Density matrix purification with rigorous error control

Density matrix purification, although being a powerful tool for linear scaling construction of the density matrix in electronic structure calculations, has been limited by uncontrolled error accumulation. In this article, a strategy for the removal of small matrix elements in density matrix purification is proposed with which the forward error can be rigorously controlled. The total forward error is separated into two parts, the error in eigenvalues and the error in the occupied invariant subspace. We use the concept of canonical angles to measure and control differences between exact and approximate occupied subspaces. We also analyze the conditioning of the density matrix construction problem and propose a method for calculation of interior eigenvalues to be used together with density matrix purification.     

X-ray absorption and resonant Auger spectroscopy of O2 in the vicinity of the O 1s-->sigma* resonance: experiment and theory

We report on an experimental and theoretical investigation of x-ray absorption and resonant Auger electron spectra of gas phase O(2) recorded in the vicinity of the O 1s-->sigma(*) excitation region. Our investigation shows that core excitation takes place in a region with multiple crossings of potential energy curves of the excited states. We find a complete breakdown of the diabatic picture for this part of the x-ray absorption spectrum, which allows us to assign an hitherto unexplained fine structure in this spectral region. The experimental Auger data reveal an extended vibrational progression, for the outermost singly ionized X (2)Pi(g) final state, which exhibits strong changes in spectral shape within a short range of photon energy detuning (0 eV>Omega>-0.7 eV). To explain the experimental resonant Auger electron spectra, we use a mixed adiabatic/diabatic picture selecting crossing points according to the strength of the electronic coupling. Reasonable agreement is found between experiment and theory even though the nonadiabatic couplings are neglected. The resonant Auger electron scattering, which is essentially due to decay from dissociative core-excited states, is accompanied by strong lifetime-vibrational and intermediate electronic state interferences as well as an interference with the direct photoionization channel. The overall agreement between the experimental Auger spectra and the calculated spectra supports the mixed diabatic/adiabatic picture.     

Synergizing Electron and Heat Flows in Photocatalyst for Direct Conversion of Captured CO2

We report a ternary hybrid photocatalyst architecture with tailored interfaces that boost the utilization of solar energy for photochemical CO₂ reduction by synergizing electron and heat flows in the photocatalyst. The photocatalyst comprises cobalt phthalocyanine (CoPc) molecules assembled on multiwalled carbon nanotubes (CNTs) that are decorated with nearly monodispersed cadmium sulfide quantum dots (CdS QDs). The CdS QDs absorb visible light and generate electron-hole pairs. The CNTs rapidly transfer the photogenerated electrons from CdS to CoPc. The CoPc molecules then selectively reduce CO₂ to CO. The interfacial dynamics and catalytic behavior are clearly revealed by time-resolved and in situ vibrational spectroscopies. In addition to serving as electron highways, the black body property of the CNT component can create local photothermal heating to activate amine-captured CO₂, namely carbamates, for direct photochemical conversion without additional energy input.     

Recent advances in "formal" ruthenium-catalyzed [2+2+2] cycloaddition reactions of diynes to alkenes

"Formal" and standard RuII-catalyzed [2+2+2] cycloaddition of 1,6-diynes to alkenes gave bicyclic 1,3-cyclohexadienes in relatively good yields. When terminal 1,6-diynes 1 were used, two isomeric bicyclic 1,3-cyclohexadienes 4 or 6 were obtained, depending on the acyclic or cyclic nature of the alkene partner. When unsymmetrical substituted 1,6-diynes 7 were used, the reaction with acyclic alkenes took place regio- and stereoselectively to afford bicyclic 1,3-cyclohexadienes 8. A cascade process that behaves as a "formal" RuII-catalyzed [2+2+2] cycloaddition explained these results. Initially, a Ru-catalyzed linear coupling of 1,6-diynes 1 and 7 with acyclic alkenes occurs to give open 1,3,5-trienes of type 3, which after a thermal disrotatory 6e(-) pi-electrocyclization led to the final 1,3-cyclohexadienes 4 and 8. When disubstituted 1,6-diyne 10 was used with electron-deficient alkenes, new exo-methylene cyclohexadienes 12 arose from a competitive reaction pathway.     

Mathematical programming based heuristics for the 0–1 MIP: a survey

The 0–1 mixed integer programming problem is used for modeling many combinatorial problems, ranging from logical design to scheduling and routing as well as encompassing graph theory models for resource allocation and financial planning. This paper provides a survey of heuristics based on mathematical programming for solving 0–1 mixed integer programs (MIP). More precisely, we focus on the stand-alone heuristics for 0–1 MIP as well as those heuristics that use linear programming techniques or solve a series of linear programming models or reduced problems, deduced from the initial one, in order to produce a high quality solution of a considered problem. Our emphasis will be on how mathematical programming techniques can be used for approximate problem solving, rather than on comparing performances of heuristics.     

Syntheses,Structures, and Luminescent Properties of Two Cadmium(II) Coordination Compounds based on a Sulfonate Functionalized Terpyridine Ligand

The coordination compounds [Cd(TBDS)(H₂O)₂]_n ( 1 ) and Cd(TBDS)(bpy)₂(H₂O) · 3H₂O ( 2 ) {H₂TBDS = 4‐([4,2′:6′,4′′‐terpyridine]‐4′‐yl)benzene‐1,3‐disulfonic acid, bpy = 2,2′‐bipyridine} were synthesized under hydrothermal conditions. Single crystal X‐ray diffraction analyses revealed that compound 1 is a twofold interpenetrating 3D framework with 4‐connected dia topology, whereas compound 2 is a mononuclear compound, which packed with each other via hydrogen‐bonding interactions to construct a three‐dimensional supramolecular structure, and contained unusual meso‐helical chains. Additionally, the luminescence properties and thermal stabilities of 1 and 2 were investigated.     

Single‐Crystal to Single‐Crystal Linker Substitution,Linker Place Exchange,and Transmetalation Reactions in Interpenetrated Pillared–Bilayer Zinc(II) Metal–Organic Frameworks

A twofold interpenetrated pillared–bilayer framework, {[Zn₃( L )₂( L₂ )(DMF)] ? (18DMF)(6H₂O)}_n ( 1 ), has been synthesized from the ligands tris(4′‐carboxybiphenyl)amine ( H₃L ) and 1,2‐bis(4‐pyridyl)ethylene ( L₂ ). The structure contains [Zn₃(COO)₆] secondary building units (SBUs), in which three Zn^II ions are almost linear with carboxylate bridging. This framework undergoes reversible pillar linker substitution reactions at the terminal Zn^II centers with three different dipyridyl linkers of different lengths to afford three daughter frameworks, 2 – 4 . Frameworks 2 – 4 are interconvertible through reversible linker substitution reactions. Also, competitive linker‐exchange experiments show preferential incorporation of linker L₃ in the parent framework 1 . The larger linker L₅ does not undergo such substitution reactions and framework 5 , which contains this linker, can be synthesized solvothermally as a twofold interpenetrated structure. Interestingly, when framework 5 is dipped in a solution of L₃ in DMF, linker substitution takes place as before, but linker L₅ now moves and diagonally binds two Zn^II centers to afford 6 as a nonpenetrated single framework. This linker place exchange reaction is unprecedented. All of these reactions take place in a single‐crystal to single‐crystal (SC‐SC) manner, and have been observed directly through X‐ray crystallography. In addition, each 3D framework undergoes complete copper(II) transmetalation.     

An A‐Site Mixed‐Ammonium Solid Solution Perovskite Series of [(NH2NH3)x(CH3NH3)1−x][Mn(HCOO)3] (x=1.00–0.67)

The A‐site mixed‐ammonium solid solutions of metal–organic perovskites [(NH₂NH₃)_x(CH₃NH₃)_1?x][Mn(HCOO)₃] (x=1.00–0.67) exhibit para‐ to ferroelectric diffuse phase transitions with lowered transition temperatures from x=1.00 to 0.67. These properties are due to the decreased framework distortion and polarization in their low temperature ferroelectric phases caused by the increased CH₃NH₃⁺ concentration.     

Large eddy simulations of targeted electromagnetic control of buoyancy-driven turbulent flow in a slender enclosure

We conducted a large eddy simulation (LES) of a locally applied electromagnetic control of turbulent thermal convection of an electrically conductive fluid (electrolyte solution) inside of a slender enclosure. Generic configurations, consisting of two or three magnets of opposite polarities located below the lower wall, and two oppositely charged electrodes along the side walls, are considered. The neutral situation (pure thermal convection) is selected to be in turbulent regime at Ra = 10⁷, Pr = 7. A magnetically extended Smagorinsky type model for the subgrid turbulent stresses and a simple-gradient diffusion model for the subgrid turbulent heat fluxes are used. Different intensities of applied DC current through electrodes are imposed. The effects of the resulting Lorentz force on flow, turbulence reorganisation and wall-heat transfer are analysed. It is demonstrated that significant flow and turbulence structure reorganisation takes place in the proximity of the lower horizontal wall and in the central parts of the enclosure—even for weak DC current of I = 1 A. Significant turbulence increase, generated by the elevated electromagnetic mixing, produced significant enhancements of the wall-heat transfer—up to 70% for the 2-magnet configuration.     

CS-MRI 中评价随机欠采样矩阵的新方法

在压缩感知-磁共振成像(CS-MRI)中,随机欠采样矩阵与重建图像质量密切相关．而选取随机欠采样矩阵一般是通过计算点扩散函数(PSF),以可能产生的伪影的最大值为评价参数,评估欠采样对图像重建的影响,然而最大值只反应了伪影的最坏情况．该文引入了两种新的统计学评价参数平均值(MV)和标准差(SD),其中平均值评估了伪影的平均大小,标准差可以反映伪影的波动情况．该文分别使用这3种参数对小鼠和人体脑部MRI数据以不同的采样比率进行CS图像重建,实验结果表明,当采样比率不低于4倍稀疏度时,使用平均值获得了质量更优的重建图像．因此,通过稀疏度先验知识指导合理选取采样比率,并以平均值为评价参数选取随机欠采样矩阵,能够获得更优的CS-MRI重建图像．