Behind the success of modified coupled-cluster methods: addition by subtraction

ABSTRACT

Modified coupled-cluster (CC) methods such as linearized coupled-cluster doubles (LinCCD), approximate coupled pair (ACP D14), 2CC (from nCC family), parameterized CCSD (pCCSD) and distinguishable cluster (DCSD) can have their advantages over general CC methods. Though these methods include connected clusters of single and double excitations at most, distinguishable cluster, parameterized CC and approximate coupled pair methods, in particular, have been shown to produce quantitatively correct results in benchmark studies. To put these methods on a stronger foothold, it is essential to understand the rationale for their success: mimicking the effect of connected triple excitations. We exploit the relation between CC and many body perturbation theory (MBPT) in general, and between CCSD and MBPT(4)/MP4 in particular, to take a step towards bringing clarity to this persisting conundrum. Our aim here is to look for numerical signs of ‘addition by subtraction’ or ‘inclusion by deletion’ effect that is likely behind the success of these modified CCD or CCSD methods. We achieve this by revisiting well-studied examples of single and multiple bond dissociation and comparing the performance of these modified CCSD methods with higher-level CC methods. Though our results are qualitative in nature, we hope this would lead to more rigorous analysis in future studies.     

A note on fractional $${\varvec{}}$$-Lalacian roblems with singular weights

We study a class of fractional p-Laplacian problems with weights which are possibly singular on the boundary of the domain. We provide existence and multiplicity results as well as characterizations of critical groups and related applications.     

Application of the Tris(acetylacetonato)iron(III)/(II) Redox Couple in p‐Type Dye‐Sensitized Solar Cells

An electrolyte based on the tris(acetylacetonato)iron(III)/(II) redox couple ([Fe(acac)₃]^0/1?) was developed for p‐type dye‐sensitized solar cells (DSSCs). Introduction of a NiO blocking layer on the working electrode and the use of chenodeoxycholic acid in the electrolyte enhanced device performance by improving the photocurrent. Devices containing [Fe(acac)₃]^0/1? and a perylene–thiophene–triphenylamine sensitizer (PMI–6T–TPA) have the highest reported short‐circuit current (J_SC=7.65 mA cm^?2), and energy conversion efficiency (2.51 %) for p‐type DSSCs coupled with a fill factor of 0.51 and an open‐circuit voltage V_OC=645 mV. Measurement of the kinetics of dye regeneration by the redox mediator revealed that the process is diffusion limited as the dye‐regeneration rate constant (1.7×10⁸ M ^?1 s^?1) is very close to the maximum theoretical rate constant of 3.3×10⁸ M ^?1 s^?1. Consequently, a very high dye‐regeneration yield (>99 %) could be calculated for these devices.     

Solution‐Based Synthesis of Layered Intergrowth Compounds of the Homologous PbmBi2nTe3n+m Series as Nanosheets

Layered intergrowth compounds in the homologous Pb_mBi_2nTe_3n+m family are interesting because they are examples of natural heterostructures. We present a simple solution‐based synthesis of two‐dimensional nanosheets of PbBi₂Te₄, Pb₂Bi₂Te₅, and PbBi₆Te₁₀ layered intergrowth compounds, which are members of the Pb_mBi_2nTe_3n+m [that is, (PbTe)_m(Bi₂Te₃)_n] homologous series. Few‐layer nanosheets exhibit narrow optical band gaps (0.25–0.7 eV) with semiconducting electronic‐transport properties.     

Efficient passivation of SnO2 nano crystallites by Indoline D-149 via dual chelation

For the first time in SnO₂ based dye solar cells, here we report, efficiency exceeding 3% of the cells consisting with Indoline D-149 dye with unmodified SnO₂ nano-crystallites. The cells sensitized with metal free D-149 dye together with liquid electrolyte comprising with 0.5 M tetrapropyl ammonium iodide and 0.05 M iodine in a mixture of acetonitrile and ethylene carbonate (1:4 by volume) delivered a short circuit current density of 10.4 mA cm^?2 with an open circuit voltage of 530 mV under the illumination of 100 mW cm^?2 (AM1.5) having an efficiency of 3.1%. As evident from the FTIR measurement, strong surface passivation of recombination centers of SnO₂ crystallites due to the dual mode of attachment of dye molecules to the surface of SnO₂ via both COOH and S–O direct bond might be the possible reason for this enhancement in these SnO₂ based cells.     

An Indium‐Seamed Hexameric Metal–Organic Cage as an Example of a Hexameric Pyrogallol[4]arene Capsule Conjoined Exclusively by Trivalent Metal Ions

A hexameric metal–organic nanocapsule is assembled from pyrogallol[4]arene units, which are stitched together with indium ions. This indium‐seamed capsule is the first instance of a M₂₄L₆ type hexameric coordination cage held together exclusively by trivalent metal ions. Explicitly, unlike previously reported pyrogallol[4]arene‐based metal‐seamed capsules, the current In³⁺ seamed capsule is entirely supported by O→In coordinate bonds. This work demonstrates the important proof of concept of the ability of pyrogallol[4]arene to react with metals in higher oxidation states to assemble into atomically‐precise hexameric coordination cages. As such, these results open up exciting avenues toward the assembly of previously unanticipated metal–organic capsules, for example offering inspiration for tackling metals exhibiting high valence states such as in the lanthanide and actinide series.     

On the existence and uniqueness of the optimal central bank intervention policy in a forex market with jumps

We study a central bank intervention (CBI) problem in the foreign exchange market when the exchange rate follows a jump-diffusion process and show that the optimal CBI policy is a control-band policy. Our main contribution is a rigorous proof of the existence and uniqueness of the optimal CBI policy.     

X-ray absorption spectral analyses by theoretical calculations for TiO2 and Ni-doped TiO2 thin films on glass plates.

Ni L- and Ti L-edge as well as Ti K-edge X-ray absorption experiments for TiO2 thin films and Ni-doped TiO2 thin films coated on glass plates were performed using synchrotron radiation to investigate the structures around Ni and Ti ions in the films. The obtained spectra were compared with the results of theoretical calculations. It has consequently been found that the spectral features were affected by a change in the oxidizing form of Ni ions due to hydrogen reduction, by the charge variation and/or slight orbital splitting of Ti ions, and by the magnitude of the interaction between the center Ti ion and neighboring Ti ions.     

Characterization of crystalline and amorphous content in pharmaceutical solids by dielectric thermal analysis

Morphological and thermodynamic transitions in drugs as well as their amorphous and crystalline content in the solid state have been distinguished by thermal analytical techniques, which include dielectric analysis (DEA), differential scanning calorimetry (DSC), and macro-photomicrography. These techniques were used successfully to establish a structure versus property relationship with the United States Pharmacopeia standard set of active pharmaceutical ingredient (API) drugs. A distinguishing method is the DSC determination of the amorphous and crystalline content which is based on the fusion properties of the specific drug and its recrystallization. The DSC technique to determine the crystalline and amorphous content is based on a series of heat and cool cycles to evaluate the drugs ability to recrystallize. To enhance the amorphous portion, the API is heated above its melting temperature and cooled with liquid nitrogen to ?120 °C (153 K). Alternatively a sample is program heated and cooled by DSC at a rate of 10 °C min^?1. DEA measures the crystalline solid and amorphous liquid API electrical ionic conductivity. The DEA ionic conductivity is repeatable and differentiates the solid crystalline drug with a low conductivity level (10^?2 pS cm^?1) and a high conductivity level associated with the amorphous liquid (10⁶ pS cm^?1). The DSC sets the analytical transition temperature range from melting to recrystallization. However, analysis of the DEA ionic conductivity cycle establishes the quantitative amorphous and crystalline content in the solid state at frequencies of 0.10–1.00 Hz and to greater than 30 °C below the melting transition as the peak melting temperature. This describes the “activation energy method.” An Arrhenius plot, log ionic conductivity versus reciprocal temperature (K^?1), of the pre-melt DEA transition yields frequency dependent activation energy (E _a, J mol^?1) for the complex charging in the solid state. The amorphous content is inversely proportional to the E _a where the E _a for the crystalline form is higher and lower for the amorphous form with a standard deviation of ±2%. There was a good agreement between the DSC crystalline melting, recrystallization, and the solid state DEA conductivity method with relevant microscopic evaluation. An alternate technique to determine amorphous and crystalline content has been established for the drugs of interest based on an obvious amorphous and crystalline state identified by macro-photomicrography and compared to the conductivity variations. This second “empirical method” correlates well with the “activation energy” method.     

Purely infinite corona algebras of simple C*-algebras

In this paper, we study the problem of when the corona algebra of a non-unital C*-algebra is purely infinite. A complete answer is obtained for stabilisations of simple and unital algebras that have enough comparison of positive elements. Our result relates the pure infiniteness condition (from its strongest to weakest forms) to the geometry of the tracial simplex of the algebra, and to the behaviour of corona projections, despite the fact that there is no real rank zero condition.