Theoretical and Experimental Studies on Circular Dichroism of Carbo

Article pubs.acs.org/JPCA

Theoretical and Experimental Studies on Circular Dichroism of Carbo[n]helicenes Yoshito Nakai, Tadashi Mori,* and Yoshihisa Inoue* Department of Applied Chemistry, Graduate School of Engineering, Osaka University, 2-1 Yamada-oka, Suita, Osaka 565-0871, Japan S Supporting Information *

ABSTRACT: The chiroptical properties of a series of carbo[n]helicenes (n = 4− 10) were investigated by the state-of-the-art approximate coupled cluster and density functional theory calculations. The theoretical calculation at the RI-CC2/ TZVPP//DFT-D2-B97-D/TZVP level nicely reproduced the experimental CD spectra in both excitation energy and rotational strength without any shift or scaling. These calculations afforded the electric and the magnetic transition dipole moment vectors in [n]helicenes, allowing us to discuss the observed rotational strengths as a function of the number of benzene rings. Although the observed CD intensity was not immediately correlated to any of the calculated parameters, the anisotropy (g) factor of the 1Bb band and the specific rotation were found inversely proportional to n and nicely correlated with the helical pitch, but discontinuous at n = 6, where the aromatic rings start to overlap. In contrast, the g factor at the 1Ba band was rather insensitive to n. It was also revealed that the excitation energies of the 1Bb and 1Ba bands are inversely proportional to n over the entire range of n examined. The theoretical predictions also enabled us to rectify the erroneous experimental CD spectra of [5]- and [6]helicenes reported earlier, by using the enantiopure samples resolved by chiral HPLC.

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INTRODUCTION First principle calculations have been established as a very powerful tool in modern organic chemistry not only for calculating the geometry and energy of a given molecule in high accuracy but also for assessing its physical and chemical properties in reasonable accuracies.1 Therefore, the use of quantum calculations, at different hierarchies of ansatz, becomes a routine work in structural elucidation and conformational analysis of small molecules, host−guest or supramolecular systems, and even biomolecules such as protein binding research. Nonetheless, we are not totally free from the necessity to compare with and reproduce the relevant experimental observations and any departure from the theory is usually (if not always) ascribed to the failure of the theoretical models employed. Such a situation happens indeed in the case of the calculations associated with excited states (i.e., UV−vis and circular dichroism (CD) spectra in this work), as the theoretical calculations of these spectra have to take into account the (theoretically more demanding) electronically excited states.2 Although the advances in time-dependent density functional theory have enabled us to sensibly reproduce the experimental UV−vis and CD spectra for a number of small- to medium-sized molecules, a closer look at the scene behind reveals that it is away from the complete success. Thus, the TD-DFT calculated spectra are often scaled in intensity and shifted in energy to match the experimental ones, and more seriously the results are strongly dependent on the functionals employed.3 Despite this trick, the method is useful for the determination of absolute configuration, the elucidation of the nature of transition, and other practical purposes, in a reasonable computational times or resources. © 2012 American Chemical Society

Helicenes are ortho-fused nonplanar polyaromatics, which possess unique helical chirality (Chart 1).4 Helicenes have recently been employed in various areas of chemical sciences, including asymmetric catalysis,5 molecular recognition, and supramolecular chemistry.6 As early as mid-50s, the first synthesis and optical resolution of carbo[6]helicene (CH[6]) was achieved by Newman and Lednicer.7 In a couple of decades to follow, a number of helicene homologues were prepared by the groups of Martin,8 Wynberg,9 Laarhoven,10 and Katz.11 More recently, the transition metal-catalyzed [2+2+2]cycloisomerization has become available for the preparation of various helicene derivatives.12 For example, a chiral [11]helicene analog, possessing an anthracene unit in the middle, was prepared by this procedure.13 Utilizing the exceptionally strong Cotton effect (CE) of helicene,14 circularly polarized light was employed as a tool for enantioselectively photodecomposing racemic helicenes, but the results were not very satisfactory.15 Optically enriched helicene analogs were also prepared by using chiral transitionmetal catalysts with some success.16 However, a more general and effective method to obtain a series of enantiopure helicenes is the optical resolution of racemic samples by preparative HPLC with appropriate chiral stationary phases. Indeed, the optical resolutions of carbo[n]helicenes (CH[n]) of up to n = 14 have already been achieved in analytical scales by using a riboflavin-coated silica gel column.17 Consequently, the experimental CD spectra of enantiomeric helicenes are available Received: May 10, 2012 Revised: June 5, 2012 Published: June 13, 2012 7372

dx.doi.org/10.1021/jp304576g | J. Phys. Chem. A 2012, 116, 7372−7385

The Journal of Physical Chemistry A

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Chart 1. Structures of Carbo[n]helicenes (CH[n]; n = 3−10) Examined in This Studya

a

Phenanthrene (CH[3]), though not chiral, is included as the smallest member of the carbo[n]helicene family for a comparison purpose.

Table 1. Comparison of Selected Structural Parameters Found Experimentally in X-ray Crystallographic Structures with Those from Theoretical Calculations Optimized at Different Levels for Carbo[n]helicenes CH[n] (n = 3−10)a helicene

theory (level) or X-ray

r1/Å

r2/Å

θ/°

CH[3]

DFT-D2-B97-D/TZVP X-rayc DFT-D2-B97-D/TZVP X-rayd DFT-B3-LYP/TZVP DFT-D2-B97-D/TZVP SCS-MP2/TZVPP X-raye

3.009 2.977 3.060 3.039 2.962 2.952 2.900 2.922 2.925 2.954 3.248 3.117 3.062 3.215 3.978 3.849 3.788 3.849 3.828 3.754 4.776 5.497 5.743 5.719

5.781 5.742 5.497 5.446 4.642 4.612 4.544 4.577 4.590 4.659 4.528 4.238 4.130 4.576 5.563 5.252 5.149 5.285 5.241 5.249 6.885 7.809 7.735 7.717

0.0 1.1 19.6 17.3/19.0b 18.1, 30.2 18.4, 30.0 18.3, 29.9 18.4/20.1, 27.9b 19.1, 29.7 17.1/17.0, 32.3b 13.6, 29.6 14.8, 27.6 15.8, 26.9 11.3/15.2, 30.0/30.3b 16.2, 25.6, 28.6 19.2, 24.9, 24.4 20.7, 24.5, 22.9 16.9/21.9, 25.9/26.0, 23.6b 6.4/20.6, 21.9/34.6, 22.2b 18.7/18.6, 23.4/23.6, 25.5b 18.6, 27.6, 23.1 17.0, 26.9, 25.9, 22.3 17.8, 25.7, 25.3, 25.3 17.7/21.4, 24.0/23.8, 26.6/24.5, 25.1/26.8b

CH[4] CH[5]

CH[6]

CH[7]

CH[8] CH[9] CH[10]

DFT-B3-LYP/TZVP DFT-D2-B97-D/TZVP SCS-MP2/TZVPP X-rayf DFT-B3-LYP/TZVP DFT-D2-B97-D/TZVP SCS-MP2/TZVPP X-rayg X-rayh DFT-D2-B97-D/TZVP DFT-D2-B97-D/TZVP DFT-D2-B97-D/TZVP X-rayi

a r1: nonbonded C(1)−C(2n+4) distance. r2: nonbonded C(2)−C(2n+3) distance. θ: dihedral angle of the edge of the inner helix, starting from C(1). bPair(s) of different values were reported, due to the deviation from the C2 point group. cReference 29. dReference 30. eThree independent coordinates for two different crystals were reported in ref 31. fReference 32. gTwo independent coordinates were reported in ref 33. hAdditional structure reported in ref 34. iReference 35.

for CH[5]−CH[9] in the literature but have not been reported for smaller and larger ones. In this combined theoretical and experimental study, we wanted to provide a comprehensive and convergent view of the chiroptical properties, i.e., CD and optical rotation (OR), of the whole carbo[n]helicene (CH[n]) series (Chart 1). Throughout the work, the theoretical chiroptical properties were calculated and presented for (P)-(+)-enantiomers of CH[n]. Previously, similar systematic studies were conducted by theory but at lower levels.18−21 We now wish to demonstrate that the approximate coupled cluster linear response theory calculations for CH[5]−CH[9] successfully reproduce the experimental

UV−vis and CD spectra not only in pattern but also in excitation energy and rotational strength, which made us to revise the experimental CD intensities of CH[5] and CH[6] reported earlier. The excellent agreement of the theoretical with the experimental spectra for all of CH[5]−CH[9] prompted us to further extend the theoretical calculations to lower and higher homologues down to CH[3] and up to CH[10], results of which disclosed simple relationships of the anisotropy (g) factor and the OR values with the number of benzene rings and also on the helical pitch. 7373



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COMPUTATIONAL METHODS All calculations were performed on Linux-PCs by using the TURBOMOLE 6.10 or later program suite.22 The resolution of identity (RI) approximation 23 was employed for the perturbative corrections in all the calculations throughout this study to facilitate the computational efficiency without any significant loss of accuracy, and the corresponding auxiliary basis-sets were taken from the TURBOMOLE basis-set library. Geometries were fully optimized at the dispersion-corrected density functional theory (second generation, DFT-D2)24,25 at the B97-D/TZVP26 level (in standard notation: H, [3s1p], C, [5s3p1d], which is an AO basis-set of valence triple-ξ quality) using C2 symmetry constraint. The convergence criterion for the optimization regarding the change of total energy between two subsequent optimization cycles was set to 10−7 Eh. Selected helicenes (CH[5], CH[6], and CH[7]) were also optimized at the conventional DFT (B3-LYP27/TZVP) and more theoretically accurate spin-component scaled second-order Møller− Plesset perturbation theory (SCS-MP228/TZVPP26) levels (H, [3s2p1d], C, [5s3p2d1f] that has additional p/d and d/f functions on hydrogen and carbon atoms, respectively). Note that X-ray structures are always deviated from the ideal C2 symmetry mostly due to the packing forces,29−35 and therefore we employed the calculated C2 geometry in the following (chir)optical property calculations, which better represents the equilibrium structure in solution. Among the selected calculation levels, the DFT-D2 method provided the best results in terms of sufficient accuracy in interatomic distances and dihedral angles (as compared with the X-ray structures, especially for higher helicene homologues) and cost-efficiency (Table 1). It was recently shown that the TD-DFT estimates for smaller helicenes CH[5]−CH[7] are significantly dependent on the starting geometries, and the dispersion correction plays a crucial role in geometry optimizations for precisely predicting the optical rotations.36 Our own spectral calculations based on the different geometries (i.e., DFT, DFT-D2, and SCS-MP2), however, revealed that the differences are not substantial in the UV−vis and CD spectral calculations; rather, they were much more dependent on the choice of theoretical levels (e.g., TD-DFT or RI-CC2) (Figure S8 in the Supporting Information). All excited-state calculations were performed with the above DFT-D2 optimized ground-state geometries, thus corresponding to the vertical transition approximation. The UV−vis and CD spectra were calculated by the time-dependent, secondorder approximate coupled-cluster singles and doubles model,37 in conjunction with the resolution-of-identity method (RI-CC2 method).38 Despite the scaling of ∼N5 and increased computation times, the results obtained by the RI-CC2 method are considered most accurate with the current computational resources, especially for larger helicene molecules. The calculated dipole operator (r) in (more robust) length expression and angular momentum (L) were converted numerically to the electric (μe) and the magnetic (μm) transition dipole moments, respectively.39 Strictly speaking, the electric dipole operators in length representation and angular momentum are origin-dependent, and (chir)optical properties can only be compared to the experiment when they are origin-independent. However, the length- and velocitygauge values converge to the same value in the complete basisset limit, and in fact, most of the calculated rotational strengths of the dipole-length expression only differed from the dipole-

velocity form by less than (and mostly much less than) 10% when using relatively large triple-ξ type AO basis sets. The basis-set dependence in our RI-CC2 calculations was more rigorously tested with carbo[6]helicene (CH[6]) by using various basis sets different in size, e.g., SVP, aug-SVP, TZVP, TZVPP, and aug-TZVPP (SVP, TZVP, and TZVPP basis-sets are available in TURBOMOLE basis-set library; a prefix aug denotes adding of the diffuse spd-functions taken from the Dunning’s correlation consistent aug-cc-pVTZ basis-set).40 Although the oscillator and rotational strengths were calculated with little or no difference among the basis sets, the transition energies were expressively shifted as the basis-set size increased (Figure S8 in Supporting Information). The TZVPP basis set was found well suited for an effective and sufficiently accurate description of the CD spectra of current helicene homologues. Forty excitations were considered in all helicenes calculated in this study. The UV−vis and CD spectra were simulated by overlapping Gaussian functions for each transition where the width of the band at 1/e height is fixed at 0.5 eV.41 This value is purely empirical and has no rigorous ground but is able to successfully reproduce and match to the experimental UV−vis and CD spectra, facilitating the interpretation of the spectra. For a comparison purpose, the spectra of CH[6] were also simulated on the basis of time-dependent DFT methods employing the various hybrid functionals such as BH-LYP,42 PBE0,43 and B3-LYP, as well as by the time-dependent doublehybrid DFT (B2-PLYP),44,45 all with the TZVP basis-set (Figure S7 in Supporting Information). Due to the systematic errors found in the TD-DFT calculated transition energies, the theoretical spectra had to be shifted by −0.2 to +0.8 eV to match the 1Bb transition maxima (see figure captions for details). The effect of solvent was insignificant, which was experimentally and theoretically (COSMO46 model at the TDDFT-BH-LYP/TZVPP level) examined (Figures S6 and S8 in Supporting Information). The theoretical spectra of CH[5]− CH[10] at the B2-PLYP level were also compared with those obtained with the RI-CC2 method (Figure S10 in Supporting Information). The optical (specific) rotations (ORs) at the sodium-D and Hg resonance lines (589.3 and 578.0 nm, respectively) were calculated by the TD-DFT method with the BH-LYP and B3-LYP functionals using Dunning’s16 aug-ccpVDZ basis set.47 It is also to note that these calculations of ORs were performed with the TURBOMOLE ver. 6.31 to avoid wrong outputs in signs in earlier versions.

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RESULTS Structures of Carbo[n]helicenes. a. Experimental versus Theroetical Structures. The deviations in calculated excitation energy and intensity of UV−vis and CD spectra are larger in general than that in geometry.2 It has been shown recently that the calculated ORs are dependent on the geometries employed. For instance, appreciable underestimations of ORs were noted for medium-sized helicenes such as CH[6] and CH[7], when the dispersion-corrected DFT geometries were used.36,48 In our own research on donor−acceptor cyclophanes, the calculated ORs also showed similar geometry dependence and the sign opposite to the experimental one was obtained in some extreme cases.47 Accordingly, it is worthwhile to discuss briefly the geometries of helicene molecules used for the subsequent calculations of (chir)optical properties. However, small differences in geometry, arising from the use of different theoretical levels, turned out to be insignificant in the calculation of CD spectra of (at least, pristine) carbo[n]helicenes (vide infra). 7374



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smaller aromaticity, found for the central, rather than terminal, rings are in line with the above-mentioned larger deformation of the central rings. A similar tendency was observed for the NICS values, which is more complicated to comprehensively interpret but has been discussed in detail for helicenes and related acenes in a recent paper.54 For geometrical considerations, the bond distance is a more sensible parameter than the dihedral angle. As shown in Table 1, two nonbonded intramolecular distances (r1 and r2) progressively increased with n, but no straightforward correlation was found, probably due to the rather arbitrary deviation of each carbon atom. The incremental stabilization energy (and the accompanying structural changes), as well as the other physicochemical properties, are known to converge at around [14]helicene.49 To better describe the convergent behavior, we now introduce a new parameter “effective carbon volume (Vc),” which is obtained by dividing the van der Waals molecular volume (V) by the number of total carbon atoms: Vc = V/(4n + 2). We may further define a related parameter “effective volume increment (4Vc)” upon each addition of a fused benzene ring. The Vc value thus obtained is expected to function not only as a measure of the incremental volume change upon helix elongation but also as an index of the convergence of helical structure. As shown in Figure 1 (left), an

The X-ray crystallographic structures of common helicene molecules have been reported in the literature.29,31−35 The structures, however, always deviate more or less from the ideal C2-symmetry, due in principle to the packing forces. In addition, the X-ray crystallographic studies on CH[5] and CH[7] unveiled the existence of two different crystal forms (and three different geometries), which makes things more complicated than conceived; see the selected geometrical parameters summarized in Table 1. Due to the deformation and the polymorphism, it is inappropriate to directly use the solidstate structures for the theoretical calculations of spectra. Hence, the theoretically predicted C2-symmtrical structures were employed as the equilibrium structures in the present study. For the geometrical optimization of helicenes, we selected dispersion-corrected density functional theory (the second generation, DFT-D2) with B97-D functional and Ahlrichs’ TZVP basis-set.24 As demonstrated previously,49,50 the structures of helicenes are best reproduced by the DFT-D method, in particular for higher homologues with overlapped benzene rings. The differences of the experimental versus DFTD2 calculated C−C bonds and nonbonded distances are well less than 1% for most of the helicenes (excepting the error of ca. 3% for CH[6], probably due to the packing forces in the Xray structure).32 The calculated dihedral angles around the inner helix edge are generally in good agreement with the experiment within 2−3° errors, which are smaller than the expected deviation from C2-symmetry (2−5°, Table 1). These DFT-D2 structures are qualitatively reliable enough for the subsequent calculations of UV−vis and CD spectra (vide infra). The conventional DFT (B3-LYP/TZVP) and more expensive spin-component scaled second-order Møller−Plesset perturbation theory (SCS-MP2/TZVPP)28 were also tested in selected helicenes for a comparison purpose (Table 1). As expected, the conventional DFT method overestimated the intramolecular distances, whereas SCS-MP2 slightly underestimated them. b. Carbo[n]helicene Homologues. The effects of increasing number of benzene rings (n) on the structures of carbo[n]helicenes were systematically investigated (Table 1 and Tables S1 and S2 in Supporting Information). The dihedral angles of the edge of the inner helix is one of the most frequently used essential parameters for structural argument.51 As a general trend, the dihedral angle (17−20°) including the terminal ring is much smaller than those (20−30°) including only the inner rings, although the individual value shows significant deviations. Because these angles represent only the carbon atoms positioned on the edge of the inner helix, we also compared the angles (ψ) between the mean planes of neighboring rings, which are obtained by the least-squares fit of six carbon atoms in the ring.51 The calculated angle ψ turned out to be appreciably larger in the central rings by 2−3° than in the terminal ones, indicating that the inner rings are slightly more distorted. Interestingly, the ψ at the central rings converged to almost the same value of ca. 13° in both smaller (CH[4]− CH[6]) and larger helicenes (CH[7]−CH[10]), revealing insignificant effect of the overlapping benzene rings on ψ. The aromatic distortion in the helicene homologues was also assessed by several aromaticity indexes. Thus, the harmonic oscillator model of aromaticity (HOMA)52 and the nucleusindependent chemical shifts at the ring center [NICS(0)], as well as at 1 Å above and below the ring [NICS(1)], were calculated at the B3-LYP/6-311+G(d) level53 for the DFT-D2optimized geometries of helicenes (Tables S3 and S4, Supporting Information). The smaller HOMA values, i.e.,

Figure 1. (a) Plots of the “effective carbon volume (Vc)”, obtained by dividing the van der Waals molecular volume (V) by the number of carbon atoms (4n + 2), as a function of the reciprocal ring number (1/ n) for carbo[n]helicene (solid circle) and carbo[n]acene (open circle) series (n = 4−10). (b) Plots of the inner and center helical pitches (rpinner, rpcenter) of carbo[n]helicenes (n = 4−10), calculated by using the geometry of inner carbon atoms (red) and the geometry of mean centers of benzene rings (blue).

excellent linear correlation of Vc with the reciprocal ring number (1/n) was obtained for the entire helicene series examined, i.e., CH[4]−CH[10], which allows us to predict the limiting effective carbon volume (Vc∞) of 10.97 Å3 and the limiting volume increment (4Vc∞) of 43.9 Å3 at infinite n. As anticipated, the Vc values calculated for linear [n]acenes are slightly greater than those for the corresponding [n]helicenes to reach a larger Vc∞ of 11.10 Å3 at infinite n. The helical pitch rp, obtained by least-squares-fitting the helix geometry to a regular screw-type curve defined by z = rp × sin−1[y/(x2 + y2)0.5], is a superior parameter for globally understanding the features of helical structure.55 Hence, two pitch lengths calculated by using the inner carbon atoms (rpinner) and the mean center of each benzene ring (rpcenter) were plotted against the reciprocal ring number (1/n) in Figure 1 (right). Both pitch lengths progressively increased until the overlap of aromatic rings begins (n ≤ 6) but showed distinctly different dependencies thereafter, indicating a strong impact of ring overlap on the helix structure. The linear and exponential extrapolation of the 7375



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Figure 2. Comparison of (a) experimental and (b) theoretical CD spectra of CH[4]−CH[10]. Experimental CD spectra for CH[7]−CH[9] (in chloroform)60 were taken from the literature, whereas those for CH[5] (in 98:2 n-hexane/2-propanol at 0 °C) and CH[6] (in acetonitrile at 25 °C) were obtained in this study. The theoretical spectra were calculated at the RI-CC2/TZVPP//DFT-D2-B97-D/TZVP level.

inner and center pitches to infinite n led to the ultimate value of rpinner = rpcenter = 3.5 Å for [∞]helicene. UV−Vis and CD Spectra of Carbo[n]helicenes. As a consequence of the C 2-symmetric structure, the main transitions of CH[n] observed in the UV−vis and CD spectra can be categorized into A (C2-axis polarized) and B (perpendicular to the A-axis) symmetry groups. For instance, fairly strong negative and positive Cotton effects (CEs) were observed at around 250 and 320 nm in (P)-(+)-CH[6], which are assigned as 1Ba and 1Bb transitions, respectively, by the Platt’s nomenclature.56 These apparently coupled CEs were commonly observed for all the examined carbo[n]helicenes (excepting CH[3] and CH[4]), and the signs of these CEs can be readily used as a tool for determining the absolute configuration of helicenes (Figure 2). The smaller CEs observed for the 1La and 1Lb transitions are difficult in general to explain quantitatively (vide infra). In the following, we will discuss the experimental and theoretical CD spectra of a series of CH[n] in detail. a. Experimental Spectra. Figure 2 (left) illustrates the experimental CD spectra of CH[5]−CH[9] (see Figure S11 in Supporting Information for the corresponding UV−vis spectra). Direct comparison of the CD spectra of CH[5]− CH[9] reveals some general trends for the first strong CE (and the corresponding absorption) at the 1Bb transition. Thus, the excitation energy and molar extinction coefficient (transition probability) gradually decrease with increasing ring number n, whereas the CD intensity does not change systematically and is kept almost constant for larger helicenes (n ≥ 6). These UV− vis and CD spectral features will be discussed in detail in the theoretical CD spectrum section. However, the absolute CD intensities of these reported spectra may have to be (re)examined with caution, because the claimed optical purities do not appear to be fully guaranteed for some of the enantiomeric CH[n] samples, due to the possible thermal instability and/or the inappropriate method of optical resolution employed. It is thus important to carefully examine the experimental details. In the early studies on the experimental CD spectra of CH[5] (measured in 2,2,4trimethylpentane at 25 °C)18,57 and CH[6] (measured in methanol at 25−26 °C),58 the racemic samples were optically resolved through fractional crystallization of the corresponding diastereomeric salts with 2-(2,4,5,7-tetranitro-9fluorenylideneaminooxy)propionic acid. The resolved samples were considered to be optically pure, as the specific rotation showed saturation behavior after repeated recrystallization. During the course of the present study, we noticed that the CD

intensities reported for CH[5] and CH[6] were inconsistent with the theoretical values calculated by us, whereas those for higher helicenes were nicely reproduced by the theoretical calculations, demonstrating the suitability and reliability of the theoretical method chosen and casting some doubts about the optical purities of the samples reported in the old literature. We therefore decided to reexamine the CD spectra of CH[5] and CH[6] by using enantiomerically pure samples resolved by modern (but now routine) chiral HPLC technique. Thus, racemic CH[5] and CH[6] samples prepared by the conventional procedures (see Supporting Information) were subjected to chiral HPLC on a Daicel Chiralpak IB column to obtain enantiopure CH[5] and CH[6]. Although the CH[6] enantiomers were totally stable at ambient temperatures, the enantiomeric CH[5] gradually racemized upon storage (with a half-life of 50 min at 25 °C) but was reasonably stable at 0 °C. This result was compatible with the results of earlier semiempirical study on the racemization energies of a series of helicenes.59 The enantiomeric purities of the samples thus obtained were further confirmed by analytical chiral HPLC after resolution and also after the CD spectral measurement in the case of CH[5]. The CD spectra of enantiopure CH[5] (in a 98:2 mixture of n-hexane and 2-propanol at 0 °C) and CH[6] (in acetonitrile at 25 °C) thus obtained are shown in Figure 2. As anticipated from the rigid structure, the CD spectra of helicenes were scarcely dependent on solvent polarity (Figure S6 in Supporting Information). The revised CD spectrum of CH[6] was essentially identical in shape to that in the literature, whereas the enantiopure CH[5] showed a considerably different profile from the reported one, particularly in the short wavelength region. Crucially, the absolute CD intensities newly obtained were substantially smaller than the value reported previously for CH[5] (Δεext308 nm: 154 versus 328 M−1 cm−1) but larger for CH[6] (Δεext325 nm: 259 versus 196 M−1 cm−1). It is likely that the CH[6] sample prepared by the recrystallization of a diastereomeric salt was not sufficiently optically pure and hence afforded the smaller CD intensities. On the other hand, it seems difficult to immediately rationalized the different CD spectral profile and higher intensity reported for CH[5].57 Despite the thermal instability of enantiomeric CH[5] at ambient temperatures,57 curiously the CD spectrum was recorded at 25 °C; this, however, should not lead to a different CD profile or a larger intensity but afford a correct CD profile with a reduced intensity as a consequence of the thermal racemization. Therefore, we cannot rule out the possible 7376



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chirality of helicenes. These theoretical calculations, however, were not successful in quantitatively reproducing the CD spectra, in particular the CD intensity. A pioneering CD calculation, using the CC2 method with smaller basis-sets, has recently been performed to give a satisfactory result for CH[6], but unfortunately no detailed inspection or correlation analysis was made in the context of the whole helicene series.69 We may conclude therefore that essentially no systematic investigation has been done so far on the theoretical CD spectra of a series of carbo[n]helicenes calculated by the nonempirical theoretical method, in particular at the (more demanding) coupled cluster levels (vide supra). Despite the great success of the TD-DFT method in theoretically evaluating a variety of molecular properties,3 the search for an exchange−correlation functional suitable for predicting the desired properties with a reasonable accuracy is still a current challenge. Because the exchange−correlation functional is not exact, it is necessary or even recommended to play with several functionals and also to check the basis-set dependence to confirm the suitability of the method chosen for the specific purpose. Hence, the TD-DFT calculations on CH[6] were briefly examined by using a variety of functionals with different fractions of exact exchange for comparison with our coupled cluster results (Figure S7 in Supporting Information). Our previous experience suggests that the amount of exact exchange in the DFT functionals plays a substantial role and incorporating 30−50% exchange always leads to acceptable results.45,70 Thus, all of the selected functionals with certain amounts of HF exchange reasonably reproduced the experimental CD spectrum of CH[6], whereas the BH-LYP (50% exact exchange) and B2-PLYP (53%) methods overestimate and the B3-LYP (20%) and PBE0 (25%) methods slightly underestimate the experimental CD intensities. The typical bisignate CE pattern of 1Bb/1Ba bands was correctly reproduced if arbitrary energy-shift and intensityscaling, which depend on the functionals chosen, were applied (see the caption of Figure S7 in Supporting Information). The CE sign of weak 1Lb band was not correctly predicted with the latter two functionals. The long-range separated functionals such as LC-B3LYP and CAM-BLYP may be potential alternatives to better describe the electronic transitions for certain difficult cases,71 but further assessment of such methods on the present system was beyond the scope of this study. Although there are many examples of successful reproduction and interpretation of the CD spectra of chiral molecules by the cost-efficient yet reliable TD-DFT method, the coupled cluster methods are certainly preferred (where possible) for such molecules that possess well-behaved ground states as well as excited states reasonably well described by single excitation. The effect of solvent was examined theoretically by COSMO model at the TD-DFT-BH-LYP/TZVPP level for CH[6].42,46 There found insignificant solvent effect especially in the predicted CD spectra, as has been also confirmed by experiment (Figures S6 and S8 in Supporting Information). Finally, we compared the results of the TD-DFT and RICC2 calculations with the experimental CD spectra of CH[5]− CH[9] (Figure S10 in Supporting Information) to find that the coupled cluster methods are obviously superior to the TD-DFT method, affording much better agreements in energy and intensity with the experimental values for CH[5]−CH[9] and also a reasonable prediction for CH[10]. Our benchmark tests to assess the performance of the RI-CC2 calculations examined the effects of the starting geometry and the dependence on the

contamination of the CH[5] sample by unidentified optically active impurity/ies in the old measurement. CH[7], CH[8], and CH[9], enantiomers of which separately crystallize as conglomerates, were optically resolved by the repeated partial resolution from supersaturated solutions (more than 20 times for CH[8]) until the constant specific rotations were reached. Thus, the optical purities of these samples used for the CD measurements were regarded quantitative.60 The theoretical calculations also afforded comparable CD intensities (vide infra), supporting high purities of these samples. Next, we briefly discuss the Cotton effects of the 1Ba band and of much smaller 1Lb and 1La bands. The excitation energy of the 1Ba band gradually shifted to the red with increasing n. Although the absolute intensities of the 1Ba and 1Bb bands were comparable to each other, the profile was more complex for the 1 Ba band, being composed of several components. Furthermore, the molar extinction coefficient and molar circular dichroism did not systematically vary with n. The 1La band does not appear to be particularly useful, as the theoretically predicted rotational strength was much smaller (by 2−3 orders of magnitude) than those of the 1Ba and 1Bb transitions (Table S6 in Supporting Information) and usually hidden under the much stronger 1Bb transition (in this connection, note that the shoulder in the 1Bb band of CH[6] at ∼350 nm is considered vibrational in origin).19 The 1Lb band is similarly weak (Table S6 in Supporting Information) but can be analyzed in detail, if well separated from the nearby strong 1B transitions. The sign of the 1Lb band was a critical function of the angle of the relevant electric and magnetic transition dipole moments, and found sensitive to the electronic perturbation (such as substitution).61 CH[4] is chiral but has not been optically resolved so far.62 CH[3], known as phenanthrene, is not chiral but may be regarded as the smallest member of carbo[n]helicene series. Therefore, we make brief comments on these compounds. If one introduces some substituents (such as methyl) to CH[3] and CH[4], the helical chirality is generated or stabilized. Thus, (P)- and (M)-4,5-dimethylphenanethrene (DM-CH[3]), resolved by chiral HPLC below −70 °C, were subjected to the CD spectral measurement in a mixture of ethanol and n-hexane at −60 °C to exhibit mirror-imaged, coupled intense CD signals, from which the absolute configurations were successfully determined.63 The optical resolution and CD spectral studies of 1,12-dimethylbenzo[c]phenanthrene-5-acetic acid (DM-CH[4]-CO2H)64 and of 1-fluoro-12-methylbenzo[c]phenanthrene (FM-CH[4])65 were also reported in the literature. The CD spectra, in particular the CE at the 1Bb band (Δε299 nm = +46 M−1 cm−1 for DM-CH[4]-CO2H and Δε290 nm = +68 M−1 cm−1 for FM-CH[4]), resembled the theoretical one calculated for parent CH[4] (Δε269 nm = +43 M−1 cm−1) with a slight shift in excitation energy. b. Theoretical Methods Suitable for Calculating CD Spectra of Helicenes: A Test with CH[6]. Recently, a variety of theoretical methods have been employed in the calculation of chiroptical properties, such as electronic and vibrational CD, optical rotatory dispersion, OR, and Raman optical activity.66 Due to the relatively large size of helicenes, most of the earlier theoretical studies have employed the empirical and semiempirical methods.18−20,67 Only recently, the TD-DFT studies on CH[5] and CH[6],68 as well as CH[7]21 have been published. All of the theoretical studies successfully predicted the unique feature of the strong bisignate positive/negative CEs at the 1Bb/1Ba bands, which are derived from the inherent 7377


−3.0 −8.4 −5.0 −4.1 −7.8 −6.9 −6.1

−199 −382 −267 −278 −302 −214 −100 (c) (−376) (−272) (−455) (−364) (−189)

+47.6 (c) (−7.8) (−5.3) (−5.4) (−6.9) (−6.0)

+33.1 (+34.0) +40.2 (+40.7)

+0.61 (c) +4.3 (+4.2) +8.0 (+9.2) +22.3 (+20.7)

10−3g

+261

+273 (+282) +237 (+273)

+43 (c) +189 (+161) +257 (+259) +263 (+242)

Δε/M−1 cm−1

1.6 2.0 4.5 4.0 3.0 1.9 0.31

|μm| Bb Band 1.2 2.1 4.7 8.3 3.1 3.9 6.5 2.4 3.9 8.4 1 Ba Band 0.09 0.62 0.57 0.66 0.57 0.62 0.58

1

7.9 6.7 4.2 4.3 0.56d 0.64d 1.3 0.33d 0.33d 0.85

|μe|

180 180 180 180 180 180 180

90 85 77 69 48 51 39 29 16 15

θ/deg

HO−2 → LU+3 (45.1%), HO−3 → LU+2 (23.9), HO−7 → LU+1 (18.9%) HO−2 → LU+3 (29.2%), HO−3 → LU+2 (19.6%), HO−1 → LU+4 (10.5%) HO−2 → LU+2 (64.0%), HO → LU+3 (13.0%) HO−1 → LU+3 (48.1%), HO−4 → LU (13.1%), HO−5 → LU+1 (10.4%) HO → LU+4 (31.8%), HO−4 → LU+1 (21.6%), HO−5 → LU (14.4%) HO−5 → LU+3 (32.8%), HO−3 → LU+4 (13.9%), HO−4 → LU (10.5%) HO−1 → LU+3 (45.1%), HO−3 → LU+3 (16.5%)

HO−1 → LU+1 (40.7%), HO → LU (27.8%) HO → LU+1 (46.3%), HO−1 → LU (46.3%) HO → LU+1 (51.9%), HO−1 → LU (36.7%) HO → LU+1 (48.6%), HO−1 → LU (39.6%) HO−1 → LU (89.5%) HO → LU+1 (56.3%), HO−2 → LU (29.3%) HO−1 → LU+1 (49.5%), HO → LU (37.2%) HO → LU (84.5%) HO−1 → LU+1 (46.9%), HO−2 → LU (43.2%) HO−1 → LU+1 (41.7%), HO → LU (27.2%), HO−2 → LU (18.3%)

configurationb

Excitation wavelength (λ), molar extinction coefficient (ε) and ellipticity (Δε), anisotropy factor (g = Δε/ε), electric (μe) and magnetic (μm) transition dipole moments in atomic unit, and their angles (θ) calculated at the RI-CC2/TZVPP level. In the parentheses, the experimental spectral data cited from the literature (CH[3],62 CH[4],74 and CH[7]−CH[9]60) or obtained in this work (CH[5] and CH[6]) are shown. The 1Ba band of CH[3] was not well-defined. bRelevant molecular orbital configurations and relative amplitudes (in the parentheses) of the major contributions (≥10%). cTwo separate transitions were found contributed to the 1Bb band. dNot observed or not reported.

a

(c) (483) (51700) (84200) (52500) (31700)

176 194 233 262 280 282 309

CH[4] CH[5] CH[6] CH[7] CH[8] CH[9] CH[10]

66400 45500 53400 67900 38700 31100 16300

5480

403

CH[10]

(c) (206) (246) (270) (288) (297)

8260 (8300) 5890 (6700)

(67000) (79400) (38200) (28300) (11700)

371 (372) 389 (390)

74500 70500 43500 32300 11800

CH[8] CH[9]

(250) (290) (310) (324) (348)

ε/M−1 cm−1

234 269 298 317 351

λ/nm

CH[3] CH[4] CH[5] CH[6] CH[7]

helicene

Table 2. Theoretical CD Spectral Parameters for Carbo[n]helicenes CH[3]−CH[10] at the 1Bb and 1Ba Bandsa

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Table 3. Experimental and Theoretical Specific Rotations for Carbo[n]helicenes CH[4]−CH[10]a specific rotation/deg cm3 g−1 dm−1 theoretical helicene

light source

CH[4]

Na-D Hg Na-D

CH[5]

Hg CH[6]

CH[7] CH[8]

Na-D Hg Na-D Hg Na-D Hg

CH[9]

Na-D Hg

CH[10]

Na-D Hg

experimental (conditions)

b

+2760 +2160 +2270 +1670 +3760 +3707

(c 0.013, n-hexane:2-propanol =98:2)c (c 0.29, 2 °C)d (c 0.29, 2 °C)d (2,2,4-trimethylpentane, 26 °C)e ± 20 (c 0.0025, acetonitrile)c ± 12 (c 0.082)f

+6200 +5900 +6690 +6900 +7170 +7500 +8100 +8300 +8300 +8940

± ± ± ± ± ± ± ± ± ±

200 200 100 200 100 100 200 100 100 100

(20 °C)g (c 0.06)h (c 0.02)i (c 0.043)h (c 0.02)i (c 0.02)i (c 0.061)h (c 0.02)i (c 0.02)i (c 0.02)i

B3-LYP/augD

BH-LYP/augD

+880 +900 +2970 (+2880)j

+2430 (+2360)j

+3090

+2520

+4760 (+4530)j

+3570 (+3400)j

+5030 +6690 (+6100)j +7260 +8170 +8890

+3750 +4660 (+4280)j +4990 +5480 +5870

+9000 +9790

+6030 +6430

+9790 +10100

a

Specific rotation at the wavelength of sodium-D (589 nm) or Hg resonance (578 nm) line. The theoretical specific rotation [α] was calculated by the TD-DFT method with B3-LYP or BH-LYP functional by using the Dunning’s aug-cc-pVDZ (augD) basis-set. bExperimental [α] values measured in chloroform and at 25 °C, unless otherwise indicated. Concentration in g (100 mL)−1. cThis work. dReference 79. eReference 57. f Reference 7. gReference 80. hReference 60. iReference 81. jGauge-invariant atomic orbitals were employed for the TD-DFT calculations. Geometries were optimized at the B3-LYP-D2/6-311G(d,p) level. See ref 36.

basis-sets (Figure S9, Supporting Information). The CD spectra calculated for the DFT-D2 and SCS-MP2 method-based geometries are slightly red-shifted and smaller in intensity at the 1Bb band than the result calculated for the geometry optimized by the conventional DFT method. As already pointed out,70 the different starting geometries did not greatly affect the overall spectral profile (only affording a slightly better match for the DFT-D2/SCS-MP2 geometry), which is in stark contrast to the OR calculation of helicenes.36,48 Most of the CD intensities were already converged with the use of double-ξ SVP basis-sets, and the very expensive aug-TZVPP basis-sets gave the theoretical CD spectrum quite similar to that obtained with the TZVP/TZVPP basis-sets, showing very minor differences only in the high-energy region (200−250 nm). These results encouraged us to choose the RI-CC2/TZVPP// DFT-D2/TZVP level of theory for the systematic theoretical investigations on the CD spectra of the carbo[n]helicene family. The only empirical manipulation employed in this study is the expansion of the theoretically obtained rotational strength to approximate the vibrational consequence of the helicene molecule by applying the Gaussian band half-width of 0.25 eV. There have been a number of reports that pointed out that the molecular vibration plays considerable effects on the predicted (chir)optical properties.72 Although the vibrational consequence was taken into account in some advanced studies on smaller molecules,73 application of such a theoretical treatment is not feasible on these (large) helicene molecules and is beyond the scope of this work. c. Theoretical UV−Vis and CD Spectra of Carbo[n]helicenes (n = 3−10). Taking into account the results of the above preliminary examinations, we carried out the theoretical calculations for the whole series of CH[3]−CH[10] at the RI-

CC2/TZVPP level. The theoretical CD spectra thus obtained are shown in Figure 2 (right), along with the experimental ones (Figure 2, left); for the corresponding UV−vis spectra, see Figure S11 in Supporting Information. The characteristic bisignate CEs for the 1Bb and 1Ba bands of the helicenes larger than CH[5] were precisely reproduced in excitation energy, sign, and absolute rotational strength; for a numerical comparison, see Table 2. The assignment of the 1Ba band was more difficult because of the significant overlap of closely located transitions but was achieved by performing the configuration analysis of the theoretically calculated transitions and further reinforced by the linear correlation of the excitation energy with the reciprocal ring number, 1/n (vide infra). There were some larger deviations at shorter wavelengths ( 0. The angle θ exceeded 90° at CH[6] and further increased thereafter, endowing negative CE for the 1Lb band of CH[6] and beyond. Experimentally, the CE observed for 1Lb band was negative in sign for CH[6] in accordance with the theoretical prediction but became positive in sign for CH[8], whereas the band was not clearly identified for CH[7] and CH[9] due to the serious overlap with neighboring 1Ba/1Bb bands (Table S6 in Supporting Information). As the electric and magnetic transition dipoles of forbidden 1La and 1Lb transitions are also determined by the helical structure, the CEs of these bands are potentially useful for structural elucidation of helicene molecules. However, the CE intensity is generally very weak and affected by closely located intense transition(s) and environmental factors, and hence the absolute value (and even the sign) of the observed CE are not considered as good measures of the helicene structure, unless the effect of nearby transitions and environmental factors can be rigorously extruded. Excitation Energies of 1Ba and 1Bb Transitions. The helicene series suffered the effect of delocalization to show systematic bathochromic shifts of the 1Ba and 1Bb bands (Figure 2 and Table 2). The experimental excitation energies of 1Ba and 1 Bb bands are plotted against 1/n to afford good linear correlations over the entire range of n (n ≤ 9) (Figure 5, left). Such a linear dependence has also been reported for a series of linear acenes,83 as well as ortho-84 and para-phenylenes.85 Although TD-DFT methods usually fail to predict the singlet excitation energies of low-lying 1La and 1Lb states in oligoacenes86 (for range-separated hybrid functional to mitigate these deficiencies, see ref 87; the failure has been ascribed recently88 to the disguised charge-transfer-like character), the coupled cluster method86 appropriately reproduced the experimental excitation energies, showing a linear dependence against 1/n (Figure 5, left). The effective conjugation length of carbo[n]helicene was estimated as ≈50 at the 1Bb band by the least-squares fitting of these theoretical data to the exponential function (Figure S13 in Supporting Information).89 This is in good agreement with the earlier theoretical calculations at the semiempirical level that predicted the convergence of excitation energy at n ≈ 40.67 The present value is somewhat larger than those reported for ortho- and para-phenylenes (∼10) or oligothiophenes (∼20),90 most probably due to the effective intramolecular 3-D overlap for larger helicenes. The good linear correlations of both theoretical and experimental excitation energies with 1/n provided the converged transition energies (wavelengths) of the 1Ba and 1Bb bands of 1.91 eV (649 nm) and 2.06 eV (601 nm), respectively, for [∞]helicene. This also predicts a switching of the 1Ba and 1Bb excitation energies at around [70]helicene. Anisotropy (g) Factors of 1Bb and 1Ba Bands. We now discuss the CD intensity of the 1Bb and 1Ba bands as a function of n. The CD intensity (Δε) as well as the anisotropy factor (g = Δε/ε) are plotted against n in Figure S14 in Supporting Information and the relevant data are summarized in Table 2. For the 1Bb band, the Δε value gradually increased up to n = 6 to reach a plateau of ∼260 M−1 cm−1 after n ≥ 6. This trend obviously contradicts the previous theoretical prediction that increasing ring number n in carbo[n]helicene,19 as well as elongating pitch distance in carbo[6]helicene,67 progressively increase the rotational strength and CD intensity. In sharp

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CONCLUSIONS Helicenes have attracted considerable attention for their unique helical chirality. Nevertheless, no comprehensive high-precision study on the structure-chiroptics relationship was available, which prompted us to perform the state-of-the-art theoretical CD spectral calculations for a series of carbo[n]helicenes CH[n]. In this combined theoretical and experimental study on the (chir)optical properties of CH[3]−CH[10], we have revealed the following (mostly) new aspects: (1) The experimental CD spectra of CH[5] and CH[6] reported earlier turned out to be erroneous in intensity (and also in shape for CH[5]). The enantiopure CH[5] and CH[6] newly prepared exhibited the chiroptical properties coherent to the rest of the carbo[n]helicene series. (2) The excitation energies (wavelengths) of both 1Ba and 1 Ba bands are linearly correlated with the reciprocal number of benzene rings (1/n) over the entire range of n examined (n = 4−10) to converge to 1.9 eV (650 nm) and 2.1 eV (600 nm), respectively, at n = ∞. The effective conjugation length is estimated as n ≈ 50, which is much larger than that for acenes, probably due to the effective intramolecular (helical) overlap. (3) The approximate linear response coupled cluster method at the RI-CC2/TZVPP level to calculate the optimized geometries with the dispersion-corrected DFT method 7382



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Notes

beautifully reproduced the experimental CD spectra of all the experimentally available helicenes (CH[5]−CH[9]), affording the exact excitation energies and rotational strengths without applying any energy shift or intensity scaling. (4) For (P)-helicenes, the tangential transition dipole of the 1 Bb state leads to counterclockwise charge rotation. The electric transition dipole is almost perpendicular to the magnetic transition dipole for smaller helicenes, which is progressively aligned to the parallel direction with increasing n to afford more intensified positive CE. The anisotropy (g) factor of the 1Bb transition is linearly correlated with 1/n, when n ≥ 6. An exceptionally large g factor of ∼0.1 (as an allowed, nonexciton coupled transition) is predicted by extrapolating the regression line to infinite n. For smaller helicenes (n < 6), the g factor is also proportional to 1/n but the slope is much smaller. (5) The rotational strength is a function of the electric and magnetic transition dipoles (|μe| and |μm|) as well as the angle between them (θ). A general correlation with n is found only for the cos θ value, but not for the individual moments μe and μm. Nevertheless, a mutual compensation of these parameters leads to a good linear correlation of the g factor with 1/n for n ≥ 6. (6) The g factor of the 1Ba band is insensitive to the helicene size n. The CEs of the forbidden 1Lb and 1La bands are structure-sensitive but are not suitable for structural elucidation due to the spectral overlap with the much stronger 1Bb/1Ba transitions. (7) The experimental and theoretical specific rotations are also proportional to 1/n, again for larger CH[n]s (n ≥ 6). The specific rotations calculated by the TD-DFT method at the B3-LYP/aug-cc-pVDZ level are systematically deviated from the experimental values, but both values are correlated by the equation: [α]Dexp = 0.84 × [α]DDFT. (8) The discontinuous alterations of chiroptical properties observed consistently at n = 6 are ascribed to the sudden change in helicene structure, in particular the leap of the helical pitch, upon completion of the first helix at CH[6]. The chiroptical properties display nice linear relationships with 1/n at n ≥ 6, assuring good reliable predictions for unavailable CH[n]s. These findings convince us that the chiroptical properties of helicenes are controllable by adjusting the helical pitch. Experimentally, this is not a trivial task but still seems achievable by using some tricks, for example, alkylation or heteroatom substitution at the terminal or central rings. Further studies along these lines are currently in progress.

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The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Financial supports of this research by Grant-in-Aid for Scientific Research (No. 23350018, 24655029, and 21245011) from JSPS, the Mitsubishi Chemical Corporation Fund, the Sumitomo Foundation, the Shorai Foundation for Science and Technology, and the Kurata Memorial Hitachi Science and Technology Foundation are gratefully acknowledged.

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ASSOCIATED CONTENT

S Supporting Information *

Details of preparation, enantiomer separation, and experimental NMR, UV−vis, and CD spectra of CH[5] and CH[6], as well as details of theoretical calculations for CH[3]−CH[10]. This information is available free of charge via the Internet at http:// pubs.acs.org.

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REFERENCES

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. 7383



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