Molecular QTAIM Topology Is Sensitive to Relativistic Corrections

The topology of the molecular electron density of benzene dithiol gold cluster complex Au₄−S−C₆H₄−S′−Au′₄ changed when relativistic corrections were made and the structure was close to a minimum of the Born–Oppenheimer energy surface. Specifically, new bond paths between hydrogen atoms on the benzene ring and gold atoms appeared, indicating that there is a favorable interaction between these atoms at the relativistic level. This is consistent with the observation that gold becomes a better electron acceptor when relativistic corrections are applied. In addition to relativistic effects, here, we establish the sensitivity of molecular topology to basis sets and convergence thresholds for geometry optimization.     

Through-Space Spin Coupling in a Silver(II) Porphyrin Dimer upon Stepwise Oxidations: AgII⋅⋅⋅AgII,AgII⋅⋅⋅AgIII,and AgIII⋅⋅⋅AgIII Metallophilic Interactions

Metallophilic interactions between closed-shell metal ions are becoming a popular tool for a variety of applications related to high-end materials. Heavier d⁸ transition-metal ions are also considered to have a closed shell and can be involved in such interactions. There is no systematic investigation so far to estimate the structure and energy characteristics of metallophilic interactions in Ag^II/Ag^II (d⁹/d⁹), Ag^III/Ag^III (d⁸/d⁸), and mixed-valent Ag^II/Ag^III (d⁹/d⁸) complexes, which have been demonstrated in the present study. Both interporphyrinic and intermetallic interactions were investigated on stepwise oxidation by using a rigid ethene-bridged cis silver(II) porphyrin dimer and the results compared with those for highly flexible ethane-bridged analogues. By controlling the nature of chemical oxidants and their stoichiometry, both 1e and 2e oxidations were done stepwise to generate Ag^II/Ag^III mixed-valent and Ag^III/Ag^III porphyrin dimers, respectively. Unlike all other ethene-bridged metalloporphyrin dimers reported earlier, in which 2e oxidation stabilizes only the trans form, such an oxidation of silver(II) porphyrin dimer stabilizes only the cis form because of the metallophilic interaction. Besides silver(II) ⋅⋅⋅ silver(II) interactions in cis silver(II) porphyrin dimer, stepwise oxidations also enabled us to achieve various hitherto-unknown silver(II) ⋅⋅⋅ silver(III) and silver(III) ⋅⋅⋅ silver(III) interactions, which thereby allow significant modulation of their structure and properties. The strength of Ag ⋅⋅⋅ Ag interaction follows the order Ag^II/Ag^II (d⁹/d⁹)<Ag^II/Ag^III (d⁹/d⁸)<Ag^III/Ag^III (d⁸/d⁸). Single-crystal XRD, X-ray photoelectron spectroscopy (XPS), ¹H NMR and EPR spectroscopy, and variable-temperature magnetic investigations revealed various oxidation states of silver and metallophilic interactions, which are also well supported by computational analysis.     

New classes of second order difference equations solvable by factorization method

Under some assumptions we find a general solution of the factorization problem for a family of second order difference equations.     

Inner-Sphere Oxygen Activation Promoting Outer-Sphere Nucleophilic Attack on Olefins

Alkoxylation and hydroxylation reactions of 1,5-cyclooctadiene (cod) in an iridium complex with alcohols and water promoted by the reduction of oxygen to hydrogen peroxide are described. The exo configuration of the OH/OR groups in the products agrees with nucleophilic attack at the external face of the olefin as the key step. The reactions also require the presence of a coordinating protic acid (such as picolinic acid (Hpic)) and involve the participation of a cationic diolefin iridium(III) complex, [Ir(cod)(pic)₂]⁺, which has been isolated. Independently, this cation is also involved in easy alkoxy group exchange reactions, which are very unusual for organic ethers. DFT studies on the mechanism of olefin alkoxylation mediated by oxygen show a low-energy proton-coupled electron-transfer step connecting a superoxide–iridium(II) complex with hydroperoxide–iridium(III) intermediates, rather than peroxide complexes. Accordingly, a more complex reaction, with up to four different products, occurred upon reacting the diolefin–peroxide iridium(III) complex with Hpic. Moreover, such hydroperoxide intermediates are the origin of the regio- and stereoselectivity of the hydroxylation/alkoxylation reactions. If this protocol is applied to the diolefin–rhodium(I) complex [Rh(pic)(cod)], free alkyl ethers ORC₈H₁₁ (R=Me, Et) resulted, and the reaction is enantioselective if a chiral amino acid, such as l -proline, is used instead of Hpic.     

Electronic Structure of N-Bridged High-Valent Diiron-Oxo

Density functional theory (DFT) and an advanced ab initio technique based on density matrix renormalization group (DMRG-CASPT2) were employed to investigate a reactive N-bridged high-valent diiron-oxo species involved in H-abstraction reactions. We studied in detail two important doublet states, the ground state with two iron(IV) centers and a mixed valence Fe^V-Fe^IV excited state. We found that the latter state is low-lying. Furthermore, its electronic structure and spin density imply that it has significantly higher H-abstraction reactivity than the ground state. This low-lying excited state might be the reason behind the high oxidation reactivity of this diiron-oxo species towards methane.     

Red shifting of absorption maxima of phenothiazine based dyes by incorporating electron-deficient thiadiazole derivatives as π-spacer

This study was carried out to design phenothiazine based dyes by incorporating electron-deficient thiadiazole derivatives as π-spacer. Density functional theory and time-dependent density functional theory calculations of the geometries, electronic structures and absorption spectra of the dyes before and after binding to titanium oxide were carried out. Effects of the electron-deficient units on the spectra and electrochemical properties have been investigated. Compared with the reference compound CS1A, Dyes 1–4 display remarkably enhanced spectral responses in the red portion of the solar spectrum. The newly designed dyes demonstrate desirable energetic and spectroscopic parameters, and may lead to efficient metal-free organic dye sensitizers for DSSCs.     

Weak Pnictogen Bond with Bismuth: Experimental Evidence Based on Bi−P Through-Space Coupling

To study pnictogen bonding involving bismuth, flexible accordion-like molecular complexes of the composition [P(C₆H₄-o-CH₂SCH₃)₃BiX₃], (X=Cl, Br, I) have been synthesised and characterised. The strength of the weak and mainly electrostatic interaction between the Bi and P centres strongly depends on the character of the halogen substituent on bismuth, which is confirmed by single-crystal X-ray diffraction analyses, DFT and ab initio computations. Significantly, ²⁰⁹Bi–³¹P through-space coupling (J=2560 Hz) is observed in solid-state ³¹P NMR spectra, which is so far unprecedented in the literature, delivering direct information on the magnitude of this pnictogen interaction.     

Diastereoselective Synthesis of Polysubstituted Piperidines through Visible-Light-Driven Silylative Cyclization of Aza-1,6-Dienes: Experimental and DFT Studies

A visible-light-driven radical silylative cyclization of aza-1,6-dienes featuring an acrylonitrile or acrylate moiety and an electron-neutral olefin was developed, which allows for stereoselective synthesis of densely functionalized piperidines in a highly atom-economical manner. Depending on the substitution pattern of the electron-neutral olefin, poor-to-excellent diastereoselectivity was observed. It was suggested that the 6-exo-trig cyclization was initiated by a chemoselective addition of silyl radical toward electron-deficient olefin and the geometry of the remaining olefin is closely associated with the cis-stereoselectivity. DFT calculations supported that a transition state with a cyano group locating at the axial position of the forming piperidine ring might be involved, in which either the increase of 1,3-diaxial repulsion or the lack of hydrogen bonding interaction will diminish diastereoselectivity.     

Optimal recovery of integral operators and its applications

In this paper we present the solution to a problem of recovering a rather arbitrary integral operator based on incomplete information with error. We apply the main result to obtain optimal methods of recovery and compute the optimal error for the solutions to certain integral equations as well as boundary and initial value problems for various PDE’s.