The coupled-cluster formalism – a mathematical perspective

ABSTRACT

The Coupled-Cluster (CC) theory is one of the most successful high precision methods used to solve the stationary Schrödinger equation. In this article, we address the mathematical foundation of this theory with focus on the advances made in the past decade. Rather than solely relying on spectral gap assumptions (non-degeneracy of the ground state), we highlight the importance of coercivity assumptions – Gårding type inequalities – for the local uniqueness of the CC solution. Based on local strong monotonicity, different sufficient conditions for a local unique solution are suggested. One of the criteria assumes the relative smallness of the total cluster amplitudes (after possibly removing the single amplitudes) compared to the Gårding constants. In the extended CC theory the Lagrange multipliers are wave function parameters and, by means of the bivariational principle, we here derive a connection between the exact cluster amplitudes and the Lagrange multipliers. This relation might prove useful when determining the quality of a CC solution. Furthermore, the use of an Aubin–Nitsche duality type method in different CC approaches is discussed and contrasted with the bivariational principle.     

Acoustic phonon impact on the inter-Coulombic decay process in charged quantum dot pairs

ABSTRACT

Recently, highly accurate multi-configuration time-dependent Hartree electron dynamics calculations demonstrated the efficient long-range energy transfer inter-Coulombic decay (ICD) process to happen in charged semiconductor quantum dot (QD) pairs. ICD is initiated by intraband photoexcitation of one of the QDs and leads to electron emission from the other within a duration of about 150 ps. On the same time scale electronically excited states are reported to relax due to the coupling of electrons to acoustic phonons. Likewise, phonons promote ionisation. Here, the QDs' acoustic breathing mode is implemented in a frozen-phonon approach. A detailed comparison of the phonon effects on electron relaxation and emission as well as on the full ICD process is presented, which supports the previous empirical finding of ICD being the dominant decay channel in paired QDs. In addition the relative importance of phonon–phonon, phonon–electron and electron–electron interaction is analysed.     

Intermolecular interactions between natural humic substances and tricyclic antidepressants

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Trimetallic NiCoM catalysts (M = Mn,Fe, Cu) for methane conversion into synthesis gas

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S‐Adenosyl Methionine Cofactor Modifications Enhance the Biocatalytic Repertoire of Small Molecule C‐Alkylation

A tandem enzymatic strategy to enhance the scope of C‐alkylation of small molecules via the in situ formation of S‐adenosyl methionine (SAM) cofactor analogues is described. A solvent‐exposed channel present in the SAM‐forming enzyme SalL tolerates 5′‐chloro‐5′‐deoxyadenosine (ClDA) analogues modified at the 2‐position of the adenine nucleobase. Coupling SalL‐catalyzed cofactor production with C‐(m)ethyl transfer to coumarin substrates catalyzed by the methyltransferase (MTase) NovO forms C‐(m)ethylated coumarins in superior yield and greater substrate scope relative to that obtained using cofactors lacking nucleobase modifications. Establishing the molecular determinants that influence C‐alkylation provides the basis to develop a late‐stage enzymatic platform for the preparation of high value small molecules.     

Structural studies and biological evaluation of Co (II), Ni (II) and Cu (II) complexes of carbohydrazone derived from ethyl acetoacetate in addition to crystallographic description of La (III) or Sm (III) catalytic activity abnormal product

New carbohydrazone ligand derived from the condensation of carbohydrazide and ethyl acetoacetate, diethyl 3,3′‐(carbonylbis (hydrazin‐2‐yl‐1‐ylidene))(3E,3′E)‐dibutyrate (H₄EBC), and its divalent Co, Ni and Cu chelates have been isolated and characterized utilizing convenient methods. ¹H‐NMR spectrum of H₄EBC revealed the abundance of the enol isomer in solution, which was the opposite to what was shown by the solid IR. This was supported by comparing the theoretical IR of both keto and enol forms. In [Ni(H₄EBC)Cl₂(H₂O)]·2H₂O, H₄EBC acts as a neutral NON tridentate ligand via the (C=O)_carbonyl oxygen atom besides the two (C=N)_azomethine nitrogen atoms, while in [Co(H₄EBC)Cl₂(2H₂O)]·2H₂O, H₄EBC behaves as a neutral NN bidentate ligand through the two azomethine groups. Magnetic measurements inherent to their electronic spectra show that both Ni (II) and Co (II) chelates have octahedron coordination frameworks. On the other hand, the ligand behaves as a binegative tetradentate in [Cu₂(H₄EBC)Cl₂]·H₂O via the deprotonated (C=O)_carbonyl groups of the ethyl acetoacetate framework and the two (C=N)_azomethine groups. In the latter complex, the carbonyl group of the carbohydrazide moiety is converted to hydroxyl group. Cu (II) complex has a tetrahedral geometry according to ESR and electronic spectral data. The reaction of H₄EBC with SmCl₃·6H₂O or LnCl₃·7H₂O gave single crystals of abnormal product (C₁₆H₁₆N₄O₄). The packing diagram of this crystal has a chain structure. The photoluminescence spectra of [Cu ₂ (H ₄ EBC)Cl ₂ ]·H ₂ O , [Co(H ₄ EBC)Cl ₂ (H ₂ O) ₂ ]·2H ₂ O and [Ni(H ₄ EBC)Cl ₂ (H ₂ O)]·2H ₂ O display emission broad‐bands at 342, 321 and 337 nm, respectively. The microbial behavior of the synthesized moieties was investigated against various bacterial and fungal strains. [Cu₂(H₄EBC)Cl₂]·H₂O complex shows the same activity as ampicillin towards Escherichia coli and Staphylococcus aureus with inhibition zones of 26 and 22 mm, respectively. Antioxidant activity is determined using bleomycin‐dependent DNA damage assay besides erythrocyte hemolysis. Finally, in vitro cytotoxic activities against two different cell lines have been examined.     

Comparative study between two fabricated potentiometric sensors to enhance selectivity towards ferrous ions

Electroanalytical methods are highly selective for measuring electrical quantities including the charge, potential and current with their relation to chemical parameters. They are widely applied in various fields such as biochemical analysis, industrial quality control and environmental monitoring. They have many advantages over other techniques in that they are not time consuming and are specific for certain oxidation states of certain elements which give these techniques high selectivity and sensitivity features. This paper is based on two parts: the first part describes the fabrication of screen‐printed electrodes (SPEs) modified with methyl red as electroactive material, while second part describes the preparation and characterization of Fe(II)–methyl red complex using various spectroscopic tools, the complex being used for the construction of carbon paste electrodes (CPEs). The two proposed electrodes were successfully applied for the determination of Fe(II) in water and pharmaceutical (pharovit) samples. The electrodes under investigation show potentiometric response for Fe(II) in the concentration range 8.0 × 10^?7–1.0 × 10^?2 and 5.0 × 10^?7–1.0 × 10^?2 M at 25°C for SPE and CPE, respectively, and the electrode response is independent of pH in the range 1.5–7.0. These sensors show Nernstian slopes of 29.1 ± 0.2 and 29.7 ± 0.16 mV decade^?1 with detection limit values of 8.0 × 10^?7 and 5.0 × 10^?7 M for SPE and CPE, respectively. These electrodes show fast response time of 6 and 4 s and exhibit a lifetime of 100 and 30 days for SPE and CPE, respectively. The mechanism of chemical reaction between modifier and Fe(II) on the SPE surface was studied using infrared spectra, scanning electron microscopy and energy‐dispersive X‐ray analysis. The proposed potentiometric method was validated according to the IUPAC recommendations. The results obtained using the proposed sensors were comparable with those obtained with inductively coupled plasma analysis.     

Design and Synthesis of Aromatic Polyesters Bearing Pendant Clickable Maleimide Groups

A bisphenol bearing pendant maleimide group, namely, N‐maleimidoethyl‐3, 3‐bis(4‐hydroxyphenyl)‐1‐isobenzopyrrolidone (PPH‐MA) was synthesized starting from phenolphthalein. Aromatic (co)polyesters bearing pendant maleimide groups were synthesized from PPH‐MA and aromatic diacid chlorides, namely, isophthaloyl chloride (IPC), terephthaloyl chloride (TPC), and 50:50 mol % mixture of IPC and TPC by low temperature solution polycondensation technique. Copolyesters were also synthesized by polycondensation of different molar proportions of PPH‐MA and bisphenol A with IPC. Inherent viscosities and number‐average molecular weights of aromatic (co)polyesters were in the range of 0.52–0.97 dL/g and 20,200–32,800 g/mol, respectively indicating formation of medium to reasonably high‐molecular‐weight polymers. ¹³C NMR spectral analysis of copolyesters revealed the formation of random copolymers. The 10% weight loss temperature of (co)polyesters was found in the range 470–484 °C, indicating their good thermal stability. A selected aromatic polyester bearing pendant maleimide groups was chemically modified via thiol‐maleimide Michael addition reaction with two representative thiol compounds, namely, 4‐chlorothiophenol and 1‐adamantanethiol to yield post‐modified polymers in a quantitative manner. Additionally, it was demonstrated that polyester containing pendant maleimide groups could be used to form insoluble crosslinked gel in the presence of a multifunctional thiol crosslinker. © 2018 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2019 , 57, 630–640     

Strong red emissions induced by Pt–Pt interactions in binuclear cycloplatinated(II) complexes containing bridging diphosphines

A series of dinuclear cycloplatinated(II) complexes with general closed formula of [Pt₂Me₂(C^N)₂(μ‐P^P)] (C^N = 2‐vinylpyridine (Vpy), 2,2′‐bipyridine N‐oxide (O‐bpy), 2‐(2,4‐difluorophenyl)pyridine (dfppy); P^P = 1,1‐bis(diphenylphosphino)methane (dppm), N,N‐bis(diphenylphosphino)amine (dppa)) are reported. The complexes were characterized by means of NMR spectroscopy. Due to the presence of dppm and dppa with short backbones as bridging ligands, two platinum centres are located in front of each other in these complexes so a Pt…Pt interaction is established. Because of this Pt…Pt interaction, the complexes have bright orange colour under ambient light and are able to strongly emit red light under UV light exposure. These strong red emissions originate from a ³MMLCT (metal–metal‐to‐ligand charge transfer) electronic transition. In most of these complexes, the emissions have unstructured bell‐shaped bands, confirming the presence of large amount of ³MMLCT character in the emissive state. Only the complexes bearing dfppy and dppa ligands reveal dual luminescence: a high‐energy structured emission originating from ³ILCT/³MLCT (intra‐ligand charge transfer/metal‐to‐ligand charge transfer) and an unstructured low‐energy band associated with ³MMLCT. In order to describe the nature of the electronic transitions, density functional theory calculations were performed for all the complexes.