Article Cite This: J. Phys. Chem. C 2017, 121, 25494-25502
pubs.acs.org/JPCC
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, New York 10003 United States § Research Organization for Nano and Life Innovation, Waseda University, Tokyo 162-0041, Japan S Supporting Information *
ABSTRACT: 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 nonresonant 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 division-of-time polarimeters. The absolute structure of crystalline benzil was established for the first time. The optical rotation (OR) of (+)-crystalline benzil (space group P3121) 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.
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INTRODUCTION 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, the imperfect quality of optical components and polarimetric settings, and 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. In solution, only an average value is obtained, without an understanding of what is being averaged. 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 (C6H5C(O)−C(O)C6H5), space group P31(2)21,6,7 is a consequential substance in the history of OA; it served as a bridge between well-studied α-quartz and carbonbased compounds. Ever since Biot observed that many organic substances when dissolved rotate the plane of polarized light,8 © 2017 American Chemical Society
he was keen to reconcile the behavior of solutions of chiral molecules with that of chiral crystals. While fused quartz is optically inactive, its crystalline counterpart 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, Biot thought organic substances seemed to have an intrinsic OA associated with individual molecules and that molecular OA was a signature of a 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, 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 of quartz, since 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. We now know that benzil, an equilibrium racemic mixture in solution, can be trapped in homochiral conformations in Received: September 5, 2017 Revised: October 14, 2017 Published: October 18, 2017 25494
DOI: 10.1021/acs.jpcc.7b08831 J. Phys. Chem. C 2017, 121, 25494−25502
Article
The Journal of Physical Chemistry C ⎡ Itotal ⎤ ⎢ ⎥ ⎢ I0 ° − I90 ° ⎥ S=⎢ ⎥ ⎢ I45 ° − I −45 ° ⎥ ⎢I ⎥ ⎣ RCP − ILCP ⎦
conglomerate crystals. We also know that even achiral crystal structures, of point group symmetries D2d, S4, C2v, and CS, are optically active along 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 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 studied more than that of any other organic crystal;13,31−39 however, unlike quartz, its anisotropy has resisted characterization40−42 while continuing to prompt discussion.43 In the absence of this off-axis measurement of OA, interpretations will be 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 Münster20 obtained a credible value for the off-axis OA of quartz using null polarimetry. This benchmark was reestablished by a variety of polarimetric methods21−27 and as a function of wavelength, i.e. ORD.28−30 The 1988 measurement of Kobayashi et al.25 employed the so-called high-accuracy universal polarimeter (HAUP) method in which stable highintensity 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 method 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 dye-intercalate of K4Nb6O17,50 γglycine,51 salicylidenephenylethylamine,52 and alanine.53 Laminated collagen membranes were also examined.54 Most recently, 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 transformation matrix, which transforms an incoming Stokes vector Sin into an outgoing Stokes vector Sout according to Sout = MSin. A Stokes vector describes the polarization state of light:
(1)
and the elements of S are light intensity differences 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 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 outgoing quantities. In both the Jones and Stokes−Mueller formalisms, the functions of the transmitted intensity were taken to secondorder,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 are
