Cyclopentadienyl Complexes of the Alkaline Earths in Light of the Periodic Trends

The electron-rich cyclopentadienyl and the analogous indenyl and fluorenyl ligands (collectively denoted here as Cp’) have been impactful in stabilizing electron-deficient metal centers including the highly electropositive alkaline earths. Being in the s-block, the group 2 metals follow a major periodic variation in their atomic and ionic properties which is reflected in those Cp’ compounds. This article presents an overview of this class of compounds for all the five metals from beryllium to barium (radium is excluded for its radioactivity), highlighting their systematic variation.     

Application of an efficient multireference approach to free-base porphin and metalloporphyrins: ground, excited, and positive ion states

The improved virtual orbital-complete active space configuration interaction (IVO-CASCI) method is applied to determine the geometries of the ground state of free-base porphin and its metal derivatives, magnesium and zinc porphyrins. The vertical excitation energies and ionization potentials are computed at these optimized geometries using an IVO-based version of multireference Mo?ller-Plesset (IVO-MRMP) perturbation theory. The geometries and excitation energies obtained from the IVO-CASCI and IVO-MRMP methods agree well with experiment and with other correlated many-body methods. We also provide the ground state vibrational frequencies for free-base porphin and Mg-porphyrin. All frequencies are real in contrast to self-consistent field treatments which yield an imaginary frequency. Ground state normal mode frequencies (scaled) of free-base porphin and magnesium porphyrin from IVO-CASCI and complete active space self-consistent field methods are quite similar and are consistent with Becke-Slater-Hartree-Fock exchange and Lee-Yang-Parr correlation density functional theory calculations and with experiment. In addition, geometries are determined for low-lying excited state triplets and for positive ion states of the molecules. To our knowledge, no prior experimental and theoretical data are available for these excited state geometries of magnesium and zinc porphyrins. Given that the IVO-CASCI and IVO-MRMP computed geometries and excitation energies agree favorably with experiment and with available theoretical data, our predicted excited state geometries should be equally accurate.     

Ultrafast electron transfer in a nanocavity. dimethylaniline to coumarin dyes in hydroxypropyl gamma-cyclodextrin

Photoinduced electron transfer (PET) from N,N-dimethylaniline (DMA) to four coumarin dyes (C151, C481, C153, and C480) inside the cavity of hydroxypropyl gamma-cyclodextrin (hpCD) is studied using femtosecond upconversion. The rate of PET is found to be nonexponential and to vary significantly with the coumarin dyes. The rate for C481 is 100 times faster than that for C480. The PET rate displays a bell-shaped dependence on the free energy change and thus reveals a Marcus-type inverted region. The anisotropy decay of the four dyes in hpCD are found to be very similar, and hence the observed variation in the rate of PET is not due to variation in rotational diffusion of the acceptors (coumarin dyes).     

Extending asymmetric convergence and Cauchy condition using ideals

In this paper we use the notion of ideals to extend the convergence and Cauchy conditions in asymmetric metric spaces. The asymmetry (or rather, absence of symmetry) of these spaces makes the whole treatment different from the metric case and we use a genuinely asymmetric condition called (AMA) to prove many results and show that certain classic results fail in the asymmetric context if the assumption is dropped.     

CO-Induced Dinitrogen Fixation and Cleavage Mediated by Boron

The boron atoms react with carbon monoxide and dinitrogen forming the end-on bonded NNBCO complex in solid neon or in nitrogen matrices. The NNBCO complex rearranges to the (η²-N₂)BCO isomer with a more activated side-on bonded dinitrogen ligand upon visible light excitation. (η²-N₂)BCO and its weakly CO-coordinated complexes further isomerize to the NBNCO and B(NCO)₂ molecules with N−N bond being completely cleaved under UV light irradiation. The geometries, energies and vibrational spectra of the molecules are calculated with quantum chemical methods and the electronic structures are analyzed with charge- and energy-partitioning methods.     

Optimal harvesting and complex dynamics in a delayed eco-epidemiological model with weak Allee effects

In this article, an eco-epidemiological system with weak Allee effect and harvesting in prey population is discussed by a system of delay differential equations. The delay parameter regarding the time lag corresponds to the predator gestation period. Mathematical features such as uniform persistence, permanence, stability, Hopf bifurcation at the interior equilibrium point of the system is analyzed and verified by numerical simulations. Bistability between different equilibrium points is properly discussed. The chaotic behaviors of the system are recognized through bifurcation diagram, Poincare section and maximum Lyapunov exponent. Our simulation results suggest that for increasing the delay parameter, the system undergoes chaotic oscillation via period doubling. We also observe a quasi-periodicity route to chaos and complex dynamics with respect to Allee parameter; such behavior can be subdued by the strength of the Allee effect and harvesting effort through period-halving bifurcation. To find out the optimal harvesting policy for the time delay model, we consider the profit earned by harvesting of both the prey populations. The effect of Allee and gestation delay on optimal harvesting policy is also discussed.