On the origin of optical activity in crystal structures

Chiral plasmonic sensing: From the perspective of light-matter interaction

Molecular chirality is represented as broken mirror symmetry in the structural orientation of constituent atoms and plays a pivotal role at every scale of nature. Since the discovery of the chiroptic property of chiral molecules, the characterization of molecular chirality is important in the fields of biology, physics, and chemistry. Over the centuries, the field of optical chiral sensing was based on chiral light-matter interactions between chiral molecules and polarized light. Starting from simple optics-based sensing, the utilization of plasmonic materials that could control local chiral light-matter interactions by squeezing light into molecules successfully facilitated chiral sensing into noninvasive, ultrasensitive, and accurate detection. In this Review, the importance of plasmonic materials and their engineering in chiral sensing are discussed based on the principle of chiral light-matter interactions and the theory of optical chirality and chiral perturbation; thus, this Review can serve as a milestone for the proper design and utilization of plasmonic nanostructures for improved chiral sensing.

Chirality-Induced Selectivity of Phonon Angular Momenta in Chiral Quartz Crystals

A generation, propagation, and transfer of phonon angular momenta are examined on thermal transport in chiral insulative and diamagnetic crystals of α-quartz. We found that thermally driven phonons carry chirality-dependent angular momenta in the quartz crystals and they could be extracted from the quartz as a spin signal. Namely, chirality-induced selectivity of phonon angular momenta is realized in the chiral quartz. We argue that chiral phonons available in chiral materials could be a key element in triggering or enhancing chirality-induced spin selectivity with robust spin polarization and long-range spin transport found in various chiral materials.

Chiral Mesostructured Inorganic Materials with Optical Chiral Response

Fabricating chiral inorganic materials and revealing their unique quantum confinement-determined optical chiral responses are crucial tasks in the multidisciplinary fields of chemistry, physics, and biology. The field of chiral mesostructured inorganic materials started from the synthesis of individual nanocrystals and evolved to include their assembly from metals, semiconductors, ceramics, and inorganic salts endowed with various chiral structures ranging from atomic to micron scales. This tutorial review highlights the recent research on chiral mesostructured inorganic materials, especially the novel expression of mesostructured chirality and endowed optical chiral response, and it may inspire us with new strategies for the design of chiral inorganic materials and new opportunities beyond the traditional applications of chirality. Fabrication methods for chiral mesostructured inorganic materials are classified according to chirality type, scale, and symmetry-breaking mechanism. Special attention is given to highlight systems with original discoveries, exceptional phenomena, or unique mechanisms of optical chiral response for left- and right-handedness.

Chiral phonons: circularly polarized Raman spectroscopy and ab initio calculations in a chiral crystal tellurium

Recently, phonons with chirality (chiral phonons) have attracted significant attention. Chiral phonons exhibit angular and pseudoangular momenta. In circularly polarized Raman spectroscopy, the peak split of the Γ 3 $$ {\Gamma}_3 $$ mode is detectable along the principal axis of the chiral crystal in the backscattering configuration. In addition, peak splitting occurs when the pseudoangular momenta of the incident and scattered circularly polarized light are reversed. Until now, chiral phonons in binary crystals have been observed, whereas those in unary crystals have not been observed. Here, we observe chiral phonons in a chiral unary crystal Te. The pseudoangular momentum of the phonon is obtained in Te by an ab initio calculation. From this calculation, we verified the conservation law of pseudoangular momentum in Raman scattering. From this conservation law, we determined the handedness of the chiral crystals. We also evaluated the true chirality of the phonons using a measure with symmetry similar to that of an electric toroidal monopole.

Calculating temperature-dependent X-ray structure factors of α-quartz with an extensible Python 3 package

A Python 3 software package for precise calculation of X-ray structure factors of α-quartz over a wide temperature range is presented. α-Quartz was chosen because of its practical application in high-resolution X-ray spectroscopy, but this software package can be easily extended to other crystals.

The design of X-ray optics based on diffraction from crystals depends on the accurate calculation of the structure factors of their Bragg reflections over a wide range of temperatures. In general, the temperature dependence of the lattice parameters, the atomic positions and the atomic thermal vibrations is both anisotropic and nonlinear. Implemented here is a software package for precise and flexible calculation of structure factors for dynamical diffraction. α-Quartz is used as an example because it presents the challenges mentioned above and because it is being considered for use in high-resolution X-ray spectroscopy. The package is designed to be extended easily to other crystals by adding new material files, which are kept separate from the package’s stable core. Python 3 was chosen as the language to allow the easy integration of this code into existing packages. The importance of a correct anisotropic treatment of the atomic thermal vibrations is demonstrated by comparison with an isotropic Debye model. Discrepancies between the two models can be as much as 5% for strong reflections and considerably larger (even to the level of 100%) for weak reflections. A script for finding Bragg reflections that backscatter X-rays of a given energy within a given temperature range is demonstrated. The package and example scripts are available on request. Also discussed, in detail, are the various conventions related to the proper description of chiral quartz.

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.

Terahertz optical Hall effect in p-type monolayer hexagonal boron nitride on fused silica substrate

We demonstrate for the first time, to the best of our knowledge, that the optical Hall effect (OHE) can be observed in p-type monolayer (ML) hexagonal boron nitride (hBN) on a fused silica substrate by applying linearly polarized terahertz (THz) irradiation. When ML hBN is placed on fused silica, in which the incident pulsed THz field can create local and transient electromagnetic dipoles, proximity-induced interactions can be presented. The Rashba spin-orbit coupling can be enhanced, and the in-plane spin component can be induced, along with the lifting of valley degeneracy. Thus, in the presence of linearly polarized THz radiation, the nonzero transverse optical conductivity (or Hall conductivity) can be observed. We measure the THz transmission through ML hBN/fused silica in the temperature range from 80 to 280 K by using THz time-domain spectroscopy in combination with an optical polarization examination. The Faraday ellipticity and rotation angle, together with the complex longitudinal and transverse conductivities, are obtained. The temperature dependence of these quantities is examined. The results obtained from this work indicate that ML hBN is a valleytronic material, and proximity-induced interactions can lead to the observation of OHE in the absence of an external magnetic field.

Getting the Right Grip? How Understanding Electrophile Selectivity Profiles Could Illuminate Our Understanding of Redox Signaling

Significance: Electrophile signaling is coming into focus as a bona fide cell signaling mechanism. The electrophilic regulation occurs typically through a sensing event (i.e., labeling of a protein) and a signaling event (the labeling event having an effect of the proteins activity, association, etc.). Recent Advances: Herein, we focus on the first step of this process, electrophile sensing. Electrophile sensing is typically a deceptively simple reaction between the thiol of a protein cysteine, of which there are around 200,000 in the human proteome, and a Michael acceptor, of which there are numerous flavors, including enals and enones. Recent data overall paint a picture that despite being a simple chemical reaction, electrophile sensing is a discerning process, showing labeling preferences that are often not in line with reactivity of the electrophile. Critical Issues: With a view to trying to decide what brings about highly electrophile-reactive protein cysteines, and how reactive these sensors may be, we discuss aspects of the thermodynamics and kinetics of covalent/noncovalent binding. Data made available by several laboratories indicate that it is likely that specific proteins exhibit highly stereo- and chemoselective electrophile sensing, which we take as good evidence for recognition between the electrophile and the protein before forming a covalent bond. Future Directions: We propose experiments that could help us gain a better and more quantitative understanding of the mechanisms through which sensing comes about. We further extoll the importance of performing more detailed experiments on labeling and trying to standardize the way we assess protein-specific electrophile sensing.

Chiral Surface and Geometry of Metal Nanocrystals

Chirality is a basic property of nature and has great importance in photonics, biochemistry, medicine, and catalysis. This importance has led to the emergence of the chiral inorganic nanostructure field in the last two decades, providing opportunities to control the chirality of light and biochemical reactions. While the facile production of 3D nanostructures has remained a major challenge, recent advances in nanocrystal synthesis have provided a new pathway for efficient control of chirality at the nanoscale by transferring molecular chirality to the geometry of nanocrystals. Interestingly, this discovery stems from a purely crystallographic outcome: chirality can be generated on high-Miller-index surfaces, even for highly symmetric metal crystals. This is the starting point herein, with an overview of the scientific history and a summary of the crystallographic definition. With the advance of nanomaterial synthesis technology, high-Miller-index planes can be selectively exposed on metallic nanoparticles. The enantioselective interaction of chiral molecules and high-Miller-index facets can break the mirror symmetry of the metal nanocrystals. Herein, the fundamental principle of chirality evolution is emphasized and it is shown how chiral surfaces can be directly correlated with chiral morphologies, thus serving as a guide for researchers in chiral catalysts, chiral plasmonics, chiral metamaterials, and photonic devices.

Chiral Surface and Geometry of Metal Nanocrystals

Chirality is a basic property of nature and has great importance in photonics, biochemistry, medicine, and catalysis. This importance has led to the emergence of the chiral inorganic nanostructure field in the last two decades, providing opportunities to control the chirality of light and biochemical reactions. While the facile production of 3D nanostructures has remained a major challenge, recent advances in nanocrystal synthesis have provided a new pathway for efficient control of chirality at the nanoscale by transferring molecular chirality to the geometry of nanocrystals. Interestingly, this discovery stems from a purely crystallographic outcome: chirality can be generated on high-Miller-index surfaces, even for highly symmetric metal crystals. This is the starting point herein, with an overview of the scientific history and a summary of the crystallographic definition. With the advance of nanomaterial synthesis technology, high-Miller-index planes can be selectively exposed on metallic nanoparticles. The enantioselective interaction of chiral molecules and high-Miller-index facets can break the mirror symmetry of the metal nanocrystals. Herein, the fundamental principle of chirality evolution is emphasized and it is shown how chiral surfaces can be directly correlated with chiral morphologies, thus serving as a guide for researchers in chiral catalysts, chiral plasmonics, chiral metamaterials, and photonic devices.

Net atomic charges, electric moments, and sign and magnitude of optical rotatory power in α-TeO2 at 296 K

Optical activity is determined from a point charge model in one enantiomorph of a chiral and semiconducting α-TeO2 crystal. Net atomic charges of Te and O atoms are iterated and electric moments derived. Second electric moments in the principal axis directions are calculated and their ratio is fitted by comparison with the corresponding ratio of the optical refraction indices. The components of the axial vectors are calculated and converted to the gyration tensor components. The optical rotatory power in the positive direction of the optic axis is determined, and the sense of optical rotation is defined from transformations of polar vectors of first rank of the TeO2 groups and visually confirmed in both enantiomorphs.

Supramolecular chirality: a caveat in assigning the handedness of chiral aggregates

The handedness of a supramolecular chiral aggregate is often assigned based on the sign of circular dichroism spectra, adopting the exciton chirality method. However, the method does not properly account for the nature of intermolecular interactions. We introduce a generalized picture on the use of the sign of chiral signals in determining the helicity of chiral aggregates, rooted in the exciton model, supported by TD-DFT results.

Twins in YAl3(BO3)4 and K2Al2B2O7 Crystals as Revealed by Changes in Optical Activity

Many borate crystals feature nonlinear optical properties that allow for efficient frequency conversion of common lasers down into the ultraviolet spectrum. Twinning may degrade crystal quality and affect nonlinear optical properties, in particular if crystals are composed of twin domains with opposing polarities. Here, we use measurements of optical activity to demonstrate the existence of inversion twins within single crystals of YAl 3 (BO 3 ) 4 (YAB) and K 2 Al 2 B 2 O 7 (KABO). We determine the optical rotatory dispersion of YAB and KABO throughout the visible spectrum using a spectrophotometer with rotatable polarizers. Space-resolved measurements of the optical rotation can be related to the twin structure and give estimates on the extent of twinning. The reported dispersion relations for the rotatory power of YAB and KABO may be used to assess crystal quality and to select twin-free specimens.

Syntheses, Structures, and Properties of Non-Centrosymmetric Quaternary Tellurates Bi MTeO6 ( M = Al, Ga)

Single crystals of two new metal tellurates Bi MTeO₆ ( M = Al, Ga) with a honeycomb layered structure were obtained by the molten flux method and characterized. The Bi MTeO₆ compounds both crystallize into a non-centrosymmetric trigonal space group of P312 (no. 149) with cell parameters of a = 5.0667(8) Å, c = 4.9920(16) Å and a = 5.107(3) Å, c = 4.932(6) Å, respectively. The non-centrosymmetry of BiAlTeO₆ and BiGaTeO₆ originates from the packing order of the octahedra. In these two structures, TeO₆ octahedra and MO₆ octahedra share edges and form a honeycomb open-framework with [Te MO₆]_∞ layers. The layers of [ MTeO₆]_∞ and [BiO₆]_∞ alternate and are connected along the c-axis by corner-sharing oxygen atoms to form the three-dimensional framework. The chiral compound BiGaTeO₆ exhibits a powder second harmonic generation (SHG) response of ∼0.2 times that of potassium dihydrogen phosphate (KDP) and an absorption edge of 355 nm.

Correct interpretation of diffraction properties of quartz crystals for X-ray optics applications. Corrigendum

Errors about left-handed (laevorotatory) quartz and right-handed (dextrorotatory) quartz in the paper by Huang, Gog, Kim, Kasman, Said, Casa, Wieczorek, Hönnicke & Assoufid [J. Appl. Cryst. (2016), 51, 140–147] are corrected.

Confusion over the description of the quartz structure yet again

In a recent paper [Huang, Gog, Kim, Kasman, Said, Casa, Wieczorek, Hönnicke & Assoufid (2018). J. Appl. Cryst. 51, 140–147], a description of the structure of quartz was given that is incorrect. There is a long history of such errors in publications describing the quartz structure. This was fully and correctly discussed in 1978 [Donnay & Le Page (1978). Acta Cryst. A34, 584–594], and yet these errors still persist. In the present paper the description by Huang et al. is corrected and the seminal work of Donnay and Le Page revisited.

Magnetic Skyrmion Formation at Lattice Defects and Grain Boundaries Studied by Quantitative Off-Axis Electron Holography

We use in situ Lorentz microscopy and off-axis electron holography to investigate the formation and characteristics of skyrmion lattice defects and their relationship to the underlying crystallographic structure of a B20 FeGe thin film. We obtain experimental measurements of spin configurations at grain boundaries, which reveal inversions of crystallographic and magnetic chirality across adjacent grains, resulting in the formation of interface spin stripes at the grain boundaries. In the absence of material defects, we observe that skyrmions lattices possess dislocations and domain boundaries, in analogy to atomic crystals. Moreover, the distorted skyrmions can flexibly change their size and shape to accommodate local geometry, especially at sites of dislocations in the skyrmion lattice. Our findings provide a detailed understanding of the elasticity of topologically protected skyrmions and their correlation with underlying material defects.

Cooperative expression of atomic chirality in inorganic nanostructures

Cooperative chirality phenomena extensively exist in biomolecular and organic systems via intra- and inter-molecular interactions, but study of inorganic materials has been lacking. Here we report, experimentally and theoretically, cooperative chirality in colloidal cinnabar mercury sulfide nanocrystals that originates from chirality interplay between the crystallographic lattice and geometric morphology at different length scales. A two-step synthetic scheme is developed to allow control of critical parameters of these two types of handedness, resulting in different chiral interplays expressed as observables through materials engineering. Furthermore, we adopt an electromagnetic model with the finite element method to elucidate cooperative chirality in inorganic systems, showing excellent agreement with experimental results. Our study enables an emerging class of nanostructures with tailored cooperative chirality that is vital for fundamental understanding of nanoscale chirality as well as technology applications based on new chiroptical building blocks.

Optically active metasurface with non-chiral plasmonic nanoantennas

We design, fabricate, and experimentally demonstrate an optically active metasurface of λ/50 thickness that rotates linearly polarized light by 45° over a broadband wavelength range in the near IR region. The rotation is achieved through the use of a planar array of plasmonic nanoantennas, which generates a fixed phase-shift between the left circular polarized and right circular polarized components of the incident light. Our approach is built on a new supercell metasurface design methodology: by judiciously designing the location and orientation of individual antennas in the structural supercells, we achieve an effective chiral metasurface through a collective operation of nonchiral antennas. This approach simplifies the overall structure when compared to designs with chiral antennas and also enables a chiral effect which quantitatively depends solely on the supercell geometry. This allows for greater tolerance against fabrication and temperature effects.

PolaBer: a program to calculate and visualize distributed atomic polarizabilities based on electron density partitioning

This paper describes the program PolaBer, which calculates atomic polarizability tensors from electric field perturbations of a partitioned electron density distribution. Among many possible partitioning schemes, PolaBer is currently using the quantum theory of atoms in molecules and it is interfaced to programs that apply such a partitioning. The calculation of the atomic tensors follows the idea suggested by Keith [The Quantum Theory of Atoms in Molecules: From Solid State to DNA and Drug Design, (2007), edited by C. F. Matta & R. J. Boyd. Weinheim: Wiley-VCH], which enables the removal of the intrinsic origin dependence of the atomic charge contributions to the molecular dipole moment. This scheme allows the export, within chemically equivalent functional groups, of properties calculated from atomic dipoles, such as for example the atomic polarizabilities. The software permits visualization of the tensors and calculation of straightforward optical properties of a molecule (like the molar refractive index) or a crystal (assuming the molecule in a given crystal lattice).

Crystal optics of D-mannitol, C6H14O6: crystal growth, structure, basic physical properties, birefringence, optical activity, Faraday effect, electro-optic effects and model calculations

Large single crystals of optical quality were grown from aqueous solutions. The structure [Berman, Jeffrey and Rosenstein, Acta Crystallogr. B24 (1968) 442] was reinvestigated and refined in space group P212121 to an R(F)-value of 0.0276. Thermal expansion, refractive indices, dielectric constants, optical activity, Faraday effect and electro-optic effects were experimentally determined. Simple model calculations based on structural information and empirical data are compared with the observed anisotropy of the experimental results. Non-linear optical properties were estimated from a dipole-dipole model which uses polarizability volumes of the atoms [Devarajan and Glazer, Acta Crystallogr. A42 (1986) 560] and in which electron-cloud shifting by a simulated electrical field is introduced.

Determination of the absolute chirality of tellurium using resonant diffraction with circularly polarized x-rays

Many proteins, sugars and pharmaceuticals crystallize into two forms that are mirror images of each other (enantiomers) like our right and left hands. Tellurium is one enantiomer having a space group pair, P3(1)21 (right-handed screw) and P3(2)21 (left-handed screw). X-ray diffraction with dispersion correction terms has been playing an important role in determining the handedness of enantiomers for a long time. However, this approach is not applicable for an elemental crystal such as tellurium or selenium. We have demonstrated that positive and negative circularly polarized x-rays at the resonant energy of tellurium can be used to absolutely distinguish right from left tellurium. This method is applicable to chiral motifs that occur in biomolecules, liquid crystals, ferroelectrics and antiferroelectrics, multiferroics, etc.

Optical rotation in RbTiOAsO4 (point group mm2)

Measurement of optical rotation in RbTiOAsO4 (RTA) with the tilter method resulted in an optical rotation of ρ 12= +17(3)o/mm at a wavelength of 670nm, when a (100) sample was tilted about [001]. A tilt about [010] showed no rotation, as expected from the directional dependence of optical rotation calculated from the tensor in point group mm2. The absolute Miller-indices of the sam-les were found using X-ray anomalous scattering. The calculations with a dipole-dipole model show that the As5+-ions in RTA correlate with the main structural contribution of the optical rotation. However, there seems to be an even larger intrinsic contribution due to the Ti4+ – ions as a result of the distorted octahedral co-ordination with oxygen.

Internal dynamics and optical rotations predicted for O(h)- and O-symmetric cubanes

B3LYP/6-31G(d) calculations find that cubanes, persubstituted with NO2 or BF2 groups, are predicted to undergo near-barrierless, internal disrotations. However, as a consequence of the intrinsically higher energies of eclipsed conformations for threefold than for twofold rotors, the threshold mechanisms for octamethyl-, octakis(trifluoromethyl)-, octakis(trichloromethyl)-, octakis(tribromomethyl)-, octasilylcubane, and octakis(trichlorosilyl)cubane are calculated to be mono- or conrotation. The cubanes with the larger substituents are predicted to be O-symmetric, resolvable, and thus optically active.

Optical rotation of achiral compounds

Oriented achiral molecules and crystals with D(2d) symmetry or one of its non-enantiomorphous subgroups, S(4), C(2v), or C(s), can rotate the plane of transmitted polarized light incident in a general direction. This well-established fact of crystal optics is contrary to the teaching of optical activity to students of organic chemistry. This Minireview gives an overview of the measurement and calculation of the chiroptical properties of some achiral compounds and crystals. Methane derivatives with four identical ligands related by reflection symmetry are quintessential optically inactive compounds according to the logic of van't Hoff. Analysis of the optical activity of simple achiral compounds such as H(2)O and NH(3) provides general aspects of chiroptics that are not readily broached when considering chiral compounds exclusively. We show here, through the use of group theoretical arguments, the transformation properties of tensors, and diagrams, why some achiral, acentric compounds are optically active while others are not.

Resonant diffraction of circularly polarized x-rays by a chiral crystal (low quartz)

A correlation in x-ray resonant scattering between crystal chirality and circular polarization (helicity) is explored in the context of an analysis of Bragg diffraction from low quartz (α-SiO(2)). There is a one-to-one correlation between chirality and helicity when one resonant event is present in diffraction and thus, in this simple case, resonant Bragg diffraction of circularly polarized x-rays is a direct probe of crystal chirality. The presence of more than one resonant event is shown to add phase relations to the scattering amplitude and then coupling of helicity and chirality is no longer transparent.

Right handed or left handed? Forbidden x-ray diffraction reveals chirality

Enantiomers, or stereoisomers, have crystal structures that are mirror images of each other and are thus handed, like our right and left hands. The physical properties of enantiomers are identical except for optical activity, which rotates linearly polarized light by equal amounts but in opposite directions. While conventional x-ray Bragg diffraction can determine crystal structures, it does not distinguish between right- and left-handed crystals. We show resonant Bragg diffraction using circularly polarized x rays reveals the handedness of crystals by coupling x-ray helicity to a crystal screw axis. The intensity of resonantly allowed reflection of alpha-quartz is well described by an admixture of a parity-even and a parity-odd process. Our results are of general importance and demonstrate a new method to directly study chiral motifs in structures that include biomaterials, liquid crystals, magnets, multiferroics, etc.

Solid- and Solution-State Studies of the Novel μ-Dicyanamide-Bridged Dinuclear Spin-Crossover System {[(Fe(bztpen)]2[μ-N(CN)2]}(PF6)3⋅n H2O

The mononuclear diamagnetic compound {Fe(bztpen)[N(CN)2]}(PF6)CH3OH (1) (bztpen = N-benzyl-N,N',N'-tris(2-pyridylmethyl)ethylenediamine) has been synthesized and its crystal structure studied. Complex 1 can be considered to be the formal precursor of two new dinuclear, dicyanamide-bridged iron(II) complexes with the generic formula {[(Fe(bztpen)]2[mu-N(CN)2]}(PF6)3 x n H2O (n = 1 (2) or 0 (3)), which have been characterized in the solid state and in solution. In all three complexes, the iron atoms have a distorted [FeN6] octahedral coordination defined by a bztpen ligand and a terminal (1) or a bridging dicyanamide ligand (2 and 3). In the solid state, 2 and 3 can be considered to be molecular isomers that differ by the relative position of the phenyl ring of the two {Fe(bztpen)[N(CN)2]}+ halves (cis and trans, respectively). Depending on the texture of the sample, 2 exhibits paramagnetic behavior or displays a very incomplete spin transition at atmospheric pressure. Complex 3 undergoes a gradual two-step spin transition with no observed hysteresis in the solid state. Both steps are approximately 100 K wide, centered at approximately 200 K and approximately 350 K, with a plateau of approximately 80 K separating the transitions. The crystal structure of 3 has been determined in steps of approximately 50 K between 400 K and 90 K, which provides a fascinating insight into the structural behavior of the complex and the nature of the spin transition. Order-disorder transitions occur in the dicyanamide bridge and the PF6(-) ions simultaneously, with the spin-crossover behavior suggesting that these transitions may trigger the two-step character. In solution, 2 and 3 display very similar continuous spin conversions. Electrochemical studies of 2 and 3 show that the voltammograms are typical of dimeric systems with electronic coupling of the metals through the dicyanamide ligand.

Optical activity induced by helical arrangements of tryptamine and 4-chlorobenzoic acid in their cocrystal

Optical rotatory powers of chiral cocrystals formed from the achiral molecules tryptamine and 4-chlorobenzoic acid were determined by the HAUP (high accuracy universal polarimeter) method. These cocrystals belonged to space group P2(1)2(1)2(1), and their absolute configuration was confirmed by the Flack parameter. In the M-crystal, 2-fold helical arrangements are formed in a counterclockwise direction between the two components through the quaternary ammonium salt bridge, hydrogen bond, and the aromatic pi-piinteraction along the c axis, while clockwise helices alone exist in the P-crystal. Large rotatory powers rho(3)(M) = -355 and rho(3)(P) = +352 deg mm(-)(1) were obtained along the c axis in the M- and P-crystal, respectively, at 632.8 nm and 303 K. The magnitude was 10 to 100 times larger than those for ordinary organic crystals. Further, it was confirmed that the negative sign was induced by the counterclockwise helical structures and the positive sign by the clockwise helices. In contrast, the rotations along the a and b axis which are in perpendicular directions to the screw axis were rho(1)(M) = +138, rho(1)(P) = -140 deg mm(-)(1), and rho(2)(M) = -56, rho(2)(P) = +58 deg mm(-)(1), much smaller than rho(3)(M) and rho(3)(P) . The results revealed that the helically arranged aromatic pi electrons as well as the helical ionic and hydrogen bond networks in the crystal contributed to the enhancement of the magnitude of these rotations.

CD spectra of solid-state samples

Solid-state CD spectroscopy can provide valuable information on conformation, intermolecular interactions, including chirality induction, and enantioselective reactions which occur specifically in the solid state. The technique can, however, suffer from serious artifacts. Some examples of solid-state CD are given and potential artifacts are discussed. Copyright 2000 Wiley-Liss, Inc.

Light propagation in cubic and other anisotropic crystals

A consistent multipole theory is presented to describe light propagation in non-absorbing non-magnetic crystals. Although valid for the 32 crystal classes, the theory is applied here to all except the five members of the triclinic and monoclinic systems. To account for the birefringence that has been observed in certain cubic crystals and also for the predicted Jones birefringence, the theory has to allow for electric octopoles and magnetic quadrupoles induced by the light wave. At the earlier stage of electric quadrupoles and magnetic dipoles, it is able to describe optical activity in crystals. An expression for this is derived which, when electric quadrupole contributions are omitted, yields the familiar Nye result. As a criterion for the correct inclusion in the theory of all relevant induced multipole moments, tensor expressions for observables are shown to be independent of the choice of origin. Finally, the concepts of O-ray and E-ray are found to break down beyond the electric dipole approximation and alternatives are proposed.