Chiroptical anisotropy of crystals and molecules.

Optical activity, a foundational part of chemistry, is not restricted to chiral molecules although generations have been instructed otherwise. A more inclusive view of optical activity is valuable because it clarifies structure-property relationships however, this view only comes into focus in measurements of oriented molecules, commonly found in crystals. Unfortunately, measurements of optical rotatory dispersion or circular dichroism in anisotropic single crystals have challenged scientists for more than two centuries. New polarimetric methods for unpacking the optical activity of crystals in general directions are still needed. Such methods are reviewed as well as some of the 'nourishment' they provide, thereby inviting to new researchers. Methods for fitting intensity measurements in terms of the constitutive tensor that manifests as the differential refraction and absorption of circularly polarized light, are described, and examples are illustrated. Single oriented molecules, as opposed to single oriented crystals, can be treated computationally. Structure-property correlations for such achiral molecules with comparatively simple electronic structures are considered as a heuristic foundation for the response of crystals that may be subject to measurement.

ROY revisited, again: the eighth solved structure.

X-ray powder diffraction and crystal structure prediction (CSP) algorithms were used in synergy to establish the crystal structure of the eighth polymorph of 5-methyl-2-[(2-nitrophenyl)amino]-3-thiophenecarbonitrile (ROY), form R05. R05 crystallizes in the monoclinic space group P21 with lattice parameters a = 11.479(4) Å, b = 11.030(1) Å, c = 10.840(6) Å, ß = 118.23(1)°. This is both the first acentric ROY polymorph, and the first with Z' > 1. The torsion angles defined by the S-C-N-C atom sequence of each molecule in the asymmetric unit (R05-1 and R05-2) are 44.9° and -34.0°. These values are between those previously determined for the red and orange forms of ROY. The crystal packing and intermolecular interactions in R05 are explained herein through Hirshfeld surface analysis and an updated energy stability ranking is determined using computational methods. Although the application of CSP was critical to the structure solution of R05, energy stability rankings determined using a series of DFT van der Waals (vdW)-inclusive models substantially differ from experiment, indicating that ROY polymorphism continues to be a challenge for CSP.

Revisiting polarimetry near the isotropic point of an optically active, non-enantiomorphous, molecular crystal.

Accurate polarimetric measurements of the optical activity of crystals along low symmetry directions are facilitated by isotropic points, frequencies where dispersion curves of eigenrays cross and the linear birefringence disappears. We report here the optical properties and structure of achiral, uniaxial (point group D2d ) potassium trihydrogen di-(cis-4-cyclohexene-1,2-dicarboxylate) dihydrate, whose isotropic point was previously detected (S. A. Kim, C. Grieswatch, H. Küppers, Zeit. Krist. 1993; 208:219-222) and exploited for a singular measurement of optical activity normal to the optic axis. The crystal structure associated with the aforementioned study was never published. We report it here, confirming the space group assignment I 4¯c2, along with the frequency dependence of the fundamental optical properties and the constitutive tensors by fitting optical dispersion relations to measured Mueller matrix spectra. k-Space maps of circular birefringence and of the Mueller matrix near the isotropic wavelength are measured and simulated. The signs of optical rotation are correlated with the absolute crystallographic directions.

Double cone of eigendirections in optically active ethylenediammonium selenate crystals.

Circular birefringence (CB) is generally responsible for only a small perturbation to the state of light polarization in crystals that also exhibit linear birefringence (LB). As such, the magnetoelectric tensor of gyration, which gives rise to CB and optical activity, is less well determined than the electric permittivity tensor in optical models of the Mueller matrix. To visualize the effect of the magnetoelectric tensor on polarimetric measurements, reported here are experimental mappings of the Mueller matrix and of the CB in a new chiral crystal with accidental null LB at an accessible optical frequency. Single crystals of ethylenediammonium selenate (EDSeO4) were synthesized and characterized by X-ray diffraction and Mueller matrix measurements in transmission and reflection. The crystals are isomorphous with the corresponding sulfate salt. They are tetragonal, space group P41(3)212. The constitutive relations of EDSeO4 were recovered using a partial wave summation of incoherent reflections. The extraordinary and ordinary refractive indices cross at 364 nm (3.41 eV), a scenario commonly called the 'isotropic point' or 'iso-index point'. At this wavelength, the magnetoelectric tensor fully describes the polarization transformation, giving rise to a double cone of eigendirections.

Dichroism in Helicoidal Crystals.

Accounting for the interactions of light with heterogeneous, anisotropic, absorbing, optically active media is part of the characterization of complex, transparent materials. Stained biological structures in thin tissue sections share many of these features, but systematic optical analyses beyond the employ of the simple petrographic microscopes have not be established. Here, this accounting is made for polycrystalline, spherulitic bundles of twisted d-mannitol lamellae grown from melts containing light-absorbing molecules. It has long been known that a significant percentage of molecular crystals readily grow as helicoidal ribbons with mesoscale pitches, but a general appreciation of the commonality of these non-classical crystal forms has been lost. Helicoidal crystal twisting was typically assayed by analyzing refractivity modulation in the petrographic microscope. However, by growing twisted crystals from melts in the presence of dissolved, light-absorbing molecules, crystal twisting can be assayed by analyzing the dichroism, both linear and circular. The term "helicoidal dichroism" is used here to describe the optical consequences of anisotropic absorbers precessing around radii of twisted crystalline fibrils or lamellae. d-Mannitol twists in two polymorphic forms, α and δ. The two polymorphs, when grown from supercooled melts in the presence of a variety of histochemical stains and textile dyes, are strongly dichroic in linearly polarized white light. The bis-azo dye Chicago sky blue is modeled because it is most absorbing when parallel and perpendicular to the radial axes in the respective spherulitic polymorphs. Optical properties were measured using Mueller matrix imaging polarimetry and simulated by taking into account the microstructure of the lamellae. The optical analysis of the dyed, patterned polycrystals clarifies aspects of the mesostructure that can be difficult to extract from bundles of tightly packed fibrils.

Long-range modulation of a composite crystal in a five-dimensional superspace.

The intergrowth crystal of n-tetracosane/urea presents a misfit parameter, defined by the ratio γ = ch /cg (chost/cguest), that is very close to a commensurate value (γ ≅ 1/3). High-resolution diffraction studies presented here reveal an aperiodic misfit parameter of γ = 0.3369, which is found to be constant at all temperatures studied. A complex sequence of structural phases is reported. The high temperature phase (phase I) exists in the four-dimensional superspace group P6122(00γ). At Tc1 = 179(1) K, a ferroelastic phase transition increases the dimension of the crystallographic superspace. This orthorhombic phase (phase II) is characterized by the five-dimensional (5D) superspace group C2221(00γ)(10δ) with a modulation vector ao* + cm* = ao* + δ · ch*, in which the supplementary misfit parameter is δ = 0.025(1) in host reciprocal units. This corresponds to the appearance of a modulation of very long period (about 440 ± 16 Å). At Tc2 = 163.0(5) K, a 5D to 5D phase transition leads to the crystallographic superspace group P212121(00γ)(00δ) with a very similar value of δ. This phase transition reveals a significant hysteresis effect.

Model for photoinduced bending of slender molecular crystals.

The growing realization that photoinduced bending of slender photoreactive single crystals is surprisingly common has inspired researchers to control crystal motility for actuation. However, new mechanically responsive crystals are reported at a greater rate than their quantitative photophysical characterization; a quantitative identification of measurable parameters and molecular-scale factors that determine the mechanical response has yet to be established. Herein, a simple mathematical description of the quasi-static and time-dependent photoinduced bending of macroscopic single crystals is provided. This kinetic model goes beyond the approximate treatment of a bending crystal as a simple composite bilayer. It includes alternative pathways for excited-state decay and provides a more accurate description of the bending by accounting for the spatial gradient in the product/reactant ratio. A new crystal form (space group P21/n) of the photoresponsive azo-dye Disperse Red 1 (DR1) is analyzed within the constraints of the aforementioned model. The crystal bending kinetics depends on intrinsic factors (crystal size) and external factors (excitation time, direction, and intensity).

A molecular "phase ordering" phase transition leading to a modulated aperiodic composite in n-heptane/urea.

n-Heptane/urea is an aperiodic inclusion compound in which the ratio of host and guest repeats along the channel axis is very close to unity and is found to have a constant value (0.981) from 280 K to 90 K. Below 280 K, two phase transitions are observed. The first (T(c1) = 145 K) is a ferroelastic phase transition that generates superstructure reflections for the host while leaving the guest with 1D order. The second (T(c2) = 130 K) is a "phase ordering" transition to a four-dimensional structure (P2(1)11(0ßγ)) with pronounced host-guest intermodulation and a temperature dependent phase shift between guests in adjacent channels.