Nonet State Research Articles

3,4-Dimethylenecyclobutene: A Building Block for Design of Macrocycles with Excited State Aromatic Low-Lying High-Spin States.

3,4-Dimethylenecyclobutene (DMCB) is an unusual isomer of benzene. Motivated by recent synthetic progress to substituted derivatives of this scaffold, we carried out a theoretical and computational analysis with a particular focus on the extent of (anti)aromatic character in the lowest excited states of different multiplicities. We found that the parent DMCB is non-aromatic in its singlet ground state (S0), lowest triplet state (T1), and lowest singlet excited state (S1), while it is aromatic in its lowest quintet state (Q1) as this state is represented by a triplet multiplicity cyclobutadiene (CBD) ring and two uncoupled same-spin methylene radicals. Interestingly, the Q1 state, despite having four unpaired electrons, is placed merely 4.8 eV above S0, and there is a corresponding singlet tetraradical 0.16 eV above. The DMCB is potentially a highly useful structural motif for the design of larger molecular entities with interesting optoelectronic properties. Here, we designed macrocycles composed of fused DMCB units, and according to our computations, two of these have low-lying nonet states (i. e., octaradical states) at energies merely 2.40 and 0.37 eV above their S0 states as a result of local Hückel- and Baird-aromatic character of individual 6π- and 4π-electron monocycles.

Existence of the critical endpoint in the vector meson extended linear sigma model

The chiral phase transition of the strongly interacting matter is investigated at nonzero temperature and baryon chemical potential mu_B within an extended (2+1) flavor Polyakov constituent quark-meson model which incorporates the effect of the vector and axial vector mesons. The effect of the fermionic vacuum and thermal fluctuations computed from the grand potential of the model is taken into account in the curvature masses of the scalar and pseudoscalar mesons. The parameters of the model are determined by comparing masses and tree-level decay widths with experimental values in a chi^2-minimization procedure which selects between various possible assignments of scalar nonet states to physical particles. We examine the restoration of the chiral symmetry by monitoring the temperature evolution of condensates and the chiral partners' masses and of the mixing angles for the pseudoscalar eta-eta' and the corresponding scalar complex. We calculate the pressure and various thermodynamical observables derived from it and compare them to the continuum extrapolated lattice results of the Wuppertal-Budapest collaboration. We study the T-mu_B phase diagram of the model and find that a critical end point exists for parameters of the model, which give acceptable values of chi^2.

DFT and TD-DFT study on structures, related energies, frontier molecular orbitals and UV–Vis spectra of [M(Tp)(PPh3)(Cl)(L)] (M = Ru and Fe; L = C3H4N2 and C13H11N)

Density functional theory (DFT) and time-dependent density functional theory (TD-DFT) with the DZVP/DZVP2 all-electron mixed basis sets are used to study the related energies, structures, frontier molecular orbitals and UV–Vis spectra for [M(Tp)(PPh3)(Cl)(L)] (M=Ru and Fe; L=C3H4N2 and C13H11N). The related energies between the singlet state (low-spin) and nonet state (high-spin) for these complexes are reported. Because of the low related energies, these complexes are expected to be in the singlet state (low-spin). The calculated structural parameters for complexes 1 and 3 (Ru-based) are in very good agreement with the experimental values, and the geometries of complexes 2 and 4 (Fe-based) have been studied as well. The metal–ligand bond distances for the Fe-based complexes are predicted to be slightly shorter than those of the Ru-based complexes due to the small spatial extent of the 3d wave functions of the Fe atom. These complexes display a HOMO of metal d and π(Cl) orbitals in character, and the LUMO is contributed by metal d and π∗(PPh3) or π∗(C13H11N) orbitals. The HOMO–LUMO energy gap (ΔEL–H) can be reduced by a π-electron rich ligand (such as C13H11N) and a low electronegativity metal atom (such as Fe). A π-electron rich ligand (such as C13H11N) can increase the electron accepting ability, which leads to more electrons being pumped into the π∗(PPh3) and π∗(C13H11N) orbitals and results in a red-shift and intensity-enhanced absorption in the UV–Vis spectrum. The UV–Vis absorption intensity can be enhanced by solvent (such as CH3OH) as well as resulting in a blue-shift, which suggests that it is due to the polarizability and dielectric strength of the solvent. Owing to the low electronegativity of the Fe atom, a red-shift occurs in the UV–Vis spectra for complexes 2 and 4. The primary absorption features for complexes 1 and 3 are attributed to MLCT/LLCT transitions; on the other hand, a MLCT transition results in the primary absorption features for complexes 2 and 4. Our results show that Ru can be replaced by the inexpensive Fe as the photo-sensitizer. In addition, these Ru- and Fe-based complexes are good candidates for photo-sensitizers in DSSCs due to rich absorption bands and strong absorption intensities in the visible region.

Competition between surface chemisorption and cage formation in Fe12O12 clusters

The electronic and geometrical structures of the clusters composed of 12 iron and 12 oxygen atoms are obtained using all-electron density functional theory. It is found that the states with geometrical structures corresponding to oxygen chemisorbed on the ground-state Fe12 cluster surface (Fe12O12) are close in total energy to the states whose geometrical configurations are hollow cages (FeO)12. The lowest total energy state is the ferrimagnetic triplet state of Fe12O12. A ferrimagnetic nonet state of (FeO)12 is only marginally higher in total energy. The clusters are rich in nearly degenerate isomers. Oxygen adsorption dramatically quenches the spin of Fe12 clusters.

Formation and Structure of Co2O4: A Combined IR Matrix Isolation and Theoretical Study

The formation and structure of dicobalt tetroxide (Co₂O₄) has been investigated using matrix isolation in solid neon and argon coupled to infrared spectroscopy and quantum chemical methods. It is found that Co₂O₄ can be formed by dimerization of cobalt dioxide without activation energy by diffusion of ground state CoO₂ molecules at 9 K in the dark. The IR data on eight fundamentals, isotopic effects and quantum chemical calculations are both consistent with a centro-symmetrical structure with two pairs of equivalent oxygen atoms, engaged in a stronger terminal Co-O bond and in a weaker bridging Co-O-Co position. Evidence for other, metastable states is also presented, but the data are not conclusive. The electronic structure and formation pathway has been investigated using the Tao-Perdew-Staroverov-Scuseria/triple-zeta valence polarived basis set (TPSS/TZVP) and broken symmetry unrestricted density functional theory (BS-UDFT) approach and the ground electronic state is predicted to be an open shell ¹Ag singlet with the quintet, triplet, septet, and nonet states above by 3.3, 4.9, 9.3, and 27.7 kcal/mol, respectively, but certainly has a complex multireference character that hinders the use of more precise multireference approaches. Different formation pathways have been considered, and the 2(O═Co═O) → Co₂O₄ dimerization reaction is found to be the only barrierless channel and to be strongly exothermic. Comparisons with another transition metal (TM) oxide system (V₂O₄) suggests that the difference in predicted ground state geometries in TM₂O₄ systems might be due in HOMO-LUMO shapes of the isolated dioxide subunits and optimal overlap configurations.

Density Functional Theory Study on the Mechanism of the Reductive Cleavage of CO2 by a Bis-β-Diketoiminatediiron Dinitrogen Complex

Density functional theory has been used to analyze the detailed reaction mechanism for the reductive cleavage of CO(2) by a dinitrogen bridged bis-beta-diketoiminatediiron complex, L(tBu)Fe-N(2)-FeL(tBu) (I), recently reported by Holland and co-workers. A number of pathways have been investigated and the most likely mechanism correlates well with experimental evidence. A rationale has been provided for the binding of CO(2), the release of CO, and the ready formation of CO(3)(2-). Our results show that the insertion of CO(2) into the diiron complex is the rate determining step of the reductive cleavage reaction. An intramolecular reduction step from the reduced dinitrogen bridge is proposed which serves to increase the activation of CO(2). This is followed by an intersystem crossing from the septet to the nonet state which acts as a driving force for the subsequent release of CO. The overall reductive cleavage reaction is exergonic by 120 kJ/mol, and further reaction of the released CO with the starting diiron complex is also predicted to be strongly exergonic.

Indications of the possible observation of the lowest-lying1−+QCD state

We discuss properties of 1 - + exotic mesons within the framework of the QCD field-theoretic approach. We estimate the mass of the lowest-lying 1 -+ exotic meson using renormalization-improved QCD sum rules, and find that the mass lies around 1.26 ± 0.15 GeV, in good agreement with the π 1 (1400) data. This state should be expected in QCD. We find that the mass for the lowest-lying strange 1 -+ meson is 1.31 ± 0.19 GeV. Our result hints that the K*(1410) may be the lowest-lying 1 -+ nonet state.

Density Functional and Ab Initio Study of Cr(CO)n (n = 1−6) Complexes

Cr(CO)n (n = 1-6) systems were studied for all possible spin states using density functional and high-level ab initio methods to provide a more complete theoretical understanding of the structure of species that may form during ligand dissociation of Cr(CO)6. We carried out geometry optimizations for each system and obtained vibrational frequencies, sequential bond dissociation energies (BDE), and total CO binding energies. We also compared the performance of various DFT functionals. Generally, the ground states of Cr(CO)6, Cr(CO)5, and Cr(CO)4, whose spin multiplicity is a singlet, are in good agreement with both previous theoretical results and currently available experimental data. Calculations on Cr(CO)3, Cr(CO)2, and CrCO provide new findings that the ground state of Cr(CO)3 might be a quintet with C2v symmetry instead of a singlet with C3v symmetry, and the ground state of Cr(CO)2 is not a linear quintet, as suggested by previous DFT calculations, but rather a linear septet. We also found that nonet states of Cr(CO)2 and CrCO display partial C-O bond breakage.

Spin Polarization Effect for Molecule Fe2

Density functional method (B3p86) was used to optimize the structure of the molecule Fe2. The result showed that the ground electronic state for the molecule Fe2 is nonet state instead of septet state, which indicates that there is a spin polarization effect in the molecule Fe2, i.e., in which there are 8 parallel spin electrons. In this case, the number of the unpaired d-orbit electrons is the largest, and these electrons occupy different spatial orbitals so that the energy of the molecule Fe2 is minimized. Meanwhile, the spin pollution was not found because the wave functions of the ground state do not mix with those of the higher energy states. In addition, the Murrell-Sorbie potential functions with the parameters for the ground electronic state and other exited electronic states of the molecule Fe2 were derived. The dissociation energy, equilibrium bond length and the vibration frequency for the ground electronic state of the molecule Fe2 are 3.5522 eV, 0.2137 nm and 292.914 cm1, respectively. Its force constants f2, f3 and f4 are 1.4115102 aJ=nm2, 37.1751103 aJ=nm3 and 98.7596104 aJ=nm4, respectively. The other spectroscopic parameters ee,Be and e for the ground electronic state of Fe2 are 0.3522, 0.0345 and 0.4963104 cm1, respectively.

Interaction between heterobinuclear molecules and nature of the ground spin state in oximato-bridged [Cu IIM II] 2 bis-binuclear complexes (M=Cu, Ni, Mn): crystal structure of [Cu(pdmg)Ni(Me 3[12]N 3)(EtOH)](ClO 4) 2

Two new heterobimetallic complexes [Cu(pdmg)Ni(Me 3[12]N 3)(CH 3CH 2OH)](ClO 4) 2 ( 2) and [Cu(pdmg)Mn(bipy) 2](ClO 4) 2 · H 2O ( 3) (H 2pdmg=3,9-dimethyl-4,8-diazaundeca-3,8-diene-2,10-dione dioxime; Me 3[12]N 3=2,4,4-trimethyl-1,5,9-triazacyclododeca-1-ene; bipy=2,2′-bipyridyl) have been prepared and characterized. The structure of 2 has been determined by single-crystal X-ray diffraction methods. It consists of [Cu(pdmg)Ni(Me 3[12]N 3)(CH 3CH 2OH)] 2+ cations and non-coordinated perchlorate anions. The [Cu(pdmg)(CH 3CH 2OH)] complex coordinates to the [Ni(Me 3[12]N 3)] 2+ fragment to afford the binuclear unit doubly-bridged by oximato groups in cis arrangement. The coordination geometry around the copper atom is square-pyramidal, whereas the nickel atom exhibits a trigonal-bipyramidal surrounding. The intramolecular Cu–Ni distance is 3.810(6) Å. In the crystal, two [Cu IINi II] dimeric units are related through an inversion center, giving rise to a bis-binuclear entity with a relatively short intermolecular Cu–Cu separation of 4.175(6) Å. Variable-temperature magnetic susceptibility measurements (2.0–300 K) for 2 correspond to an almost isolated Cu(II)Ni(II) pair with an intrapair interaction parameter J=−143.6(2) cm −1. However, the EPR spectrum at 4.2 K is that of a triplet spin state arising from the interaction between the two doublet spin states within the [Cu IINi II] 2 bis-binuclear entity. The magnetic properties of 3 unambiguously reveal the bis-binuclear nature of this compound, as is the case for the related homometallic complex [Cu(pdmg)Cu(bipy)(H 2O) 2](ClO 4) 2 · H 2O ( 1). The intra- ( J) and interpair ( j) interaction parameters for 3, as deduced from the analysis of its magnetic susceptibility data in the temperature range 2.0–300 K, are −50.9(2) and 1.50(2) cm −1, respectively. The field dependence of the magnetization of 3 at 2.0 K corresponds to that of a nonet state arising from the interaction between two quintuplet spin states within the [Cu IIMn II] 2 bis-binuclear entity. The interaction between the heterobinuclear Cu(II)Mn(II) molecules and its influence on the nature of the ground spin state for 3 are analyzed and discussed in the framework of a spin polarization scheme.

Wide scalar gluonium and the quark-antiquark scalar nonet

The couplings of scalar gluonium as well as quark-antiquark scalar nonet states to the pseudoscalar mesons are discussed on the basis of the low-energy theorems of broken chiral symmetry and scale invariance implemented using phenomenological Lagrangians. Mixing between pure gluonium σ and theSU(3)F singlet quarkoniumS0 is considered. Taking for the masses ofS0 and σ the values based on estimates of the quark model and of recent QCD lattice calculations, respectively, and using the “standard” values of the gluon condensate then the mixture ofS0 and σ in the physical statesG and ɛ is predicted to be approximately half- and- half. We predictG to have properties consistent with the GAMSf0(1590) meson, while ɛ is predicted to be the wide effective gluonium state below 1 GeV. On this basis we suggest a possible consistent description of the whole scalar xxxxx nonet. The picture containsS*(975) neither as xxxxxxx nor asgg state and we support thus still more exotic interpretation of theS*(975) effect.

Electron spin resonance line shapes of randomly oriented molecules in septet and nonet states by a perturbation approach

The electron spin resonance line shapes of randomly oriented molecules in septet and nonet states are analyzed in terms of the formulas derived from a perturbation treatment to third-order in the fine-structure energy. The method is applied to a ground-state septet hydrocarbon, 3, 3′-diphenylmethylenebis (phenylmethylene), and a ground-state nonet hydrocarbon, m-phenylenebis[(diphenylmethylen-3-yl)methylene], randomly oriented in mixed polycrystalline powders of benzophenone. It is shown that the g factor and the fine-structure parameters are determined from the line shapes of a K-band spectrum with nearly the same accuracy as in a single-crystal experiment. Extra lines have been observed in addition to the canonical lines corresponding to the external magnetic field along the principal axes of the fine-structure tensor. The appearance of extra lines in the spectra of septet and nonet molecules is discussed relative to the third-order perturbation theory.

Zeros in the Scattering Amplitudes of Two Pseudoscalar Mesons in the Nonet States

The low-energy pseudoscalar-meson-pseudoscalar-meson scatterings are investigated phenomenologically in terms of the forward dispersion relations. Using the scattering lengths given by the current algebra, it is shown that there exists one general feature common to the scattering amplitudes in the nonet states, namely, that the effective-range functions $(\frac{2p}{W})cot\ensuremath{\delta}$ decrease rather rapidly above threshold. It is suggested that this behavior can be explained by assuming the existence of a zero in the scattering amplitude. Another argument which requires these nonet zeros is given in the framework of the theory of complex angular momenta.