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Optical Activity Anisotropy of Benzil Kenta Nakagawa, Alexander T. Martin, Shane M. Nichols, Veronica L. Murphy, Bart Kahr, and Toru Asahi J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b08831 • Publication Date (Web): 18 Oct 2017 Downloaded from http://pubs.acs.org on October 30, 2017

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The Journal of Physical Chemistry

Optical Activity Anisotropy of Benzil Kenta Nakagawa,† Alexander T. Martin,‡ Shane M. Nichols,‡ Veronica L. Murphy,‡ Bart Kahr,∗,‡,† and Toru Asahi∗,†,¶ †Department of Advanced Science and Engineering, Graduate School of Advanced Science and Engineering, Waseda University, Tokyo 162-8480, Japan ‡Department of Chemistry, New York University, New York, NY 10003 USA ¶Research Organization for Nano and Life Innovation, Waseda University, Tokyo 162-0041, Japan E-mail: [email protected]; [email protected]

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Abstract

Introduction

Optical activity (OA) along the optic axis of crystalline benzil has been measured by many over the past 150 years. However, the OA anisotropy remains uncharacterized due to difficulties in sample preparation as well as competition with linear birefringence (LB). The challenges associated with measuring OA along low-symmetry directions in crystals have too often left scientists with only average values of non-resonant OA in solution, i.e. specific rotations, which continue to resist interpretation in terms of structure. Measuring OA anisotropy has been facilitated by recent advances in polarimetry and optical modeling and here we compare results from two distinct divisionof-time polarimeters. The absolute structure of crystalline benzil was established for the first time. The optical rotation (OR) of (+)-crystalline benzil (space group P 31 21) perpendicular to the optic axis at the sodium D-line is −24.6 ± 1.1◦ /mm. A spectroscopic optical model in the transparent region of the crystal is provided. Electronic structure calculations of OR inform the polarimetric measurements and point to the necessity of developing linear response theory with periodic boundary conditions in order to interpret the results of chiroptical measurements in crystals.

Arago discovered optical rotatory dispersion (ORD) by passing linearly polarized light along the optic axis of quartz in 1811, 1,2 but he could not measure the off-axis value because of the competition with linear birefringence (LB) that dominates the perturbation to the polarization state of light. Thus began two centuries of woe in the measurement of the optical activity (OA) of single crystals in general directions. 3 Modest OA in the presence of LB manifests as a slight ellipticity in the eigenpolarization states, 4 the measurement of which can easily be affected by imperfections within a crystal and on its surface, by the imperfect quality of optical components and polarimetric settings, as well as the spatial and temporal coherence of the light source. 5 These obstacles to the measurement of OA in crystals have thwarted structural interpretations of non-resonant OA in solution, a consequence of molecules rapidly, randomly reorienting. Understanding light-matter interactions requires unpacking the average by measuring the anisotropy, a task made possible by the organization of molecules in crystals. Crystalline benzil (C6 H5 C(O)-C(O)C6 H5 ), space group P 31(2) 21, 6,7 is a consequential substance in the history of OA; it served as a bridge between well-studied α-quartz and carbon-based compounds. Ever since Biot observed that many organic substances, when dissolved, rotate the plane of polarized light, 8 he was keen to reconcile

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the behavior of solutions of chiral molecules with that of chiral crystals. While fused quartz is optically inactive, its crystalline counterpart 110 exhibits OA as a consequence of the dissymmetric arrangement of its SiO2 components in the solid state, quite like Pasteur’s spiral staircase made from achiral steps. 9 However, organic substances, so thought Biot, seemed to have an intrinsic OA associated with individual molecules. Biot believed that molecular OA was a signature of a 115 vital force directing matter. 10,11 Uniaxial organic crystals, such as tetragonal strychnine sulfate hexahydrate, 12 were long known to exhibit OA along an optic axis. When dissolved, OA persisted. Des Cloizeaux, Biot’s student, 120 first measured the OA of benzil, also a decidedly organic compound, along the optic axis, 13,14 but benzil was more like quartz than strychnine in that it lost its OA upon dissolution. In fact, Des Cloizeaux considered benzil an organic analogue 125 of quartz; both crystalline substances have 32 (D3 ) point symmetry, large benzil crystals can be grown from solution that match the size of quartz, 15,16 and rotatory powers at 589 nm are comparable along their optic axes. 130 We now know that benzil, an equilibrium racemic mixture in solution, can be trapped in homochiral conformations in conglomerate crystals. We also know that even achiral crystal structures, of point group symmetries D2d , S4 135 C2v , and CS , may be optically active for certain directions. 17,18 Of course, the necessary and sufficient conditions for OA in solution and in organized media only came into focus long after the early scientists who struggled with the apparent 140 benzil conundrum. 19 The OA of quartz has been more closely studied than that of any other inorganic crystal and it has been the model compound for measurements of OA anisotropy. 20–30 The OA of benzil has been 145 studied more than that of any other organic crystal, 13,31–39 however, unlike quartz, its anisotropy has resisted characterization 40–42 while continuing to prompt discussion. 43 In the absence of this offaxis measurement of OA, interpretations will be 150 forever incomplete, as will be the analogy between quartz and benzil. Here, we compare ORD measurements along the low-symmetry direction of crystalline benzil by two polarimetric methods

accompanied by electronic structure calculations of the benzil molecule in its crystal conformation as well as aggregates of molecules.

Single Crystal Polarimetry Given the troublesome history of the measurement of OA in crystals, some background is required to appreciate where we stand. From the time of Arago’s discovery, 123 years passed before Szivessy and Münster 20 obtained a credible value for the off-axis OA of quartz using null polarimetry. This benchmark was reestablished by a variety of polarimetric methods 21–27 and as a function of wavelength (ORD). 28–30 The 1988 measurement of Kobayashi et al. 25 employed the so-called High Accuracy Universal Polarimeter (HAUP) method in which stable high intensity light sources (lasers) were combined with accurate electrophotometry, for the measurement of transmitted light intensity as a function of the azimuthal orientation of a linear polarizer and analyzer. 44–46 HAUP promised to be a general solution to the determination of the OA of anisotropic crystals 47 breaking a log-jam of accumulated pessimism. In fact, the majority of crystals whose OA anisotropy has been determined, while still comparatively few in number, were analyzed by the HAUP method. 3,48 The Generalized HAUP or G-HAUP 49 was developed to account for dissipative as well as dispersive optical effects. It has been applied to OA measurements of various crystals such as a dyeintercalate of K4 Nb6 O17 , 50 γ-glycine, 51 salicylidenephenylethylamine 52 and alanine. 53 Laminated collagen membranes were also examined. 54 Most recently, a rapid HAUP was developed using dispersive detection to a CCD array (CCD-HAUP). 55 A variant of the HAUP for measuring crystals in non-normal incidence accounts for the refraction of the primary beam. 17,56,57 The HAUP method takes the Jones matrix as its point of departure for transparent crystals. 58 Other researchers have measured OA in oriented systems by using the competing Stokes-Mueller calculus, 59 better adapted to imperfect samples that can be depolarizing. 60–63 Polarimeters were constructed to extract harmonics of the time varying signals in the expressions for the Mueller matrix. 64–66 The Mueller matrix, M, is a 4 × 4 polarization trans-


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formation matrix, which transforms an incoming 195 Stokes vector (Sin ) into an outgoing Stokes vector (Sout ) according to Sout = MSin . A Stokes vector describes the polarization state of a light source,   Itotal 200  I0◦ − I90◦    S= , (1) I45◦ − I−45◦  IRCP − ILCP and the elements of S are light intensity differences 205 between the various polarization states. Here, Itotal is the total intensity of the light source, I0◦ − I90◦ is the intensity difference between horizontal and vertical linearly polarized light, I45◦ − I−45◦ is the intensity difference between linearly polarized 210 light in the +45◦ and −45◦ azimuthal planes, and IRCP − ILCP is the intensity difference between right and left circularly polarized light. The elements of the Mueller matrix represent projections of the incoming Stokes vector quantities onto the 215 outgoing quantities. In both the Jones and Stokes-Mueller formalisms, the functions of the transmitted intensity were taken to second order 62 and approximations were required to simplify analyses. The truncation of high-order terms is strictly applicable only in the small angle limit where the optical properties 220 are < 0.5 rad. 67 Most preferable is the inversion of Mueller matrix by taking the matrix logarithm, 68 or analytically, 67 to deliver the fundamental optical properties. These analyses require no approximations. Of the polarimetric methods compared in the following, the first arises out of the HAUP tradition, and the second uses 225 polarimeters with a considerably more complex light modulation scheme that delivers the full normalized Mueller matrix. 29,69 The latter method was applied to quartz most recently. 29,30

X-ray Diffraction (XRD) XRD analysis was performed with a single crystal diffractometer (R-AXIS RAPID-II, Rigaku, Tokyo, Japan), confirming the space group P 31(2) 21. While the structure of benzil has been established previously, 70 here the absolute structure was determined for the first time, and correlated to the sign of optical rotation (OR).

Atomic Force Microscopy (AFM) The (001) benzil surfaces were characterized by AFM (Bruker MultiMode 8 AFM, Billerica, MA, USA) at room temperature in contact mode with high-speed ScanAsyst.

Polarimetry

Materials and Methods 230

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exposing large (001) or (100) faces. The mis-cut from the intended crystallographic orientation was determined prior to optical characterization with a polarized-light microscope (DMLP, Leica, Hesse, Germany) equipped with a Berek compensator. To reduce sample thickness and to generate smooth surfaces, plates of benzil were polished with SiC (grain diameter 9 and 5 µm), Al2 O3 (3 and 1 µm), and Fe2 O3 (0.3 µm) lapping films (3M, Minneapolis, USA). Despite careful preparation, the lapping films invariably produce surface features sufficiently rough to scatter visible light. The most transparent surfaces were obtained by wetting the finest lapping films with a few drops of ethanol. The final thickness of each sample was measured with a signal digimatic indicator (Absolute, Mitutoyo, Kanagawa, Japan). Three distinct single-crystalline polished slabs of benzil were chosen for polarimetric measurement; the extrinsic properties of each are discussed in the following sections.

Crystal Growth and Sample Preparation Single crystals of benzil (Wako, Osaka, Japan) were grown by slow evaporation from acetone 235 solution at 25◦ C. Thin single crystalline plates (5 mm × 5 mm × 1 mm) were cut with a razor blade,

Two polarimetric methods were implemented to measure the optical properties of crystalline benzil. Generally, a polarimeter consists of a light source, a polarization state generator (PSG), a polarization state analyzer (PSA), and a detector. The G-HAUP employs a simple optical configuration that contains only two optical elements: a GlanThompson polarizer serves as the PSG and a


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calculate the LB and ORD, 1/2

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LB = ǫ33 − ǫ11 πd ORDc = (2α11 ) λ πd (α11 + α33 ) ORDa = λ

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(4a) (4b) (4c)

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where d is the sample thickness and λ is the wavelength of light. Fig. 2 shows the calculated LB and ORD spectra from the 4PEM measurements in 420 blue. The off-axis value for OR was determined to be −24.6◦ /mm ± 1.1◦ /mm at the sodium D-line. See SI for full polarimetric analysis and discussion of error. 425

Evaluation of Optical Measurements 380

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The G-HAUP and 4PEM polarimeter determinations of LB perpendicular to the optic axis, and ORD along the optic axis, were in suitable 430 agreement with one another and with values extracted from the literature; these are relatively easy measurements. It is likely that the measurements of crystal thickness represent the greatest errors. Polishing, moreover, sometimes creates 435 either a slight gradient in thickness or induces a slight curvature which can cause beam steering or beam divergence, respectively. The G-HAUP and 4PEM polarimeter values for ORD along the low-symmetry a-axis were likewise in reasonable agreement, though the G-HAUP measurement of this sample was unstable below 550 nm. 440 Another significant difference between the two techniques is that the G-HAUP analysis, while offering precise measurement of optical rotation, requires normal incidence and therefore two distinctly cut and polished samples to establish the 445 two independent tensor components. The 4PEM polarimeter analysis is corrected for non-normal incidence and therefore a single sample cut will suffice. Cutting and polishing soft crystals suited to extremely accurate light transmission measure450 ments is demanding and is often the rate limiting step in analyses of this kind. The preparation of fewer plane parallel slabs is a major time savings. Moreover, even if time and effort were not a consideration, anisotropy renders cuts in some di455 rections very difficult to obtain while maintaining

the structural integrity of the sample. Previously, enantiomorphous domains of benzil were grown from the melt as thin linearly birefringent films. These were studied by Mueller matrix imaging polarimeters, but individual domains were not single crystals and the crystallographic directions were not identified, making it difficult to connect the OA measured in these experiments with the results herein. 82–84 In principle, α of any uniaxial crystal can be obtained from a measurement along the optic axis, which delivers α11 , and a spectrum of the isotropic average, αavg = tr(α)/3 = (2α11 + α33 )/3. Therefore, Castaño measured the average spectrum of a finely ground benzil powder suspended in Nujol. 40 These measurements focused on the CD at ca. 400 nm involving S1 to T1 absorption. In the 1970s, before the development of general strategies for measuring OR in crystals of general symmetry, there were two attempts to measure the off-axis value for benzil, both of which gave values of the correct sign but far from the values reported here, 41,85 and far from one another. The latter was a much more credible measurement. Moreover, the authors took advantage of the surrendipitous isotropic point 79 in the real part of the dielectric permittivity tensor for a better measure of the CD along a low symmetry direction.

Electronic Structure Calculations The electronic structure of benzil crystals was described in detail. 33 Attempts to interpret anomalous ORD in benzil were first based on semiempirical wavefunctions. 32 However, any theoretical analysis naturally delivers the anisotropy of the OA. Most recently, time dependent density functional and linear response theories have tackled the chiroptical properties of molecules from first principles, 71,72 methods that are now standard in widely available electronic structure computing programs. But, there is a dearth of data on crystals, a consequence of the aforementioned linear anisotropies. The second rank pseudo-axial gyration tensors that are delivered by contemporary quantum calculations are invariably averaged to give pseudo-scalars corresponding to specific rotations, generally the only quantities for which we have data. Most of the fruits of computation


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are never reported. We were optimistic that benzil crystals might be well interpreted in terms of the chiroptical properties of molecules summed under the rotational symmetries of the crystal point group. Tensors for organic crystals are few and far between, but most are salts (e.g. calcium strontium acetate) 86 with long range electrostatic interactions or are rich in O-H...O hydrogen bonds: triglycine sulfate, 45 L-tartaric acid, 87 sodium ammonium L-tartrate (ammonium Rochelle salt), 88 D-mannitol, 89 Larginine phosphate, 90 an oxoamide, 91 L-glutamic acid, 92 L-aspartic 93 acid, and a cocrystal of Ltryptamine and 4-chlorobenzoic acid. 94 Benzil and 4-methylbenzophenone 95 are the only such examples for which dispersion forces dominate the interactions between molecules. Therefore, we calculated the chiroptical response of one molecule of benzil in its crystallographic conformation, and the expectation for one unit cell by rotating the OR tensor of one molecule around the crystallographic threefold axis to generate the symmetry related tensors. These were then summed. The result was compared to a calculation of one whole unit cell, Z = 3, in which the three molecules selected were related to one another by the screw axis denoted by the orange symbol in Fig. 1a. These results are expressed in atomic units of bohr4 at 589 nm, and are summarized in Table 2. Also, an explicit sum over 1000 excited states was computed for one 510 molecule. The summations were nearly converged but not completely. Nevertheless, these values are given parenthetically in Table 2. The gyration tensor computed by Gaussian, and that typically reported in the computational liter- 515 ature, operates on the wavevector (k), such that the value of ORD in any direction is given by ˆ T gk, ˆ where k ˆ is the unit wavevector. In g′ = k other words, g ′ is proportional to ORD along the direction of k. The tensor g and α are related by 520 equations given elsewhere. 79 A single benzil molecule has dyad (twofold) symmetry only but the molecular twofold axis in this calculation was not parallel to any of the Cartesian axes. The eigenvalues of this tensor were 525 −7.83, 0.065, 17.38 bohr4 and the molecule is plotted with the representation surface of this tensor in Fig. 4. The smallest eigenvalue corresponds to the gyration along the twofold axis, almost zero.

Table 2. Electronic Structure Calculation Results

gxx gyy gzz gxy gxz gyz Eig.e

Iso.f

1 mol. (SOS)a 9.8 (11.3) 3.7 (4.1) -3.3 (-5.7) 5.3 (6.3) -8.4 (-7.9) -4.9 (-4.5) -7.8 (-9.1) 0.7 (-0.5) 17.4 (18.3) -3.4 (-3.2)

1 mol. PCb 8.3 3.9 -3.5 3.7 -8.7 -5.0 -8.8 1.8 15.7 -2.9

3 mol.c 0.2 -10.0 36.8 -8.9 -1.2 3.7 -15.3 5.2 37.2 -9.0

per mol. symm.d 6.7 6.7 -3.3 0 0 0 6.7 6.7 -3.3 -3.4

a

The linear response gyration tensor for one molecule in the crystallographic coordinate system and parenthetically the computed gyration tensor from a sum-over-1000 excited states; note: g ′ ∝ −OR. b The linear response gyration tensor with a polarizable continuum (PC, acetone ǫ = 20.7). c Three molecules in one unit cell computed as a supramolecule by linear response theory. d Symmetrized tensor per molecule by adding the tensor from the first column after rotations of +2π/3 and −2π/3. e Eigenvalues. f Isotropic average (negated by convention).

For one molecule, the largest gyration tensor element is perpendicular to the central C-C bond, and the second largest element, about half of the former but of opposite sign is in the direction almost along the central C-C bond. The third Cartesian direction is about zero. Interpreting this tensor in terms of a small number of excited states is difficult because, unlike simple hydrocarbons investigated previously, 96,97 a great number of states contribute to the long wavelength value of benzil. For instance, the gxx tensor element for one molecule which has a value of 9.8 bohr4 requires summing the contributions from 100 excited states at a minimum. Between 100 and 500 excited states the value oscillates within 20% of the linear response value, and between 500 and 1000 it oscillates within 10%. A simple sum of symmetry related tensors to satisfy the crystallographic symmetry is not anywhere near the linear response calculation for three molecules in one unit cell, because these three molecules are related by a screw axis, not a proper rotation. Thus, three molecules is merely a trimer with a dyad axis running through the


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specifications. This material is available free of charge via the Internet at http://pubs.acs. org/.

(5) Cloude, S. R. Polarisation: Applications in Remote Sensing; Oxford University Press: Oxford, UK, 2014.

Acknowledgement We thank Professor M. D. 590 Ward for the use of his AFM and Dr. J. Yang for his assistance. This work was supported in the USA by the National Institutes of Health (5R21GM107774-02), the National Science Foundation (DMR-1105000), an NSF Predoctoral Fellowship to SMN (DGE-12342536), a Margaret 595 Strauss Kramer Fellowship and a Margaret and Herman Sokol Fellowship from the NYU Department of Chemistry to ATM. The Japanese contributions to this study were financially supported by the High-Tech Research Center (TWIns), the Consolidated Research Institute for Advanced 600 Science and Medical Care (ASMeW), the Global COE for Practical Chemical Wisdom, the Leading Graduate Program in Science and Engineering, The Global University Project, Waseda University, from the Ministry of Education, Culture, Sports, Science and Technology, Japan and the grant- 605 in-aid from the Mitsubishi Materials Corporation (Tokyo, Japan).

(6) Allen, N. C. B. CI. The crystal structure of benzil. Lond. Edin. Dubl. Phil. Mag. J. Sci. 1927, 3, 1037–1040.

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Optical Activity Anisotropy of Benzil - The Journal of Physical

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