D3h Symmetry Research Articles

Bare and ligand protected planar hexacoordinate silicon in SiSb3M3 + (M = Ca, Sr, Ba) clusters.

The occurrence of planar hexacoordination is very rare in main group elements. We report here a class of clusters containing a planar hexacoordinate silicon (phSi) atom with the formula SiSb3M3+ (M = Ca, Sr, Ba), which have D3h (1A1′) symmetry in their global minimum structure. The unique ability of heavier alkaline-earth atoms to use their vacant d atomic orbitals in bonding effectively stabilizes the peripheral ring and is responsible for covalent interaction with the Si center. Although the interaction between Si and Sb is significantly stronger than the Si–M one, sizable stabilization energies (−27.4 to −35.4 kcal mol−1) also originated from the combined electrostatic and covalent attraction between Si and M centers. The lighter homologues, SiE3M3+ (E = N, P, As; M = Ca, Sr, Ba) clusters, also possess similar D3h symmetric structures as the global minima. However, the repulsive electrostatic interaction between Si and M dominates over covalent attraction making the Si–M contacts repulsive in nature. Most interestingly, the planarity of the phSi core and the attractive nature of all the six contacts of phSi are maintained in N-heterocyclic carbene (NHC) and benzene (Bz) bound SiSb3M3(NHC)6+ and SiSb3M3(Bz)6+ (M = Ca, Sr, Ba) complexes. Therefore, bare and ligand-protected SiSb3M3+ clusters are suitable candidates for gas-phase detection and large-scale synthesis, respectively.

Energy Spectrum and Optical Absorption Spectrum of Fullerene C-=SUB=-26-=/SUB=- within the Hubbard Model

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 in the approximation of static fluctuations. 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. Keywords: Hubbard model, Green's functions, energy spectrum, nanosystems, fullerene C26.

Path-dependency of energy decomposition analysis & the elusive nature of bonding.

Here, we provide evidence of the path-dependency of the energy components of the energy decomposition analysis scheme, EDA, by studying a set of thirty-one closed-shell model systems with the D2h symmetry point group. For each system, we computed EDA components from nine different pathways and numerically showed that the relative magnitudes of the components differ substantially from one path to the other. Not surprisingly, yet unfortunately, the most significant variations in the relative magnitudes of the EDA components appear in the case of species with bonds within the grey zone of covalency and ionicity. We further discussed that the role of anions and their effect on arbitrary Pauli repulsion energy components affects the nature of bonding defined by EDA. The outcome variation by the selected partitioning scheme of EDA might bring arbitrariness when a careful comparison is overlooked.

Energy Spectrum and Optical Absorption Spectrum of exohedral Fullerene C-=SUB=-50-=/SUB=-Cl-=SUB=-10-=/SUB=- within the Hubbard Model

Energy spectra of fullerene C50 and exohedral fullerene C50Cl10 with the D5h symmetry groups have been obtained within the Hubbard model and static fluctuation approximation. The energy states have been classified using the methods of group theory, and the allowed transitions in the energy spectra of molecules C50 and C50Cl10 have been determined. On the basis of the energy spectrum of exohedral fullerene C50Cl10 is given an interpretation of experimentally observed optical absorption bands molecule C50Cl10. Keywords: Hubbard model, Green's functions, energy spectrum, fullerenes, nanosystems, fullerene C50, exohedral fullerene C50Cl10.

Modulation of the magnetic dynamics of pentagonal-bipyramidal Co(II) complexes by fine-tuning the coordination microenvironment.

Four air-stable mononuclear Co(II) complexes, with the formulas [Co(dapbh)(H2O)(CH3OH)] (1), [Co(Hdapbh)(N3)(CH3OH)]·(CH3OH) (2), [Co(H2aapbh)(CH3OH)2]·(NO3)2 (3) and [Co(H2bapbh)(H2O)(NO3)]·(NO3) (4), have been synthesized and structurally characterized by single crystal X-ray diffraction. In all of the complexes, the Co(II) centers constrained by the rigid pentadentate ligand H2LR with two protonable hydrogens adopt a heptacoordinated pentagonal-bipyramidal geometry. The combined analyses of magnetic data and ab initio calculations unveil large easy-plane magnetic anisotropies for these complexes (D = +37.338, +37.273, +41.138 and +41.139 cm-1 for 1-4, respectively), which indicate that the chemical alterations of the equatorial ligand and the ligand field strength in the axial positions synergistically fine-tune the magnitude of the D values. Magnetic investigations demonstrate the field-induced single-ion magnetic behavior in complexes 1, 2 and 4 with diverse energy barriers (Ueff) of 12.25 for 1, 44.15 for 2 and 48.72 K for 4, corresponding to the geometrical distortion of the heptacoordinated Co(II) ion. That is, the greatest deviation from the ideal D5h symmetry in 4 is responsible for the highest barrier.

Энергетический спектр и спектр оптического поглощения экзоэдрального фуллерена С-=SUB=-50-=/SUB=-Cl-=SUB=-10-=/SUB=- в модели Хаббарда

Energy spectra of fullerene C50 and exohedral fullerene С50Cl10 with the D5h symmetry groups have been obtained within the Hubbard model and static fluctuation approximation. The energy states have been classified using the methods of group theory, and the allowed transitions in the energy spectra of molecules C50 and С50Cl10 have been determined. On the basis of the energy spectrum of exohedral fullerene С50Cl10 is given an interpretation of experimentally observed optical absorption bands molecule С50Cl10.

Modular Synthesis of Tetraurea and Octaurea Macrocycles Encoded with Specific Monomer Sequences

Modular Synthesis of Tetraurea and Octaurea Macrocycles Encoded with Specific Monomer Sequences

Multiplicity, Parity and Angular Momentum of a Cooper Pair in Unconventional Superconductors of D4h Symmetry: Sr2RuO4 and Fe-Pnictide Materials

Sr2RuO4 and Fe-pnictide superconductors belong to the same point group symmetry D4h. Many experimental data confirm odd pairs in Sr2RuO4 and even pairs in Fe-pnictides, but opposite conclusions also exist. Recent NMR results of Pustogow et al., which revealed even Cooper pairs in Sr2RuO4, require reconsideration of symmetry treatment of its SOP (superconducting order parameter). In the present work making use of the Mackey–Bradley theorem on symmetrized squares, a group theoretical investigation of possible pairing states in D4h symmetry is performed. It is obtained for I4/mmm , i.e., space group of Sr2RuO4, that triplet pairs with even spatial parts are possible in kz direction and in points M and Y. For the two latter cases pairing of equivalent electrons with nonzero total momentum is proposed. In P4/nmm space group of Fe- pnictides in point M, even and odd pairs are possible for singlet and triplet cases. It it shown that even and odd chiral states with angular momentum projection m=±1 have nodes in vertical planes, but Eg is nodal , whereas Eu is nodeless in the basal plane. It is also shown that the widely accepted assertion that the parity of angular momentum value is directly connected with the spatial parity of a pair is not valid in a space-group approach to the wavefunction of a Cooper pair.

Periodoannulenes: A Generalized Annulene-within-an-Annulene Paradigm for Combined σ and π Ring Currents.

Periodoannulene molecules and ions CxIxq in planar geometry offer examples of systems with the potential for outer σ and inner π ring-current double aromaticity, given a sufficient overlap of tangential pσ-orbital manifolds on the large atoms of the outer cycle. Previous theoretical work indicated concentric diatropic currents in the dication C6I62+. Ab initio ipsocentric calculations support an account in terms of frontier-orbital selection rules for current contributions in C6I62+ (and radical C6I6+, implicated in recent experimental work on the oxidation of periodobenzene). A σ/π analogue of the annulene-within-an-annulene model is applied here to periodo systems based on cyclooctatetraene. Model species C8I8q with charges q = 0, +1, +2, +4, -2 and structures constrained to a planar D4h symmetry exhibit maps with all combinations of σ/π con- and counter-rotation, comprising global σ ring currents on the iodine perimeter and central π ring currents on the carbocycle. All can be rationalized by the separate application of the tropicity selection rules to the two subsystems, whether in singlet or triplet states.

Infrared Spectroscopy and Bonding of the B(NN)3+ and B2(NN)3,4+ Cation Complexes.

The boron-dinitrogen cation complexes B(NN)3+ and B2(NN)3,4+ are produced in the gas phase and are studied by infrared photodissociation spectroscopy in the N-N stretching vibrational frequency region. The geometric and electronic structures are determined by comparison of the experimental spectra with density functional theory calculations. The B(NN)3+ cation is characterized to have a closed-shell singlet ground state with planar D3h symmetry. The B2(NN)3+ cation is determined to have a B═B bonded (NN)2BBNN structure with C2v symmetry. Two isomers of the B2(NN)4+ cation contribute to the experimental spectrum. One is a N2-tagged complex involving a B2(NN)3+ core ion. Another one is a B-B bonded B2(NN)4+ complex with a planar D2h structure. Bonding analyses reveal that the B-NN interactions in these complexes come mainly from covalent orbital interactions, with the NN → B σ donation being stronger than the B → NN π back-donation.

Evaluation of photoluminescence and scintillation properties of Yb<sup>2+</sup>-doped SrCl<sub>2−</sub><i><sub>x</sub></i>Br<i><sub>x</sub></i> crystals

Photoluminescence and scintillation properties are reported for SrCl2−xBrx:Yb2+ (x = 0, 0.3, 1.4, 1.6, and 2.0) crystals grown by a self-seeding solidification method. SrCl2−xBrx have been reported to crystallize in some structural types with different local site symmetries depending on the Cl/Br ratio. Taking advantage of this property, we can control the crystal structure and the local Yb2+ site symmetry of SrCl2−xBrx:Yb2+ by changing the compositions and investigate the behaviors of the spin-allowed and spin-forbidden transitions dependent on the local site symmetry. For photoluminescence and scintillation, both spin-allowed and spin-forbidden Yb2+ 5d–4f transitions were observed for SrCl2:Yb2+ with local Oh symmetry and SrCl0.4Br1.6:Yb2+ and SrBr2:Yb2+ with local C4h symmetry, whereas only spin-forbidden Yb2+ 5d–4f transition was observed for SrCl1.7Br0.3:Yb2+ and SrCl0.6Br1.4:Yb2+ with local D2h symmetry. The spin-allowed transitions were observed in crystals with higher local site symmetry. Light yields of SrCl2−xBrx:Yb2+ (x = 0, 0.3, 1.4, 1.6, and 2.0) were (21000 to 71000) photons/MeV. Crystals with higher local site symmetry, which showed the spin-allowed transitions, had relatively high light yields. Among them, SrCl0.4Br1.6:Yb2+ showed a light yield of 71000 photons/MeV, which is higher than those of previously reported Yb2+-doped scintillators, for example, SrI2:Yb2+ (56000 photons/MeV) and CsBa2I5:Yb2+ (54000 photons/MeV).

Chirality and Relativistic Effects in Os3(CO)12.

The energy and structural parameters were obtained for all forms of the carbonyl complex of osmium Os3(CO)12 with D3h and D3 symmetries using density functional theory (DFT) methods. The calculations took into account various levels of relativistic effects, including those associated with nonconservation of spatial parity. It was shown that the ground state of Os3(CO)12 corresponds to the D3 symmetry and thus may be characterized either as left-twisted (D3S) or right-twisted (D3R). The D3S↔D3R transitions occur through the D3h transition state with an activation barrier of ~10–14 kJ/mol. Parity violation energy difference (PVED) between D3S and D3R states equals to ~5 × 10−10 kJ/mol. An unusual three-center exchange interaction was found inside the {Os3} fragment. It was found that the cooperative effects of the mutual influence of osmium atoms suppress the chirality of the electron system in the cluster.

Molecular Structure, Thermodynamic and Spectral Characteristics of Metal-Free and Nickel Complex of Tetrakis(1,2,5-thiadiazolo)porphyrazine.

The Knudsen effusion method with mass spectrometric control of the vapor composition was used to study the possibility of a congruent transition to the gas phase and to estimate the enthalpy of sublimation of metal-free tetrakis(1,2,5-thiadiazolo)porphyrazine and its nickel complex (H2TTDPz and NiTTDPz, respectively). The geometrical and electronic structure of H2TTDPz and NiTTDPz in ground and low-lying excited electronic states were determined by DFT calculations. The electronic structure of NiTTDPz was studied by the complete active space (CASSCF) method, following accounting dynamic correlation by multiconfigurational quasi-degenerate second-order perturbation theory (MCQDPT2). A geometrical structure of D2h and D4h symmetry was obtained for H2TTDPz and NiTTDPz, respectively. According to data obtained by the MCQDPT2 method, the nickel complex possesses the ground state 1A1g, and the wave function of the ground state has the form of a single determinant. Electronic absorption and vibrational (IR and resonance Raman) spectra of H2TTDPz and NiTTDPz were studied experimentally and simulated theoretically.

Stationary Points on Potential Energy Surface of Cyclic C3H3 with Coupled-Cluster Approaches and Density Functional Theory.

Cyclic C3H3 is the simplest cyclic hydrocarbon, but its configuration is complicated. The ground 2E″ state at the equilateral triangle geometry with D3h symmetry undergoes both Jahn-Teller (JT) distortion and pseudo-Jahn-Teller (PJT) distortion to structures with C3v, C2v, Cs, or C2 symmetry. Previous works using complete active space self-consistent field (CASSCF) or multiconfiguration SCF (MCSCF) differ on the characteristics of these structures. To clarify the characteristics of these stationary points on the potential energy surface (PES) of this radical, coupled-cluster methods CCSD, CCSD(T), and EOMEA/IP-CCSD as well as density functional theory are employed to calculate their geometries, harmonic frequencies, and relative energies. Deformations between these stationary points due to JT and PJT effects are analyzed in detail. Most of the results with these methods are consistent with each other, except for the b2 mode of the 2B1 state with C2v symmetry. CCSD and CCSD(T) provide an imaginary frequency for this vibrational mode, while it is calculated to be real with the other methods as well as with EOM-CCSDT-3. This may be related to unstable reference in CCSD and CCSD(T) calculations. On the other hand, most of the employed exchange-correlation functionals provide reliable results on the characteristics of these stationary points. Our results show that the 2A' state with Cs symmetry is the only minimum structure on the PES of cyclic C3H3. The 2A2 and 2B1 states of the C2v structure are second-order saddle points, while both the 2A state of the C2 structure and the 2A″ state of the Cs structure are transition states connecting the global minimum 2A' state.

Homogeneous-like Alkyne Selective Hydrogenation Catalyzed by Cationic Nickel Confined in Zeolite

The selective hydrogenation of alkynes to their corresponding alkenes is an important type of organic transformation, which is currently accomplished by modified palladium catalysts. Herein, we rep...

Vibrational Hamiltonian of Naphthalene (C10H8) Using Dynamical U(2) Lie Algebras

This article is the first to demonstrate the application of dynamical U(2) Lie algebras to model a vibrational Hamiltonian of naphthalene (C10H8), a prototype polycyclic aromatic hydrocarbon molecule containing a fused pair of benzene rings, in the gas phase having considerable astrophysical interest. A vibrational Hamiltonian that preserves the D2h symmetry of naphthalene is modeled using 19 coupled one-dimensional Morse oscillators to describe the eight C-H single bonds, the eleven C-C aromatic bonds, and their dynamic interactions, making use of the Casimir and Majorana operators. Results indicate that the dynamical U(2) Lie algebraic Hamiltonian has successfully reproduced the vibrational frequencies at the 48 fundamental excitations near to the level of spectroscopic accuracy, as well as predicted their first three overtones. The observed degeneracy of the stretching, bending, and combination vibrations at the fundamental and lower overtone excitations are expected to modify the shape of the two major bands (centered at 782 cm−1 and 3065 cm−1), and several minor bands in the infrared absorption spectrum of naphthalene in the gas phase.

Thiazolo[5,4‑d]thiazole linked conjugated microporous polymer photocatalysis for selective aerobic oxidation of amines

Recently, conjugated microporous polymers (CMPs) comprised of thiazolo[5,4-d]thiazole (TzTz) linkages have received much attention due to their excellent photoelectric properties. Herein, the polycondensation of dithiooxamide and benzyl aldehydes of C2, C3, and D2h symmetry afforded three TzTz-linked CMPs, namely TzTz-CMP-1, TzTz-CMP-2, and TzTz-CMP-3. Importantly, the porous and flexible characteristics of TzTz-linked CMPs enable the smooth selective aerobic oxidation of amines in ethanol (C2H5OH), a clean but redox-active solvent. All three TzTz-linked CMPs significantly surpass the benchmark mesoporous graphite carbonnitride (mpg-C3N4) photocatalyst. Intriguingly, TzTz-CMP-2 displays the best photocatalytic activity for the blue-light-mediated selective transformation of primary and secondary amines into imines. The conversions of amines were up to 90% with excellent selectivities for imines. This work highlights that CMPs with TzTz linkages may offer efficient photocatalytic selective transformations under genuinely ambient conditions.

Iron‐Iron Bond Lengths and Bond Orders in Diiron Lantern‐Type Complexes with High Spin Ground States

AbstractDiiron paddlewheel‐ or lantern‐type complexes comprise an interesting subclass of binuclear iron complexes, existing with digonal, trigonal, and tetragonal ligand arrays. Experimentally known members show Fe−Fe bonds of lengths ranging from 2.13 to 2.73 Å, with Fe−Fe bond orders ranging from 0.5 to 2. Truncated models for 30 experimentally characterized diiron paddlewheel‐type complexes have been studied by DFT using the M06‐L functional, reproducing the Fe−Fe bond lengths quite well. In addition, we use DFT to treat three series of model diiron complexes Fe2Lx (x=2, 3, 4) in various low‐lying spin states, L being the unsubstituted formamidinate, guanidinate, and formate ligands (along with a series of axially ligated formate complexes) in order to predict ground state spin multiplicities, Fe−Fe bond lengths, and features of the ligand arrays. The ground states all have high spin multiplicities (septets, octets, and nonets). Formal bond order (fBO) values are suggested for the Fe−Fe bonds in these 61 complexes using an electron bookkeeping procedure, in addition to the Fe−Fe bond orders obtained by metal‐metal MO analysis for ground state species. Fe−Fe bond orders up to 3 are noted in some excited states. Deviations from D3h and D4h symmetry are noted for many trigonal and tetragonal complexes, being attributed to inherent Jahn‐Teller distortions. The formamidinate and guanidinate series show many similarities, while the formate series differs from these two in several aspects. From these results, ranges are derived for Fe−Fe bond lengths of orders 0.5, 1.0, 1.5, 2.0, 2.5 and 3.0. The Fe−Fe bond length ranges for these non‐carbonyl lantern complexes are found to be appreciably lower than the corresponding ranges for diiron complexes with carbonyl ligands as compiled earlier from computational and experimental results.

Correction to Synthesis and Some Reactions of Hexaazatriphenylene Hexanitrile, a Hydrogen-Free Polyfunctional Heterocycle with D3h Symmetry

Correction to Synthesis and Some Reactions of Hexaazatriphenylene Hexanitrile, a Hydrogen-Free Polyfunctional Heterocycle with D3h Symmetry

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.