Observer-based output feedback control design for a fractional ODE and a fractional PDE cascaded system.

This paper considers a new bi-directional cascaded system of a fractional ordinary differential equation (FODE) and a fractional partial differential equation (FPDE) which interacts at an intermediate point. The space-dependent coefficients, interaction between the FODE and FPDE at an intermediate point and the presence of fractional calculus makes the FODE-FPDE cascaded system, representative. In this note, we first apply an invertible integral transformation to convert the system into a FODE-FPDE coupled system, as the target system, which is Mittag-Leffler stable.

Electronic effects on atom tunneling: conformational isomerization of monomeric para-substituted benzoic acid derivatives.

We present the first generation and spectroscopic identification of the higher-lying E conformer of the simplest aromatic carboxylic acid, benzoic acid (1a), as its O-deuterated isotopologue (E)-d(1)-1a using matrix-isolation techniques; the parent (E)-1a could not be observed because of fast H-tunneling to the more stable conformer (Z)-1a. Even deuterated (E)-d(1)-1a converts quickly back to (Z)-d(1)-1a through D-tunneling with a half-life (τ) of ∼12 min in Ar at 11 K. Tunneling computations using an Eckart barrier in conjunction with a CCSD(T)/cc-pVTZ//MP2/cc-pVDZ + ZPVE intrinsic reaction path revealed that τ of (E)-1a is only ∼10(-5) min, in marked contrast to those of simple aliphatic acids, which are in the range of minutes.

Understanding the torquoselectivity in 8pi-electrocyclic cascade reactions: synthesis of fenestradienes versus cyclooctatrienes.

Unusual and novel polycyclic cyclooctatrienes, fenestradienes, and fenestrenes form readily from trienynes depending on the structure of the starting trienynes and the reaction conditions. The experimentally observed high torquoselectivities and complete diastereoselectivities of the 8pi-electrocyclization products have been thoroughly studied using density functional computations at B3PW91/6-31G(d,p). The different P- and M-helical topologies for the Mobius aromatic transition structures are the origin of the observed torquoselectivities in the cyclooctatrienes.

Non-Kekulé N-substituted m-phenylenes: N-centered diradicals versus zwitterions.

The relationship between the structures and electronic ground state properties of non-Kekulé-type N-substituted m-phenylenes was studied utilizing density functional theory (DFT), with the aim of determining the factors that lead to ground state triplet diradicals. At B3LYP/6-311G(d,p)//B3LYP/6-311G(d,p) we identified octahydropyridoquinoline with an exceptionally large singlet-triplet energy separation of +27.9 kcal mol(-1), in favor of the triplet.

3,5,7,9-Substituted hexaazaacridines: toward structures with nearly degenerate singlet-triplet energy separations.

Toward the goal of preparing stable, neutral open-shell systems, we synthesized a novel series of p-phenyl-substituted 3,5,7,9-hexaazaacridine and 3,5,7,9-hexaazaanthracene derivatives. The effects of substitution on the molecular electronic properties were probed both experimentally and computationally [B3LYP/6-311G(d,p)//B3LYP/6-31G(d,p)]. While the experimentally prepared structures already have small (20-25 kcal/mol) singlet-triplet energy gaps, systems with even smaller (<9 kcal/mol) singlet-triplet energy separations can be realized through systematic variation of the substituent numbers, types, and patterns.