A nonsymmetric matrix with integer eigenvalues

A nonsymmetric N?×?N matrix with elements as certain simple functions of N distinct real or complex numbers r ₁, r ₂, …, r_N is presented. The matrix is special due to its eigenvalues???the consecutive integers 0,1,2, …, N?1. Theorems are given establishing explicit expressions of the right and left eigenvectors and formulas for recursive calculation of the right eigenvectors. A special case of the matrix has appeared in sampling theory where its right eigenvectors, if properly normalized, give the inclusion probabilities of the conditional Poisson sampling design.     

Three new ɑ-pyrone derivatives induced by chemical epigenetic manipulation of Penicillium herquei,an endophytic fungus isolated from Cordyceps sinensis

Abstract

Chemical epigenetic manipulation was applied to explore secondary metabolite of an endophytic fungus Penicillium herquei, which was obtained from the fruiting body of Cordyceps sinensis, and three previously undescribed polyketides with pyran-2-one scaffold were isolated from its fermentation broth containing 10?mg/L 5-aza-2-deoxycytidine (a frequently-used DNA methyltransferase inhibitor). The structures of these new compounds were identified by extensive spectroscopic analyses, and their absolute configurations were elucidated by quantum chemical ECD calculations.     

Catalytic activation of nitrobenzene on PVP passivated silver cluster: A DFT investigation

Poly(N‐vinyl‐2‐pyrrolidone) (PVP) has been used extensively to stabilize the surface of noble metal nanoparticles against aggregation and also to produce anisotropic nanostructures. Naturally, it is very important to understand the effect of such surface stabilization by PVP on the catalytic activity of these nanoparticles. This communication investigates through DFT calculations the electronic properties of PVP stabilized 13‐atom Ag cluster for catalytic activation of nitrobenzene (NB). These computations suggest that poly(N‐vinyl‐2‐pyrrolidone) (PVP) interact with silver (Ag) cluster mainly through oxygen atom and acts not only as a stabilizer to prevent the aggregation of Ag clusters but also as an electron donor to activate the Ag clusters for further reaction. Natural Bonding Orbital (NBO) calculations show that catalytic activation of NB by PVP passivated Ag cluster occurs due to interaction of the oxygen of the nitro group with the Ag cluster. Weak back donation of electrons from M(dπ) orbital of Ag to antibonding σ* of one of the N O bond, facilitates the formation of the nitroso intermediate. To understand the extent and the nature of this interaction better, vibrational frequency calculation of nitrobenzene association with Ag13‐2PVP cluster is carried out. Red shift in the frequencies is consequence of strong interaction with that of silver cluster present in Ag13‐2PVP‐NB model.     

Liquid Crystals Posessing 1,2,4-Trisubstituted Benzene Derivatives

Abstract

The present work deals with synthesis of two homologous series possessing ester and amide linkage and a large lateral aryl substituent. The large lateral group is attached to the main molecule through an amide linkage. Mesogenic amides are rare even when the amide linkage is present in the main molecular framework. However, in the present work the compounds containing amide linkage in lateral moiety also exhibit mesophases of high thermal stability.     

Synthesis of New β,β′-Diketodithioethers via Swern Oxidation and Study of Their Hydrazone Formation Rate

The synthesis of β,β′-diketodithioethers 4b–j from corresponding β,β′-dihydroxydithioethers 3b–j was carried out by a Swern oxidation using DMSO-oxalyl chloride as oxidizing agent. β,β′-Dihydroxydithioethers 3b–j were prepared by the reaction of two molar equivalents of epoxides 1b–j with dimercaptoethane 2 in the presence of a saturated aqueous solution of potassium carbonate. The reactivity behavior of imine formation of the β,β′-diketodithioethers 4b–j by 2,4-dinitrophenylhydrazine was also investigated, and a mechanism was proposed by using molecular orbital (MO) calculations. To confirm the proposed mechanism, the role of the thia function to activate hydrazone formation by measuring HOMO-LUMO energy levels was also demonstrated.     

The cell effect in adamantane adsorption on graphitized thermal carbon black

Nonequivalence of the nodal and bridging carbon atoms of the adamantane molecule during adsorption on graphitized thermal carbon black was shown. The nonequivalence is related to a special type of intermolecular interaction, the cell effect. Based on the experimental data and the molecular statistical calculations of Henry's constants, the parameters of atomatom potentials for the nodal carbon atoms in the adamantane molecule were found. This atom-atom potential differs from that known for the carbon atom in the sp³-hybridization. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 5, pp. 849–853, May, 2000.     

Theoretical Study of the Germylene Insertion Reaction into the A‐H Bond of First‐Row and Second‐Row AHn Hydrides

The insertion of dimethylgermylene into the A–H bond of AHn hydrides is calculated using the CCSD(T) method in comparsion with the density functional theory (B3LYP) with the 6‐311G* basis set. The B3LYP values reproduce the CCSD(T) results very well. The present theoretical calculations suggest that (a) for germylene insertions there is a very clear trend toward lower activation barriers and more exothermic interactions on going from left to right along a given row, and (b) for the second‐row hydrides, the insertion reactions are more exothermic than for the first‐row hydrides, and the reaction barriers are lower.     

Structural and Theoretical Insights into the AIE Attributes of Phosphindole Oxide: The Balance Between Rigidity and Flexibility

Multiple intramolecular motions consume the excited‐state energy of luminogenic molecules upon photoexcitation and lower the emission efficiency. The low frequency rotational motion of aromatic rings can be facilely restricted by steric constraint in the condensed phase, but the high frequency bond stretching motion can hardly be suppressed by aggregation. In this work, three phosphorus‐containing heterocycles, 1,2,3,4,5‐pentaphenylphosphole‐1‐oxide (PPPO), 1,2,3‐triphenylphosphindole‐1‐oxide (TPPIO), and 1,2,3‐triphenylphosphindole (TPPI), were synthesized and characterized. Their optical properties, crystal‐packing manners, electronic features, and fluorescence dynamics were systematically investigated, and theoretical calculations were performed to decipher structure–property relationships. The results reveal that these luminogens are weak emitters in solutions but show strong emission in aggregates, exhibiting obvious aggregation‐induced emission (AIE) features. The aggregation‐insensitive stretching motion, which is dominant in PPPO, is lowered in TPPIO, enabling TPPIO to fluoresce much more efficiently than PPPO in aggregates. The stretching motion is even more lowered in TPPI, but its relatively planar conformation suffers emission quenching due to strong π–π stacking interactions in aggregates. Therefore, a twisted molecular conformation consisting of a rigid stator and a rotatable periphery is demonstrated to be a rational design for more efficient AIE luminogens.     

Formation of polymer-modified electrodes from 2-mercaptobenzoxazole in aqueous solution

A polymer-modified electrode can be formed from 2-mercaptobenzoxazole (MBO) on glassy carbon (GC) electrodes in aqueous solution. Film formation occurs during prolonged cycling with positive scan limits above +600 mV vs. SCE. The main redox process is the oxidation of MBO to bis(benzoxazolyl) disulfide and the re-reduction to MBO. However, several side reactions including polymerization are observed. A density functional calculation of the MBO radical shows that there is a considerable spin density not only at the sulfur atom but also at the nitrogen atom and at some of the carbon atoms. Therefore ring-ring coupling products other than the disulfide can be formed which may further react to the polymer film. Notably, FTIR spectra indicate substitution at the nitrogen atom. The coupling would explain the occurrence of both thione and bridging sulfur as well as amine and imine nitrogen in the formed polymer. These binding states in the film have been identified by X-ray photoelectron spectroscopy (XPS). Elemental sulfur could not be detected by cyclic voltammetry or XPS of cooled samples. The polymer film is not redox active and non-conducting, as illustrated by the self-limiting growth and the diminishing currents during the potentiodynamic film growth. The film is impermeable for anions. At pH 7 the film is permeable for cations, while it is impermeable for anions and cations at pH 4. Electronic Publication