Phase transition in the one-dimensional pair-hopping model with unusual one-electron hopping

By modifying the conventional one-electron hopping behavior, we study effects of an occupation-dependent hopping on the ground state of the half-filled one-dimensional pair-hopping model. At weak coupling, the use of bosonization and renormalization-group analysis techniques helps to derive the phase diagram. Such unusual hopping is shown to drive a spin-gap transition and to introduce a new region where the triplet superconducting instability dominates for positively small pair-hopping interaction.     

Theory of chemical bonds in metalloenzymes XXII: a concerted bond-switching mechanism for the oxygen–oxygen bond formation coupled with one electron transfer for water oxidation in the oxygen-evolving complex of photosystem II

ABSTRACT

QM(UB3LYP)/MM(AMBER) calculations were performed for the locations of the transition structure (TS) of the oxygen–oxygen (O–O) bond formation in the S₄ state of the oxygen-evolving complex (OEC) of photosystem II (PSII). The natural orbital (NO) analysis of the broken-symmetry (BS) solutions was also performed to elucidate the nature of the chemical bonds at TS on the basis of several chemical indices defined by the occupation numbers of NO. The computational results revealed a concerted bond switching (CBS) mechanism for the oxygen–oxygen bond formation coupled with the one-electron transfer (OET) for water oxidation in OEC of PSII. The orbital interaction between the σ-HOMO of the Mn(IV)₄–O₍₅₎ bond and the π*-LUMO of the Mn(V)₁=O₍₆₎ bond plays an important role for the concerted O–O bond formation for water oxidation in the CaMn₄O₆ cluster of OEC of PSII. One electron transfer (OET) from the π-HOMO of the Mn(V)₁=O₍₆₎ bond to the σ*-LUMO of the Mn(IV)₄–O₍₅₎ bond occurs for the formation of electron transfer diradical, where the generated anion radical [Mn(IV)₄–O₍₅₎]^-? part is relaxed to the ?Mn(III)₄?…?O₍₅₎^- structure and the cation radical [O₍₆₎=Mn(V)₁]⁺ ? part is relaxed to the ⁺O₍₆₎–Mn(IV)₁? structure because of the charge-spin separation for the electron-and hole-doped Mn–oxo bonds. Therefore, the local spins are responsible for the one-electron reductions of Mn(IV)₄->Mn(III)₄ and Mn(V)₁->Mn(IV)₁. On the other hand, the O₍₅₎^- and O₍₆₎⁺ sites generated undergo the O–O bond formation in the CaMn₄O₆ cluster. The Ca(II) ion in the cubane- skeleton of the CaMn₄O₆ cluster assists the above orbital interactions by the lowering of the orbital energy levels of π*-LUMO of Mn(V)₁=O₍₆₎ and σ*-LUMO of Mn(IV)₄–O₍₅₎, indicating an important role of its Lewis acidity. Present CBS mechanism for the O–O bond formation coupled with one electron reductions of the high-valent Mn ions is different from the conventional radical coupling (RC) and acid-base (AB) mechanisms for water oxidation in artificial and native photosynthesis systems. The proton-coupled electron transfer (PC-OET) mechanism for the O–O bond formation is also touched in relation to the CBS-OET mechanism.     

The maximum multiplicity of the largest k-th eigenvalue in a matrix whose graph is acyclic or unicyclic

Given a graph $G$ we are interested in studying the symmetric matrices associated to $G$ with a fixed number of negative eigenvalues. For this class of matrices we focus on the maximum possible nullity. For trees this parameter has already been studied and plenty of applications are known. In this work we derive a formula for the maximum nullity and completely describe its behavior as a function of the number of negative eigenvalues. In addition, we also carefully describe the matrices associated with trees that attain this maximum nullity. The analysis is then extended to the more general class of unicyclic graphs. Further our work is applied to re-describing all possible partial inertias associated with trees, and is employed to study an instance of the inverse eigenvalue problem for certain trees.     

Ligands Based on Phosphine-Stabilized Aluminum(I), Boron(I), and Carbon(0)

A systematic quantum chemical study of the bonding in d⁶-transition-metal complexes, containing phosphine-stabilized, main-group-element fragments, (R₃P)₂E, as ligands (E=AlH, BH, CH⁺, C), is reported. By using energy decomposition analysis, it is demonstrated that a strong M−E bond is accompanied by weak P−E bonds, and vice versa. Although the Al−M bond is, for example, found to be very strong, the weak Al−P bond suggests that the corresponding metal complexes will not be stable towards phosphine dissociation. The interaction energies for the boron(I)-based ligand are lower, but still higher than those for two-carbon-based ligands. For neutral ligands, electrostatic interactions are the dominating contributions to metal–ligand bonding, whereas for the cationic ligand a significant destabilization, with weak orbital and even weaker electrostatic metal–ligand interactions, is observed. Finally, for iron(II) complexes, it is demonstrated that different reactivity patterns are expected for the four donor groups: the experimentally observed reversible E−H reductive elimination of the borylene-based ligand (E=BH) exhibits significantly higher barriers for the protonated carbodiphosphorane (CDP) ligand (E=CH) and would proceed through different intermediates and transition states. For aluminum, such reaction pathways are not feasible (E=AlH). Moreover, it is demonstrated that the metal hydrido complexes with CDP ligands might not be stable towards reduction and isomerization to a protonated CDP ligand and a reduced metal center.     

Oxidative dehydrogenation of n-octane over a vanadium–magnesium oxide catalyst: Influence of the gas hourly space velocity

Oxidative dehydrogenation (ODH) of n-octane was carried out over a vanadium–magnesium oxide catalyst in a continuous flow fixed bed reactor. The catalyst was characterized by ICP–OES, powder XRD and SEM. The catalytic tests were carried out at different gas hourly space velocities (GHSVs), viz. 4000, 6000, 8000, and 10,000 h^?1. The best selectivity for octenes was obtained at the GHSV of 8000 h^?1, while that for C8 aromatics was attained at the GHSV of 6000 h^?1 at high temperatures (500 and 550 °C). The catalytic testing at the GHSV of 10,000 h^?1 showed the lowest activity, while that at the GHSV of 4000 h^?1 consistently showed the lowest ODH selectivity. Generally, the best ODH performance was obtained by the catalytic testing at the GHSVs of 6000 and 8000 h^?1. No phasic changes were observed after the catalytic testing.     

New lower bounds on the radius of spatial analyticity for the KdV equation

The radius of spatial analyticity for solutions of the KdV equation is studied. It is shown that the analyticity radius does not decay faster than $t^{?1/4}$ as time t goes to infinity. This improves the works of Selberg and da Silva (2017) [30] and Tesfahun (2017) [34]. Our strategy mainly relies on a higher order almost conservation law in Gevrey spaces, which is inspired by the I-method.     

Ab initio and Monte Carlo studies of phase transitions and magnetic properties of YCrO3: Heisenberg model

By using the density functional theory (DFT) and Monte Carlo simulations (MCS) with the Heisenberg model, we have studied magnetic properties of the bulk perovskite YCrO₃. The exchange couplings of the Heisenberg model and the magnetic anisotropy are investigated. The 110 direction in the crystalline structure of the compound has shown the minimum energy, it is the easy magnetic direction. Using Monte Carlo simulations, the magnetizations behavior, the effects of system parameters and the critical exponents of the compound YCrO₃ are implemented. It is shown that the bulk perovskite YCrO₃ belongs to the 3D Heisenberg universality class.