Spectral and scattering theory for a Schrödinger operator with a class of momentum-dependent long-range potentials

Let be the selfadjoint operator for the static electromagnetic field where W _j for 0, 1, 2, ..., n is a sum of (i) a short-range potential and (ii) a smooth long-range potential decreasing at as |x|^- with in (0, 1]. Then for >1/2, asymptotic completeness holds for the scattering system (H, H ₀).     

Ab Initio and DFT Studies on CO2 Interacting with Znq+–Imidazole (q=0, 1, 2) Complexes: Prediction of Charge Transfer through σ‐ or π‐Type Models

Using first‐principles methodologies, the equilibrium structures and the relative stability of CO₂@[Zn^q+Im] (where q=0, 1, 2; Im=imidazole) complexes are studied to understand the nature of the interactions between the CO₂ and Zn^q+–imidazole entities. These complexes are considered as prototype models mimicking the interactions of CO₂ with these subunits of zeolitic imidazolate frameworks or Zn enzymes. These computations are performed using both ab initio calculations and density functional theory. Dispersion effects accounting for long‐range interactions are considered. Solvent (water) effects were also considered using a polarizable continuum model approach. Natural bond orbital, charge, frontier orbital and vibrational analyses clearly reveal the occurrence of charge transfer through covalent and noncovalent interactions. Moreover, it is found that CO₂ can adsorb through more favorable π‐type stacking as well as σ‐type hydrogen‐bonding interactions. The inter‐monomer interaction potentials show a significant anisotropy that might induce CO₂ orientation and site‐selectivity effects in porous materials and in active sites of Zn enzymes. Hence, this study provides valuable information about how CO₂ adsorption takes place at the microscopic level within zeolitic imidazolate frameworks and biomolecules. These findings might help in understanding the role of such complexes in chemistry, biology and material science for further development of new materials and industrial applications.     

Theoretical analysis of the enzyme reaction processes within the multiscale porous biocatalytic electrodes

Mathematical model describing the oxidation of glucose in a multiscale porous biocatalytic electrode is discussed. The model considers herein is composed of two nonlinear differential equations accounting for reaction and diffusion within the hydrogel film. In this letter, approximate analytical expressions for the concentration of mediator, substrate and current have been obtained using the Adomian decomposition method (ADM). Furthermore, a comparison confirmed that our analytical result fitted very well with the numerical solution (Matlab). Sensitivity analysis of the parameters is also reported.     

ENSS' Theory in Long Range Scattering: Second Order Hyperbolic and Parabolic Operators

We prove asymptotic completeness using ENSS' method for h₀(P) + W_S(Q) + W_L(Q) where h₀: Rⁿ → R is a polynomial of degree 2 with lim lim_|ξ|→∞h₀(ξ)| + |Δh₀(ξ)| = ∞, W_S a short range potential and W_L a smooth long range potential.     

Non-linear analysis of Haldane kinetic model in phenol degradation in batch operations

Kinetics and Catalysis - The Haldane kinetic model of phenol biodegradation in batch operation is discussed. This kinetic is most commonly used to describe the dependence of specific growth rate on...     

A conjecture for some partial differential operators on L 2( R n)

OnX =L ²(R ⁿ), letQ = (Q ₁,Q ₂,…,Q _n) andP = (P ₁,P ₂, …,P _n) be the operators given by (Q _jf) (x) =x _jf(x),P _j = - i∂/∂x _j. For anyC ^∞ functionh:R ⁿ →R putH ₀ =h(P) andH =H ₀ + (1 +Q ²)^-δ, where δ > 1/2. By the method of scattering theory we prove thatH _ac, the absolutely continuous part ofH is unitarily equivalent toH ₀ when (a)n = 1 and (b) forn ≥ 2, whenh is in a large class of polynomials. It is conjectured that the results are true for any polynomialh. We use the techniques of Enss’ method and the idea of bound states for momentum.     

Cover Feature: Formation of Eigen or Zundel Features at Protonated Water Cluster–Aromatic Interfaces (ChemPhysChem 16/2023)

Interfacial interactions of protonated water clusters adsorbed at aromatic surfaces play an important role in biology, and in atmospheric, chemical and materials sciences. Here, we investigate the interaction of protonated water clusters ((H⁺H₂O)_n (where n=1–3)) with benzene (Bz), coronene (Cor) and dodecabenzocoronene (Dbc)). To study the structure, stability and spectral features of these complexes, computations are done using DFT-PBE0(+D3) and SAPT0 methods. These interactions are probed by AIM electron density topography and non-covalent interactions index (NCI) analyses. We suggest that the excess proton plays a crucial role in the stability of these model interfaces through strong inductive effects and the formation of Eigen or Zundel features. Also, computations reveal that the extension of the π-aromatic system and the increase of the number of water molecules in the H-bounded water network led to a strengthening of the interactions between the corresponding aromatic compound and protonated water molecules, except when a Zundel ion is formed. The present findings may serve to understand in-depth the role of proton localized at aqueous medium interacting with large aromatic surfaces such as graphene interacting with acidic liquid water. Besides, we give the IR and UV-Vis spectra of these complexes, which may help for their identification in laboratory.     

Multicomponent solid forms of the uric acid reabsorption inhibitor lesinurad and cocrystal polymorphs with urea: DFT simulation and solubility study

Lesinurad (systematic name: 2‐{[5‐bromo‐4‐(4‐cyclopropylnaphthalen‐1‐yl)‐4H‐1,2,4‐triazol‐3‐yl]sulfanyl}acetic acid, C₁₇H₁₄BrN₃O₂S) is a selective uric acid reabsorption inhibitor related to gout, which exhibits poor aqueous solubility. High‐throughput solid‐form screening was performed to screen for new solid forms with improved pharmaceutically relevant properties. During polymorph screening, we obtained two solvates with methanol (CH₃OH) and ethanol (C₂H₅OH). Binary systems with caffeine (systematic name: 3,7‐dihydro‐1,3,7‐trimethyl‐1H‐purine‐2,6‐dione, C₈H₁₀N₄O₂) and nicotinamide (C₆H₆N₂O), polymorphs with urea (CH₄N₂O) and eutectics with similar drugs, like allopurinol and febuxostat, were prepared using the crystal engineering approach. All these novel solid forms were confirmed by XRD, DSC and FT–IR. The crystal structures were solved by single‐crystal and powder X‐ray diffraction. The crystal structures indicate that the lesinurad molecule is highly flexible and the triazole moiety, along with the rotatable thioacetic acid (side chain) and cyclopropane ring, is almost perpendicular to the planar naphthalene moiety. The carboxylic acid–triazole heterosynthon in the drug is interrupted by the presence of methanol and ethanol molecules in their crystal structures and forms intermolecular macrocyclic rings. The caffeine cocrystal maintains the consistency of the acid–triazole heterosynthons as in the drug and, in addition, they are bound by several auxiliary interactions. In the binary system of nicotinamide and urea, the acid–triazole heterosynthon is replaced by an acid–amide synthon. Among the urea cocrystal polymorphs, Form I (P, 1:1) consists of an acid–amide (urea) heterodimer, whereas in Form II (P2₁/c, 2:2), both acid–amide heterosynthons and urea–urea dimers co‐exist. Density functional theory (DFT) calculations further support the experimentally observed synthon hierarchies in the cocrystals. Aqueous solubility experiments of lesinurad and its binary solids in pH 5 acetate buffer medium indicate the apparent solubility order lesinurad–urea Form I (43‐fold) > lesinurad–caffeine (20‐fold) > lesinurad–allopurinol (12‐fold) ? lesinurad–nicotinamide (11‐fold) > lesinurad, and this order is correlated with the crystal structures.     

Application of thermal analysis and kinetic predictions to YBCO films prepared by chemical solution deposition methods

Journal of Thermal Analysis and Calorimetry - Low-temperature DSC on a wide range of opal-A and opal-CT samples was carried out to estimate the proportion of crystallisable water and to determine...     

Structure, stability and spectral signatures of monoprotic carborane acid-water clusters (CBW(n), where n = 1-6)

The gas phase structure, stability, spectra, and proton transfer properties of monoprotic carborane acid-water clusters [CB(11)F(m)H(11-m)(OH(2))(1)]-(H(2)O)(n) (where m = 0, 5, and 10; n = 1-6) have been calculated using density functional theory (DFT) with the Becke's three-parameter hybrid exchange functional and Lee-Yang-Parr correlation functional (B3LYP) using 6-31+G* basis set. Results reveal that Eigen cation defects are found in CBW(n) (where n = 2-6) clusters and these clusters are significantly more stable than the non-Eigen geometry. In addition to the conventional hydrogen bond (H-bond) the role of dihydrogen bond (DHB) and halogen bond (XB) in the stabilization of these clusters can be observed from the molecular graphs derived from the atoms in molecules (AIM) analysis. Spectral information shows the features of Eigen cation and proton oscillation involved in the proton transfer process. The dissociation of proton from the perfluoro derivatives with two water molecules is more favorable when compared to the other derivatives.