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Keywords:

  • absolute configuration;
  • cyclotrimerization;
  • circular dichroism;
  • benzocyclotrimers;
  • optical rotation;
  • DFT calculations

Abstract

  1. Top of page
  2. Abstract
  3. INTRODUCTION
  4. MATERIALS AND METHODS
  5. RESULTS AND DISCUSSION
  6. CONCLUSIONS
  7. Acknowledgements
  8. LITERATURE CITED
  9. Supporting Information

The large molecules 13 (69, 90, and 102 atoms, respectively), prepared by cyclotrimerization of enantiomerically pure derivatives of (−)-bornyl acetate, show intense ECD spectra, high optical rotation (OR) values (200–1300, in absolute value) dominated in sign and order of magnitude by the lowest-energy Cotton effects, that is, they are the ideal candidates to test the reliability of our “approximate” (TDDFT/B3LYP/6-31G* or smaller basis set) approach to the calculation of chiroptical properties. As a matter of fact, a correct simulation of the OR values and ECD spectra of 1 and 2 can be obtained even using STO-3G basis set and semiempirical or molecular mechanics input geometries: for 1, at the TDDFT/B3LYP/STO-3G level, the OR values are of the order of 500–550, versus an experimental value ranging between 660 and 690, depending on the solvent. On the contrary, the case of 3 (exp. OR between −1330 and −1500) is really complex (for instance, the OR values range between −3216 and −729 (TDDFT/B3LYP/6-31G* calculations) or −1824 and −444 (TDDFT/B3LYP/STO-3G calculations)), making the comparison between calculated and experimental values more difficult. The behavior of 3 is due to its molecular flexibility, whereas 1 is a really rigid molecules and 2 behaves (vide infra) as it were a rigid system. These observations strongly indicate that the conformational freedom constitutes one of the major difficulties for a correct but simple simulation of the chiroptical properties. Chirality 21:E86–E97, 2009. © 2009 Wiley-Liss, Inc.


INTRODUCTION

  1. Top of page
  2. Abstract
  3. INTRODUCTION
  4. MATERIALS AND METHODS
  5. RESULTS AND DISCUSSION
  6. CONCLUSIONS
  7. Acknowledgements
  8. LITERATURE CITED
  9. Supporting Information

The analysis of the chiroptical properties1–3 (optical rotation, OR, optical rotatory dispersion, ORD, electronic, and vibrational circular dicroism, ECD and VCD, respectively) has for several years, constituted an useful tool to assign the molecular absolute configuration.4–8 In addition, the development of ab initio methods9 (time-dependent Hartree–Fock, TDHF, time-dependent density functional theory, TDDFT), which allow the simulation of such chiroptical properties10–14 and the commercial availability of suitable computer packages (Gaussian03,15 Dalton2.0,16 TurboMole5.1017), made this analysis safer and hence the configurational assignment derived from it more reliable. This progress makes, at least in principle, these methods accessible even to nonspecialists, such as experimental organic chemists, who are the researchers more interested in solving the problem of the assignment of the molecular absolute configuration. From this point of view, the ab initio calculation10–14 of the OR at a certain wavelength, usually 589 nm, represents a particularly appealing method to the experimental organic chemist because it requires a simple OR measurement, which can be carried out with a cheap instrument, the polarimeter, present in all the laboratories of synthetic organic chemistry and a calculation feasible by means of the above quoted computer packages with a standard desktop computer. In spite of all these progresses, some difficulties are still present. In fact, Stephens et al.18 claiming that the ab initio calculation of the OR (and of ECD) provides a reliable answer only by the use of TDDFT method with extended basis sets (i.e., including diffuse functions) propose the use of the TDDFT method with the state-of-the-art hybrid functional B3LYP19–21 and an extended basis set (aug-cc-pVDZ or higher) as a reliable and largely applicable22–57 calculation technique. Clearly, such a recipe makes compulsory the use of powerful computing systems when big-sized molecules (i.e., those having applicative interest and most common for the practicing organic chemist) are treated: this represents a clear obstacle to the diffusion of these methods among nonspecialists. The aim of this article is just to approach this problem: do some cases exist where it is possible to use smaller basis sets, without reducing the reliability of the answer? In such cases, one could do calculations even to large-size molecules with standard desktop computers, providing then an important contribution to the diffusion of these methods among the experimental organic chemists. Actually, for a few years we are involved in a research project of this type58–66: we noticed that when the OR at the sodium Dline (589 nm) is determined in sign and order of magnitude by the lowest-energy Cotton effects, even a TDDFT/B3LYP/6-31G* calculation provides the correct answer. Therefore, with this article, we intend to verify if and how much it is possible, for the molecular structures having the above required spectroscopic features, reducing the level of the quality of the treatment but obtaining completely reliable answers. This aspect is, in our opinion, very important: if it is possible to a priori provide some criteria to establish if a certain system can be treated at a low level of theory (say, TDDFT/B3LYP/6-31G* or smaller basis sets) with a safe result, we will gain a strong reduction of the computational effort and such large molecules will be treated without the use of supercomputers. In summary, to establish if and how much our “approximate” approach (i.e., the OR calculation using the TDDFT method, with the B3LYP functional, and the 6-31G* basis set or smaller) can be safely used to simulate OR values and then provide a reliable configurational assignment, we decided to study the cases of compounds 1–3 below (Chart 1) taking into account (vide infra) that these molecules are of known absolute configuration, in fact, they have been prepared from (−)-bornyl acetate, a configurationally established compound, using reactions which do not involve the stereogenic centers: as a result, the absolute configuration of 13 is the same as the starting compound and is that reported in Chart 1. Of course, this information constitutes an essential prerequisite to test the validity of our “approximate” approach. In addition, they show intense (Δϵ > 10) Cotton effects in their ECD spectra and possess high OR values (>200 deg[dm g/cm3]−1), determined in sign and order of magnitude by the lowest ECD bands. In summary, compounds 1–3 have all the necessary spectroscopic features required for the application of our “approximate” approach. In particular, we intend to test how much we can reduce the level of theory: to this end, we shall study the behavior of the very small STO-3G basis set, which, to the best of our knowledge, has not been used in the ab initio calculation of chiroptical properties.

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Chart 1. Schematic of compounds 1–3.

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MATERIALS AND METHODS

  1. Top of page
  2. Abstract
  3. INTRODUCTION
  4. MATERIALS AND METHODS
  5. RESULTS AND DISCUSSION
  6. CONCLUSIONS
  7. Acknowledgements
  8. LITERATURE CITED
  9. Supporting Information

Solvents and chemicals were used as received unless otherwise stated. THF and toluene were distilled from sodium/benzophenone under argon atmosphere. Diisopropylamine was distilled from calcium hydride under argon atmosphere. Flash chromatography was performed with 360–400 mesh silica-gel Merk 60. (+)-syn-Benzotricamphor was obtained according to literature procedures.67

(1S,4S)-5-Bromo-1,7,7-trimethylbiciclo[2.2.1]hept-5-en-2-one (5)

A slurry of endo-3-bromo-6-hydroxy-1,7,7-trimethylbiciclo[2.2.1]hept-2-ene [66] (4) (10.00 g, 43.3 mmol), N-methylmorpholine-N-oxide NMO (7.60 g, 64.9 mmol), and activated 4 Å molecular sieves (10 g) in DCM (200 ml) was stirred for 15 min in argon atmosphere. Tetrapropylammonium perrutenate (TPAP, 300 mg, 0.87 mmol) was added and the mixture was maintained under vigorous stirring for 2 h. The resulting slurry was filtered on a pad of florisil-celite, obtaining a solution that was washed with 1 M aqueous HCl (4 × 50 ml), NaHCO3 (3 × 50 ml), dried over MgSO4, and concentrated by distillation at 760 Torr. The residue was purified by flash chromatography (eluant 0.5:9.5 Et2O/n-pentane) to obtain 7.60 g (76% yield) of pale yellow oil.

[α]math image = +508 (c 1.4, CHCl3). 1H NMR (300 MHz, CDCl3): δ 5.64 (1H, dd, J = 1.3 and 1.0 Hz), 2.67 (1H, dd, J= 3.4 and 1.3 Hz), 2.27 (1H, ddd, J = 16.9, 3.4, and 1.0 Hz), 2.05 (1H, d, J = 16.9 Hz), 1.16 (3H, s), 1.05 (3H, s), 0.92 (3H, s) ppm. 13C NMR (75 MHz, CDCl3): δ 213.5, 133.1, 131.1, 67.3, 60.3, 57.3, 35.2, 19.3, 19.1, 6.9 ppm. IR (film): ν 2968, 2932, 2872, 1747, 1578, 1024 cm−1. MS (EI, 70 eV) m/z: 230–228 (M+, 6), 188–186 (M+[BOND]C2H4O, 68), 107 (100%). C10H13BrO (229.11): calcd. C 52.42, H 5.72; found C 5.31, H 5.60.

(1S,4S)-5-Bromo-1,7,7-trimethylbiciclo[2.2.1]hept-5-en-2-ethanediolacetal (6)

A mixture of 5-bromo-1,7,7-trimethylbiciclo[2.2.1]hept-5-en-2-one (5) (7.00 g, 30 mmol), ethylene glycol (4.5 ml, 79 mmol), and p-toluenesulphonic acid (600 mg, 3.10 mmol) in cyclohexane (350 ml) was refluxed for 24 h on a dropping funnel containing 4 Å molecular sieves. The mixture was poured onto saturated NaHCO3 (200 ml), washed with H2O (3 × 50 ml), dried over MgSO4, and concentrated at reduced pressure. Residual ethylene glycol was removed by azeotropic distillation in rotavapor with small portions of toluene. The resulting oil was purified by flash chromatography (eluant 1:9 Et2O/hexane) to obtain 7.13 g (85% yield) of colorless oil.

[α]math image = +126 (c 1.9, CHCl3); 1H NMR (CDCl3, 300 MHz): δ 5.83 (1H, br d, J = 1.4 Hz), 4.00–3.75 (4H, m), 2.40 (1H, dd, J = 3.7 and 1.4 Hz), 2.10 (2H, dd, J = 12.6 and 3.7 Hz), 1.63 (1H, d, J =12.6 Hz), 1.07 (3H, s), 1.02 (3H, s), 0.96 (3H, s) ppm; 13C NMR (CDCl3, 75 MHz): δ 137.1, 128.0, 119.5, 66.0, 64.4, 62.7, 59.9, 59.8, 40.1, 21.2, 20.4, 7.6 ppm; IR (film): v 2959, 2874, 1589, 1473, 1449, 1299, 1184, 1052, 988, 924, 874, 737 cm−1; MS (EI, 70 eV) m/z: 272–274 (M+,6), 186–188 (M+[BOND]C2H4O, 48), 107 (94), 86 (100). C12H17BrO2 (273.17): calcd. C 52.76, H 6.27; found C 53.11, H 6.62.

(1S,4S)-5-Bromo-6-(trimethylstannyl)-1,7,7-trimethylbiciclo[2.2.1]hept-5-en-2-ethanediolacetal (7)

To a solution of dry diisopropylamine (1.5 ml, 11.3 mmol) in dry THF (11 ml) maintained at 0°C under Ar was added dropwise n-BuLi (4.5 ml, 2.5 M in hexane, 11.3 mmol), and the mixture was maintained at 0°C for 15 min. 5-Bromo-1,7,7-trimethylbiciclo[2.2.1]hept-5-en-2-ethanediolacetal (6) (1.23 g, 4.5 mmol) was added via syringe and the mixture was stirred for an additional 15 min. Trimethyltin chloride (1.0 g, 5.0 mmol) was added in one portion and the mixture was left to rise to room temperature overnight. The resulting solution was poured onto saturated aqueous NaCl (15 ml) and extracted with Et2O (3×50 ml). Combined organic extracts were washed with H2O (3×20 ml), saturated aqueous NaCl (3×20 ml), dried over MgSO4, and concentrated in vacuum to afford an oil that was purified by flash chromatography over neutral Al2O3 to obtain 1.55 g (79% yield) of colorless crystal, m.p. 41°C.

[α]math image = +86 (c 1.1, CHCl3). 1H NMR (200 MHz, CDCl3): δ 3.99–3.69 (4H, m), 2.40 (1H, d, J = 3.6 Hz), 2.05 (1H, dd, J = 12.5 and 3.6 Hz), 1.61 (2H, dd, J = 12.5 Hz), 1.05 (3H, s), 1.00 (3H, s), 0.98 (3H, s), 0.24 (9H, s) ppm. 13C NMR (75 MHz, CDCl3): δ 149.5, 139.9, 119.1, 67.1, 65.4, 63.8, 61.6, 58.9, 40.0, 20.9, 20.0, 9.4, −7.7 ppm. IR (KBr): ν 2965, 1554, 1387, 1299, 1173, 1091, 1018, 769, 527 cm−1. MS (EI, 70 eV) m/z: 436 (M+, 1), 421 (M+[BOND]CH3, 2), 377 (5), 350 (16), 335 (53), 255 (54), 229 (64), 105 (100). C15H25BrO2Sn (435.97): calcd. C 41.32, H 5.78; found C 41.67, H 6.13.

syn-(1R,4S,5R,8S,9R,12S)-3,4,7,8,11,12-Hexahydro-2,6,10-triethanediolacetal-1,5,9,13,13′,14,14′,15,15′-nonamethyl-1,4:5,8:,9,12-trimethanotriphenylene (syn-2)

Copper(I) 2-thiophenecarboxylate (1.17 g, 6.12 mmol) was added portionwise to a solution of 5-bromo-6-(trimethylstannyl)-1,7,7-trimethylbiciclo[2.2.1]hept-5-en-2-ethanediolacetal (7) (1.77 g, 4.06 mmol) in dry NMP (6 ml), maintained at −20°C under Ar. The well-stirred mixture was maintained at −20°C for 2 h and was finally allowed to warm to room temperature overnight. The resulting slurry was diluted with 15% aqueous NH3 (20 ml), stirred for 2 h in air, and extracted with hexane (3 × 50 ml). The combined organic extracts were washed with H2O (50 ml) and saturated aqueous NaCl (50 ml), dried with MgSO4, and concentrated in vacuo to afford an oil that was purified by recrystallization from hot MeOH. Colorless crystals 480 mg (61% yield), m.p. > 260°C (MeOH).

[α]math image = +222 (c 1.2, CHCl3); 1H NMR (300 MHz, CDCl3): δ 3.98–3.68 (12H, m), 3.03 (3H, d, J = 4.2 Hz), 2.23 (3H, dd, J = 12.6 and 4.2 Hz), 1.81 (3H, d, J = 12.6 Hz), 1.20 (9H, s), 1.18 (9H, s), 0.62 (9H, s) ppm. 13C NMR (75 MHz, CDCl3): δ 140.2, 135.4, 118.5, 65.4, 64.5, 60.4, 57.8, 48.6, 41.9, 21.9, 20.2, 9.0 ppm. IR (KBr): ν 2943, 2873, 1094, 1053 cm−1. MS (EI, 70 eV) m/z: 576 (M+, 1), 532 (M+[BOND]C2H4O, 1), 490 (7), 446 (6), 404 (8), 360 (47), 318 (72), 303 (33), 289 (18), 273 (16), 259 (11), 229 (6), 86 (100), 43 (55%). C36H48O6 (576.76): calcd. C 74.97, H 8.39; found C 75.32, H 8.74.

anti-(1S,4R,5R,8S,9R,12S)-1,2,7,8,11,12-Hexahydro-3,6,10-triethanediolacetal-4,5,9,13,13′,14,14′,15,15′-nonamethyl-1,4:5,8:9,12-trimethanotriphenylene (anti-2)

Mother liquors from the crystallization of the previous product were concentrated and purified by flash chromatography (eluant Et2O/hexane 1:9) to afford 70 mg (9% yield) of colorless crystals, m.p. 224–227°C.

1H NMR (300 MHz, CDCl3): δ 4.00–3.56 (12H, series of m), 3.02 (1H, d, J = 4.2 Hz), 2.72 (1H, d, J = 4.0 Hz), 2.69 (1H, d, J = 4.0 Hz), 2.29 (1H, dd, J = 12.5 and 4.0 Hz), 2.26(1H, dd, J = 12.4 and 4.0 Hz), 2.20 (1H, dd, J = 12.5 and 4.2 Hz), 1.68 (1H, d, J = 12.5 Hz), 1.52 (1H, d, J = 12.5 Hz), 1.46 (1H, d, J = 12.4 Hz), 1.28 (6H, s), 1.22 (3H, s), 1.18 (3H, s), 1.15 (6H, s), 0.61 (3H, s), 0.59 (3H, s), 0.58 (3H, s) ppm. 13C NMR (75 MHz, CDCl3): δ 141.2, 140.3, 140.2, 137.8, 136.4, 134.6, 118. 6, 118.3, 118.2, 65.5, 65.45, 65.37, 64.0, 63.6, 63.5, 61.7, 61.4, 60.6, 58.7, 58.3 (2 overlapping C), 48.9, 48.6, 47.9, 43.2, 43.0, 42.0, 22.03, 22.00, 21.8, 20.54, 20.52, 20.2, 10.9, 10.7, 9.1 ppm. IR (KBr): ν 2947, 2875, 1098, 1049 cm−1. MS (EI, 70 eV) m/z: 574 (M+, 1), 532 (M+[BOND]C2H4O, 1), 490 (17), 446 (27), 404 (58), 360 (73), 318 (97), 303 (59), 289 (33), 259 (19), 229 (10), 86 (100), 43 (67%). C36H48O6 (576.76): calcd. C 74.97, H 8.39; found C 75.19, H 8.68.

E,E,E-(1R,4R,5R,8R,9R,12R)-3,7,11-Tribenzyliden-4,8,12-trihydro-1,5,9,13,13′,14,14′,15,15′-nonamethyl-1,4:5,8:9,12-trimethanotriphenylene (3)

A solution of (+)-syn-benzotricamphor (1) (60 mg, 0.13 mmol),68 benzaldehyde (100 mg, 0.94 mmol), and potassium tert-butanolate (60 mg, 0.53 mmol) in dry toluene (20ml) was refluxed for 24 h under argon atmosphere. The resulting mixture was poured onto water (20 ml) and extracted with Et2O (3 × 40 ml). Combined organic extracts were washed with saturated aqueous NaCl (3 × 30 ml), dried over MgSO4, and concentrated at reduced pressure. The residue was purified by flash chromatography (eluant 0.5:9.5 Et2O/hexane) and recrystallized from acetone (57 mg, 62% yield), m.p. = 176–180°C; [α]math image = −1350 (c 0.8, CHCl3); 1H NMR (300 MHz, CDCl3): δ 7.61–7.37 (15 H, series of m), 7.34 (3 H, s), 4.24 (3 H, s), 1.36 (9 H, s), 1.00 (9 H, s), 0.88 (9 H, s) ppm. 13C NMR (75 MHz, CDCl3): δ 202.4, 142.1, 138.0, 135.3, 135.1, 130.1, 129.4, 128.74, 128.69, 64.9, 61.0, 51.4, 19.7, 19.1, 8.0 ppm. IR (KBr): ν 2973, 2933, 1736, 1275, 1084, 696 cm−1. C51H48O3 (708.93): calcd. C 86.40, H 6.82; found C 86.16, H 7.08.

Computational Details

All calculations have been carried out on a simple PC endowed with a single PentiumIV 3.16 GHz processor. The preliminary conformational distribution search has been performed by Spartan02 package69 using the MMFF94s molecular mechanics force field, assuming for 13 the absolute configuration reported in Chart 1. The “systematic” option was used and search of all possible conformers has been performed, considering the degrees of freedom of system and retaining only the structures with an energy of not more than 2 kcal/mol above the most stable conformer. This analysis provided for 13 only one conformer each. These geometries have been afterward optimized by DFT/B3LYP/6-31G* of Gaussian0315 or the AM1 and PM3 methods of Spartan02,69 respectively. All conformers are real minima, no imaginary vibrational frequencies have been found. The UV, ECD, and ORD calculations have been carried out by means of TDDFT methods using the hybrid B3LYP functional and the 6-31G* as available within Gaussian03. Both velocity and length formalism have been used in ECD calculations. London orbitals (which ensures the origin independency of the results) have been used in OR calculations.

RESULTS AND DISCUSSION

  1. Top of page
  2. Abstract
  3. INTRODUCTION
  4. MATERIALS AND METHODS
  5. RESULTS AND DISCUSSION
  6. CONCLUSIONS
  7. Acknowledgements
  8. LITERATURE CITED
  9. Supporting Information

Synthesis

(+)-syn-Benzotricamphor 1 was obtained in 75% yield by Swern-oxidation of (+)-syn-benzotriborneol, according to a previously described procedure.67 Attempts to obtain ethanediol tris-acetal 2 from syn-benzotricamphor, under azeotropic removal of water, led to complex mixtures of partially condensed products. For this reason, the synthesis of the tris-acetal was achieved from a short sequence of reactions, starting from previously reported (+)-endo-5-bromoborn-5-en-2-ol 4.68 The alcohol 4 was oxidized with NMO and catalytic amounts of TPAP to afford 5 (76% yield),70 which was protected with 1,2-ethanediol to obtain 6 (85% yield).71 Acetal 6 was stannylated with LDA and chlorotrimethylstannane furnishing the vic-bromostannylolefin 7 in 79% yield.68 The cyclotrimerization of 7 was accomplished with copper(I) 2-thiophenecarboxylate (CuTC),72 to produce a 6.8:1 syn to anti ratio mixture of cyclotrimers 2 in 70% overall yields (Scheme 1). The favorable diastereoselectivity results from the presence of sterically hindered trimethyltin moiety and scarcely hindered ligating functional group in the enantiopure bicyclic olefin, as previously observed with related substrates.73, 74

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Scheme 1. Synthetic procedure for syn-2.

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The tris-benzylidene 3 was obtained by aldolic condensation of syn-benzotricamphor with benzaldehyde in the presence of potassium tert-butanolate (62% yield).75 The geometrical isomerism of the olefin moiety was assessed by NOESY experiments, showing dipolar interaction between the bridge-head hydrogen of the bornane skeleton and the ortho-hydrogens of the phenyl group (Scheme 2).

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Scheme 2. Synthesis of 3 and observed nuclear Overhauser effect.

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A final, short comment: the synthetic procedures described earlier clearly show that compounds 13 have been prepared starting from a configurationally well-known compounds, that is, (−)-bornyl acetate, using a series of transformations which do not involve the stereogenic centers, therefore, the absolute configuration of the molecules studied in this article is certain and it is that shown in Chart 1.

Experimental and Computed Chiroptical Properties of Compounds 1–3

Compound 1

Compound 1 shows [α]D = +690 (c 1.4, CHCl3) and +660 (c 0.4, CH3CN), that is, the OR in practice is independent of the solvent. This fact is very important because in this way we feel authorized to compare the experimental data in solution with the corresponding computed data in vacuo, avoiding the use of solvation models76 which make the overall treatment very heavy. The absorption and ECD spectra of 1 in acetonitrile are reported in Figure 1.

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Figure 1. Absorption (UV) and ECD (CD) spectra of 1 in acetonitrile.

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Absorption bands are observed at about 300 (ϵ 3000 ca.), 240 (ϵ 25000 ca.), and 200 nm (ϵ 20,000 ca.) to which correspond, in the ECD spectrum, Cotton effects at 300 (Δϵ + 60), 240 (Δϵ −30), and 200 nm (Δϵ – 30). The chromophore of 1 is a β,γ-unsaturated ketone, like benzonorcamphor which has been studied in detail by Mislow and coworkers.77 Following their assignments, we can state that the band at 300 is due to the n–π* transition of the ketone chromophore, whereas the bands at 240 and 200 nm are allied to π−π* transition of the benzene ring.

The lowest energy Cotton effect contributes58, 78 +909 to the OR at the sodium D line, whereas the overall contribution of the observed Cotton effects is +547, that is, the OR of 1 is determined in sign and order of magnitude by the lowest energy Cotton effects. As a consequence, 1 possesses all the features required for our “approximate” approach. Compound 1 exists as a single conformer, the structure of which, optimized at the DFT/B3LYP/6-31G* level of theory is reported in Figure 2.

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Figure 2. Structure of 1, optimized at the DFT/B3LYP/6-31G* level of theory.

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The three camphor residues assume the normal boat conformation and the three carbonyl groups are below the benzene plane. The OR values have been computed with the TDDFT/B3LYP method using as input geometries structures obtained by DFT/B3LYP/6-31G*15, the semiempirical AM1, PM3, and molecular mechanics (MMFF94s) methods of SPARTAN0269 calculations, and two different basis sets, that is, the 6-31G* one we used in our previous articles58, 60–66 and the much smaller STO-3G basis set, just to test how much the level of theory can be lowered, without reducing the reliability of the results. The results are collected in Table 1.

Table 1. OR values of 1, obtained at two different levels of theory
RunGeometry (time, h)aLevel of theoryOR (time, h)b
  • a

    cpu time to get the input geometry, by means of a Pentium D 3.20 GHz computer with 2GB RAM memory.

  • b

    cpu time to get the OR value, by means of a Pentium D 3.20 GHz computer with 2GB RAM memory.

1DFT/B3LYP/6-31G* (92)TDDFT/B3LYP/6-31G*+713 (45)
2AM1 (1)TDDFT/B3LYP/6-31G*+723 (45)
3PM3 (0.5)TDDFT/B3LYP/6-31G*+596 (45)
4MM (0.2)TDDFT/B3LYP/6-31G*+682 (45)
5DFT/B3LYP/6-31G* (92)TDDFT/B3LYP/STO3G+551 (3.3)
6AM1 (1)TDDFT/B3LYP/STO3G+542 (3.3)
7PM3 (0.5)TDDFT/B3LYP/STO3G+429 (3.3)
8MM (0.3)TDDFT/B3LYP/STO3G+523 (3.3)
9Experimental OR, chloroform +690
10Experimental OR, acetonitrile +660

The data collected in Table 1 can be discussed as follows:

  • 1
    The use of the TDDFT/B3LYP/6-31G* method upon a DFT/B3LYP/6-31G* geometry, which uses the absolute configuration reported in Chart 1, provides an OR value (+713), which is in excellent agreement with the experimental values (+690, chloroform and +660, acetonitrile), measured for 1 which possesses safely (see the Synthesis section) this absolute configuration. As a consequence, one could assign computationally the absolute configuration of a large molecule such 1, in 137 h of cpu time, by means of a Pentium D 3.20 GHz computer with 2GB RAM memory.
  • 2
    The use of input geometries obtained with the semiempirical (AM1 and PM3) or the molecular mechanics (MMFF94s force field of Spartan02) methods provide OR value in good agreement with experiment (Runs 2–4). In particular, the figures obtained with the AM1 and MM geometries are quite satisfactory (Runs 2 and 4), whereas the PM3 number is more distant (about 100 units, Run 3) from the experiment.
  • 3
    The STO-3G calculations provide OR values (for all the geometries employed, Runs 5–8) in satisfactory agreement with the experiment: in fact, sign and order of magnitude of OR are correctly reproduced, even if, from a numerical point of view, the numbers obtained with this basis set are lower than the experimental values of 100 units, on average. This result is a clear consequence of the use of a lower quality (STO-3G vs. 6-31G*) basis set.
  • 4
    It is interesting to note that the input geometry seems to play only a minor role: the calculated OR values (both at the 6-31G* and STO-3G level) are quite similar, only the PM3 geometry affords a number, which is more different from the experiment than the others. This fact could be the consequence that 1 is a really rigid system, and hence the final theoretical structure does not depend (at least to a large extent) on the optimization technique used.
  • 5
    It is really noteworthy that both at the 6-31G* and STO-3G level, using an input geometry obtained at DFT, semiempirical, or MM level, we always get the correct sign and order of magnitude of the experimental OR: this guarantees for a molecule like 1, showing the spectroscopic features discussed earlier, we can apply our “approximate” approach, obtaining a safe configurational assignment. Taking into account that the semiempirical geometry requires only less than half an hour of cpu time and the STO-3G calculation of OR can be carried out on 1 in 5 h of cpu time, we have that the absolute configuration of a molecule like 1 can be safely assigned in less than 6 h of cpu time on a standard desktop computer.

In Figure 3 are reported the experimental ultraviolet (UV) and ECD (exp. ECD) spectra of 1, together with the simulated (theor. ECD) spectrum, as obtained at the TDDFT/B3LYP/6-31G* level, length formalism, using the lowest 60 states, see Computational Section for details, on the DFT/B3LYP/6-31G* geometry.

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Figure 3. Experimental ultraviolet (UV) and ECD (exp. ECD) spectra of 1, together with the simulated (theor. ECD) spectrum, as obtained at the TDDFT/B3LYP/6-31G* level, length formalism, using the lowest 50 states, see Computational Section for details, on the DFT/B3LYP/6-31G* geometry.

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This calculation correctly reproduces number, sign, and intensities of the observed Cotton effects, even if a clear red shift79 of the theoretical bands with respect to the experimental (in particular for those at 240 and 205 nm) can be noticed. The very good agreement between calculated and experimental spectra has been obtained without the intervention of the extended basis sets, suggesting that at least for rigid molecules, with intense ECD spectra, high OR determined in sign and order of magnitude by the lowest energy Cotton effects, the use of the “approximate” method guarantees a safe configurational assignment. In Figure 1 of the Supporting Information is compared the experimental ECD spectrum of 1 with the theoretical ones (TDDFT/B3LYP/6-31G*) obtained with AM1 and PM3 geometries: the effect of the input geometry is clearly negligible. In Figure 2 of the Supporting Information is reported a comparison between experimental and calculated (TDDFT/B3LYP/STO-3G, DFT/B3LYP/6-31G* geometry) ECD spectra of 1: the theoretical spectra (both in length and velocity formalism) show very reduced intensities with respect to the experimental one. This fact explains the low OR values provided by the STO-3G calculation: ECD intensities and OR values are related by the Kronig-Kramers transforms.9, 78

Compound 2

This compound shows [α]D = +222 (c 1.2, CHCl3) and +187 (c 0.45, CH3CN), that is, the OR does not depend significantly on the solvent, so in this case as well, we shall not use the solvation models76 and we shall directly compare the experimental data in the solvent with the simulation in gas phase. In Figure 3 of the Supporting Information are reported the UV and ECD spectra of 2 in acetonitrile. Taking into account shape, position, and relative intensities of the bands, it is reasonable to assign these absorptions to π−π* transition of the benzene chromophore.80 Even if the contribution of the lowest energy transition to the OR at 589 nm is only +40, the contribution of the all Cotton effects observed in the spectrum is +203, that is, the 589 nm OR is determined in sign and order of magnitude by the lowest energy Cotton effects, and therefore, we can apply our “approximate” approach. Compound 2 exists as a single conformer (as indicated by our MMFF94s calculations, see “Computational Details”) the optimized (DFT/B3LYP/6-31G*) structure of which is reported in Figure 4: the dioxolane rings are disposed in planes almost perpendicular to that of the benzene ring and possess a prevailing sense of twist.

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Figure 4. Structure of 2, optimized at the DFT/B3LYP/6-31G* level of theory.

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OR values of 2 have been simulated at two different levels of theory. The results collected in Table 2 can be discussed as follows:

  • 1
    The OR value obtained at TDDFT/B3LYP/6-31G* upon the DFT/B3LYP/6-31G* geometry (+246) (Run 1) is in very good agreement with the experimental (+222) figure. This means that the absolute configuration of a large molecule can be safely obtained in 6 days of cpu time on our standard desktop computer. This is clearly possible because we have applied our “approximate” approach, which avoids the use of extended basis sets with diffuse functions. Quite interestingly, the “approximate” approach works very well also in the case of 2, which shows an OR significantly lower than 1 (+222 vs. +690).
  • 2
    Here, as well the quality of the input geometry does not affect so much the computed (OR) values, see Runs 2–4, for the TDDFT/B3LYP/6-31G* treatment and Runs 5–8, for the TDDFT/B3LYP/STO-3G treatment. In fact, sign and order of magnitude of the experimental OR are correctly reproduced. This fact is particularly important because we have that using the MM geometry and the STO-3G OR calculation (only 5 h of cpu time!) we can safely assign the absolute configuration of a large molecule like 2. A referee of this article was not completely satisfied with our conformational analysis of compound 2. So, following his suggestions, we repeated this step, using the “Montecarlo” option of SPARTAN02, with the MMFF94s force field. Four structures having the relative energies 0.0 (27.9% population), 0.04352 (25.9% population), 0.08946(24.0% population), 0.13766(22.2% population)) have been found. They differ for the sense of twist of the dioxolane ring: three P rings in the most stable conformer, two P and an M ring in the 0.04 conformer, 2 M and one P ring in the 0.08 conformer, and three M rings in the last one. Using these structures as input geometries, some OR calculations at the TDDFT/B3LYP/STO-3G level have been carried out. The calculated values are as follows: +194.38 for the most stable conformer, +199.71 for the second one, 205.11 for the third one, and 210.78 for the fourth one. From these figures, an average value of +195 can be calculated, which is in excellent agreement with +199, reported in Table 2. However, the most important result is that, passing from conformer 1 to conformer 4, OR varies from +194 to 211, that is, less than 10%. This means that the chiroptical properties of 2 do not depend to a significant extent on the sense of twist of the dioxolane ring: this supports our previous results on this molecule. In summary, even if 2 is not a perfectly rigid molecule, its conformers show very similar chiroptical properties, making our initial treatment acceptable.
Table 2. OR values of 2, obtained at two different levels of theory
RunGeometry (time, h)aLevel of theoryOR (time, h)b
  • a

    cpu time to get the input geometry, by means of a Pentium D 3.20 GHz computer with 2GB RAM memory.

  • b

    cpu time to get the OR value, by means of a Pentium D 3.20 GHz computer with 2GB RAM memory.

1DFT/B3LYP/6-31G* (96)TDDFT/B3LYP/6-31G*+246 (48)
2AM1 (1)TDDFT/B3LYP/6-31G*+305 (48)
3PM3 (1)TDDFT/B3LYP/6-31G*+260 (48)
4MM (0.3)TDDFT/B3LYP/6-31G*+239 (48)
5DFT/B3LYP/6-31G* (96)TDDFT/B3LYP/STO3G+211 (3.5)
6AM1 (1)TDDFT/B3LYP/STO3G+296 (3.5)
7PM3 (1)TDDFT/B3LYP/STO3G+258 (3.5)
8MM (0.3)TDDFT/B3LYP/STO3G+199 (3.5)
9Experimental OR, chloroform +222
10Experimental OR, acetonitrile +187

In Figure 4 of the Supporting Information, a comparison between the experimental and calculated (both in the length, RL, and velocity, RV, formalism) of 2 is reported: the computed ECD spectrum does not simulate the weak positive Cotton effect at 305 nm, but affords a satisfactory reproduction of the 260–200 nm range.

Compound 3

The experimental values of OR for 3 are −1350 (c 1, CHCl3) and −1535 (c 1.1, CH3CN): the change of the solvent (from chloroform to acetonitrile) induces only a small (about 10%) variation of the [α]D, so in this case as well we shall not use the solvation models and we shall compare the experimental figures in solution with the simulated ones in the gas phase. We attempted to simulate the OR data of 3 using the “approximate” approach. The measured Cotton effects (see Fig. 6) provide the following contributions to the OR at 589 nm: negative ECD band at 370 nm, −420; negative ECD band at 300 nm, −1283; positive ECD band at 275 nm, +41; positive ECD band at 230 nm, +146. So, the OR at 589 is determined, in practice, by the first two measured Cotton effects (−1703 vs. −1350), and therefore, another criterion required for the application of our “approximate” treatment is fully respected. As discussed earlier, the MM conformational analysis for 3 gave only one conformer (vide infra, for a further discussion), the structure of which have been optimized by DFT/B3LYP/6-31G*, AM1, PM3 calculations, obtaining the necessary input geometries. So, the [α]D values have been computed with the TDDFT/B3LYP method and with two different basis sets, that is, 6-31G* and STO-3G. The results are collected in Table 3.

Table 3. OR values of 3, obtained at two different levels of theory
RunGeometry (time, h)aLevel of theoryOR (time, h)b
  • a

    cpu time to get the input geometry, by means of a Pentium D 3.20 GHz computer with 2GB RAM memory;

  • b

    cpu time to get the OR value, by means of a Pentium D 3.20 GHz computer with 2GB RAM memory;

1DFT/B3LYP/6-31G* (144)TDDFT/B3LYP/6-31G*−3216 (85)
2AM1 (3)TDDFT/B3LYP/6-31G*−1372 (85)
3PM3 (2.5)TDDFT/B3LYP/6-31G*−1521 (85)
4MM (0.2)TDDFT/B3LYP/6-31G*−729 (85)
5DFT/B3LYP/6-31G* (144)TDDFT/B3LYP/STO3G−1824 (6)
6AM1 (3)TDDFT/B3LYP/STO3G−712 (6)
7PM3 (2.5)TDDFT/B3LYP/STO3G−941 (6)
8MM (0.2)TDDFT/B3LYP/STO3G−444 (6)
9Experimental OR, chloroform −1350
10Experimental OR, aceto nitrile −1535

These results can be discussed as follows:

  • 1
    The figures obtained with the 6-31G* basis set (Runs 1–4) are always larger than the values obtained with the STO-3G basis set (Runs 5–8), as already observed for 1 and 2.
  • 2
    Within the same group of calculations (6-31G* or STO-3G), the figures obtained with the 6-31G* geometry (Runs 1 and 5) are always larger than the values obtained with the AM1, PM3, and MM geometries (Runs 2–4 and runs 6–8). Note the large overestimation of run 1 versus the experimental values. This behavior is different with respect to that previously observed: the molecular geometry plays an important role in determining the theoretical ORs of 3, whereas this fact has not been observed in the case of 1 and 2, at least to such a great extent (see Table 3 vs. Tables 1 and 2).
  • 3
    It is also noteworthy that the calculated OR values of a given group have a minimum (in absolute value) for the MM geometry. Considering that the main structural difference between 3 and 1 is the addition of the benzylidene function of 3, we decided to compare the values of the dihedral angle θ (C1-C2-C3-C4, Chart 2) in the four geometries, Table 4.
    In Figure 5 are reported the OR values obtained at the TDDFT/B3LYP/6-31G* and STO-3G level versus the angle θ. As anticipated earlier, the two curves look similar, with the 6-31G* curve showing larger OR values than the STO-3G curve, both the curves have a minimum (in absolute value) in correspondence to the MM geometry, whereas the figures obtained with the semiempirical geometries are intermediate between those obtained with the DFT and MM geometries.
  • 4
    A possible explanation of the effect of the geometry on the theoretical OR values of 3 could be found just taking into account its characteristic structural feature, that is, the presence of an α,β-unsaturated ketone chromophore of 3. As, at least in principle, rotation is possible around the simple bond connecting the phenyl ring to the exocyclic C[DOUBLE BOND]C bond, 3 can be considered more flexible than 1. Therefore, the α,β-unsaturated ketone chromophore can assume different degrees of conjugation. Such chromophore, inserted in the chiral environment of 3, could assume a preferred sense of twist and form an intrinsically dissymmetric chromophore, which could strongly contribute to the OR. As a matter of fact, looking at Table 4, in the MM geometry the C[DOUBLE BOND]C double bond and the benzene ring are almost perpendicular and then not conjugated: in this case, the computed OR value is a minimum, in absolute value. On the contrary, in the other three geometries, an intrinsically twisted styrene chromophore is clearly present. This fact could determine the higher ORs predicted for the DFT and semiempirical geometries. To support this interpretation, we did some OR calculations upon a new structure of 3, obtained by rotating only one of the phenyl residues (to save computational effort!!) and reaching a dihedral angle θ of about 90°. When θ is 87° we have a structure with an energy value 2 kcal/mol over the minimum: it represents the maximum of the energy barrier for the rotation of the phenyl group which is hence almost free. In these conditions, the theoretical OR becomes −2339, that is, a figure which is much smaller (in absolute value) than the number calculated for the minimum energy geometry. Considering that we have three benzylidene groups, which can assume this geometry and the energy barrier to the rotation of the phenyl group is of the order of only 2 kcal/mol, that is, almost free rotation at room temperature, we have that the numerical difficulties observed for 3 depend on its flexibility: if the three phenyl groups rotate almost freely at room temperature, several less conjugated structures are accessible and then low values of OR are provided.
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Figure 5. Plot of OR values, calculated with the TDDFT/B3LYP/6-31G* (6-31G* curve) or the TDDFT/B3LYP/STO-3G (STO-3G curve) method versus the angle θ (C1-C2-C3-C4).

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Chart 2. Numbering of the benzylidene moiety of 3.

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Table 4. Values of the diehedral angle θ (see Chart 2) obtained in different geometries
GeometryDihedral angle θ
DFT−33
AM1−109
PM3−59
MM−81

The absorption (UV) and ECD (CD) spectra of 3 in acetonitrile are reported in Figure 6. The UV spectrum shows a first absorption at 360 nm (ϵ 2000 ca.), followed by a very broad band centered at about 290 nm (ϵ 35,000 ca.) with a clear shoulder at 275 nm (ϵ 30,000 ca.), and a last maximum at 225 nm (ϵ 35,000). Taking into account positions and relative intensities of these bands is tempting to assign the 360 nm band to the n-π* transition and the 280 and 225 nm bands to the π−π* transitions of the cisoid-α,β-unsaturated ketone chromophore.81 Based on this, the ECD band at 350 nm is related to the n-π* transition of the above quoted unsaturated ketone chromophore, whereas the very strong Cotton effects at 300 (Δϵ −150) and 280 nm (Δϵ +20) are due to the electrically allowed π−π* transitions of the same chromophore. So, the sequence of strong (Δϵ −150) negative band at 300 nm followed by a (relatively) weak (Δϵ +20) ECD band could be the components of a strongly asymmetric exciton couplet. To verify this analysis, we decided to do some DeVoe coupled oscillator ECD calculations.82–85 Each electrically allowed π−π* transition of the α,β-unsaturated ketone chromophore, located at about 300 nm and dominating the 340–240 nm spectral range, has been represented by a single dipole, located in C3 (Chart 2) and polarized along the direction connecting C3 and C1 carbon atoms (Chart 2). To each dipole was attributed an electric polarizability of 15 D2 and a half-width of 3 kK: these parameters have been obtained looking at the experimental data of some α,β-unsaturated ketones.81. In these conditions, the broad experimental UV band between 340 and 240 nm is satisfactorily reproduced (interestingly even a shoulder at 275 nm is calculated), a negative (as the experimentally observed one) CD couplet is obtained, even if the theoretical one is symmetric (−70;70) and less intense than the experimental one (−170; +20), Figure 6.

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Figure 6. Experimental absorption (exp. UV) and ECD (exp. ECD) spectra of 3, together with the DeVoe calculated absorption (DeVoe abs) and ECD (DeVoe ECD) spectra.

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Attempts at simulating the ECD spectra by means of TDDFT/B3LYP/6-31G* calculations have been carried out, using the minimum energy (DFT/B3LYP/6-31G* level) structure: Figure 7 collects the experimental ECD curve (exp. ECD) and the theoretical 6-31G* spectra (length and velocity formalism).

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Figure 7. Experimental ECD spectrum of 3 (light black line) and calculated (TDDFT//B3LYP/6-31G*) ECD spectra (RL/RV).

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First of all the two theoretical curves are almost coincident indicating the good quality of the molecular wavefunctions used. The ECD bands experimentally observed between 400 and 220 nm are reproduced in number, sign, and intensity even if a clear (20–25 nm) red shift is observed (these computations have been carried out on a AMDX86–64 dual core opteron machine and required 27 h of cpu time). This fact could contribute to the aforementioned overestimation of the OR at 589 nm. In Figure 4 of the Supporting Information is compared the experimental ECD spectrum of 3 with that obtained at the TDDFT/B3LYP/STO-3G level. The difference between the spectra obtained with the length and velocity formalism is more clear than above, indicating that the quality of the molecular wavefunction is reduced; however, the experimental broad negative band centered at 355 nm is reproduced by two theoretical Cotton effects at 405 and 305 nm, whereas the strong negative couplet-like feature at 280 nm is reproduced by a sequence of negative/positive ECD bands located at 240 nm. In summary, the experimental ECD bands are satisfactorily simulated in number, sign, and intensity even if the theoretical ones result heavily blue shifted (some 50 nm!): this blue shift could contribute to the reduced OR values obtained at the STO-3G level versus those obtained at the 6-31G* level.

CONCLUSIONS

  1. Top of page
  2. Abstract
  3. INTRODUCTION
  4. MATERIALS AND METHODS
  5. RESULTS AND DISCUSSION
  6. CONCLUSIONS
  7. Acknowledgements
  8. LITERATURE CITED
  9. Supporting Information

The theoretical analysis of the chiroptical properties of the large molecules 13 has demonstrated that in the case of rigid molecules (i.e., 1, 2), which show intense ECD spectra, high OR values (>100 deg[dm g/cm3), determined in sign and order of magnitude by the lowest-energy Cotton effects, a TDDFT/B3LYP/6-31G* calculation of OR and ECD, using DFT/B3LYP/6-31G* geometry, affords the correct answer. However, two further interesting comments have to be made: first of all, in cases like those of 1 and 2, even the small STO-3G basis set can be reliably used for OR and ECD calculations. Second, in the same cases, input geometries obtained at semiempirical and molecular mechanics level can be used as well: this means that in a few hours of CPU time on a standard desktop computer, we can have a reliable configurational assignment. The safe use of semiempirical and molecular mechanics input geometries is a consequence of the fact that the simulation of the chiroptical properties is independent, for rigid molecules like 1 and 2, of the origin of the input geometry. This result is quite important because in this way we have established some criteria to treat even complex systems at a low level of theory. This means that, in these cases, supercomputers and special calculation algorithms are not required: this is a guarantee of diffusion of these methods among the practicing organic chemists who are the people much interested in simple but reliable methods of absolute configuration assignment. More complex is the situation of a nonrigid molecule, like 3, because here even if 3 possesses intense ECD spectra, high OR values (>100°[dm g/cm3]−1), determined in sign and order of magnitude by the lowest energy Cotton effects, there is a significant dependence of the results (at least from a quantitative point of view) on the input geometry: the OR values range between −3216 and −729 (TDDFT/B3LYP/6-31G* calculations) or −1824 and −444 (TDDFT/B3LYP/STO-3G calculations). We have shown that this is due to the molecular flexibility, that is, there is (almost) free rotation around the single bond connecting the benzene ring to the double bond, making several conformers having different degrees of conjugation accessible at room temperature: this renders such a case very complex, hindering the use of our “approximate” approach. These observations strongly indicate that the conformational freedom constitutes one of the major difficulties for a correct but simple simulation of the chiroptical properties.

Acknowledgements

  1. Top of page
  2. Abstract
  3. INTRODUCTION
  4. MATERIALS AND METHODS
  5. RESULTS AND DISCUSSION
  6. CONCLUSIONS
  7. Acknowledgements
  8. LITERATURE CITED
  9. Supporting Information

The authors thank the referee of this article for his constructive comments. They also thank Professor Benedetta Mennucci, Dipartimento di Chimica e Chimica Industriale, Università di Pisa, for carrying out the TDDFT/B3LYP/ 6-31G* ECD calculation on 3.

LITERATURE CITED

  1. Top of page
  2. Abstract
  3. INTRODUCTION
  4. MATERIALS AND METHODS
  5. RESULTS AND DISCUSSION
  6. CONCLUSIONS
  7. Acknowledgements
  8. LITERATURE CITED
  9. Supporting Information
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Supporting Information

  1. Top of page
  2. Abstract
  3. INTRODUCTION
  4. MATERIALS AND METHODS
  5. RESULTS AND DISCUSSION
  6. CONCLUSIONS
  7. Acknowledgements
  8. LITERATURE CITED
  9. Supporting Information

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