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.     

Synthesis,spectral investigation and development of tetrahedral copper(II) complexes as artificial metallonucleases and antimalarial agents

Seven new copper(II) complexes of type [Cu(A)(L)]?H₂O (A = sparfloxacin, ciprofloxacin, levofloxacin, gatifloxacin, pefloxacin, ofloxacin, norfloxacin; L = 5‐[(3‐chlorophenyl)diazenyl]‐4‐hydroxy‐1,3‐thiazole‐2(3H)‐thione) were synthesized and characterized using elemental and thermogravimetric analyses, and electronic, electron paramagnetic resonance (EPR), Fourier transform infrared and liquid chromatography–mass spectroscopies. Tetrahedral geometry around copper is assigned in all complexes using EPR and electronic spectral analyses. All complexes were investigated for their interaction with herring sperm DNA utilizing absorption titration (K_b = 1.27–3.13 × 10⁵ M^?1) and hydrodynamic volume measurement studies. The studies suggest the classical intercalative mode of DNA binding. The cleavage reaction on pUC19 DNA was monitored by agarose gel electrophoresis. The results indicate that the Cu(II) complexes can more effectively promote the cleavage of plasmid DNA. The superoxide dismutase mimic activity of the complexes was evaluated by nitroblue tetrazolium assay, and the complexes catalysed the dismutation of superoxide at pH = 7.8 with IC₅₀ values in the range 0.597–0.900 μM. The complexes were screened for their in vitro antibacterial activity against five pathogenic bacteria. All the complexes are good cytotoxic agents and show LC₅₀ values ranging from 5.559 to 11.912 µg ml^?1. All newly synthesized Cu(II) complexes were also evaluated for their in vitro antimalarial activity against Plasmodium falciparum strain (IC₅₀ = 0.62–2.0 µg ml^?1). Copyright © 2015 John Wiley & Sons, Ltd.     

Feasibility of application of conductometric biosensor based on acetylcholinesterase for the inhibitory analysis of toxic compounds of different nature

This study was aimed at the development of a conductometric biosensor based on acetylcholinesterase considering the feasibility of its application for the inhibitory analysis of various toxicants. In this paper, the optimum conditions for enzyme immobilization on the transducer surface are selected as well as the optimum concentration of substrate for inhibitory analysis. Sensitivity of the developed biosensor to different classes of toxic compounds (organophosphorus pesticides, heavy metal ions, surfactants, aflatoxin, glycoalkaloids) was tested. It is shown that the developed biosensor can be successfully used for the analysis of pesticides and mycotoxins, as well as for determination of total toxicity of the samples. A new method of biosensor analysis of toxic substances of different classes in complex multicomponent aqueous samples is proposed.