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.     

Highly Proton-Conductive Zinc Metal-Organic Framework Based On Nickel(II) Porphyrinylphosphonate

The design of new solid-state proton-conducting materials is a great challenge for chemistry and materials science. Herein, a new anionic porphyrinylphosphonate-based MOF ( IPCE-1Ni ), which involves dimethylammonium (DMA) cations for charge compensation, is reported. As a result of its unique structure, IPCE-1Ni exhibits one of the highest value of the proton conductivity among reported proton-conducting MOF materials based on porphyrins (1.55×10⁻³ S cm⁻¹ at 75 °C and 80 % relative humidity).     

Tween 20-stabilized gold nanoparticles combined with adenosine triphosphate-BODIPY conjugates for the fluorescence detection of adenosine with more than 1000-fold selectivity

This study describes the development of a simple, enzyme-free, label-free, sensitive, and selective system for detecting adenosine based on the use of Tween 20-stabilized gold nanoparticles (Tween 20-AuNPs) as an efficient fluorescence quencher for boron dipyrromethene-conjugated adenosine 5′-triphosphate (BODIPY-ATP) and as a recognition element for adenosine. BODIPY-ATP can interact with Tween 20-AuNPs through the coordination between the adenine group of BODIPY-ATP and Au atoms on the NP surface, thereby causing the fluorescence quenching of BODIPY-ATP through the nanometal surface energy transfer (NSET) effect. When adenosine attaches to the NP surface, the attached adenosine exhibits additional electrostatic attraction to BODIPY-ATP. As a result, the presence of adenosine enhances the efficiency of AuNPs in fluorescence quenching of BODIPY-ATP. The AuNP-induced fluorescence quenching of BODIPY-ATP progressively increased with an increase in the concentration of adenosine; the detection limit at a signal-to-noise ratio of 3 for adenosine was determined to be 60 nM. The selectivity of the proposed system was more than 1000-fold for adenosine over any adenosine analogs and other nucleotides. The proposed system combined with a phenylboronic acid-containing column was successfully applied to the determination of adenosine in urine.