C2v Symmetry Research Articles

Exploring the methane combustion reaction: A theoretical contribution**Project supported by the National Natural Science Foundation of China (Grant Nos. 51574016 and 51604018).

This paper represents an attempt to extend the mechanisms of reactions and kinetics of a methane combustion reaction. Three saddle points (SPs) are identified in the reaction using the complete active space self-consistent field and the multireference configuration interaction methods with a proper active space. Our calculations give a fairly accurate description of the regions around the twin first-order SPs (3A′ and 3A″) along the direction of O(3P) attacking a near-collinear H–CH3. One second-order SP2nd (3E) between the above twin SPs is the result of the C3v symmetry Jahn–Teller coupling within the branching space. Further kinetic calculations are performed with the canonical unified statistical theory method with the temperature ranging from 298 K to 1000 K. The rate constants are also reported. The present work reveals the reaction mechanism of hydrogen-abstraction by the O(3P) from methane, and develops a better understanding for the role of SPs. In addition, a comparison of the reactions of O(3P) with methane through different channels allows a molecule-level discussion of the reactivity and mechanism of the title reaction.

Investigation of magneto-structural correlation based on a series of seven-coordinated β-diketone Dy(iii) single-ion magnets with C2v and C3v local symmetry.

A series of four β-diketone mononuclear Dy(iii) complexes, namely Dy(Hthd)3(MeOH)·2,5-Py (1), Dy(Hthd)3(Tppo) (2), Dy(Hthd)3(PyNO) (3), and Dy(Hthd)3(4-PyNO) (4) (Hthd = 2,2,6,6-tetramethyl-3,5-heptanedione, 2,5-Py = 2,5-pyridine, Tppo = triphenylphosphine oxide, PyNO = pyridine N-oxide, 4-PyNO = 4-methylpyridine N-oxide), have been isolated by reactions of Hthd, DyCl3·6H2O and an auxiliary ligand. X-ray crystallographic analysis revealed that complexes 1-4 are all seven-coordinated mononuclear structures with C2v or C3v local symmetry. The magnetic measurements of complexes 1-4 revealed their field-induced single-ion magnet (SIM) behavior, due to mixed low-lying states. The crystal field parameters and orientations of the magnetic easy axes were obtained from simulations of the DC magnetic data and an electrostatic model calculation. The magneto-structural correlation of seven-coordinated Dy(iii) SIMs with low-symmetry coordination environments was further discussed.

Polarization and structure dependent optical characteristics of the three-arm nanoantenna with C3v symmetry and broken symmetry

The optical properties of a three-arm plasmonic nanoantenna with and without broken symmetry were analyzed in detail. For the symmetrical structure, the local electric field can be significantly enhanced and well confined within the feed gap, whilst the extinction spectrum illustrates polarization independence. With broken symmetry, multi-wavelength resonances are observed due to the single dipole resonance and dipole–dipole coupling effect, and wide tunability is also available through minor structural adjustment. Especially when illuminated by a circularly polarized light beam, the extinction and the electric field distribution can be effectively modulated by just varying the incident wavelength.

The bismuth tetramer Bi4: the ν3 key to experimental observation.

The spectroscopic identification of Bi4 has been very elusive. Two constitutional Bi4 isomers of Td and C2v symmetry are investigated and each is found to be a local energetic minimum. The optimized geometries and vibrational frequencies of these two isomers are obtained at the CCSD(T)/cc-pVQZ-PP level of theory, utilizing the Stoll, Metz, and Dolg 60-electron effective core potential. The fundamental frequencies of the Td isomer are obtained at the same level of theory. The focal point analysis method, from a maximum basis set of cc-pV5Z-PP, and proceeding to a maximum correlation method of CCSDTQ, was employed to determine the dissociation energy of Bi4 (Td) into two Bi2 and the adiabatic energy difference between the C2v and Td isomers of Bi4. These quantities are predicted to be +65 kcal mol-1 and +39 kcal mol-1, respectively. Two electron vertical excitation energies between the Td and C2v electronic configurations are computed to be 156 kcal mol-1 for the Td isomer and 9 kcal mol-1 for the C2v isomer. The most probable approach to laboratory spectroscopic identification of Bi4 is via an infrared spectrum. The predicted fundamentals (cm-1) with harmonic IR intensities in parentheses (km mol-1) are 94(0), 123(0.23), and 167(0) for the Td isomer. The moderate IR intensity for the only allowed fundamental may explain why Bi4 has yet to be observed. Through natural bond orbital analysis, the C2v isomer of Bi4 was discovered to exhibit "long-bonding" between the furthest apart 'wing' atoms. This long-bonding is postulated to be facilitated by the σ-bonding orbital between the 'spine' atoms of the C2v isomer.

A design strategy for the construction of 2D heteropore covalent organic frameworks based on the combination of C2v and D3h symmetric building blocks

A strategy to construct heteropore covalent organic frameworks has been developed based on a desymmetrization design which takes advantage of the combination of C2v and D3h symmetries.

An ab Initio Exploration of the Bergman Cyclization.

The Bergman cyclization is an important reaction in which an enediyne cyclizes to produce a highly reactive diradical species, p-benzyne. Enediyne motifs are found in natural antitumor antibiotic compounds, such as calicheammicin and dynemicin. Understanding the energetics of cyclization is required to better control the initiation of the cyclization, which induces cell death. We computed the singlet and triplet potential energy surfaces for the Bergman cyclization of (Z)-hex-3-ene-1,5-diyne using the CCSD and EOM-SF-CCSD methods. The triplet enediyne and transition state were found to have C2 symmetry, which contrasts with the singlet reactant and transition state that possess C2v symmetry. We analyzed the frontier orbitals of both cyclization pathways to explain the large energetic barrier of the triplet cyclization. Reaction energies were calculated using CCSD(T)/cc-pVTZ single-point calculations on structures optimized with CCSD/cc-pVDZ. The singlet reaction was found to be slightly endothermic (ΔHrxn = 13.76 kcal/mol) and the triplet reaction was found to be highly exothermic (ΔHrxn = -33.29 kcal/mol). The adiabatic singlet-triplet gap of p-benzyne, computed with EOM-SF-CCSD/cc-pVTZ, was found to be 3.56 kcal/mol, indicating a singlet ground state.

Synthesis, Crystal Structure, and Chemical-Bonding Analysis of BaZn(NCN)2

The ternary carbodiimide BaZn(NCN)2 was prepared by a solid-state metathesis reaction between BaF2, ZnF2, and Li2NCN in a 1:1:2 molar ratio, and its crystal structure was determined from Rietveld refinement of X-ray data. BaZn(NCN)2 represents the aristotype of the LiBa2Al(NCN)4 structure which is unique to carbodiimide/cyanamide chemistry and is well regarded as being constructed from ZnN4 tetrahedra, sharing edges and vertices through NCN2− units to form corrugated layers with Ba2+ in the interlayer voids. Structural anomalies in the shape of the cyanamide units are addressed via IR spectrometry and DFT calculations, which suggest the presence of slightly bent N=C=N2− carbodiimide units with C2v symmetry. Moreover, chemical-bonding analysis within the framework of crystal orbital Hamilton population (COHP) reveals striking similarities between the bonding interactions in BaZn(NCN)2 and SrZn(NCN)2 despite their contrasting crystal structures. BaZn(NCN)2 is only the second example of a ternary post-transition metal carbodiimide, and its realization paves the way for the preparation of analogues featuring divalent transition metals at the tetrahedral Zn2+ site.

Molecular geometries and other properties of H2O⋯AgI and H3N⋯AgI as characterised by rotational spectroscopy and ab initio calculations.

The rotational spectra of H3N⋯AgI and H2O⋯AgI have been recorded between 6.5 and 18.5 GHz by chirped-pulse Fourier-transform microwave spectroscopy. The complexes were generated through laser vaporisation of a solid target of silver or silver iodide in the presence of an argon gas pulse containing a low concentration of the Lewis base. The gaseous sample subsequently undergoes supersonic expansion which results in cooling of rotational and vibrational motions such that weakly bound complexes can form within the expanding gas jet. Spectroscopic parameters have been determined for eight isotopologues of H3N⋯AgI and six isotopologues of H2O⋯AgI. Rotational constants, B0; centrifugal distortion constants, DJ, DJK or ΔJ, ΔJK; and the nuclear quadrupole coupling constants, χaa(I) and χbb(I) - χcc(I) are reported. H3N⋯AgI is shown to adopt a geometry that has C3v symmetry. The geometry of H2O⋯AgI is Cs at equilibrium but with a low barrier to inversion such that the vibrational wavefunction for the v = 0 state has C2v symmetry. Trends in the nuclear quadrupole coupling constant of the iodine nucleus, χaa(I), of L⋯AgI complexes are examined, where L is varied across the series (L = Ar, H3N, H2O, H2S, H3P, or CO). The results of experiments are reported alongside those of ab initio calculations at the CCSD(T)(F12*)/AVXZ level (X = T, Q).

Crystallographic properties and electronic structure of V-doped AlN films that absorb near ultraviolet-visible-infrared light

For highly efficient photoconversion devices, 3d-transition-metal-doped AlN is a candidate intermediate-band material. Here, we synthesized and investigated V-doped AlN (AlVN; V ≤ 11%) films. The optical absorption spectra of the films showed characteristic features including a peak in the infrared region and shoulders in the visible light region. These features remained essentially unchanged for the various V concentrations. X-ray diffraction (XRD), transmission electron microscopy (TEM), and V K-edge X-ray absorption fine structure (XAFS) measurements were carried out to clarify the crystallographic origin of the optical absorption features. The XRD profiles revealed that all films had a c-axis-oriented wurtzite structure. The TEM analyses supported the XRD results. The V K-edge X-ray absorption near-edge structure indicated that the V atoms in the AlN lattice were surrounded by N atoms with non-centrosymmetric conditions and had an oxidation state close to 3+. Extended XAFS (EXAFS) analyses implied that the V atoms had C3v symmetry. The results of ab initio lattice relaxation calculations for a model wurtzite structure of an Al35V1N36 supercell were consistent with the EXAFS data. Electronic structure calculations using this model showed that additional energy bands, mainly consisting of V d states, were formed in the band gap of AlN, and the Fermi level was between the additional bands. Hence, in the optical absorption spectra, the peak was explained by d-d transitions partially allowed thorough hybridization with the p component, and the shoulders were attributed to transitions from the valence band to the new bands in the band gap of AlN.

Spectra of optical absorption and energy levels diagram of Er3+ ions in bulk crystals of aluminum nitride

The absorption spectra of the Er3+ ions embedded in the AlN matrix have been investigated. The admixture of erbium was introduced in bulk AlN crystals by diffusion. The absorption lines, which are associated with the intraconfigurational electronic f–f-transitions from the ground 4 I 15/2-state to the levels of ion Er3+ excited states have been observed in the spectral range of 370–700 nm. The transitions to the state levels 4 F 9/2, 2 H 11/2, 4 F 7/2, 4 F 5/2, 2 H 9/2, and 4 G 11/2 have been investigated in detail at the temperature T = 2 K. The number of the observed lines for these transitions coincides with the theoretically possible one for the electronic f–f-transitions in the ions Er3+, which are in the crystal field with the symmetry below cubic. The narrowness of the observed lines and their number convincingly testify the replacement of preferably one regular crystalline position by erbium ions. The implementation of Er3+ in the Al3+ position with the local symmetry C 3v appears the most probable. The energy positions of the levels of excited states for the investigated transitions have been determined. The diagram of the Er3+ ion energy levels in the AlN crystals has been built.

Insights on the vibration characteristics of double-layer cable nets of D4h symmetry

Coupling shallow cable nets into multi-layer configurations offers the possibility of altering the vibration properties of single-layer systems in a beneficial way. When members of appropriate stiffness and damping characteristics are employed as coupling devices, there will be a dynamic interaction between the motions of the layers, with the combined system expected to exhibit a higher stiffness and damping response than the individual layers. Vertical coupling of two identical single-layer cable nets of C4v symmetry results in a double-layer configuration of D4h symmetry, the vertical motions of which are strongly influenced by the symmetry properties of the configuration as well as the stiffness and damping properties of the coupling members. By considering a 32-node double-layer cable net as a case study, the present investigation employs group theory to reveal important insights on the vibration characteristics of cable nets of the type in question, at the same time laying out a computational framework for an efficient vibration analysis of such systems.

MRMP2, CCSD(T), and DFT Calculations of the Isomerization Barriers for the Disrotatory and Conrotatory Isomerizations of 3-Aza-3-ium-dihydrobenzvalene, 3,4-Diaza-3-ium-dihydrobenzvalene, and 3,4-Diaza-diium-dihydrobenzvalene.

The isomerizations of 3-aza-3-ium-dihydrobenzvalene, 3,4-diaza-3-ium-dihydrobenzvalene, and 3,4-diaza-diium-dihydrobenzvalene to their respective cyclic-diene products were studied using electronic structure methods with a multiconfigurational wave function and several single reference methods. Transition states for both the allowed (conrotatory) and forbidden (disrotatory) pathways were located. The conrotatory pathways of each structure all proceed through a cyclic intermediate with a trans double bond in the ring: this trans double bond destroys the aromatic stabilization of the π electrons due to poor orbital overlap between the cis and trans π bonds. The 3,4-diaza-3-ium-dihydrobenzvalene structure has C1 symmetry, and there are four separate allowed and forbidden pathways for this structure. The 3-aza-3-ium-dihydrobenzvalene structure is Cs symmetric, and there are two separate allowed and forbidden pathways for this structure. For 3,4-diaza-3,4-diium-dihydrobenzvalene, there was a single allowed and single forbidden pathway due to the C2v symmetry. The separation of the barrier heights for all three molecules was studied, and we found the difference in activation barriers for the lowest allowed and lowest forbidden pathways in 3,4-diaza-3-ium-dihydrobenzvalene, 3-aza-3-ium-dihydrobenzvalene, and 3,4-diaza-diium-dihydrobenzvalene to be 9.1, 7.4, and 3.7 kcal/mol, respectively. The allowed and forbidden barriers of 3,4-diaza-diium-dihydrobenzvalene were separated by 3.7 kcal/mol, which is considerably less than the 12-15 kcal/mol expected based on the orbital symmetry rules. The addition of the secondary ammonium group tends to shift the conrotatory and disrotatory barriers up in energy (∼12-14 kcal/mol (conrotatory) and 5-10 kcal/mol (disrotatory) per secondary NH2 group) relative to the barriers of dihydrobenzvalene, but there is negligible effect on E,Z to Z,Z isomerization barriers, which remain in the expected range of greater than 4 kcal/mol.

Spectrally Tunable Optical Transmission of Titanium Nitride Split Ring Resonators

In this paper, the optical properties of titanium nitride split ring resonators as an intermetallic metamaterial nanostructure were studied. Our simulation shows the presence of plasmon and LC resonances in the transmission spectrum of a cell consists of four u-shape split ring resonators. The effect of different parameters of resonator such as size, periodic constant, and the material between arms in addition to the polarization of incident beam was examined on the resonance behavior of the system. Also, the optical properties of a cell consist of four complementary split ring resonators within titanium nitride thin film were investigated. An excited mode was observed at λ = 840 nm that was attributed to the plasmon resonance. Changing the arrangement and configuration of the system from C 1v to C 2v symmetry led to the presence of the LC mode beside the plasmon mode in the transmission spectrum. Also, we explored a connection between the complementary split ring resonators and orderly perforated surface plasmon systems. It was determined that a transition occurred from resonator-type to surface plasmon behavior by increasing the size of resonator above 170 nm.

Molecular structures of cobalt complexes of 2-aza-2-[p-methylbenzyl]-5,10,15,20-tetraphenyl-21-carbaporphyrin: [Co(2-NCH2-p-C6H4CH3-21-m-CH2C6H4CH3NCTPP)L] (L = Cl−, N*CS−)

Two experimentally well characterized four-coordinate complexes of the general formula [Co(2-NCH2-p-C6H4CH3-21-m-CH2C6H4CH3NCTPP)L] (with L = Cl− and N*CS− for 3 and 4) are considered for this study. The crystal structures of the paramagnetic chloro(2-aza-2-[p-methyl benzyl]-5,10,15,20-tetraphenyl-21-m-xylyl-21-carbaporphyrinato-N,N′,N″) cobalt(II) octane solvate [Co(2-NCH2-p-C6H4CH3-21-m-CH2C6H4CH3NCTPP)Cl]·0.5C8H18 (3·0.5 C8H18) and thiocyanato-N-(2-aza-2-[p-methylbenzyl]-5,10,15,20-tetraphenyl-21-m-xylyl-21-carbaporphyrinato-N,N′,N″) cobalt(II) [Co(2-NCH2-p-C6H4CH3-21-m-CH2C6H4CH3NCTPP)(NCS)] (4) were established. The geometry around the Co2+ ion in 3·0.5 C8H18 (or 4) is a distorted tetrahedron, with C2v symmetry. The magnitude of the zero-field splitting (ZFS) parameter (D) was reported to change from 44.5 cm−1 in 3 to 30.0 cm−1 in 4 through DC magnetic susceptibility determinations. The |D| value can be related to the magnitude of the ligand-field splitting parameter of the axial k-donating Cl− ligand of 3 and the axial π-accepting NCS− ligand of 4 at the cobalt sites.

Cyclotron resonance features in a three-dimensional topological insulators

The specific features of the cyclotron resonance in topological insulators of the Bi2Te3 family are analyzed. The energy spectrum of electron excitation on the surface of these compounds in a magnetic field has the C3V symmetry. With the use of quasiclassical equations of motion, which take into account the Berry curvature and magnetic moment, it is found that the cyclotron frequency spectrum contains additional harmonics due to spectrum anisotropy. An analysis of these harmonics makes it possible to reveal the contribution from the topological characteristics to the observables.

The Intermetalloid Cluster Cation (CuBi8 )3.

The reaction of Bi, BiCl3 , and CuCl in the ionic liquid [BMIm]Cl⋅4 AlCl3 (BMIm=1-n-butyl-3-methylimidazolium) at 180 °C yielded air-sensitive shiny black crystals of (CuBi8 )[AlCl4 ]2 [Al2 Cl7 ] and (CuBi8 )[AlCl4 ]3 . For both compounds X-ray diffraction on single crystals revealed monoclinic structures that contain the intermetalloid cluster (CuBi8 )3+ . It is the first pure bismuth cluster with a 3d metal and the first with a metal that does not form binary intermetallics with bismuth under ambient pressure. The cluster can be interpreted either as a copper(I) cation, η4 -coordinated by a square-antiprismatic Bi82+ polycation (Bi-Cu 267 pm), or as a nine-atomic intermetalloid nido-cluster with 22 skeletal electrons and the C4v symmetry. One of the chloride ions of a tetrahedral [AlCl4 ]- group coordinates the copper atom (Cu-Cl 228 pm) and thereby completes its 18 electron count. DFT-based calculations, followed by real-space bonding analysis, revealed a multicenter bonding situation between copper and bismuth atoms with about seven shared electrons.

Preparation and emission study of divalent samarium formed in air fired samples of Sm:Ba2B10O17

Trivalent samarium has been found to be reduced to the divalent state during the air firing process of the preparation of 5% Sm:Ba2B10O15. This is the first time that the formation of divalent samarium has been reported as a function of the preparation of this material. The product was prepared from a co-precipitated borate which was fired at 750°C with an additional 30% boric acid. The resulting product was confirmed by x-ray analysis and exhibited only divalent samarium emission. Based upon the observed emission, the primary samarium site can be assigned a site symmetry of C2v. The emitting samarium ion appears to occupy a tetrahedral boron site in this material.

Infrared Spectroscopic and Theoretical Studies on the OMF2 and OMF (M = Cr, Mo, W) Molecules in Solid Argon

Group 6 metal oxide fluoride molecules in the form of OMF2 and OMF (M = Cr, Mo, W) were prepared via the reactions of laser-ablated metal atoms and OF2 in excess argon. Product identifications were performed by using infrared spectroscopy, 18OF2 samples, and electronic structure calculations. Reactions of group 6 metal atoms and OF2 resulted in the formation of ternary OCrF2, OMoF2, and OWF2 molecules with C2v symmetry in which the tetravalent metal center is coordinated by one oxygen and two fluorine atoms. Both OCrF2 and OMoF2 are computed to possess triplet ground states, and a closed shell singlet is the ground state for OWF2. Triatomic OCrF, OMoF, and OWF molecules were also observed during sample deposition. All three molecules were computed to have a bent geometry and quartet ground state. A bonding analysis showed that the OMF2 molecules have highly ionic M-F bonds. 3OCrF2 and 3OMoF2 have an M-O double bond composed of a σ bond and a π bond. 1OWF2 has an M-O triple bond consisting of a σ bond, a π bond, and a highly delocalized O lone pair forming the other π bond. The M-O bonds in the OMF compounds have triple-bond character for all three metals.

The phase-field modeling of the self-organized phase growth with three-fold symmetry

The formation of self-organized domain patterns during polarization reversal in highly non-equilibrium switching conditions was studied by us earlier in the single crystals of lithium niobate and lithium tantalate. In this paper, we used the phase-field simulation to verify the analogy between self-organized growth of domains and new phase during the first order phase transition. The crystal symmetry C3v was taken into account. The similarity of simulated and experimentally observed shapes of isolated domains was achieved.

Geometric dependence of strong field enhanced ionization in D2O.

We have studied strong-field enhanced dissociative ionization of D2O in 40 fs, 800 nm laser pulses with focused intensities of <1-3 × 1015W/cm2 by resolving the charged fragment momenta with respect to the laser polarization. We that observe dication dissociation into OD+/D+ dominates when the polarization is out of the plane of the molecule, whereas trication dissociation into O+/D+/D+ is strongly dominant when the polarization is aligned along the D-D axis. Dication dissociation into O/D+/D+ and O+/D2+ is not seen nor is there any significant fragmentation into multiple ions when the laser is polarized along the C2v symmetry axis of the molecule. Even below the saturation intensity for OD+/D+, the O+/D+/D+ channel has higher yield. By analyzing how the laser field is oriented within the molecular frame for both channels, we show that enhanced ionization is driving the triply charged three body breakup but is not active for the doubly charged two body breakup. We conclude that laser-induced distortion of the molecular potential suppresses multiple ionization along the C2v axis but enhances ionization along the D-D direction.