Axial Chirality of Donor–Donor, Donor–Acceptor ... - ACS Publications

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Axial Chirality of Donor
Donor, Donor
Acceptor, and Tethered 1,10 -Binaphthyls: A Theoretical Revisit with Dynamics Trajectories Masaki Nishizaka, Tadashi Mori,* and Yoshihisa Inoue* Department of Applied Chemistry, Graduate School of Engineering, Osaka University, 2-1 Yamada-oka, Suita 565-0871, Japan

bS Supporting Information ABSTRACT: The circular dichroism (CD) spectra of (R)-2,20 -dimethoxy-1,10 binaphthyl (DD) and its untethered and tethered donor
acceptor analogues (DA and DA7
DA9) were investigated experimentally and theoretically. The experimental CD spectra of DD and DA resembled each other in several aspects, displaying a positive
positive
negative Cotton effect pattern in the 1 Lb
1La region and a strong negative couplet at the 1Bb band, but significantly differed in transition energy and rotatory strength. The couplet amplitude (A) of the main band was 1.6 times larger in DA than in DD, despite the comparable extinction coefficients and seemingly analogous conformations. An additional positive Cotton effect was observed at the CT (CT) band for donor
acceptor binaphthyl DA. Our theoretical prediction of the CD spectra of binaphthyls involves three sequential first principle quantum mechanics (QM) calculations. Thus, the geometry optimizations of a series of conformers with varying dihedral angles were performed by the dispersion-corrected DFT-D method using the B97-D functional and the TZV2P basis set. The potential curve as a function of the dihedral angle (θ) was obtained by using the SCS-MP2/TZVPP single-point energy calculations with and without application of the solvent correction. The CD spectrum of each conformer was independently calculated by the second-order approximate coupled cluster calculation (CC2 method) using the TZVPP basis sets and the resolution of the identity (RI-J) approximation. The (net) theoretical CD spectrum was obtained by averaging over all possible conformers, where the dynamics trajectories based on the relative SCS-MP2 energies were taken into account. By using 17 possible conformers at θ varying from 50 to 130° by 5° intervals, the experimental CD spectra were successfully reproduced in a quantitative manner, enabling us to characterize properly almost all of the important spectral features and chiroptical properties. The two-state model, reported previously, turned out to have led to the right answer with wrong reasons. The couplet sign and amplitude A are critical functions of θ and can be used not only for (qualitatively) determining the absolute configuration but also for quantitatively analyzing the binaphthyl conformations. The angle dependence of A was already argued in the classical coupled oscillator and exciton chirality theories to provide reasonable structure elucidations but only in a qualitative or semiquantitative manner. Our method is able to predict the A value quantitatively as a function of θ. For tethered binaphthyls DA7
DA9, particular care should be exercised in the conformational assessment based on the classical treatment because the amplitude A was shown to be significantly affected by the existence of the tether itself. In the present method, the couplet amplitude A was nicely related to the dihedral angle θ of DA and DD by the state-of-the-art ab initio calculations, enabling us to gain the quantitative information about the conformation of axially chiral binaphthyls. The Cotton effect at the CT band also serves as a complementary clue for elucidating the conformation of donor
acceptor binaphthyls.

’ INTRODUCTION Conformational behavior of chiral 2,20 -disubstituted-1,10 -binaphthyl is of broad interest owing to the widespread use in asymmetric catalysis, chirality sensing, supramolecular chemistry, and materials science.1 The conformational diversity of binaphthyl in condensed phase arises from the rotational freedom of the central C1
C10 bond, whereas its chirality comes from the limited rotation. Both of the s-cis and s-trans conformers are found in the solid state,2 whereas the orthogonal conformation is favored in solution.3 These apparently incoherent results are rationalized in terms of the relatively flat potential energy profile against the C2
C1
C10
C20 dihedral angle (θ).4 For deeper comprehension and more precise prediction r 2011 American Chemical Society

of the chiroptical (and other physical) properties of axially chiral binaphthyl molecules, the dynamic conformational diversity on such a flat potential surface should be appropriately taken into account because the (chir)optical properties are critical functions of the angle of the transition dipole moments of the naphthalene chromophores. We have recently reported the comparative experimental and theoretical study of the axial chirality of 2,20 -, 3,30 -, and 4,40 biphenol ethers5 to reveal that the chiroptical properties of chiral biaryls are highly angle-dependent and the weak CD intensities Received: March 24, 2011 Published: May 10, 2011 5488

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The Journal of Physical Chemistry A Chart 1. Definition of Dihedral Angle θ and Central Bond Distance r

observed are often a consequence of the overlap of oppositely signed spectra of multiple conformers. Nevertheless, the experimental spectra were well-reproduced by theory, if the proper methods of calculation were chosen with solid theoretical consideration and the contribution of each conformer was adequately incorporated. The main-band couplet at 220
230 nm is associated with the binaphthyl’s 1Bb transition,6 and the direction of polarization is assigned to the long axis of the naphthalene chromophore from the single-crystal electronic spectral examinations (Chart 1).7 Mason et al. proposed an exciton model to correlate quantitatively the couplet amplitude (A) of the 1Bb band of binaphthyl with the angle between the two transition dipole moments of naphthyl moieties.8 The major conclusions derived therefrom were that the amplitude A maximizes at ca. 70° and the CD sign is inverted at ca. 110°. The strongly coupled 1Bb band has recently also been used for the conformational analysis of photoexcited 1,10 -binaphthol.9 However, the theoretical A values calculated by the Mason’s method are considerably (more than twice) larger than the experimental ones, and the magnitude of deviation is highly substrate-dependent. In this coupled oscillator model, the direction of transition moment is not supposed to deviate from the long axis of naphthalene, despite the fact that the real transition moment is more or less tilted in substituted naphthalenes, and also the effects of other nearby transition dipoles are completely neglected. The Pariser
Parr
Pople calculation of 2,20 -dihydroxy-1,10 -binaphthyl with the composite-molecule treatment revealed that the first-order exciton interaction with nearby excited states should be incorporated to predict precisely the rotatory strength of binaphthyl derivatives.10 Consequently, the Mason’s model is valid only semiquantitatively and not suitable for predicting the dihedral angle of binaphthyl in solution. It is rather surprising that practically no comprehensive ab initio study of the chiroptical properties of 1,10 -binaphthyls has been done at the satisfactory accuracy level. In this study, we performed a comprehensive experimental and theoretical investigation of the chiroptical properties of 2,20 -dimethoxy-1,10 binaphthyl (DD) and its donor
acceptor analogues (DA, DA7
DA9) to reveal that the theoretical couplet amplitude (A), if obtained by using the state-of-the-art QM methods, is indeed the most valuable parameter for assessing the conformational behavior in solution (Chart 2).11 The previously reported two-state model, in which only s-cis and s-trans conformers optimized at the DFT-D-B97-D level were taken into consideration, turned out to have given the right answer with wrong reasons. In this study, to establish a reliable methodology for accurately predicting the CD spectra of axially chiral binaphthyls, we employed a combination of sophisticated state-of-the-art QM calculations. First, the geometry was optimized at the DFT-D-

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Chart 2. Axially Chiral Donor
Acceptor 1,10 -Binaphthyl (DA), Tethered Derivatives (DA7
DA9), and Donor
Donor Analogue (DD)

B97-D level for a set of conformers with various preset (and fixed) θ, for each of which the RI-CC2 spectrum calculation was performed, and the theoretical CD spectrum was obtained by weighted-averaging the calculated spectra over the full set of conformers on the basis of the Boltzmann population calculated from their relative SCS-MP2 energies. The essential spectral features were nicely reproduced by incorporating the dynamics trajectories of the binaphthyl conformers (vide infra). Furthermore, the CD spectra of tethered binaphthyls (DA7
DA9) were properly predicted but were appreciably deviated from those of the corresponding DA conformers at the same θ, indicating that there exists the significant effect of the nonchromophoric tether on the observed CD spectrum. More seriously, the simple coupled oscillator model was shown to be invalid at least for the axially chiral binaphthyls presented herein.

’ RESULTS AND DISCUSSION Structures of DA and DD. In the previous study, we optimized the structures of DA and DD at the DFT-D-B97-D/ TZV2P level to obtain both s-cis and s-trans conformations.12 All of the DFT methods provide reasonable structures (within a deviation of 2 to 3% in bond angle and length), which are accurate enough for the subsequent CD (thus the excited state) calculation that usually accompanies more aberrations. However, the finding that the more sophisticated method (the spincomponent scaled second-order Møller
Plesset perturbation theory, SCS-MP2),13 provided a potential energy curve for DA significantly different from that obtained by the DFT-D method12 urged us to more closely re-examine the suitability and reliability of the QM methods of choice for the current system. The SCS-MP2 method has been shown to provide the most accurate energy and thus the preferred wave function method in most medium to large organic molecules when meaningful CCSD(T)-type computations could not be performed.14 Thus, the geometries of DA and DD were reoptimized by using the SCS-MP2 method, and the geometries of the s-cis forms of DA and DD are compared in Figure 1. The SCS-MP2 method turned out to provide the s-cis conformer structures very similar to those obtained by the DFT-D method, both of which are compared with the corresponding X-ray crystallographic structures in Table 1. We were unable to find any local minimum for 5489

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Figure 1. Geometries of DA (left) and DD (right) optimized at the SCS-MP2/TZVPP level.

Table 1. Comparison of Structural/Spectral Parameters for DD, DA, and DA7
DA9a A λmax λfl Δλ λCT εCT ΔεCT DD 360 337 363 2100

DA 560 373 542 8400 379 1180 þ1.0

DA7 330 383 523 7000 389 5070 þ10.2 DA8 450 373 513 7300 369 3870 þ5.3 DA9 720 370 526 8000 368 2140 þ6.1

s-cis s-trans X-ray b s-cis s-trans X-ray b s-cis s-cis s-cis s-trans

θ

r

79.2 (79.0) 98.5 (101.9) 112.1 79.8 (76.1) ; (98.1)c 98.3 58.9 66.9 71.7 95.1

1.483 (1.490) 1.483 (1.491) 1.503 1.475 (1.479) ; (1.480)c 1.486 1.474 1.476 1.479 1.480

Couplet amplitudes at the main band (A/M
1 cm
1), the lowest energy absorption maximum (λmax/nm) and emission maximum (λfl/nm), and the Stokes shift (Δλ/cm
1) were obtained from the spectra in acetonitrile at 25 °C. The CT band absorption maximum (λCT/nm), molar extinction coefficient (εCT/M
1 cm
1), and ellipticities at the CT band (ΔεCT/M
1 cm
1) were obtained by the deconvolution of the observed spectra in dichloromethane at 25 °C. Dihedral angle (θ/°) and C1
C10 bond length (r/Å) for s-cis and s-trans conformers calculated at the SCS-MP2/TZVPP level and at the DFT-D-B97-D/TZV2P method in parentheses. b Values from the X-ray crystal structure. c Optimization failed. See the text. a

s-trans conformer of DA; the geometry optimizations of s-transDA by the SCS-MP2 method always led to the s-cis conformation. This is fairly reasonable if the single-well potential curve is considered (vide infra). The fact that the more accurate SCSMP2 method was unable to give both the s-cis and s-trans conformers as local minima clearly indicates that the previously proposed two-state model12 was not appropriate for predicting the CD spectra of these axially chiral donor
acceptor 1,10 binaphthyls. Comparison of Gas-Phase Potential Curves of DA versus DD. The potential curves were obtained for DD and DA as a function of C2(N)
C1
C10
C20 dihedral angle (θ) by the following procedures. First, a series of DD and DA conformers at varying θ were optimized by using the DFT-D-B97-D method.15 Because of the steric hindrance, 1,10 -binaphthyls are not coplanar, and θ can vary from 60 to 120°.16 Therefore, the optimization was repeated by changing θ from 50 to 130° at every 5°. The empirical dispersion-correction was employed to improve the accuracy of physical property prediction without additional computational cost.17 The Ahlrichs-type basis sets of valence triple-ζ quality18 with additional two sets of polarization functions taken

Figure 2. Comparison of the potential curves for DA (left) and DD (right) as functions of dihedral angle θ. Relative energies in the gas phase (black lines) calculated at the SCS-MP2/TZVPP//DFT-D-B97-D/ ZTV2P level and in acetonitrile (red lines) obtained by incorporating the COSMO treatment (ε = 36.64).

from the corresponding Dunning cc-pVXZ basis sets19 (leading to TZV(2d,2p) were denoted as TZV2P; in standard notation: H, [3s2p], C/N/O, [5s3p2d]) were employed for all geometry optimizations. The single-point energies were then calculated by the SCS-MP2 method13 using the basis sets of additional d/f polarization functions on hydrogen or non-hydrogen atoms (denoted as TZVPP).20 As previously mentioned, the SCSMP2/TZVPP calculations21 provided the most reliable gasphase potential curves for DA and DD against θ, as compared in Figure 2 (black). The potential curves for both of the axially chiral molecules are rather shallow, and both s-cis and s-trans conformations can freely interconvert at an ambient temperature. It is to note that the transformation to antipodal conformers is prohibited because fo the much higher energy barriers. The most stable conformers were found in the s-cis form at θ ≈ 80° for both DA and DD by the theoretical calculations in the gas phase, whereas only the s-trans conformers were found in the X-ray crystallographic structures of both DA and DD.12 The horizontal dotted lines in Figure 2 represent the boundaries of θ in DA (70
105°) and DD (60
120°) determined by the Boltzmann distribution at 25 °C (kT ≈ 0.6 kcal mol
1). DD has an almost symmetrical double-well potential, which, however, slightly favors the narrower θ due to the effective dispersion interaction of the two naphthyls. The shape of the potential curve of DD is qualitatively consistent with that of the parent 1,10 -binaphthyl obtained by using the standard density functional theory at the BPW91/631G** level.22 The estimated range of θ for DA is much narrower and more s-cis-oriented than that for DD, suggesting the possible existence of a minimum for the s-trans conformer. The minimum was, however, not found (apparently) for the s-trans conformations, contrary to the results obtained with the DFT-D potential, in which the dispersion effect seems overestimated.12 The electrostatic and donor
acceptor interactions between the quinolinium and electron-rich methoxynaphthalene moiety play some roles in stabilizing the s-cis conformations. Judging from the low oxidation potential of 2-methoxynaphthalene (Eox = 1.52 V vs SCE) and the high reduction potential of N-methylisoquinolinium (Ered =
1.15 V vs SCE),23 binaphthyl DA should bear substantial (intramolecular) donor
acceptor interaction, which was experimentally supported by the fairly large oscillator strength (log ε = 3.1) of the CT transition at ∼380 nm. In Acetonitrile. Although the ansatz involving explicit solvent molecules is required for some class of solvation issues,24 the continuum solvation model such as the conductor-like screening 5490

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Figure 3. Comparison of the theoretical versus experimental CD spectra of DA (left) and DD (right). Black: Experimental spectra in acetonitrile at 25 °C. Blue: Theoretical spectra calculated at the RICC2/TZVPP level by weighted-averaging the spectra of conformers based on the Boltzmann population obtained by using the potential curves in the gas phase (shift: 0.2 eV). Red: Theoretical spectra obtained by using the potential curves in acetonitrile.

model (COSMO) has been successfully applied to the theoretical prediction of a number of properties of organic molecules in solution.25 Thus, the solvent effects on the potential curves of DA and DD were investigated by using the COSMO procedures implemented in the TURBOMOLE package, and the (relative) SCS-MP2/TZVPP energies in acetonitrile were calculated for all optimized geometries of a given dihedral angle (vide supra) (Figure 2, red). Thus, the solvation energies, ESCS-MP2(acetonitrile)
ESCS-MP2(gas phase), for DA and DD were calculated as
41.8 and
10.2 kcal mol
1, respectively, when the dihedral angle θ = 90°. As anticipated, the solvent effect was slightly more pronounced for cationic DA, but the potential curves for DA and DD in acetonitrile were not greatly altered from those obtained in the gas phase. A closer look revealed that the potential well became slightly narrower in acetonitrile, in particular, for the s-trans of DD to give a single minimum, as was the case with DA. The influence of these changes on the predicted CD spectra, however, turned out to be nominal (vide infra). In both cases, the most stable conformers became slightly more perpendicular but still kept the s-cis form (θ ≈ 85°). These near-perpendicular conformers may be more effectively solvated because of the wider space between the aromatic planes available for solvent molecules. It is also to note that the potential curve is essentially a single well with a small shoulder on the s-trans side both in the gas phase and in acetonitrile. Experimental CD Spectra of DA and DD. The experimental CD spectra of DA and DD were obtained by using conventional cuvette (optical path length = 1 cm) in acetonitrile at 25 °C (Figure 3, black lines); the CD spectra of DA in methanol and in dichloromethane are shown in Figure S1 (left) in the Supporting Information. A small red shift of the CT band at 350
430 nm and a decrease in the intensity of the 1Lb band were induced for DA in less-polar dichloromethane than in polar acetonitrile or methanol. The main-band couplet at the 1Bb transitions in dichloromethane was difficult to compare directly because of the substantial overlap of dichloromethane absorption in this region. Further examination of the solvent effect in nonpolar solvents was not feasible because of the low solubility of cationic DA in these solvents. Because the X-ray crystallographic study revealed the s-trans conformation for DA recrystallized from ethanol,12 the solid-state CD spectrum of DA was anticipated to differ significantly from the solution spectrum. Indeed, the CD

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Figure 4. Dihedral angle dependence of the theoretical CD spectra of DA (left) and DD (right) calculated at the RI-CC2/TZVPP level (shift, 0.2 eV).

spectrum of DA in a KBr disk showed appreciable differences in shape (Figure S1, right, in the Supporting Information), the origin of which was, however, difficult to theoretically rationalize. Accordingly, we will mostly use the spectra in acetonitrile as the experimental references for the theoretical results (vide infra). Theoretical Calculations of the CD Spectra of DA and DD. (a). Calculation for Each Conformer. The theoretical CD spectra of DA and DD to be compared with the experimental ones were obtained by weighted-averaging the theoretical CD spectra of 17 conformers (with θ ranging from 50 to 130° by 5° step) on the basis of the Boltzmann populations attained by the relevant dynamics trajectories (Figure 2). The CD spectra of individual conformers of both DA and DD were calculated by the second-order approximate coupled cluster (CC2) calculations.26 The CC2 Franck
Condon excitation energies were calculated by using the TZVPP basis sets20 and the resolution of the identity (RI-J) approximation.27 The RI-CC2/TZVPP method28 is much more accurate in general than the more popular time-dependent DFT method and is thus preferred whenever applicable.29,30 The CD spectra were simulated by summing the Gaussian function for each transition from more robust length-gauge representations where the bandwidth at 1/e height is fixed at 0.4 eV. This bandwidth was chosen to better match the experimental bandwidth, intensity, or both from our previous experiences. Figure 4 illustrates the CD spectra calculated for the individual conformers, which distinctly differ from each other in shape and intensity; for the enlarged spectra, see Figures S5 and S6 in the Supporting Information. (b). Dihedral Angle Dependence of the CD Spectrum of DD. Because the exciton coupling phenomenon can be used as a convenient, sensible, and even indispensable tool for elucidating molecular geometry and conformation, the optical activity of chiral biaryls has been a target of intensive experimental studies.31 The couplet amplitude at the 1Bb transition of binaphthyls (220
230 nm) has been qualitatively discussed in terms of the coupled oscillator theory, which properly predicts the absolute configuration of various biaryls.32 In the exciton chirality theory, the couplet amplitude is a critical function of the dihedral angle of coupling transition moments, maximizing at θ ≈ 70°, and the bisignate signal changes its sign at θ ≈ 110°. Our RI-CC2 calculations (Figure 4) indicate, however, that the CD spectrum in the main-band region (210
260 nm) is not a result of simple exciton coupling but a grand total of all relevant transitions of various origins. As can be seen from the CD spectra for DD conformers (Figure 4, right), the couplet sign is negative for the conformers of θ = 50
90°, and the amplitude 5491

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Figure 5. Dihedral angle dependence of the couplet amplitude |A| at the 1Bb transition (220
230 nm) in DA and DD (left) and the CD intensity at the CT band in DA (right). The CD intensity of the positive Cotton effect at 230 nm was used in the plot for DD at θ 110
130° because no clear couplet appeared.

maximizes at θ = 70°, but the CD profile in the main-band region becomes more complicated at θ > 90°, exhibiting an apparently positive couplet at θ = 100
110° and eventually a positive
positive
negative pattern (from the longer wavelengths) at θ = 110
130°. The angle dependence of the apparent couplet amplitude is visualized for DD and DA in Figure 5 (left). The CD intensity at ∼230 nm (instead of the amplitude) of DA was used at θ = 110
130° because the 1Bb transition does not strongly couple at these angles. It is to note that this intensity plot (and thus the CD behavior predicted therefrom) is appreciably different in shape from that derived from the Mason’s method, especially on the s-trans side. Whereas the transition energy of each DD conformer is progressively shifted as a function of θ and maximizes at θ = 90° (Figure S2, right in the Supporting Information), the individual rotatory strength behaves quite inconceivably as a function of θ (Figures S3 and S4, right, in the Supporting Information). The transition nos. 7
10 are fairly strong and the summation of these transitions essentially affords a CD pattern resembling the experimentally observed in the main-band region. Thus, the profiles of the couplet amplitude and the observed CD pattern as functions of θ are not straightforward. Nevertheless, the couplet amplitude is very sensitive to the dihedral angle and still valid in evaluating the molecular conformation under the given conditions but only if combined with the proper quantum mechanical method(s). (c). Dihedral Angle Dependence of the CD Spectrum of DA. The dihedral angle dependence of couplet amplitude for DA displayed a parallel but considerably different pattern from that for DD (Figure 5, left). Thus, in sharp contrast with DD, the couplet intensity of DA monotonically decreased with increasing θ from 50 to 110° (without accompanying a maximum at 70°), and the band did not show any couplet, but a positive Cotton effect, accompanied by satellite negative Cotton effect, was observed at θ larger than 110°. The transition energy profiles of DA as a function of θ are smooth in general, mostly showing extrema at θ = 90°, as was the case with DD; see Figure S2, left, in the Supporting Information. The angle dependence of the individual rotatory strength in DA, although somewhat unpredictable, is smooth with respect to θ (Figures S3 and S4, left, in the Supporting Information). In the case of DA, three transitions (i.e., nos. 10
12, in particular, nos. 11 and 12) are responsible for the strong negative couplet in the main-band region, which rapidly grows at θ < 110°. Again, the angle dependence of the calculated CD spectra of DA is not a simple function of θ, contrary to the expectation from the simple

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coupled oscillator theory,32 where the couplet intensity is anticipated to increase progressively with decreasing θ. It is noteworthy that the calculated couplet amplitude becomes comparable for both DA and DD at near perpendicular θ of 75
110°. This angle range covers most of the conformations of DA (∼85%) and DD (∼80%) that contribute to the weighted averaging based on the Boltzmann population at ambient temperature (vide infra). These results not only confirm that the main-band couplets of both DA and DD are quite sensible to the dihedral angle but also demonstrate that the combined experimental and theoretical analyses proposed above greatly contribute to the quantitative evaluation of the conformational behavior of biaryls. In the case of DA, the CT band observed at ∼3.0 eV (in theory) or ∼370 nm (in experiment) can also be used as an additional convenient tool for analyzing conformational changes. The rotatory strength or Cotton effect of the CT band gradually decreases as the dihedral angle increases (Figure 5, right). Despite the modest CD intensity (Δε ≈ (20 M
1 cm
1), the Cotton effect at the CT band, which is readily separable from the other high-energy transitions and alternating in sign at θ ≈ 90°, is valuable and convenient in elucidating the equilibrium between the s-cis and s-trans forms. Apart from the main 1Bb and low-lying CT transitions, the 1La and 1Lb transitions were also revealed to vary significantly with θ (Figure 4 and Figures S5 and S6 in the Supporting Information). However, their weak intensities and considerable overlaps in the experimental CD spectra obviously disturb the reliable band assignment and conformation analysis, rendering these bands less important. (d). Simulation of the Theoretical CD Spectra Considering the Conformer Ensemble. As mentioned above, both DA and DD have fairly flat potential energy profiles against θ (Figure 2), and the individual theoretical CD spectra of DA and DD conformers are considerably different in shape and intensity. This means that the conventional two-state model, dealing with only the s-cis and s-trans conformers, may not be the most appropriate approximation, and instead the ensemble model, considering all energetically attainable conformers, is a better approach to more realistically simulate the experimental CD spectra.12 The QM/MM MD method that intertwines the advantages of the QM (in terms of accuracy) and MD techniques (to generate a dynamics trajectory) has been applied to several biomolecular systems for the better prediction of spectroscopic properties.33 In this study, we applied similar averaging technique to the simulation of theoretical CD spectra using the potential curves shown in Figure 2 as a dynamics trajectory. Thus, the RICC2/TZVPP calculated spectra for 17 conformers were averaged, taking into account the Boltzmann distribution based on the SCS-MP2/TZVPP relative energies. The details of the relative energies and the populations applied are tabulated in Table S1 in the Supporting Information. In Figure 3, the averaged CD spectra of DA and DD thus obtained are compared with the experimental ones measured in acetonitrile. The spectra in blue and red are the theoretical simulations based on the relative SCS-MP2 energies in the gas phase and in acetonitrile, respectively. The two calculated spectra were almost identical, which may be anticipated from the similarity of the potential curves in both phases (Figure 2). For DD, two positive Cotton effects were followed by a weak negative one (at 1Lb and 1La band region), excepting the slight deviation in intensity in the first band. More importantly, the 5492

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Figure 6. Comparison of the theoretical and experimental CD spectra of DA7
DA9. Black: Experimental spectra in acetonitrile at 25 °C. Red: Theoretical spectra at the RI-CC2/TZVPP level obtained for the optimized structures of DA7
DA9 at the DFT-D-B97-D/TZV2P level (shift: 0.2 eV). Blue: Theoretical spectra calculated for the DA conformers at θ = 60°, 65°, and 70°, which are equivalent in dihedral angle to DA7, DA8, and DA9, respectively.

negative couplet at the main band, which is essential for the conformational assessment, was nicely reproduced (in both energy splitting and relative intensity). The successful reproduction of the CD spectra validates all of our assumptions employed in the evaluation of the spectra, that is, the geometrical optimization by the DFT-D method, the energy calculation at the SCSMP2 level, and the CD calculation at the RI-CC2 level. Thus, we can safely conclude that 2,20 -dimethoxy-1,10 -binaphthyl DD bears a very flat potential against the torsion angle around the central C1
C10 bond. In the experimental spectrum of DA, (1) the CT band observed at ∼380 nm gives a positive Cotton effect, (2) the subsequent 1Lb and 1La bands (250
350 nm) show a positive
positive
negative CD pattern (from longer wavelength), as is the case with DD, and (3) the 1Bb band gives a strong negative couplet, which is more intensive than that of DD (Figure 3 and Table 1). The spectrum simulation for cationic DA (Figure 3, left) was apparently less satisfactory than that for neutral DD (Figure 3, right). However, closer examinations reveal that the abovementioned most important features (1)
(3) are properly reproduced at least semiquantitatively. The theoretical CT band appears at appreciably longer wavelengths than the experimental one, which is at least partially due to the arbitrary 0.2 eV red shift to match the main-band couplet. Thus, the theoretical CT band transition, if shifted by
0.2 eV, shows a good agreement with the experiment, whereas the couplet peaks (at 1Bb) disagree, suggesting less-accurate evaluation of the transition energies in the theory. Nevertheless, the signs and magnitudes of the mainband couplet and of CT band were properly reproduced, indicating that our protocol for the conformational averaging is quantitatively correct. The Cotton effects of the 1La and 1Lb transitions were not completely reproduced in energy (overestimated in theory) but were correct in sign and therefore readily assignable to the experiment. These less significant deviations may be attributed to several factors such as zero-point vibration, temperature effect, and residual correlation effect.34 The strong negative couplet at the 1Bb band, which is essential in determining the conformation of axially chiral 1,10 -binaphthyls, was completely reproduced both in split energy and in magnitude. The excellent reproducibility of the Cotton effects at both the 1Bb and CT bands supports our theoretical model and procedures, in which biaryl DA is freely rotating around the central C1
C10 band, but the potential is rather shallower and the s-cis conformation is favored.

CD Spectra of Tethered Donor
acceptor Analogues DA7
DA9. To elucidate further the effects of conformation

on the chiroptical behavior of this class of compounds, we synthesized a series of tethered donor
acceptor binaphthyls DA7
DA9 with much reduced freedoms and experimentally and theoretically investigated their chiroptical properties.35 The experimental spectra were obtained in acetonitrile at 25 °C and compared with the theoretical ones obtained at the RI-CC2/ TZVPP//DFT-D-B97-D/TZV2P level (Figure 6). The theoretical calculations demonstrated that the tether length critically affects the dihedral angle of DA7
DA9 to reduce θ from 80° for nontethered DA to 72° for DA9, to 67° for DA8 and then to 59° for DA7. These smaller dihedral angles of DA7
DA9 should lead to strong coupling of the 1Bb transition. Indeed, the couplet amplitude was a critical function of the tether length to grow smoothly with shrinking tether (Table 1). Fluorescence spectral studies showed that the Stokes shift in acetonitrile is also a smooth function of the dihedral angle in the ground state, decreasing in the order DA > DA9 > DA8 > DA7 (Table 1 and Figure S7 in the Supporting Information). The Stokes shift appears to reflect the degree of conformational flexibility in the excited state. Because the amplitude is expected to be larger for the binaphthyls with deeper potential-well and for the conformers with narrower θ, the experimental CD spectral couplet amplitudes of DA7
DA9 (330, 450, and 720 M
1 cm
1) are rather inconsistent with the theoretical expectations for untethered DA (770, 750, and 710 M
1 cm
1), for which the intrinsic effects of the tether atoms on the CD spectra are likely to be responsible (vide infra). In the calculated CD spectra of DA7
DA9 (Figure 6, red), the CT band was underestimated in transition energy, as was the case with DA, but was nicely reproduced in both sign and intensity. The negative Cotton effect observed at ∼320 nm for all DA7
DA9 was poorly reproduced by the theory. The 1La and 1Lb transitions cannot be used for the conformation analyses because of the weak intensity and severe overlap. In contrast, the negative couplet at the main band, which is important as a sensible parameter in the binaphthyl system, was reproduced satisfactorily. In these calculations for DA7
DA9, the conformer population was not taken into consideration (in contrast with the DA and DD cases), yet it provided the excellent agreement. This is consistent with the fact that these tethered derivatives are much more restricted in conformation than DA or DD, although some disagreement in amplitude may mean a partial failure of this assumption. 5493

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The Journal of Physical Chemistry A We have discussed above the CD spectra of DA7
DA9 in terms of the dihedral angle and the degree of freedoms altered by tethering the two naphthyls. Certainly, these are the major factors influencing the CD spectral behavior of DA, but the tethering modification inevitably introduces the linker atoms to the binaphthyl chromophore. Hence, it is interesting or even essential to assess the effect of the tether itself on the CD spectrum of DA. In Figure 6, the experimental spectra of DA7
DA9 (black lines) were compared with the theoretical spectra of the DA conformers with matching θ of 60, 65, and 70° (blue lines), respectively. As can be seen from Figure 6, the CD spectra of the respective DA conformers (blue) show greater deviations in intensity (main band, excepting DA9) and transition energy (CT band) than those calculated for DA7
DA9. As shown in Figure 5, the theory predicts smaller couplet amplitudes for DA conformers as the dihedral angle increases from 60 to 70°, which corresponds to the change from DA7 to DA9. In reality, the totally opposite trend was observed in the experimental CD spectra of DA7
DA9 (Table 1), and the couplet intensity decreased in the order DA9 > DA8 > DA7, which was nicely reproduced in the calculated CD spectra of DA7
DA9. The only advantage of using DA conformers for calculation is that the weak negative Cotton effect at 320 nm was nicely reproduced for reasons not known. However, the fact that the CD spectra calculated for DA conformers, with equivalent dihedral angles but lacking a tether, gave a much poorer match with the experiment led us to the important conclusion that the tethering substitution plays double roles in determining the chiroptical properties, thus by reducing the conformational freedoms and also by attaching an optically transparent group to the chromophore. This means that the conventional theoretical approach to the chiroptical property simulation considering only the “essential” chromophore(s) extracted from the whole system is invalid and probably misleading. Instead, the whole system including apparently “non-chromophoric” moiety(ies), along with the dynamics trajectories, should also be taken into account in the theoretical calculations to obtain more accurate predictions.

’ CONCLUSIONS The chiroptical properties of axially chiral 1,10 -binaphthyls with 2,20 -donor/donor (DD), donor/acceptor (DA), and tethering (DA7
DA9) substituents were comparatively investigated experimentally and theoretically to reveal that the width and depth of the potential well against the dihedral angle θ, the dynamics trajectory, and the tether (if introduced) jointly play critical and decisive roles in determining the CD spectral behavior. The theoretical CD spectrum was obtained by Boltzmann weighted-averaging the component CD spectra calculated for all conformers over θ = 50
130° at every 5° on the basis of the dynamics trajectory obtained by using the high-level ab initio energy calculations. Essentially, our approach involves the three successive QM calculations: the geometry optimization (with a fixed dihedral angle) at the DFT-D-B97-D/TZV2P level, the relative energy calculation at the SCS-MP2/TZVPP level, and the spectroscopic property calculation at the RI-CC2/TZVPP level. The potential curve for DA was shown to be much narrower and appreciably shifted to the s-cis side (smaller θ) than that for DD, providing a structural basis for the stronger couplet amplitude of the 1Bb transition in DA. The averaged CD spectra, incorporating the conformer distribution, excellently

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reproduce the experimental spectra of both DA and DD. Despite the rather coarse conformer sampling at every 5°, most of the important spectral features of chiral binaphthyls were correctly predicted. The conventional two-state model turned out to have led to the right answer with wrong reasons. Thus, the DFT-DB97-D method afforded two optimized s-cis and s-trans conformations as local minima, and averaging the theoretical spectra calculated for these conformers nicely coincided with the experimental ones in DA and DD. (For comparison, see Figure S8 in the Supporting Information.) However, the more sophisticated QM method failed to reproduce the double-well potential, affording the s-cis conformer as a single global minimum. This result does not immediately exclude the existence of s-trans conformer, for example, in crystals, but the validity of the twostate model should be carefully examined when applied to the conformation analysis of 1,10 -binaphthyls. The theoretical RI-CC2 calculations of DA and DD conformers using dynamics trajectory revealed the limitations of the classical semiquantitative couplet-amplitude prediction based on the coupled oscillator theory. The global profile of the couplet amplitude against θ significantly differs for DA and DD at the extreme angles of 110° but resembles each other at angles in between. In the case of DA, the Cotton effect of the CT band, located at the longest wavelengths, provides an additional clue for elucidating the conformational changes.36 The CT band may be more advantageous than the main band couplet because the Cotton effect smoothly diminishes its intensity with increasing θ to invert the sign from positive to negative at 90°. The CD spectral studies on DA7
DA9 provided further insight into the conformation of tethered binaphthyls and the chiroptical consequences of tethering substitution. Thus, the couplet amplitude was critically affected not only by the tether length (to alter θ) but also by the atoms incorporated in the linker. The latter fact indicates that the conventional exciton theory, taking into account only the “essential” chromophores, is simply not enough to achieve the reliable simulation of biaryl conformers, and the combined use of sophisticated QM methods is strongly recommended for more reliable prediction of the energies, conformer population, and physical, in particular, chiroptical, properties of axially chiral biaryls. In conclusion, the couplet amplitude of the 1Bb transition is not a simple function of the dihedral angle but is still a convenient indispensable tool for elucidating the conformational features and the physical properties of biaryls if the dynamics trajectories of conformers and the effects of the “transparent” substituent attached to the chromophore are properly deliberated in the appropriate QM calculations.

’ ASSOCIATED CONTENT

bS

Supporting Information. Details of general experimental procedure and computations, additional experimental spectra, theoretical calculations, and the coordinates of the optimized geometries for DD, DA, and DA7
DA9. This material is available free of charge via the Internet at http:// pubs.acs.org.

’ AUTHOR INFORMATION Corresponding Author

*Fax: þ81-6-6879-7923. E-mail: [email protected]. 5494

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