Calculation of electric multipole moment integrals with the different screening parameters via the Fourier transform method

Three‐center electric multipole moment integrals over Slater‐type orbitals (STOs) can be evaluated by translating the orbitals on one center to the other and reducing the system to an expansion of two‐center integrals. These are then evaluated using Fourier transforms. The resulting expression depends on the overlap integrals that can be evaluated with the greatest ease. They involve expressions for STO with different screening parameters that are known analytically. This work gives the overall expressions analytically in a compact form, based on Gegenbauer polynomials. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012     

Theoretical Investigation on Electronic Transition of Tris(8-quinolinolate) Aluminum Grafted on Poly(p-phenylenevinylene) Units with the Localized-density-matrix Method

An unsystematic molecule PPV‐Alq₃ [3‐(4‐((E)‐2‐(8‐hydroxy‐3‐(4‐styrylstyryl)quinolin‐Alq₂‐6‐yl)vinyl)‐ styryl)‐6‐(4‐styrylstyryl)quinolin‐8‐olate‐Alq₂; q=8‐quinolinolate], which combines poly(p‐phenylenevinylene) with tris(8‐quinolinolate)aluminum, has been studied using a localized‐density‐matrix method. The absorption spectra and electronic transition properties were analyzed and compared with both intermediate neglect of the differential overlap method and the localized‐density‐matrix method. Great efforts have been made on investigating conjugated system on the absorption properties as these can be particularly important for many applications. Two different absorptions of the special molecule, tris(8‐quinolinolate)aluminum grafted on poly(p‐phenylenevinylene) units, were further discussed with density matrices. For the molecule, the first absorption peak is at 413 nm near the purple light. Two 8‐hydroxyquinolines have very slight electronic transition properties. Another absorption peak is at 237 nm. The second characteristic peak of molecule is completely different from that of the first one, which comes from contribution of 8‐hyroxyquinolines in the two different side chains. Our studies show that electronic transition properties of poly(p‐phenylenevinylene) can be effectively tuned by grafting tris(8‐quinolinolate)‐aluminum on poly(p‐phenylenevinylene) from the standpoint of transition energies, frontier molecular orbitals and density matrices.     

Topology of dynamical lattice configurations including results from dynamical overlap fermions

We investigate how the topological charge density in lattice QCD simulations is affected by violations of chiral symmetry caused by the fermion action. To this end we compare lattice configurations generated with a number of different actions including first configurations generated with exact dynamical overlap quarks. We visualize the topological profiles after mild smearing. In the topological charge correlator we measure the size of the positive core, which is known to shrink to zero extension in the continuum limit. To leading order we find the core size to scale linearly with the lattice spacing with the same coefficient for all actions, even including quenched simulations. In the subleading term the different actions vary over a range of about 10%. Our findings suggest that non-chiral lattice actions at current lattice spacings do not differ much for observables related to topology, both among themselves and compared to overlap fermions.     

Hard–soft modeling parallel factor analysis to solve equilibrium processes

PARAFAC model is the most famous model for analyzing three‐way data. However, this method does not converge to chemically meaningful solutions when applied to three‐way problems involving rank overlap profiles at least in one mode. Rank overlap can be simply found where components have similar spectral profiles or analytes appearing in identical proportions throughout an experiment. However, an appropriate selection of the initial parameters and constraints such as non‐negativity and unimodality can still make PARAFAC model useful in this regard. Although such constraints reduce rotational freedom in PARAFAC solution, they are generally insufficient to wholly eliminate the rotational problem. The goal of the present paper is to incorporate hard modeling constraint in the soft‐modeled PARAFAC algorithm to overcome non‐uniqueness problem in the equilibrium processes involving linearly dependent factors at least in one mode. The hard constraint is introduced to force some or all of the concentration profiles to fulfill an equilibrium model that is refined at each iteration cycle of the optimization process of PARAFAC. The proposed approach is called hard–soft PARAFAC (HSPARAFAC). When the rank overlap species obeys equilibrium model in HSPARAFAC, the unique results are obtained even in the presence of non‐modeled interferences. The new modification in the treatment of equilibrium data sets yields more satisfactory results than the exclusive PARAFAC algorithm. Simulated and real examples with rank overlap problem are used to confirm this statement. Copyright © 2011 John Wiley & Sons, Ltd.