Structures and binding energies for complexations of different spin states of Ni+ and Ni2+ to aromatic molecules

Abstract

Density functional theory calculations, using the B3LYP parameterisation, were performed to determine structures, vibrational frequencies, and binding energies for complexation of Ni⁺ and Ni²⁺ cations with benzene and naphthalene molecules and clusters. The calculations employed the Stuttgart basis set with ECP pseudo potentials for the Ni cations and basis sets of at least triple ζ plus polarisation, and diffuse quality for C and H. The effect of electron correlation on non-bonded interactions was accounted for by the Grimme GD3 dispersion correction. Counterpoise computations were made for BSSE. Comparison between experiment and theory provide fascinating new insight into the bonding for these prototypical organometallic (OM) complexes. These structures have a sandwich topology, indicating major structural reorganisations occuring when benzene or naphthalene interact with Ni cations. Adiabatic electron affinities and ionisation potentials agree well with experiment when available. Binding energies were also determined, providing insight into the stability of the complexes. The results presented here provide important information for future studies to address additional investigations of both problems of the electronic structure properties of these complexes, as well as the role of the polycyclic aromatic hydrocarbons (PAHs) in the interstellar medium (ISM) and soot formation in combustion. The Ni⁺/Ni²⁺ + aromatic organometallic bonding is of the same order of stability as an aromatic C–H bond. Such bonding modifies the IR spectrum of the complexed aromatic molecules by enhancing the 3.3?μm feature and decreasing the C–H bands in the 11–12?μm range (γ C–H). Organometallic complexation reactions may contribute significantly to metal depletion in the ISM.     

New results on the cp-rank and related properties of co(mpletely )positive matrices

Copositive and completely positive matrices play an increasingly important role in Applied Mathematics, namely as a key concept for approximating NP-hard optimization problems. The cone of copositive matrices of a given order and the cone of completely positive matrices of the same order are dual to each other with respect to the standard scalar product on the space of symmetric matrices. This paper establishes some new relations between orthogonal pairs of such matrices lying on the boundary of either cone. As a consequence, we can establish an improvement on the upper bound of the cp-rank of completely positive matrices of general order and a further improvement for such matrices of order six.     

The Ordered Gradual Covering Location Problem on a Network

In this paper we develop a network location model that combines the characteristics of ordered median and gradual cover models resulting in the Ordered Gradual Covering Location Problem (OGCLP). The Gradual Cover Location Problem (GCLP) was specifically designed to extend the basic cover objective to capture sensitivity with respect to absolute travel distance. The Ordered Median Location problem is a generalization of most of the classical locations problems like p-median or p-center problems. The OGCLP model provides a unifying structure for the standard location models and allows us to develop objectives sensitive to both relative and absolute customer-to-facility distances. We derive Finite Dominating Sets (FDS) for the one facility case of the OGCLP. Moreover, we present efficient algorithms for determining the FDS and also discuss the conditional case where a certain number of facilities is already assumed to exist and one new facility is to be added. For the multi-facility case we are able to identify a finite set of potential facility locations a priori, which essentially converts the network location model into its discrete counterpart. For the multi-facility discrete OGCLP we discuss several Integer Programming formulations and give computational results.     

Conjugate addition of allyl stannanes with concomitant triflation

A new method for the conjugate addition of allyltributylstannane with concomitant triflation is described. This reaction works with functionalized enones, enals, enoates, and vinylogous esters. The resulting vinyl triflates can be used for intramolecular Heck reactions to afford the products of 5-exo-trig cyclization.