 1, a heterocyclic amine containing two stereogenic N atoms, is predicted from ab initio Density Functional Theory (DFT), using the B3PW91 and B3LYP functionals and the 6-31G* basis set. Vibrational unpolarized absorption and vibrational circular dichroism (VCD) spectra are predicted thence. In the case of VCD, Atomic Axial Tensors (AATs) are calculated using Gauge-Invariant Atomic Orbitals (GIAOs). The predicted structure is in excellent agreement with the X-ray structure of 1. The predicted vibrational spectra are in excellent agreement with experimental spectra of CCl4 and CS2 solutions of 1, supporting the identicalness of the crystalline and solution conformations of 1. No evidence of additional conformations of 1 in solution is found. The VCD spectra require the assignment of the (R,R)/(S,S) absolute configuration to (-)/(+)-1, opposite to that obtained from the electronic circular dichroism spectrum by Mason et al. and in accord with that obtained from X-ray crystallography of a salt of 1 containing monoprotonated 1, 2, and a chiral anion by Wilen et al. The structure of 2 predicted by DFT is also in excellent agreement with the X-ray structure.
Introduction Tro¨ger’s Base,1 1, is a chiral heterocyclic amine containing two stereogenic N atoms:
Figure 1. Atom numbering of 1.
Resolution of 1 was reported in 1944 by Prelog and Wieland.2 The absolute configuration of (+)-1 was determined to be (R,R) by Mason et al. in 19673 from its near-ultraviolet electronic circular dichroism (CD), using the “Coupled Oscillator” (CO) or “Exciton Coupling” methodology.4,5 The X-ray structure of racemic 1 was reported by Wilcox/Larson and Wilcox in 1985/ 1986.6,7 In 1991, the X-ray structure of a salt, containing monoprotonated (+)-1, 2, and the monoanion, 3, of (-)-1,1′binaphthalene-2,2′-diyl hydrogen phosphate, 4, was reported by Wilen et al.8 Given the R absolute configuration of (-)-4, the * To whom correspondence should be addressed: stephens@ chem1.usc.edu. (1) Tro¨ger, J. J. Prakt. Chem. 1887, 36, 225. (2) Prelog, V.; Wieland, P. HelV. Chim. Acta 1944, 27, 1127. (3) Mason, S. F.; Vane, G. W.; Schofield, K.; Wells, R. J.; Whitehurst, J. S. J. Chem. Soc. B 1967, 553. (4) Charney, E. The Molecular Basis of Optical ActiVity: Optical Rotatory Dispersion and Circular Dichroism, Wiley: 1979, Chapter 4, p 110. (5) Harada, N.; Nakanishi, K. Circular Dichroic Spectroscopy: Exciton Coupling in Organic Stereochemistry; University Science Books: Mill Valley, CA, 1983. (6) Wilcox, C. S. Tetrahedron Lett. 1985, 26, 5749. (7) Larson, S. B.; Wilcox, C. S. Acta Crystallogr. Sect. C 1986, C42, 224. (8) Wilen, S. H.; Qi, J. Z.; Williard, P. G. J. Org. Chem. 1991, 56, 485.
(S,S) absolute configuration was deduced for (+)-1, opposite to that reported earlier by Mason et al.3 We report a study of the structure and absolute configuration of 1 using ab initio vibrational spectroscopy. The structure,
Figure 2. The B3PW91/6-31G* structure of (R,R)-1. (a) The entire molecule, as viewed with N1C9 and N5C9 eclipsed. (b) The N1C2C3C4N5C9 ring conformation.
10.1021/ja993678r CCC: $19.00 © 2000 American Chemical Society Published on Web 02/29/2000
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Table 1. Frequencies, Dipole Strengths, and Rotational Strengths of 1a expt
B3PW91
B3LYP
modeb
ν
D
R
ν
D
R
ν
D
R
87 86 85 84 83 82 81 80 79 78 77 76 75 74 73 72 71 70 69 68 67 66 65 64 63 62 61 60 59 58 57 56 55 54 53 52 51 50 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33c 32c 31c 30c 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14
1620 1616 1578 1575 1497 1492 1478 1462 1458 1443 1440 1439 1435 1415 1412 1378 1376 1360 1345 1326 1324 1301 1297 1291 1265 1259 1250 1240 1225 1206 1192 1164 1148 1142 1114 1099 1094 1066 1044 1038 1018 997 990 970 964 951 943 939 919 899 873 870 832 824 806 748 739 730 721 715 691 636 584 570 561 529 511 476 470 456 431 423 411 384
1.3 1.4 2.0 0.8 225.6 312.2 16.3 13.0 28.0 7.1 4.2 50.2 7.7 5.2 65.4 1.5 11.1 14.7 33.6 111.3 42.1 23.0 23.8 36.8 6.3 16.0 8.1 9.6 18.2 230.7 54.0 17.0 14.0 36.1 90.6 58.6 31.8 86.5 11.1 18.1 4.1 9.4 10.4 39.5 105.8 170.8 60.7 13.2 2.1 118.9 9.5 36.3 247.8 117.0 25.0 29.3 36.4 4.0 3.5 27.0 16.9 128.5 104.0 62.6 33.9 43.3 43.7 5.2 25.7 27.7 24.0 32.4 81.4 22.2
3.0 -8.9 -2.4 3.6 300.7 -360.8 2.1 -5.9 -40.4 -27.8 13.1 14.7 -0.5 -21.3 -10.5 0.2 6.0 -2.8 81.3 0.8 -17.3 -14.9 -53.3 -98.0 -5.2 -20.2 -15.9 16.5 -12.5 66.0 100.8 18.4 -32.4 12.9 101.5 -40.8 -52.3 -29.0 -9.8 -8.9 -14.1 -72.3 -62.6 69.3 104.2 -70.2 -44.3 10.1 -2.2 -101.5 5.9 7.8 -91.0 26.4 22.2 36.3 0.9 14.8
1686 1685 1639 1636 1553 1548 1525 1523 1517 1510 1510 1500 1497 1466 1462 1436 1436 1407 1400 1383 1376 1359 1353 1337 1306 1300 1291 1274 1263 1249 1230 1199 1183 1177 1145 1135 1134 1094 1069 1069 1040 1031 1026 994 989 977 957 957 940 924 891 889 846 841 823 760 757 745 740 731 704 644 595 580 572 532 518 482 475 462 434 430 413 389
0.6 12.5 2.6 14.2 133.0 362.7 2.0 53.6 2.5 13.6 16.8 29.1 3.7 8.1 90.2 0.1 4.0 22.9 23.1 100.2 0.4 94.4 10.7 38.3 4.9 2.2 8.4 0.4 8.0 299.6 32.5 21.3 7.4 34.4 102.5 0.1 67.9 37.0 10.8 35.4 2.2 1.3 27.2 77.9 77.8 237.0 1.0 1.7 0.6 94.7 3.4 11.7 233.4 74.6 5.4 35.9 6.2 1.0 1.7 21.4 6.3 73.2 50.6 20.6 10.3 21.6 35.0 2.4 18.6 7.7 8.9 6.7 37.2 23.8
8.3 -20.2 -10.1 8.7 148.0 -191.9 14.4 -43.3 -10.6 3.6 -2.1 8.0 -1.2 -4.2 -20.6 0.2 0.2 -5.2 43.1 2.7 -4.3 -36.2 -10.4 -80.6 -5.5 -1.8 -5.4 2.9 -14.2 70.6 84.5 -0.7 -16.1 6.9 33.7 3.2 -42.5 -13.0 -2.0 -7.5 -4.9 11.5 -85.3 94.3 55.5 -114.7 -2.2 2.2 -3.4 -48.1 2.1 14.2 -127.0 12.6 -14.7 5.7 0.6 2.1 -6.0 -22.8 -1.2 2.2 -1.1 33.8 -15.8 -4.5 -8.2 -1.1 -20.8 -1.6 -6.3 5.9 46.6 -3.3
1674 1672 1626 1624 1548 1543 1530 1527 1524 1515 1515 1507 1505 1462 1458 1444 1443 1410 1391 1375 1372 1347 1342 1333 1306 1301 1286 1265 1257 1242 1225 1193 1181 1177 1139 1122 1122 1091 1075 1075 1038 1033 1027 993 983 967 957 956 935 915 894 892 847 843 822 759 755 744 738 731 699 644 597 582 573 535 519 484 477 464 435 432 414 391
0.4 10.8 2.1 12.7 120.0 316.1 0.6 52.8 0.0 8.4 16.0 29.4 2.2 8.1 85.5 0.2 10.1 35.6 22.0 119.7 5.5 58.6 5.6 32.0 1.4 4.1 10.6 4.9 6.6 337.8 36.3 16.0 2.6 26.0 99.8 8.6 60.8 49.8 7.3 28.9 2.8 3.7 28.7 57.5 88.7 255.5 1.0 0.4 0.3 131.3 2.8 10.7 196.8 62.7 12.4 31.3 6.7 0.0 3.3 21.9 7.9 74.9 45.5 15.7 6.5 22.2 31.0 2.8 15.7 8.2 6.2 5.2 31.6 18.3
6.2 -17.3 -9.4 9.1 120.9 -150.0 6.2 -46.2 0.7 7.1 -6.0 3.7 -1.5 -2.2 -23.5 -0.2 -0.6 -7.3 40.5 19.7 -16.4 -54.3 -3.4 -64.2 0.2 -4.4 -11.9 8.6 -8.2 34.9 89.6 -1.5 -10.0 3.7 64.5 -31.5 -39.9 0.2 -1.7 -10.5 -10.4 19.3 -79.3 71.6 56.6 -98.2 -1.8 1.8 -2.0 -56.0 0.9 15.6 -101.4 5.0 -25.7 7.2 1.3 0.0 -6.9 -20.3 -1.8 1.3 -0.7 28.4 -12.0 -4.6 -5.7 -1.0 -17.4 -1.5 -6.1 5.2 42.6 -3.6
a Frequencies in cm-1; dipole strengths in 10-40 esu2 cm2; rotational strengths in 10-44 esu2 cm2. Calculated and experimental rotational strengths are for (R,R)-1 and (-)-1, respectively. b From Lorentzian fitting of CCl4 spectra, except where indicated.We report parameters only for bands assigned to fundamentals. Additional bands included in the fits at 1126, 1216, 1514, and 1525 cm-1 are assigned to nonfundamentals or to impurities. c From CS spectra. 2
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Figure 3. Comparison of calculated and experimental structural parameters of 1 and 2: (a) bond lengths; (b) bond angles; and (c) dihedral angles. The slopes of the lines are +1.
vibrational unpolarized absorption spectrum, and vibrational circular dichroism (VCD)9 spectrum of 1 are predicted using ab initio Density Functional Theory (DFT).10 The predicted structure is in excellent agreement with the X-ray structure.6,7 (9) (a) Stephens, P. J.; Lowe, M. A. Annu. ReV. Phys. Chem. 1985, 36, 213; (b) Nafie, L. A. Annu. ReV. Phys. Chem. 1997, 48, 357. (10) Chemical Applications of Density Functional Theory, Laird, B. B., Ross, R. B., Ziegler, T., Eds.; ACS Symposium Series 629; American Chemical Society: Washington, D. C., 1996.
The predicted vibrational spectra are in excellent agreement with the experimental spectra in solution in CCl4 and CS2. Comparison of predicted and observed VCD spectra confirms the (S,S)-(+)/(R,R)-(-) absolute configuration of 1. In addition, we have predicted the structure of monoprotonated 1, 2. The agreement with the experimental structure is excellent. Our work takes advantage of the recent development and implementation of analytical derivative techniques for the
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calculation of DFT Atomic Axial Tensors (AATs) using GaugeInvariant Atomic Orbitals (GIAOs)11 which, together with DFT harmonic force fields (HFFs) and Atomic Polar Tensors (APTs), permit the prediction of vibrational rotational strengths and VCD spectra.12 This theoretical methodology has previously been applied to a number of chiral molecules, including trans-2,3d2oxirane,11 6,8-dioxabicyclo[3.2.1]octane13 and several mono- and dimethyl derivatives,14 camphor,15 fenchone,15 R-pinene,16 phenyloxirane,17 cyclohexanone-2d1 and -trans-2,6d2,18 and 3-methylcyclohexanone.19 Methods (+)-, (-)-, and (()-1 were obtained from Aldrich and (-)-1 from Fluka and used without further purification. Specified chemical purities were: (+), >99%; (-), >99%; ((), 98% (Aldrich); (-), 99% (Fluka). Specified specific rotations were: (+), [R]20D ) +280° (c ) 0.5, hexane); (-), [R]20D ) -280° (c ) 0.5, hexane) (Aldrich) and -283° (c ) 0.3, hexane) (Fluka). Prior literature values for (+)-1 are: [R]17D ) 287 ( 7° (c ) 0.281, hexane)2; [R]25D ) 287 ( 2° (c ) 0.29, hexane).8 The latter value was obtained on (+)-1 whose enantiomeric purity was >99%.8 Aldrich and Fluka (+)- and (-)-1 can therefore be assumed to possess enantiomeric excess (ee) > 95%. Vibrational unpolarized absorption spectra of CCl4 and CS2 solutions of 1 were obtained using a Nicolet MX-1 spectrometer at 1 cm-1 resolution. VCD spectra of CCl4 and CS2 solutions of 1 were obtained using Bomem/BioTools ChiralIR spectrometers at 4 cm-1 resolution. All experiments used a variablepath cell (Graseby Specac Ltd., UK) with KBr windows. Frequencies, dipole strengths, and rotational strengths were obtained from experimental absorption and VCD spectra via Lorentzian fitting.15b,16 DFT calculations were carried out using the Gaussian program20 as described previously.11,13-19 The hybrid density functionals B3PW9121 and B3LYP22 were used together with (11) Cheeseman, J. R.; Frisch, M. J.; Devlin, F. J.; Stephens, P. J. Chem. Phys. Lett. 1996, 252, 211. (12) (a) Stephens, P. J. J. Phys. Chem. 1985, 89, 748; (b) Stephens, P. J. J. Phys. Chem. 1987, 91, 1712. (13) Stephens, P. J.; Cheeseman, J. R.; Frisch, M. J.; Ashvar, C. S.; Devlin, F. J. Mol. Phys. 1996, 89, 579. (14) (a) Ashvar, C. S.; Stephens, P. J.; Eggimann, T.; Wieser, H. Tetrahedron: Asymmetry 1998, 9, 1107. (b) Ashvar, C. S.; Devlin, F. J.; Stephens, P. J.; Bak, K. L.; Eggimann, T.; Wieser, H. J. Phys. Chem. A 1998, 102, 6842. (15) (a) Devlin, F. J.; Stephens, P. J.; Cheeseman, J. R.; Frisch, M. J. J. Am. Chem. Soc. 1996, 118, 6327; (b) Devlin, F. J.; Stephens, P. J.; Cheeseman, J. R.; Frisch, M. J. J. Phys. Chem. 1997, 101, 6322. (16) Devlin, F. J.; Stephens, P. J.; Cheeseman, J. R. Frisch, M. J. J. Phys. Chem. 1997, 101, 9912. (17) Ashvar, C. S.; Devlin, F. J.; Stephens, P. J. J. Am. Chem. Soc. 1999, 121, 2836. (18) Devlin, F. J.; Stephens, P. J. J. Phys. Chem. A 1999, 103, 527. (19) Devlin, F. J.; Stephens, P. J. J. Am. Chem. Soc. 1999, 121, 7413. (20) GAUSSIAN 95, Development version, and GAUSSIAN 98; Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Zakrzewski, V. G.; Montgomery, J. A., Jr.; Stratmann, R. E.; Burant, J. C.; Dapprich, S.; Millam, J. M.; Daniels, A. D.; Kudin, K. N.; Strain, M. C.; Farkas, O.; Tomasi, J.; Barone, V.; Cossi, M.; Cammi, R.; Mennucci, B.; Pomelli, C.; Adamo, C.; Clifford, S.; Ochterski, J.; Petersson, G. A.; Ayala, P. Y.; Cui, Q.; Morokuma, K.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Cioslowski, J.; Ortiz, J. V.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Gomperts, R.; Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham, M. A. Peng, C. Y.; Nanayakkara, A.; Gonzalez, C.; Challacombe, M.; Gill, P. M. W.; Johnson, B.; Chen, W.; Wong, M. W.; Andres, J. L.; Head-Gordon, M.; Replogle, E. S.; Pople, J. A. Gaussian, Inc.: Pittsburgh, PA, 1998. (21) Becke, A. D. J. Chem. Phys. 1993, 98, 1372, 5648. (22) Stephens, P. J.; Devlin, F. J.; Chabalowski, C. F.; Frisch, M. J. J. Phys. Chem. 1994, 98, 11623.
Figure 4. Mid-IR absorption spectrum of 1. (a) Solid line: experimental spectrum of 1 in CCl4 (0.2 M (()-1; 370-730, 815-1480, and 1525-1800 cm-1; 0.1 M (-)-1; 1480-1525 cm-1) and in CS2 (0.2 M (-)-1; 730-815 cm-1). Resolution is 1 cm-1. Dotted line: Lorentzian fit. (b) The difference between the experimental spectrum and Lorentzian fit.
the 6-31G* 23 basis set (321 basis functions). All calculations used direct, analytical derivative methods. Atomic Axial Tensors (AATs) were calculated using GIAOs; as a result, Common Origin gauge12,24 vibrational rotational strengths are originindependent. Absorption and VCD spectra were synthesized from calculated vibrational frequencies, dipole strengths, and rotational strengths, assuming Lorentzian band shapes. Results Equilibrium structures of 1 have been calculated at the B3PW91/6-31G* and B3LYP/6-31G* levels. Bond lengths, bond angles, and dihedral angles of the two structures are given in Table 1 of the Supporting Information. The atom numbering is detailed in Figure 1. The structures exhibit C2 symmetry. B3PW91 and B3LYP structures are qualitatively identical. The B3PW91 structure is illustrated in Figure 2a. The N1C2C3C4C15C16C19C17C18 and N5C6C7C8C10C11C14C12C13 moieties are very nearly planar. The N1C2C3C4N5C6C7C8 ring is boatlike. A rigid conformation is enforced by the CH2 bridge. The conformation of the C4N2 rings is shown in Figure 2b. Quantitatively, we note that B3LYP bond lengths are systematically longer than B3PW91 bond lengths, the difference varying from 0.002 to 0.008 Å; the largest differences are for bonds in the C4N2 rings. Bond angles and dihedral angles differ very little; maximum differences are 0.1 and 0.5°, respectively. (23) Hehre, W. J.; Schleyer, P. R.; Radom, L.; Pople, J. A. Ab Initio Molecular Orbital Theory, Wiley: New York, 1986. (24) Stephens, P. J.; Jalkanen, K. J.; Amos, R. D.; Lazzeretti, P.; Zanasi, R. J. Phys. Chem. 1990, 94, 1811.
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Figure 5. Mid-IR absorption spectrum of 1. (a) Experimental spectrum (from Figure 4); (b) B3PW91/6-31G* spectrum; (c) B3LYP/6-31G* spectrum. Lorentzian band shapes are used (γ ) 4.0 cm-1). Fundamentals are numbered. Asterisks denote bands not assigned as fundamentals of 1.
The maximum deviation from 0° of the dihedral angles of the C atoms of the phenyl rings is 1.0° for C10C11C12C13/ C15C16C17C18. The B3PW91/B3LYP dihedral angles C8C7C6C13/C4C3C2C18 and C8C7C10C11/C4C3C15C16 deviate from 180° by 2.5/2.2 and 2.3/2.0°, respectively. N1/N5 and C9 are on opposite sides of the N5C6C7C8/N1C2C3C4 planes, respectively. The B3PW91/B3LYP dihedral angles N5C4C3C2/ N1C8C7C6 and C3C2N1C9/C7C6N5C9 are 11.0/11.0 and 17.5/ 18.0°, respectively. The methyl groups substituted on the phenyl rings adopt conformations in which one C-H is very nearly coplanar with the adjacent phenyl ring. In the case of the methyl group substituted at C11/C16, this H is cis with respect to C10/C15. We have examined the variation in energy of 1 on rotation of the two methyl groups (maintaining C2 symmetry), at the B3PW91/6-31G* level. The barrier is 3-fold. Rotation by 180°
does not lead to a second minimum. Thus, no other inequivalent conformations of the methyl groups are predicted. Equilibrium structures have also been calculated for 2 at the B3PW91/6-31G* and B3LYP/6-31G* levels. Bond lengths, bond angles, and dihedral angles are given in Table 1 of the Supporting Information. Large changes in bond lengths on protonation of 1 occur only for the N1C2, N1C8, N1C9, and N5C9 bonds. The B3PW91/B3LYP changes are 0.053/0.054 Å, 0.044/0.046 Å, 0.089/0.096 Å, and -0.049/-0.052 Å, respectively. All other bond length changes are e0.012 Å. The largest changes in bond angles occur for C4N5C9, N5C9N1, and C18C2C3. The B3PW91/B3LYP changes are 3.0/3.0°, -3.2/-3.5°, and 2.9/2.9°, respectively. All other changes are
