D3h Symmetry Research Articles

Spectroscopic study of the Eu3+ local symmetry in EuF3 crystal

We employed the simple overlap model (SOM) with the method of equivalent nearest neighbours (MENN) to indicate the local symmetry of the Eu3+ in the europium trifluoride (EuF3) compound through two analyses based on the emission spectra. In first situation, three lines were observed at the 5D0 → 7F1 (0-1) transition. Therefore, based on the amount of non-null crystal field parameters, we indicate that the Eu ion occupies a site with distorted inversion centre as a combination of C2 and C2h symmetries, with the following charge factors: g1 = 0.438, g2 = 0.292, g3 = 0.411, g4 = 0.201, g5 = 0.396 and g6 = 0.293. In second situation, with two lines at the 0-1 transition, we suggested the luminescent site as a combination of the D3d and D3h symmetries with g1 = 0.279 and g2 = 0.495. The 7F1 manifold splitting was obtained through Auzel-Malta equation. All theoretical calculations reproduced satisfactorily the 7F1, 7F2 and 5D1 energy sublevels in good agreement with experimentals data.

A Local D4h Symmetric Dysprosium(III) Single-Molecule Magnet with an Energy Barrier Exceeding 2000 K*.

Three six-coordinate DyIII single-molecule magnets (SMMs) [Dy(Ot Bu)2 (L)4 ]+ with local D4h symmetry are obtained by optimizing the equatorial ligands. One of the compounds with L=4-phenylpyridine shows an energy barrier (Ueff ) of 2075(11) K, which is the third largest Ueff , and the first Ueff >2000 K for SMMs with axial-type symmetry so far. Ab initio analysis indicates that the exceptional uniaxial magnetic anisotropy is deeply related to the axially compressed octahedral geometry. This work provides a new insight into the local D4h symmetry for high-performance SMMs.

Analyses of the excited 5f1 optical spectra of Th3+ compounds

The electronic structure of Th(Cp″)3 (Cp″ = η5-C5H3(SiMe3-1,3), a molecule which has a 6d1 ground configuration and an excited 5f1 configuration beginning approximately 14,000 cm−1 higher, is reexamined. The ground state of the 6d1 configuration in a crystal field of D3h symmetry is shown to be an orbitally quenched 2A1ʹ state, best described as a pure 2D1/2 state. Electric dipole selection rules from this state to the states for the 5f1 configuration in a D3h crystal field result in the 5f1 truncated optical spectrum observed. The optical spectrum of the square planar Th3+ compound [Li(THF)4][Th(OAr′)4], where (OAr′ = OC6 H2tBu2-2,6-Me-4), is discussed.

Anion Photoelectron Spectroscopy and Theoretical Studies of Al4C6-/0: Global Minimum Triangle-Shaped Structures and Hexacoordinated Aluminum.

Anion photoelectron spectroscopy and theoretical calculations were used to investigate the structural and bonding properties of Al4C6-/0 clusters. The vertical detachment energy of Al4C6- was measured to be 3.36 ± 0.08 eV. The structure of the Al4C6- anion is confirmed to be a bowl-shaped distorted triangle with an Al atom at the center and three Al atoms at the vertices. The global minimum isomer of neutral Al4C6 has a planar triangle-shaped structure with D3h symmetry. Both anionic and neutral Al4C6 have a hexacoordinated Al atom surrounded by three C≡C groups. Compared with the structure of neutral Al4C6, the structure of Al4C6- is distorted due to the addition of the excess electron. The molecular orbital analysis shows that the singly occupied molecular orbital of Al4C6- mainly locates on one side of the triangle plane and the neutral Al4C6 has a large highest occupied molecular orbital and lowest unoccupied molecular orbital gap. Theoretical calculations indicate that neutral Al4C6 has some aromaticity.

Coordination-driven self-assembly of anthraquinone-based metal-organic cages for photocatalytic selective [2 + 2] cycloaddition.

Visible-light-promoted [2 + 2] cycloaddition provides a straightforward and efficient way to produce cyclobutanes, which are the core skeleton in commercial pharmaceuticals and fine chemicals. However, the control of the conformation to produce syn-head-to-head (syn-HH) cyclobutanes remains a grand challenge. In this work, we report the design and synthesis of anthraquinone-based metal-organic cages (MOCs) for the [2 + 2] photocycloaddition of chalcones to generate syn-HH cyclobutanes. Guided by the coordination-driven self-assembly strategy, one D2 and three D4h symmetric MOCs are constructed from anthraquinone-derived dicarboxylate linkers and 4-tert-butylsulfonylcalixarene capped tetrametallic clusters. The porous cages feature large hydrophobic cavities and photoactive anthraquinone units and are demonstrated to be efficient and recyclable photocatalysts for [2 + 2] cycloaddition of chalcones. The syn-HH diastereomers are obtained with up to 13 : 1 diastereomeric ratio (dr). The cage catalysts provide a well-defined confined space to accommodate the substrates, thus leading to enhanced selectivity relative to the free anthraquinone catalyst.

Nanopatterns of molecular spoked wheels as giant homologues of benzene tricarboxylic acids.

Molecular spoked wheels with D3h and Cs symmetry are synthesized by Vollhardt trimerization of C2v-symmetric dumbbell structures with central acetylene units and subsequent intramolecular ring closure. Scanning tunneling microscopy of the D3h-symmetric species at the solid/liquid interface on graphite reveals triporous chiral honeycomb nanopatterns in which the alkoxy side chains dominate the packing over the carboxylic acid groups, which remain unpaired. In contrast, Cs-symmetric isomers partially allow for pairing of the carboxylic acids, which therefore act as a probe for the reduced alkoxy chain nanopattern stabilization. This observation also reflects the adsorbate substrate symmetry mismatch, which leads to an increase of nanopattern complexity and unexpected templating of alkoxy side chains along the graphite armchair directions. State-of-the-art GFN-FF calculations confirm the overall structure of this packing and attribute the unusual side-chain orientation to a steric constraint in a confined environment. These calculations go far beyond conventional simple space-filling models and are therefore particularly suitable for this special case of molecular packing.

Энергетический спектр и спектр оптического поглощения фуллерена C-=SUB=-26-=/SUB=- в модели Хаббарда

Anticommutator Green’s functions and energy spectra of fullerene C26 and endohedral fullerene U@C26 with the D3h symmetry groups have been obtained in an analytical form within the Hubbard model and static fluctuation ap-proximation. The energy states have been classified using the methods of group theory, and the allowed transitions in the energy spectra of molecules C26 and U@C26 with the D3h symmetry groups have been determined.

Electronic transitions of tetrathiafulvalene oriented in polyethylene film. Near and vacuum UV synchrotron radiation polarization spectroscopy

The electronic spectrum of tetrathiafulvalene (TTF) oriented in a polyethylene film is characterized experimentally using synchrotron radiation linear dichroism from the near-UV to the vacuum-UV region to 56,500 cm–1 (177 nm). The non-planar TTF molecule is shown to have electronic transitions of significant intensity polarized along all three molecular symmetry axes. A procedure for processing linear dichroic data to obtain partial absorbance curves representing different polarization directions is exemplified. The overlapping contributions to eight individual spectral features are furthermore interpreted by the aid of time-dependent density functional theory using CAM-B3LYP/6-311++G(3df,3pd) with geometry optimized at the B3LYP / 6-311++G(3df,3pd) level within the C2v point group. Additional calculations using larger basis sets as well as other long-range corrected functionals (LC-ωPBE and ωB97XD) yielded similar results. The planar conformer with D2h symmetry is also considered and it is discussed that rapid equilibration via this transition state may contribute to the diffuse nature of some features of the electronic spectrum. The TTF molecule is a dynamic and 3-dimensional chromophore, and these characteristics may serve as a basis for understanding the optical properties of the numerous TTF-based materials finding applications in supramolecular chemistry, molecular electronics and beyond.

Electrochemical Synthesis of Nanostructured Rhodium Deposits from Carbamide-Chloride Melts

It has been found by spectroscopy and electrochemical voltammetry that when rhodium is anodically dissolved in a carbamide-chloride melt, [Rh(NH3)4Cl2]+ complexes of D4h symmetry are formed, which are electroactive. The electrochemical behavior of rhodium in a carbamide-chloride melt under stationary and nonstationary electrolysis conditions has been studied. It has been found that the reduction of Rh(III) complexes at the cathode is controlled by the stage involving the formation of a passive film on anodic polarization.

Cluster structure of 20Ne: Evidence for [formula omitted] symmetry

We study the cluster structure of 20Ne and show that the available experimental data can be well described by a bi-pyramidal structure with D3h symmetry. Strong evidence for the occurrence of this symmetry comes from the observation of all nine expected vibrational modes (3 singly degenerate and 3 doubly degenerate) and of six (singly degenerate) double vibrational modes. 20Ne appears to be another example of the simplicity in complexity program, in which simple spectroscopic features arise out of a complex many-body system.

Synthesis and crystal structures of novel alkali rare-earth orthoborates K3RE3(BO3)4 (RE = Pr, Nd, Sm–Lu)

We report a series of novel alkali rare-earth orthoborates K3RE3(BO3)4 (RE = Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb and Lu) prepared by high-temperature solid-state syntheses. Single crystals of K3Pr3(BO3)4, K3Er3(BO3)4, K3Tm3(BO3)4, K3Yb3(BO3)4 and K3Lu3(BO3)4 are obtained by spontaneous crystallization using a flux. Complementary single-crystal and powder X-ray diffraction measurements followed by structure refinements reveal that both Pr- and Nd-containing phases crystallize in the space group P $$\overline{1}$$ (Z = 4), whereas the other K3RE3(BO3)4 members with higher atomic number (RE = Sm–Lu) crystallize in the higher symmetry space group P21/c (Z = 8). Amid differences in the space groups, each member of the series keeps close structural correlations in their motif and connectivity. The crystal structures of K3RE3(BO3)4 (RE = Sm–Lu) consist of quasi-two-dimensional [RE8(BO3)8] layers parallel to the ab-plane which are connected by out-of-layer RE2O12 and RE2O14 dimers as well as BO3 groups in the c-direction, forming a 3D framework. On the other hand, both K3Pr3(BO3)4 and K3Nd3(BO3)4 phases are comprised of the [RE4(BO3)4] layers, indicating the absence of 21 screw axis along the b-axis. The K+ cations are located between the [RE8(BO3)8] and [RE4(BO3)4] layers, occupying the interstitial voids. All samples exhibit characteristic absorption features in the UV/Vis range relevant to the rare-earth cations, and their optical band gaps are evaluated by both conventional Tauc plot and derivation of absorption spectrum fitting (DASF) methods. The geometric deviations away from the D3h symmetry of the BO3 planar groups are verified using Fourier transformed infrared and Raman spectra, and supported by the X-ray diffraction results.

Synthesis and Properties of a Cyclohexa‐2,7‐anthrylene Ethynylene Derivative

AbstractThe synthesis of a cyclohexa‐2,7‐(4,5‐diaryl)anthrylene ethynylene (1) was achieved for the first time by using 1,8‐diaryl‐3,6‐diborylanthracene and 1,8‐diaryl‐3,6‐diiodoanthracene as key synthetic intermediates. Macrocycle 1 possesses a planar conformation of approximately D6h symmetry, because of the triple‐bond linker between the anthracene units at the 2,7‐positions. It was confirmed that macrocycle 1, bearing bulky substituents at the outer peripheral positions, behaves as a monomeric form in solution without π‐stacking self‐association. Macrocycle 1 has an inner‐cavity size that allows specific inclusion of [9]cycloparaphenylene ([9]CPP), but not [8]CPP or [10]CPP, through an aromatic edge‐to‐face CH‐π interaction.

Synthesis and Properties of a Cyclohexa-2,7-anthrylene Ethynylene Derivative.

The synthesis of a cyclohexa-2,7-(4,5-diaryl)anthrylene ethynylene (1) was achieved for the first time by using 1,8-diaryl-3,6-diborylanthracene and 1,8-diaryl-3,6-diiodoanthracene as key synthetic intermediates. Macrocycle 1 possesses a planar conformation of approximately D6h symmetry, because of the triple-bond linker between the anthracene units at the 2,7-positions. It was confirmed that macrocycle 1, bearing bulky substituents at the outer peripheral positions, behaves as a monomeric form in solution without π-stacking self-association. Macrocycle 1 has an inner-cavity size that allows specific inclusion of [9]cycloparaphenylene ([9]CPP), but not [8]CPP or [10]CPP, through an aromatic edge-to-face CH-π interaction.

Computational simulation and crystal field analysis of the Eu3+-doped LiF

The local symmetry of the Eu3+ was obtained through atomistic simulation and crystal field models applied to lanthanides. Structural properties such as lattice parameters and unit cell volume were reproduced using a set of empirical interatomic potentials with good accuracy. The LiF Anti-Schottky intrinsic defect was most favourable energetically. The solution energy obtained by bound extrinsic defects showed that the Eu3+ prefers the Li+ site compensated by lithium vacancy. Spectroscopic calculations revealed that the europium occupies a luminescent site with distorted inversion centre. A slightly distorted D4h symmetry is most favourable with the charge factors: g1 = 0.629, g2 = 0.738, g3 = 0.627 and g4 = 0.625, which reproduced satisfactorily the 7F1 manifold splitting and the 7F1, 7F2 and 5D1 energy sublevels.

Infrared spectroscopy and anharmonic theory of H3 +Ar2,3 complexes: The role of symmetry in solvation.

The vibrational spectra of H3 +Ar2,3 and D3 +Ar2,3 are investigated in the 2000 cm-1 to 4500 cm-1 region through a combination of mass-selected infrared laser photodissociation spectroscopy and computational work including the effects of anharmonicity. In the reduced symmetry of the di-argon complex, vibrational activity is detected in the regions of both the symmetric and antisymmetric hydrogen stretching modes of H3 +. The tri-argon complex restores the D3h symmetry of the H3 + ion, with a concomitant reduction in the vibrational activity that is limited to the region of the antisymmetric stretch. Throughout these spectra, additional bands are detected beyond those predicted with harmonic vibrational theory. Anharmonic theory is able to reproduce some of the additional bands, with varying degrees of success.

Synthesis of 1,8,13-Substituted Triptycenes

Abstract Triptycene is an aromatic compound with D3h symmetry, where three benzene rings are fused to a bicyclo[2.2.2]octatriene skeleton. 1,8,13-Substituted triptycenes exhibit interesting structural features: the C-1,8,13 substituents and the bridgehead C-9 position are located in the same plane. Three faces of the molecule are open for interesting interactions and applications. This paper summarizes the syntheses of 1,8,13-substituted triptycenes.

A Series of Discrete Dichloride Dihydrates: Characterisation and Symmetry Effects.

A series of three discrete dichloride dihydrates [Cl2 (H2 O)2 ]2- have been isolated with different triaminocyclopropenium (TAC) cations and with different crystallographic symmetries. The cluster exhibits D2h symmetry with the tris(dimethylamino)cyclopropenium cation [C3 (NMe2 )3 ]+ , C2h symmetry with the fluorinated cation [C3 (N(CH2 CF3 )2 )(NBu2 )2 ]+ (containing two 2,2,2-trifluoroethyl substituents) and C2v symmetry with the more fluorinated [C3 (N(CH2 CF3 )2 )2 (NBu2 )]+ cation. The effect of symmetry on the infrared spectra of the dichloride ion-pair clusters, as well as deuterated analogues, has been investigated. The D2h - and C2h -symmetric clusters each exhibit two stretching bands in the infrared at 3427 and 3368 cm-1 for D2h symmetry and 3444 and 3392 cm-1 for C2h symmetry, whereas the C2v -symmetric cluster exhibits three bands at 3475, 3426 and 3373 cm-1 . Computational studies were carried out on a [Cl2 (H2 O)2 ]2- cluster with C2v symmetry to aid the infrared band assignments.

Use of symmetry groups for generation of complex space grids and group-theoretic vibration analysis of triple-layer grids

Space grids often exhibit a highly regular structure which is formed by repeated structural units. In the past, various algorithms have been developed to generate more complex structural assemblies using simple commands. In this paper, we explore the innovative use of symmetry groups to create various configurations of space grids, ranging from rectangular grids and their variants, to triangular and hexagonal grids, as well as grid forms of more complex shape. The advantage of this approach is that the generated space grid has pre-determined symmetry properties; this represents a shift in current design philosophy. A second objective is to show how group theory may be used to simplify the vibration analysis of layered space grids. The procedure is applied to the transverse vibrations of triple-layer space grids of D2h and D4h symmetries, modelled as discrete-parameter systems. A study of the symmetry of subspace basis vectors allows some important predictions to be made on the pattern of the motions and the location of stationary nodes. It is found that the lowest and highest frequencies of space grids of this type occur in the first subspace of the system, a finding that has significant computational importance.

Analysis of Magnetoacoustic Quadrupole Resonance and Application to Probe Quadrupole Degrees of Freedom in Quantum Magnets

Motivated by the recent progress of high-frequency ultrasonic measurements, we propose a theory of magnetoacoustic resonance as a microscopic probe for quadrupole degrees of freedom hidden in magnetic materials. A local strain driven by an acoustic wave couples to electronic states of a magnetic ion through various quadrupole-strain couplings, and this provides a periodically time-dependent oscillating field. As a typical two-level system with the quadrupole, we consider a non-Kramers doublet and investigate single- and multiphonon-mediated transition processes on the basis of the Floquet theory. An analytic form of the transition probability is derived within the weak coupling theory, which helps us analyze the magnetoacoustic quadrupole resonance. We apply the theory to realistic non-Kramers doublet systems for the f2 configuration in Oh and D4h symmetries, and discuss how to identify the relevant quadrupole by controlling the quadrupole-strain coupling with an applied magnetic field in ultrasonic measurements.

Theoretical studies on dihedral angle-bending isomers of M2Pt20/− clusters

The structures and electronic properties of the gaseous M2Pt20/− clusters (M represents the alkaline earth metal) were investigated using the density functional theory (B3LYP and PBE0) and wave function theory (SCS-MP2, CCSD and CCSD (T)). The results indicate that the D2h isomers with the planar structures are more stable than the C2v isomers with smaller dihedral angles and shorter Pt-Pt bond lengths. The mutual competition of M(s,p)-Pt(5d) interaction and Pt-Pt covalent bonding contributes to the different stabilizations of the two kinds of isomers. The M(s,p)-Pt(5d) interaction favors the planar isomers with D2h symmetry, while the Pt-Pt covalent bonding leads to the C2v isomers with bending structures. Two different crossing points are determined in the potential energy curves of Be2Pt2 with the singlet and triplet states. But there is just one crossing point in potential energy curves of Ra2Pt2 and Ca2Pt2− because of flatter potential energy curves of Ra2Pt2 with the triplet state or Ca2Pt2− with quartet state. The results reveal a unique example of dihedral angle-bending isomers with the smallest number of atoms and may help the understanding of the bonding properties of other potential angle-bending isomers.