Kinetic Analysis of Excited-State Dynamics of Emissive Oligomers of Pt(II) Complex in Solution.

[Pt(NCN)MeCN]+ (NCN = 1,3-di(2-pyridyl)benzene, MeCN = acetonitrile) forms oligomers, such as dimers and trimers, in solutions due to metallophilic interactions. The emission and absorption spectra in the visible region are considerably changed by the concentrations of the solutions because the excitation energy of the oligomers is dependent on the degree of oligomerization. In this study, excited-state dynamics of [Pt(NCN)MeCN]+ in acetonitrile were investigated by time-resolved emission spectroscopy in time regions from microseconds to nanoseconds at various concentrations. The time-resolved emission spectra recorded with 355 nm photoexcitation showed the decay of the blue-green emission and the rise of the red emission in the microsecond time region. Stern-Volmer analysis of the time-resolved data at various concentrations and wavelengths provides two bimolecular rate constants (4.1 × 109 and 8.2 × 108 M-1 s-1) for the formation processes of the excited-state T1 dimer and T1 trimer, respectively. Kinetic parameters, such as the intrinsic decay rate constants of the T1 monomer, T1 dimer, and T1 trimer, and the association and dissociation rate constants of the T1 dimer and T1 trimer were estimated by fitting the time-resolved emission data at various concentrations.

Spectroscopic mapping of the gold complex oligomers (dimer, trimer, tetramer, and pentamer) by excited-state coherent nuclear wavepacket motion in aqueous solutions.

We investigate the excited-state dynamics of the [Au(CN)2-] oligomers following photo-initiated intermolecular Au-Au bond formation by carrying out femtosecond time-resolved absorption and emission measurements at various concentrations (0.080-0.6 mol dm-3) with different photoexcitation wavelengths (290-340 nm). The temporal profiles of the time-resolved absorption signals exhibit clear oscillations arising from the Au-Au stretch coherent wavepacket motion of the excited-state oligomers, which is initiated with the photo-induced Au-Au bond formation. The frequency of the observed oscillation is changed with the change of the concentration, excitation wavelength, and wavelength of the excited-state absorption monitored, reflecting the change in the size of the oligomers detected. Fourier transforms (FTs) of the oscillations provide 2D plots of the FT amplitude against the oscillation frequency versus the detected wavelengths. Because the FT amplitude exhibits a node at the peak wavelength of the absorption of the species that gives rise to the oscillation, the 2D plots enabled us to determine the peak wavelength of the excited-state absorption of the dimer, trimer, tetramer, and pentamer. We also performed femtosecond time-resolved absorption measurements for the 0.3 mol dm-3 solution with 260 nm photoexcitation, which is the condition employed in previous time-resolved X-ray studies (e.g., K. H. Kim et al. Nature, 2015, 518 (7539), 385-389). It was found that various excited-state oligomers, including the dimer, were simultaneously generated under this condition, although the analysis of the previous time-resolved X-ray studies was made by assuming that only the excited-state trimer was generated. The obtained results show that the excited-state dynamics of the trimer claimed based on the time-resolved X-ray data is questionable and that re-analysis and re-examining of its data are necessary.

Structural change dynamics of heteroleptic Cu(I) complexes observed by ultrafast emission spectroscopy.

[Cu(I)(dmp)(P)2]+ (dmp = 2,9-dimethyl-1,10-phenanthroline derivatives; P = phosphine ligand) is one of the most promising photosensitizers used in a photo-catalytic system for reducing CO2, for which the quantum yield is as high as 57%. In this work, time-resolved emission spectra of Cu(I) complexes in solutions were investigated using femtosecond fluorescence up-conversion and nanosecond time-resolved emission spectroscopic systems. The temporal profiles of emission intensities less than 10 ps in acetonitrile solution were reproduced using a tri-exponential function with three-time constants of 0.040 ps, 0.78 ps and 8.0 ps. We found that only the second time constant is dependent on the solvent (acetonitrile: 0.78 ps, butyronitrile: 1.4 ps), indicating that the 0.78 ps spectral change is attributed to the structural change of the Cu(I) complex. The oscillator strengths of transition species are derived from the intensities in the time-resolved emission spectra (species-associated spectra). Based on the oscillator strengths, we concluded that the 0.040 ps process is the Sn → S1 internal conversion and the 0.78 ps process is a structural change in the S1 state. The final time constant of 8.0 ps is assigned to the S1 → T1 intersystem crossing because the 3MLCT state (τT1 = 97 ns) is generated after the decay. The DFT calculation showed that the 0.78 ps spectral change (∼600 cm-1 redshift) is attributed to Jahn-Teller distortion around the metal center, and there is a large structural change in the ligand, which results in a large Stokes shift in the Sn state (7.3 × 103 cm-1).

Photophysical Properties of Simple Palladium(0) Complexes Bearing Triphenylphosphine Derivatives.

Pd(0) complexes with monodentate phosphine ligands, [Pd(P)n] (n = 3, 4), are well-known catalysts. However, the nature of the Pd(0) complex, especially the basic photophysical properties of the Pd(0) complexes, has not been extensively explored. In this work, we measured the general photophysical properties and crystal structures of Pd(0)-bearing PPh3 derivatives in the solid state and in solution. In the solid state, four-coordinated Pd(0) complexes exhibited blue-yellow emission. On the other hand, three-coordinated Pd(0) complexes displayed yellow-orange emission. In solution, orange emission of three-coordinated complexes was observed, and prompt fluorescence was detected using time-resolved emission spectroscopy, which suggests a thermally activated delayed fluorescence mechanism. Density functional theory (DFT) and time-dependent DFT calculations show that the difference in the transition mechanism between the [Pd(PPh3)4] and [Pd(PPh3)3] complexes explains the different emission colors. The emitting states of both complexes have metal-to-ligand charge-transfer character, but the metal-centered d → p transition is considerably incorporated for emission of the tris complex.

Through-Space Charge Transfer in Copper Coordination Networks with Copper-Halide Guest Anions.

We prepared coordination networks that show relatively strong emission with through-space charge-transfer (TSCT) transitions. Thermolysis of a kinetically assembled network with Cu2Br2 dimer connectors, which was assembled from a CuBr cluster and the Td ligand 4-4-tetrapyridyltetraphenylmethane (4-TPPM), generated a highly luminescent network composed of Cu+ connectors and 4-TPPM linkers with CuBr2- guests. We clarified that the electronic transitions in this network include TSCT in addition to the typical metal-ligand charge transfer (MLCT) observed in conventional Cu complexes.

Coherent Vibration and Femtosecond Dynamics of the Platinum Complex Oligomers upon Intermolecular Bond Formation in the Excited State.

Femtosecond time-resolved absorption and picosecond time-resolved emission measurements were carried out for highly concentrated aqueous solutions of K2 [Pt(CN)4 ] to investigate excited-state dynamics of the [Pt(CN)4 2- ] oligomers formed with metallophilic interactions. Time-resolved absorption spectra exhibit complicated dynamics that are represented with five time constants. Among them, the 90-ps and 400-ps dynamics were assigned to the S1 → T1 intersystem crossing of the trimer and tetramer coexisting in the solution by comparison with the fluorescence decays. Clear oscillations of transient absorption were observed in the first few picoseconds, and the frequency-detected-wavelength 2D analysis revealed that the 135-cm-1 and 65-cm-1 oscillations arise from the Pt-Pt stretch motions of the S1 trimer and S1 tetramer, respectively. The obtained time-resolved spectroscopic data provide a clear view of the excited-state dynamics of the [Pt(CN)4 2- ] oligomers in the femto-/picosecond time region.

Tracking Photoinduced Au-Au Bond Formation through Transient Terahertz Vibrations Observed by Femtosecond Time-Domain Raman Spectroscopy.

Real-time observation of chemical bond formation and subsequent nuclear rearrangements is an ultimate goal of chemical science. Yet, such attempts have been hampered by the technical difficulty of triggering bond formation at well-defined, desired timing. The trimer of dicyanoaurate complex ([Au(CN)2-]3) is an ideal system for achieving this aim because the tight covalent Au-Au bonds are formed upon photoexcitation. Despite the apparent simplicity of the system, however, recent time-resolved studies failed to construct a consistent picture of its ultrafast dynamics. Here, we report femtosecond time-domain Raman tracking of ultrafast structural dynamics of the [Au(CN)2-] trimer upon photoinduced Au-Au bond formation. The obtained Raman data reveal that the Au-Au breathing vibration at ∼90 cm-1 exhibits a gradual frequency upshift in a few picoseconds, demonstrating a continuous bent-to-linear structural change on the triplet-state potential energy surface upon the Au-Au bond formation. The comprehensive ultrafast spectroscopic study settles the controversy on this prototypical molecular assembly.

Enhancement of the Photofunction of Phosphorescent Pt(II) Cyclometalated Complexes Driven by Substituents: Solid-State Luminescence and Circularly Polarized Luminescence.

Ligand functionalization is an attractive strategy for enhancing the performance of metal-based phosphorescent emitters. Here, we report the synthesis and characterization of cyclometalated Pt(II) complexes Pt3 and Pt4 containing organosilyl-substituted (2-(2-thienyl)pyridine) ligands and compare their properties with those of Pt1 (no substituent) and Pt2 (organocarbon substituent). The photophysical characteristics of these molecules, including their absorption and phosphorescence spectra, phosphorescence quantum yield and lifetime, were investigated. The molecular structures were revealed by X-ray diffraction analysis. Under UV light irradiation, Pt2-Pt4 emitted intense orange phosphorescence in the solid state because of the bulkiness of their side chains (up to ΦP: 0.49). Optically pure (-)-(S)Si-Pt4 and (+)-(R)Si-Pt4 were prepared using the optically active ligands (+)-L4 and (-)-L4, respectively. The chiroptical properties of (+)-(R)Si-Pt4, which has an asymmetric silicon atom, were investigated. Circular dichroism and circularly polarized luminescence measurements showed that these structural motifs are suitable for applications in chiroptical phosphorescent materials.

Observation of Circularly Polarized Luminescence of the Excimer from Two Perylene Cores in the Form of [4]Rotaxane.

A perylene-based [4]rotaxane was synthesized by the Sonogashira coupling of the 2:2 inclusion complex consisting of two alkynylperylenes and two γ-cyclodextrins with terphenyl-type stopper molecules. The [4]rotaxane showed orange emission attributable to the spatially restricted alkynylperylene excimer with a high fluorescence quantum yield of Φf =0.15. The excimer emission was circularly polarized as a result of the asymmetrically twisted perylene pair under the influence of chirality of γ-cyclodextrin. The glum value of the excimer emission was determined to be -2.1×10-2 at 573 nm, as large as those of the corresponding known pyrene-based series. This is the first example, in which circularly polarized luminescence was clearly observed from the excimer of a pair of perylene cores.

Aggregation-Induced Fluorescence-to-Phosphorescence Switching of Molecular Gold Clusters.

Aggregation-induced optical responses are ubiquitous among a wide range of organic and inorganic compounds. Here, we demonstrate an unprecedented effect of aggregation on the photoluminescence (PL) profiles of [core + exo]-type [Au8]4+ clusters, which displayed a change in the dominant PL emission mode from fluorescence to phosphorescence-type upon aggregation. In solvents in which cluster molecules are highly soluble and exist as monomers, they displayed single PL bands at ∼600 nm at ambient temperatures. However, in solvents in which cluster molecules are less soluble and cluster aggregation is induced, a new PL band at ∼700 nm also emerged. Lifetime measurements revealed that the PL emissions at ∼600 and ∼700 nm had fluorescence and phosphorescence characters, respectively. Studies of the excitation spectra suggested that organized cluster assemblies were responsible for the lower-energy emission at ∼700 nm and had exceptionally high emission activity. Accordingly, intense phosphorescence-type emissions were observed in the solid state in which the quantum efficiencies were higher by two orders of magnitude than those of the corresponding monomeric forms in solution. This work provides an example of the critical effects of cluster aggregation events on their optical properties and shows the potential of such effects in the design of cluster-based materials with unique functions and properties.

Multifunctional Octamethyltetrasila[2.2]cyclophanes: Conformational Variations, Circularly Polarized Luminescence, and Organic Electroluminescence.

Both symmetrical and unsymmetrical cyclophanes containing disilane units, tetrasila[2.2]cyclophanes 1-9, were synthesized. The syn and anti conformations and the kinetics of inversion between two anti-isomers were investigated by X-ray diffraction and variable-temperature NMR analysis, respectively. The flipping motion of two aromatic rings was affected by the bulkiness of the aromatic moiety (1 vs 6), the phase (solid vs solution), and the inclusion by host molecules (1 vs 1⊂[Ag2L]2+). The photophysical, electrochemical, and structural properties of the compounds were thoroughly investigated. Unsymmetrical tetrasila[2.2]cyclophanes 5-8 displayed blue-green emission arising from intramolecular charge transfer. Compound 6 emitted a brilliant green light in the solid state under 365 nm irradiation and showed a higher fluorescence quantum yield in the solid state (Φ = 0.49) than in solution (Φ = 0.05). We also obtained planar chiral tetrasila[2.2]cyclophane 9, which showed interesting chiroptical properties, such as a circularly polarized luminescence (CPL) with a dissymmetry factor of |glum| = ca. 2 × 10-3 at 500 nm. Moreover, an organic green light-emitting diode that showed a maximum external quantum efficiency (ηext) of ca. 0.4% was fabricated by doping 4,4'-bis(2,2'-diphenylvinyl)-1,1'-biphenyl with 6.

Access to Chiral Silicon Centers for Application to Circularly Polarized Luminescence Materials.

Asymmetric arylation of secondary silanes catalyzed by a Pd-chiral phosphoramidite complex was developed for application to low-molecular-weight circularly polarized luminescence (CPL) materials. The asymmetric arylation provided a convenient, efficient synthetic method for a variety of chiral tertiary silanes (2-21), which were key intermediates for preparing the quaternary silicon center. A stepwise, one-pot procedure was used to transform the appropriate aryl iodide to the quaternary silane (22) with good yield and enantioselectivity. Among compounds synthesized in this work, four optically pure tertiary silanes (18-21) were selected to investigate the relationship between the structure and optical properties. Optically pure (S,S)-21 displayed the highest CPL emission with a high fluorescence quantum yield (glum: +0.008, ΦF: 0.42). This simple molecular design provides new strategies for developing small organic CPL dyes.

Methanol-Triggered Turn-On-Type Photoluminescence in L-Cysteinato Palladium(II) and Platinum(II) Complexes Supported by a Bis(diphenylphosphine) Ligand.

The selective detection of methanol by photoluminescence under environmental conditions has been a great challenge for materials science. Herein, a reversible, turn-on-type photoluminescence triggered by methanol vapor in square-planar palladium(II) and platinum(II) complexes, newly prepared from [MCl2(1,3-bis(diphenylphosphino)propane)] and L-cysteine, is reported. Both the "turn-on" and "turn-off" states of the complexes were crystallographically characterized, which revealed the presence of intermolecular OH···O and CH···π interactions between methanol and the complex molecules in the turn-on state. These interactions prevent the vibrational quenching of the luminescence, leading to the turn-on-type luminescence in this system.

Photochemical Properties and Reactivity of a Ru Compound Containing an NAD/NADH-Functionalized 1,10-Phenanthroline Ligand.

An NAD/NADH-functionalized ligand, benzo[b]pyrido[3,2-f][1,7]-phenanthroline (bpp), was newly synthesized. A Ru compound containing the bpp ligand, [Ru(bpp)(bpy)2](2+), underwent 2e(-) and 2H(+) reduction, generating the NADH form of the compound, [Ru(bppHH)(bpy)2](2+), in response to visible light irradiation in CH3CN/TEA/H2O (8/1/1). The UV-vis and fluorescent spectra of both [Ru(bpp)(bpy)2](2+) and [Ru(bppHH)(bpy)2](2+) resembled the spectra of [Ru(bpy)3](2+). Both complexes exhibited strong emission, with quantum yields of 0.086 and 0.031, respectively; values that are much higher than those obtained from the NAD/NADH-functionalized complexes [Ru(pbn)(bpy)2](2+) and [Ru(pbnHH)(bpy)2](2+) (pbn = (2-(2-pyridyl)benzo[b]-1.5-naphthyridine, pbnHH = hydrogenated form of pbn). The reduction potential of the bpp ligand in [Ru(bpp)(bpy)2](2+) (-1.28 V vs SCE) is much more negative than that of the pbn ligand in [Ru(pbn)(bpy)2](2+) (-0.74 V), although the oxidation potentials of bppHH and pbnHH are essentially equal (0.95 V). These results indicate that the electrochemical oxidation of the dihydropyridine moiety in the NADH-type ligand was independent of the π system, including the Ru polypyridyl framework. [Ru(bppHH)(bpy)2](2+) allowed the photoreduction of oxygen, generating H2O2 in 92% yield based on [Ru(bppHH)(bpy)2](2+). H2O2 production took place via singlet oxygen generated by the energy transfer from excited [Ru(bppHH)(bpy)2](2+) to triplet oxygen.

Considerable Enhancement of Emission Yields of [Au(CN)2(-)] Oligomers in Aqueous Solutions by Coexisting Cations.

The photophysical properties of [Au(CN)2(-)] oligomers in aqueous solutions were investigated as functions of coexisting cations as well as the viscosity and temperature of solutions. A solution of [Au(CN)2(-)] in the concentration range of 0.03-0.2 mol/dm(3) exhibited emission peaks at 460-480 nm because of the presence of oligomers larger than trimers. Although the emission yields (ϕem) of K[Au(CN)2] solutions were <1%, it considerably increased to 43% when 1.0 mol/dm(3) tetraethylammonium chloride (Et4NCl) was added. The lifetimes of the main emission bands were also significantly varied with additional salts, e.g., KCl, 15 ns; Et4NCl, 520 ns. The time-resolved emission measurements of [Au(CN)2(-)] in a water/glycerol mixture indicated that the lifetimes were almost directly proportional to the inverse of the viscosity of the solution. On the other hand, the intrinsic lifetimes of dimers and trimers with weak emission in shorter wavelength regions were very short and independent of the viscosity of the solutions and coexisting cations (dimer, ∼25 ps; trimer, ∼2 ns). These results indicated that the deactivation of the excited-state [Au(CN)2(-)]n oligomers (n ≥ 4) was dominated by the dissociation of the oligomers to a shorter species (dimer or trimer). The hydrophobic interactions between tetraalkylammonium cations and CN ligands remarkably stabilized the larger oligomers and suppressed the dissociation of the excited-state oligomers, which enhanced the emission yield of the oligomers. This work provides a new method of "exciplex tuning" by changing the environment of excited-state [Au(CN)2(-)]n oligomers.

Coherent vibration and ultrafast dynamics upon bond formation in excited dimers of an Au(I) complex.

Au-Au bond strengthening in photoexcited dimers of an Au(I) complex is captured in solution as oscillations of femtosecond absorption signals. The subsequent dynamics, when compared to the trimer's data, confirm that the bent-to-linear structural change of the trimer occurs in the first few picoseconds.

Very Long-Lived Photoinduced Charge-Separated States of Triphenylamine-Naphthalenediimide Dyads in Polymer Matrices.

Photoinduced electron transfer was studied in dyads (dyad1 and dyad2) containing triphenylamine (MTA) and naphthalenediimide (MNDI) linked with oligo(phenyleneethynylene) dispersed in rigid polymer matrices of polystyrene (PS), poly(vinyl chloride), and poly(methyl methacrylate). Photoexcitation of these dyads yielded long-lived charge-separated (CS) states involving MTA+ and MNDI-. The quantum yields of charge separation in dyad1 and dyad2 were approximately 0.4 and 0.3, respectively, in the polymer matrices. The CS lifetime for dyad2 in PS was longer (400 ms) than those in poly(vinyl chloride) (120 ms) and poly(methyl methacrylate) (65 ms) at 298 K. In addition, CS state had a very long lifetime of 5.4 s in glassy toluene at 100 K. Below glass transition temperatures, polymer side chain motions with various relaxation rates should affect the charge recombination processes. The energy gap (ΔG) and outer-sphere reorganization energy (λ) in the charge recombination process were estimated using a slow-frequency component for dielectric constants. By use of ΔG and λ values, the matrix dependence of the CS lifetimes was successfully rationalized based on Marcus theory, and the charge recombination process in PS with low polarity and high polarizability should be in a deeper inverted region than the other polymer matrices. It also suggested that the rigidity of the polymer effectively suppressed intramolecular motions promoting the charge recombination process.

Specific chiral sensing of amino acids using induced circularly polarized luminescence of bis(diimine)dicarboxylic acid europium(III) complexes.

The circularly polarized luminescence (CPL) from [Eu(pda)2](-) (pda = 1,10-phenanthroline-2,9-dicarboxylic acid) and [Eu(bda)2](-) (bda = 2,2'-bipyridine-6,6'-dicarboxylic acid) in aqueous solutions containing various amino acids was investigated. The europium(III) complexes exhibited bright-red luminescence assignable to the f-f transition of the Eu(III) ion when irradiated with UV light. Although the luminescence was not circularly polarized in the solid state or in aqueous solutions, in accordance with the achiral crystal structure, the complexes exhibited detectable induced CPL (iCPL) in aqueous solutions containing chiral amino acids. In the presence of L-pyrrolidonecarboxylic acid, both [Eu(pda)2](-) and [Eu(bda)2](-) showed similar iCPL intensity (glum ∼ 0.03 for the (5)D0 → (7)F1 transition at 1 mol·dm(-3) of the amino acid). On the other hand, in the presence of L-histidine or L-arginine, [Eu(pda)2](-) exhibited intense CPL (glum ∼ 0.08 for the (5)D0 → (7)F1 transition at 0.10 mol·dm(-3) of the amino acid), whereas quite weak CPL was observed for [Eu(bda)2](-) under the same conditions (glum < 0.01). On the basis of analysis of the iCPL intensities in the presence of 12 amino acids, [Eu(pda)2](-) was found to be a good chiral CPL probe with high sensitivity (about 10(-2) mol·dm(-3)) and high selectivity for L-histidine at pH 3 and for L-arginine at pH 7. The mechanism of iCPL was evaluated by analysis of the fine structures in the luminescence spectra and the amino acid concentration dependence of glum. For the [Eu(pda)2](-)-histidine/arginine systems, the europium(III) complexes possess coordination structures similar to that in the crystal with slight distortion to form a chiral structure due to specific interaction with two zwitterionic amino acids. This mechanism was in stark contrast to that of the europium(III) complex-pyrrolidonecarboxylic acid system in which one amino acid coordinates to the Eu(III) ion to yield an achiral coordination structure.

Direct observation of hole shift and characterization of spin states in radical ion pairs generated from photoinduced electron transfer of (phenothiazine)(n)-anthraquinone (n = 1, 3) dyads.

Photoinduced intramolecular electron transfer of dyad PTZ3-PTZ2-PTZ1-B-AQ consisting of phenothiazine trimer (PTZ3-PTZ2-PTZ1), bicyclo[2.2.2]octane (B), and anthraquinone (AQ) was investigated. After excitation (∼20 ps) of the AQ moiety in THF, a metastable radical ion pair (RIP) PTZ3-PTZ2-PTZ1(+)-B-AQ(-) appeared at ∼620 nm. From 500 ps to 6 ns the spectrum changed to a new absorption (∼950 nm), which was assigned to the hole-shifted stable RIP state PTZ3-PTZ2(+)-PTZ1-B-AQ(-). The time constant of the hole-shift process was determined to be 6.0 ns. The hole-shifted RIP state had a lifetime (τ) of 250 ns and was characterized by spin-polarized signals as a spin-correlated radical pair (SCRP) by means of time-resolved ESR. These results were compared with those for the phenothiazine monomer analog PTZ-B-AQ, which also produced the RIP state PTZ(+)-B-AQ(-) with τ = 1.9 µs. Time-resolved ESR showed an all emission signal pattern showing the triplet mechanism of PTZ-B-(3)AQ* → (3)[PTZ(+)-B-AQ(-)]. The origin of the difference in the lifetimes between the trimer and the monomer RIP states was discussed from various points of view, including free energy difference in the RIP states, reorganization energy difference in the charge recombination process, and the spin-state difference. Of these, the spin-state difference effect provided the most reasonable explanation.

A doubly alkynylpyrene-threaded [4]rotaxane that exhibits strong circularly polarized luminescence from the spatially restricted excimer.

The Sonogashira coupling of γ-CD-encapsulated alkynylpyrenes with terphenyl-type stopper molecules gave a doubly alkynylpyrene-threaded [4]rotaxane. The rotaxane showed only excimer emission, with a high fluorescence quantum yield of Φf =0.37, arising from the spatially restricted excimer within the cavity of the γ-CD. The excimer emission suffered little from self-quenching up to a concentration of 1.5×10(-5) M and was circularly polarized with a high glum  value of -1.5×10(-2) . The strong circularly polarized luminescence may result from the two stacked pyrenes existing in the rotaxane in an asymmetrically twisted manner.