Optical Activity Anisotropy of Benzil - The Journal of Physical

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...
2 downloads 10 Views 2MB Size
Subscriber access provided by United Arab Emirates University | Libraries Deanship

Article

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

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a free service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are accessible to all readers and citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

The Journal of Physical Chemistry C is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 16

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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]

5

10

15

20

25

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

30

35

40

45

50

55

ACS Paragon Plus Environment

1

The Journal of Physical Chemistry

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

60

65

70

75

80

85

90

95

100

105

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 M¨unster 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-

ACS Paragon Plus Environment

2

Page 2 of 16

Page 3 of 16

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

155

160

165

170

175

180

185

The Journal of Physical Chemistry

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

190

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

ACS Paragon Plus Environment

3

The Journal of Physical Chemistry

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 ACS Paragon Plus Environment

Page 4 of 16

Page 5 of 16

The Journal of Physical Chemistry

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 ACS Paragon Plus Environment

The Journal of Physical Chemistry

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 ACS Paragon Plus Environment

Page 6 of 16

Page 7 of 16

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

The Journal of Physical Chemistry

calculate the LB and ORD, 1/2

410

1/2

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

375

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

415

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

385

390

395

400

405

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, Casta˜no 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

ACS Paragon Plus Environment

7

The Journal of Physical Chemistry

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

460

465

470

475

480

485

490

495

500

505

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

ACS Paragon Plus Environment

8

Page 8 of 16

Page 9 of 16

The Journal of Physical Chemistry

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 ACS Paragon Plus Environment

The Journal of Physical Chemistry

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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.

References 610

570

575

(1) Arago, J. D. F. Sur une modification remarquable qu’´eprouvent les rayons lumineux dans leur passage a` travers certains corps diaphanes, et sur quelques autres nouveaux ph´enom`enes d’optique. M´em. Inst. 1811, 1, 93–134. 615 (2) Kahr, B.; Arteaga, O. Arago’s best paper. ChemPhysChem 2012, 13, 79–88.

580

585

Page 10 of 16

(3) Kaminsky, W. Experimental and phenomenological aspects of circular 620 birefringence and related properties in transparent crystals. Rep. Prog. Phys. 2000, 63, 1575–1640. (4) Nye, J. F. Physical Properties of Crystals: Their Representation by Tensors and Ma- 625 trices, 2nd ed.; Oxford University Press: Oxford, 1985.

(7) Brown, C. J.; Sadanaga, R. The crystal structure of benzil. Acta. Cryst. 1965, 18, 158–164. (8) Biot, J.-B. Ph´enom`enes de polarisation successive, observ´es dans des fluides homog`enes. Bull. Soc. Philomath. 1815, 190– 192. (9) Pasteur, L. Researches on the molecular asymmetry of natural organic products, (Alembic club reprints); Simpkin, Marshall, Hamilton, Kent & Co: London, 1897. (10) Japp, F. R. President of the Section. Rep. 68th Brit. Assoc. Adv. Sci. 1898, 813. (11) Levitt, T. The Shadow of Enlightenment Optical and Political Transparency in France 1789-1848, 1st. ed.; Oxford University Press: Oxford, 2009. (12) Pope, W. J. LXI. Substances exhibiting circular polarisation both in the amorphous and crystalline states. J. Chem. Soc. Trans. 1896, 69, 971–980. (13) Cloizeaux, A. D. Sur l’existence du pouvoir rotatoire dans les cristaux de benzile. C. R. Hebd. Acad. Sci 1869, 68, 308–310. (14) Cloizeaux, A. D. Sur les propri´et´es optiques du benzile et de quelques corps de la famille du camphre, a` l’´etat de cristaux et a` l’´etat de dissolution. C. R. Hebd. Acad. Sci 1870, 70, 1209–1213. (15) Scheffen-Lauenroth, T.; Klapper, H.; Becker, R. A. Growth and perfection of organic crystals from undercooled melt: I. Benzil. J. Cryst. Growth 1981, 55, 557–570. (16) Yadav, H.; Sinha, N.; Kumar, B. Growth and characterization of piezoelectric benzil single crystals and its application in microstrip

ACS Paragon Plus Environment

10

Page 11 of 16

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

630

635

640

645

The Journal of Physical Chemistry

tensors of α-quartz by the HAUP. J. Appl. Cryst. 1988, 21, 479–484.

patch antenna. CrystEngComm 2014, 16, 10700–10710. (17) Claborn, K.; Cedres, J. H.; Isborn, C.; Zozulya, A.; Weckert, E.; Kaminsky, W.; 675 Kahr, B. Optical Rotation of Achiral Pentaerythritol. J. Am. Chem. Soc. 2006, 128, 14746–14747.

(26) Gomez, P.; Hernandez, C. High-accuracy universal polarimeter measurement of optical activity and birefringence of α-quartz in the presence of multiple reflections. J. Opt. Soc. Am. B 1998, 15, 1147–1154.

(18) Claborn, K.; Isborn, C.; Kaminsky, W.; Kahr, B. Optical rotation of achiral com- 680 pounds. Angew. Chem. Int. Ed. 2008, 47, 5706–5717.

(27) Hern´andez-Rodr´ıguez, C.; G´omezGarrido, P. Optical anisotropy of quartz in the presence of temperature-dependent multiple reflections using a high-accuracy universal polarimeter. J. Phys. D: Appl. Phys. 2000, 33, 2985–2994.

(19) O’Loane, J. K. Optical activity in small molecules, nonenantiomorphous crystals, and nematic liquid crystals. Chem. Rev. 685 1980, 80, 41–61. ¨ (20) Szivessy, G.; M¨unster, C. Uber die Pr¨ufung der Gitteroptik bei aktiven Kristallen. Ann. Phys. Leipzig 1934, 412, 703–736. 690

650

(21) Bruhat, G.; Grivet, P. Le pouvoir rotatoire du quartz pour des rayons perpendiculaires a´ l’axe optique et sa dispersion dans l’ultraviolet. J. Phys. Radium 1935, 6, 12–26.

655

(22) Konstantinova, A. F.; Ivanov, N. R.; 695 Grechushnikov, B. N. Optical activity in crystals in directions different from optic axis. 1. Uniaxial crystals. Kristallografiya 1969, 14, 283–292.

660

665

670

(23) Konstantinova, A. F.; Nabatov, B. V.; 700 Evdishchenko, E. A.; Konstantinov, K. K. Modern application packages for rigorous solution of problems of light propagation in anisotropic layered media: II. Optically active crystals. Cryst. Reports 2002, 47, 815–823. 705 (24) Horinaka, H.; Tomii, K.; Sonomura, H.; Miyauchi, T. A New Method for Measuring Optical Activity in Crystals and Its Application to Quartz. Jap. J. Appl. Phys. 1985, 24, 755–760. 710 (25) Kobayashi, J.; Asahi, T.; Takahashi, S.; Glazer, A. M. Evaluation of the systematic errors of polaimetric measurements: Application to measurements of the gyration

(28) Kobayashi, J.; Takahashi, T.; Hosokawa, T.; Uesu, Y. A new method for measuring the optical activity of crystals and the optical activity of KH2 PO4 . J. Appl. Phys. 1978, 49, 809–815. (29) Arteaga, O.; Canillas, A.; Jellison, G. E. Determination of the components of the gyration tensor of quartz by oblique incidence transmission two-modulator generalized ellipsometry. Appl. Opt. 2009, 48, 5307–5317. (30) Arteaga, O.; Freudenthal, J.; Kahr, B. Reckoning electromagnetic principles with polarimetric measurements of anisotropic optically active crystals. J. Appl. Cryst. 2012, 45, 279–291. (31) Chandrasekhar, S. The rotatory dispersion of benzil. Proc. Indian Acad. Sci. 1954, 39, 243–253. (32) Kizel, V. A.; Krasilov, Y. I.; Shamraev, V. N. The optical activity which originates in the crystalline state. Optika i Spektroskopiya 1964, 17, 863–870. (33) Chaudhuri, N. K.; El-Sayed, M. A. Molecular Origin of the Optical Rotatory Dispersion of the Benzil Crystal. J. Chem. Phys. 1967, 47, 1133–1143. (34) Deutsche, C. W. Theory of optical activity of crystalline benzil. J. Chem. Phys. 1970, 53, 1134–1149.

ACS Paragon Plus Environment

11

The Journal of Physical Chemistry

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

715

ˇ ıha, J.; Vyˇs´ın, I. Optical activity of benzil (35) R´ crystal. Physica 2001-2002, 40-41, 9–22. ˇ ıha, J.; Vyˇs´ın, I. Optical activity of benzil (36) R´ crystal. Czech. J. Phys. 2003, 53, 727–742.

720

725

730

735

740

760

ˇ ıha, J.; Vyˇs´ın, I.; Lapˇsansk´a, H. Theory, (37) R´ Measurement, and Origin of Optical Activity in Benzil Crystal. Mol. Cryst. Liq. Cryst. 765 2005, 442, 181–201. (38) Harada, T.; Kuroda, R.; Moriyama, H. Solid-state circularly polarized luminescence measurements: Theoretical analysis. Chem. Phys. Lett. 2012, 530, 126–131. 770 (39) Harada, T.; Hayakawa, H.; Watanabe, M.; Takamoto, M. A solid-state dedicated circularly polarized luminescence spectrophotometer: Development and application. Rev. Sci. Instrm. 2016, 87, 075102–075109. 775 (40) Casta˜ no, F. Complete circular dichroism tensor parameter in uniaxial crystals— I theory: Application to benzil and αNiSO4 ·6H2 O. Spectrochim. Acta A 1969, 25A, 401–405. 780 (41) Fontaine, D.; Billard, J. Measurement of crystalline optical rotatory power for benzil and guanidine carbonate. Comptes rendus hedb. seances acad. sci. serie B 1970, 270, 288.

750

755

Birefringence of Crystals. I. Principles and Construction. J. Appl. Cryst. 1983, 16, 204– 211. (45) Kobayashi, J.; Uesu, Y.; Takehara, H. A new optical method and apparatus ‘HAUP’ for measuring simultaneously optical activity and birefringence of crystals. II. Application to triglycine-sulphuric acid (NH2 CH2 CO2 H)3 ·H2 SO4 . J. Appl. Cryst. 1983, 212–219. (46) Kobayashi, J.; Kumomi, H.; Saito, K. Improvement of the accuracy of HAUP, highaccuracy universal polarimeter: Application to ferroelectric [N(CH3 )4 ]2 ZnCl4 . J. Appl. Cryst. 1986, 19, 377–381. (47) Asahi, T.; Kobayashi, J. In Introduction to Complex Mediums for Optics and Electromagnetics; Weiglhofer, W. S., Lakhtakia, A., Eds.; SPIE Press, 2003. (48) Nichols, S.; Martin, A.; Choi, J.; Kahr, B. Gyration and Permittivity of Ethylenediammonium Sulfate Crystals. Chirality 2016, 28, 460–465. (49) Kobayashi, J.; Asahi, T.; Sakurai, M.; Takahashi, M.; Okubo, K. Optical properties of superconducting Bi2 Sr2 CaCu2 O8 . Phys. Rev. B 1996, 53, 11784–11795.

785

745

Page 12 of 16

(42) Moxon, J. R. L.; Renshaw, A. R.; Tebbutt, I. J. The simultaneous measurement of optical activity and circular dichroism in birefringent linearly dichroic crystal sections. II. Description of apparatus and re- 790 sults for quartz, nickel sulphate hexahydrate and benzil. J. Phys. D: Appl. Phys. 1991, 24, 1187–1192.

(50) Tanaka, M.; Nakamura, N.; Koshima, H.; Asahi, T. An application of the advanced high-accuracy universal polarimeter to the chiroptical measurement of an intercalated compound K4 Nb6 O17 with high anisotropy. J. Phys. D: Appl. Phys. 2012, 45, 175303– 175310.

ˇ ıha, J.; Vavˇr´ıhkov´a, H. An (43) Vyˇs´ın, I.; R´ alternative method of dispersion relations 795 derivation in the crystalline optical activity in the direction perpendicular to the optic axis. Optik 2007, 118, 407–417.

(51) Ishikawa, K.; Tanaka, M.; Suzuki, T.; Sekine, A.; Kawasaki, T.; Soai, K.; Shiro, M.; Lahav, M.; Asahi, T. Absolute chirality of the γ-polymorph of glycine: correlation of the absolute structure with the optical rotation. Chem. Commun. 2012, 48, 6031–6033.

(44) Kobayashi, J.; Uesu, Y. A New Optical Method and Apparatus ‘HAUP’ for Mea- 800 suring Simultaneously Optical. Activity and

(52) Takanabe, A.; Tanaka, M.; Johmoto, K.; Uekusa, H.; Mori, T.; Koshima, H.; Asahi, T. Optical Activity and Optical

ACS Paragon Plus Environment

12

Page 13 of 16

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

805

810

815

The Journal of Physical Chemistry

Anisotropy in Photomechanical Crystals of Chiral Salicylidenephenylethylamines. J. 845 Am. Chem. Soc. 2016, 138, 15066–15077.

(62) Schellman, J.; Jensen, H. P. Optical spectroscopy of oriented molecules. Chem. Rev. 1987, 87, 1359–1399.

(53) Ishikawa, K.; Terasawa, Y.; Tanaka, M.; Asahi, T. Accurate measurement of the optical activity of alanine crystals and the determination of their absolute chirality. J. Phys. Chem. Solids 2017, 104, 257–266. 850

(63) Kim, M.; Keller, D.; Bustamante, C. Differential polarization imaging. I. Theory. Biophys. J. 1987, 52, 911–927.

(54) Nakagawa, K.; Lovelady, H. H.; Tanaka, Y.; Tanaka, M.; Yamato, M.; Asahi, T. A high-accuracy universal polarimeter study of optical anisotropy and optical activity 855 in laminated collagen membranes. Chem. Commun. 2014, 50, 15086–15089. (55) Takanabe, A.; Koshima, H.; Asahi, T. Fasttype high-accuracy universal polarimeter using charge-coupled device spectrometer. 860 AIP Advances 2017, 7, 025209–025214.

820

825

(56) Kaminsky, W.; Glazer, A. M. Measurement of optical rotation in crystals. Ferroelectrics 1996, 183, 133–141. (57) Kim, D.-Y.; Kaminsky, W.; Glazer, A. M. A low-temperature tilter system and its application to the measurement of the anisotropy of optical rotation in K2 ZnCl4 in the vicinity of the phase transition at 145 K. Phase Transitions 2001, 73, 533–563.

865

835

(58) Brosseau, C. Fundamentals of Polarized Light: A Statistical Optics Approach, 1st. eds.; Wiley-Interscience: New York, 1998. (59) Perez, J. J. G.; Ossikovski, R. Polarized Light and the Mueller Matrix Approach (Se- 875 ries in Optics and Optoelectronics); CRC Press: Boca Raton, Florida, 2016. (60) Jensen, H. P.; Schellman, J. A.; Troxell, T. Modulation Techniques in Polarization Spectroscopy. Appl. Spectroscopy 880 1978, 32, 192–200.

840

(65) Mickols, W.; Tinoco, I.; Katz, J. E.; Maestre, M. F.; Bustamante, C. Imaging differential polarization microscope with electronic readout. Rev. Sci. Instr. 1985, 56, 2228–2236. (66) Kuroda, R.; Harada, T.; Shindo, Y. A solidstate dedicated circular dichroism spectrophotometer: Development and application. Rev. Sci. Instrum. 2001, 72, 3802– 3810. (67) Arteaga, O. Mueller matrix polarimetry of anisotropic chiral media. Ph.D. thesis, University of Barcelona, 2010.

870

830

(64) Shindo, Y.; Ohmi, Y. New polarizationâĂŘmodulation spectrometer for simultaneous circular dichroism and optical rotary dispersion measurements (I): Instrument design, analysis, and evaluation. Rev. Sci. Instrum. 1985, 56, 2237–2242.

(68) Azzam, R. M. A. Propagation of partially polarized light through anisotropic media with or without depolarization: A differential 4 × 4 matrix calculus. J. Opt. Soc. Am. 1978, 68, 1756–1767. (69) Arteaga, O.; Freudenthal, J.; Wang, B.; Kahr, B. Mueller matrix polarimetry with four photoelastic modulators: theory and calibration. Appl. Opt. 2012, 51, 6805– 6817. (70) More, M.; Odou, G.; Lefebvre, J. Structure determination of benzil in its two phases. Acta Cryst. 1987, B43, 398–405. (71) Polavarapu, P. L. Chiroptical Spectroscopy: Fundamentals and Applications; CRC Press: Boca Raton, Florida, 2017.

(61) Shindo, Y.; Nakagawa, M.; Ohmi, Y. On the problems of CD spectropolarimeters. II: Artifacts in CD spectrometers. Appl. Spectroscopy 1985, 39, 860–868.

ACS Paragon Plus Environment

13

The Journal of Physical Chemistry

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

885

890

895

900

905

910

915

920

(72) Srebro-Hooper, M.; Autschbach, J. Calculating Natural Optical Activity of Molecules 930 from First Principles. Ann. Rev. Phys. Chem. 2017, 68, 399–420. (73) Bryant, W. M. D. Optical Crystallographic Studies with the Polarizing Microscope. IV. Axial Dispersion with Change of Sign. 935 Other Dispersion Measurements. J. Am. Chem. Soc. 1943, 65, 96–102. (74) Jelley, E. Application of Grating Microspectrograph to Problem of Identifying Organic Compounds. Ind. Eng. Chem. Anal. Ed. 940 1941, 13, 196–203. (75) Mackay, T. G.; Lakhtakia, A. Electromagnetic Anisotropy and Bianisotropy: A Field Guide; World Scientific Publishing Company, 2009. 945 (76) Postava, K.; Yamaguchi, T.; Kantor, R. Matrix description of coherent and incoherent light reflection and transmission by anisotropic multilayer structures. Appl. Opt. 2002, 41, 2521–2531. 950 (77) Nichols, S.; Arteaga, O.; Martin, A.; Kahr, B. Measurement of transmission and reflection from a thick anisotropic crystal modeled by a sum of incoherent partial waves. J. Opt. Soc. Am. A 2015, 32, 2049– 955 2057. (78) Martin, A. T.; Nichols, S. M.; Tan, M.; Kahr, B. Mueller matrix modeling of thick anisotropic crystals with metallic coatings. Appl. Surf. Sci. 2017, 421, 578–584.

960

(79) Martin, A. T.; Nichols, S. M.; Li, S.; Tan, M.; Kahr, B. Double cone of eigendirections in optically active ethylenediammonium selenate crystals. J. Appl. Cryst. 2017, 50, 1117–1124. 965

925

(80) Arteaga, O.; Canillas, A. Analytic inversion of the Mueller-Jones polarization matrices for homogeneous media. Opt. Lett. 2010, 35, 559–561. (81) Fowler, F. E. Smithsonian Physical Tables, 970 7th Revised Ed.; Smithsonian Institution, 1921; Vol. 71.

(82) Arteaga, O.; El-Hachemi, Z.; Canillas, A.; Rib´o, J. M. Transmission Mueller matrix ellipsometry of chirality switching phenomena. Thin Solid Films 2011, 519, 2617– 2623. (83) Arteaga, O. Number of independent parameters in the Mueller matrix representation of homogeneous depolarizing media. Opt. Lett. 2013, 38, 1131–1133. (84) Arteaga, O.; Baldr´s, M.; Ant´o, J.; Canillas, A.; Pascual, E.; Bertran, E. Mueller matrix microscope with a dual continuous rotating compensator setup and digital demodulation. Appl. Opt. 2014, 53, 2236– 2245. (85) Kaldybaev, K. A.; Konstantinova, A. F.; Perekalina, Z. B.; Grechushnikov, B. N.; Kalinkina, I. N. Optical activity and circular dichroism in benzil. Sov. Phys. Cryst. 1978, 23, 438–442. (86) Matsuda, K.; Sugiya, H.; Kobayashi, J. Optical activity of Ca2 Sr(C2 H5 COO)6 . Ferroelectrics 1990, 107, 39–44. (87) Mucha, D.; Stadnicka, K.; Kaminsky, W.; Glazer, A. M. Determination of optical activity in monoclinic crystals of tartaric acid, using the ‘tilter’ method. J. Phys.: Condensed Matter 1997, 9, 10829–10842. (88) Brozek, Z.; Stadnicka, K.; Lingard, R. J.; Glazer, A. M. Determination of the Gyration Tensor Components of Ammonium Rochelle Salt. J. Appl. Cryst. 1995, 28, 78– 85. (89) Kaminsky, W.; Glazer, A. M. Crystal optics of D-mannitol, C6 H14 O6 : crystal growth, structure, basic physical properties, birefringence, optical activity, Faraday effect, electro-optic effects and model calculations. Zeit. Kristallographie 1997, 212, 283–296. (90) Herreros-C´edres, J.; Hern´andezRodr´ıguez, C.; Guerrero-Lemus, R. Optical Activity of Deuterated Analog of L-Arginine Phosphate Single Crystals. Mater. Sci. Forum 2005, 480-481, 43–52.

ACS Paragon Plus Environment

14

Page 14 of 16

Page 15 of 16

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

975

980

The Journal of Physical Chemistry

(101) Vaccaro, P. H. In Comprehensive (91) Asahi, T.; Nakamura, M.; Kobayashi, J.; Chiroptical Spectroscopy, Volueme 1; Toda, F.; Miyamoto, H. Optical Activity of1015 Berova, N., Polavarapu, P. L., Nakanishi, K., Oxo Amide Crystals. J. Am. Chem. Soc. Woody, R. W., Eds.; Wiley: Hoboken, New 1997, 119, 3665–3669. Jersey, 2012. (92) Asahi, T.; Utsumi, H.; Itagaki, Y.; Kagomiya, I.; Kobayashi, J. Optical Activity of Crystalline Glutamic Acids. Acta Cryst. 1996, A52, 766–769. (93) Asahi, T.; Takahashi, M.; Kobayashi, J. The Optical Activity of Crystalline L-Aspartic Acid. Acta Cryst. 1997, A53, 763–771.

985

990

995

(94) Koshima, H.; Nagano, M.; Asahi, T. Optical activity induced by helical arrangements of tryptamine and 4-chlorobenzoic acid in their cocrystal. J. Am. Chem. Soc. 2005, 127, 2455–2463. (95) Kaminsky, W.; Weckert, E.; Kutzke, H.; Glazer, A. M.; Klapper, H. Non-linear optical properties and absolute structure of metastable 4-methyl benzophenone. Zeit. Kristallographie 2006, 221, 294–299. (96) Murphy, V. L.; Kahr, B. H¨uckel Theory and Optical Activity. J. Am. Chem. Soc. 2015, 137, 5177–5183. (97) Murphy, V. L.; Reyes, A.; Kahr, B. Aromaticity and Optical Activity. J. Am. Chem. Soc. 2016, 138, 25–27.

1000

1005

1010

(98) Neugebauer, J. Induced Chirality in Achiral Media - How Theory Unravels Mysterious Solvent Effects. Angew. Chem. Int. Ed. 2007, 46, 7738–7740. (99) Mukhopadhyay, P.; Zuber, G.; Wipf, P.; Beratan, D. N. Contribution of a Solutes Chiral Solvent Imprint to Optical Rotation. Angew. Chem. Int. Ed. 2007, 46, 6450– 6452. (100) Lahiri, P.; Wiberg, K. B.; Vaccaro, P. H.; Caricato, M.; Crawford, T. D. Large solvation effect in the optical rotatory dispersion of norbornenone. Angew. Chem. Int. Ed. 2014, 53, 1386–1389.

ACS Paragon Plus Environment

15

The Journal of Physical Chemistry

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 ACS Paragon Plus Environment

Page 16 of 16