The electronic structure of Ti2 and Ti2(+)

The Ti(2) and Ti(2)(+) molecular systems have been studied through multireference variational and single reference coupled-cluster methods coupled with large basis sets. Potential energy curves have been constructed for 30 (Ti(2)) and 2 (Ti(2)(+)) states and the usual spectroscopic parameters have been extracted. The main feature of the potential curves is the existence of van der Waals minima (Ti(2)) around 7 bohr irrespective of the molecular symmetry, and 4s(2)-4s(1) interactions (Ti(2)(+)) around 6 bohr. Numerous avoided crossings lead to stronger covalent bonds emanating from 4s(1)-4s(1) atomic distributions. The X-state of the neutral species is formally a (3)Δ(g) state with the first excited state lying within 1 kcal/mol. The removal of the symmetry defining e(-) leads to the X(2)Σ(g)(+) state of Ti(2)(+).     

Elektrometrie

Ohne Zusammenfassung     

Algorithms for large scale set covering problems

This paper is concerned with the set covering problem (SCP), and in particular with the development of a new algorithm capable of solving large-scale SCPs of the size found in real-life situations. The set covering problem has a wide variety of practical applications which, in general, yield large and sparse instances, normally with hundreds of rows and thousands of columns. In this paper, we present an algorithm capable of solving problems of this size and test problems up to 400 rows and 4000 columns are solved. The method developed in this paper consists of a tree-search procedure based on a combination of decomposition and state space relaxation which is a technique developed for obtaining lower bounds on the dynamic program associated with a combinatorial optimization problem. The large size SCPs are decomposed into many smaller SCPs which are then solved or bounded by state space relaxation (SSR). Before using the decomposition and SSR, reductions both in the number of columns and the number of rows of the problem are made by applying Lagrangian relaxation, linear programming and heuristic methods.     

Extensions to a Lagrangean relaxation approach for the capacitated warehouse location problem

In this paper we present a lower bound for the capacitated warehouse location problem based upon the Lagrangean relaxation of a mixed-integer formulation of the problem, where we use subgradient optimisation in an attempt to maximise this lower bound. Problem reduction tests based upon this lower bound and the original problem are given. Incorporating this bound and the reduction tests into a tree search procedure enables us to solve problems involving up to 50 warehouses and 150 customers.     

A restricted Lagrangean approach to the traveling salesman problem

We describe an algorithm for the asymmetric traveling salesman problem (TSP) using a new, restricted Lagrangean relaxation based on the assignment problem (AP). The Lagrange multipliers are constrained so as to guarantee the continued optimality of the initial AP solution, thus eliminating the need for repeatedly solving AP in the process of computing multipliers. We give several polynomially bounded procedures for generating valid inequalities and taking them into the Lagrangean function with a positive multiplier without violating the constraints, so as to strengthen the current lower bound. Upper bounds are generated by a fast tour-building heuristic. When the bound-strengthening techniques are exhausted without matching the upper with the lower bound, we branch by using two different rules, according to the situation: the usual subtour breaking disjunction, and a new disjunction based on conditional bounds. We discuss computational experience on 120 randomly generated asymmetric TSP's with up to 325 cities, the maximum time used for any single problem being 82 seconds. This is a considerable improvement upon earlier methods. Though the algorithm discussed here is for the asymmetric TSP, the approach can be adapted to the symmetric TSP by using the 2-matching problem instead of AP.Research supported by the National Science Foundation through grant no. MCS76-12026 A02 and the U.S. Office of Naval Research through contract no. N0014-75-C-0621 NR 047-048.     

Magnetically modified single and turbostratic stacked graphenes from tris(2,2'-bipyridyl) iron(II) ion-exchanged graphite oxide

Loading of graphite oxide (GO) with tris(2,2'-bipyridyl) iron(II) ions and subsequent calcination affords a novel graphene-based composite with magnetic and electrically conductive properties. The pH of the starting aqueous suspension and the washing procedure play a crucial role in the successful immobilization of the iron precursor, which is mainly governed by ion exchange. The complex is intercalated between the graphene oxide layers, where it adopts a distorted conformation. Rapid heating of this solid results in the deflagration of GO and the formation of ultrafine ( d = 2-14 nm) Fe2O3 particles with maghemite as the dominant phase. The superparamagnetic maghemite crystals are dispersed uniformly in the high-surface-area diamagnetic matrix built up from single or turbostratic stacked graphenes.     

High-stability hydrogenated silicon-carbon clusters: a full study of Si2C2H2 in comparison to Si2C2, C2B2H4, and other similar species

The structural and electronic characteristics of the Si2C2H2 and Si2C2 clusters are studied by ab initio calculations based on coupled cluster and density functional theory using the hybrid B3LYP functional. In addition, similar species, such as SiC2H2 and Si3C2H2, are also studied for comparison. It is illustrated that the lowest energy structures of all three hydrogenated clusters, which have the general form Si(n)(CH)2, n = 1, 2, 3, are fully analogous to the structures of the corresponding organometallic isovalent carboranes. The most stable structure of Si2C2H2 is obtained by attaching two hydrogens onto the carbon atoms of a higher energy (+1.5 eV) planar trapezoidal structure of Si2C2, followed by geometry optimization which leads to puckering of the planar structure. Furthermore, it is demonstrated that Si2C2H2 and the other two "similar" hydrogenated clusters are much more stable than the corresponding bare nonhydrogenated clusters. Comparison of Si2C2H2 and C2B2H4 shows that their structural and bonding similarity includes also nuclear rearrangement similarity. The two species are isomerizable with an energy difference between their lowest energy puckered 1,2- and 1,3-isomers of about +/-0.3 eV. It is suggested that SiC2H2, Si2C2H2, and Si3C2H2 are special cases of a larger class of stable clusters. It is speculated on the basis of the calculated infrared spectrum that Si2C2H2 and perhaps other members of this class of clusters could be found in appreciable abundance in interstellar space.     

Some physicochemical aspects of nanoparticulate magnetic iron oxide colloids in neat water and in the presence of poly(vinyl alcohol)

The preparation of magnetic iron oxide colloids directly from the coprecipitation of Fe (2+) and Fe (3+) species at different temperatures may lead to crystallites of higher size as the temperature of the reaction increases. On the other hand, dynamic light scattering investigations and dielectric measurements rather point to the similar colloidal size of the entities existing in their aqueous or solid-state dispersions, irrespective of the size of the primary nanocrystallites. Significant enhancement of the stability of the colloids, even in the presence of high electrolyte concentrations, is furnished after the addition of relatively small amounts of poly(vinyl alcohol), and the stabilization mechanism is discussed in terms of the various forces participating in the system. The experimental results suggest that the increased colloidal stability is triggered from the particles' decrease of velocity rather than from steric (entropic) effects originating from polymer absorption.     

Stabilization of flat aromatic Si6 rings analogous to benzene: ab initio theoretical prediction

It is shown by ab initio calculations, based on density functional (DFT/B3LYP), and high level coupled-cluster [CCSD(T)] and quadratic CI [QCISD(T)] methods, that flat aromatic silicon structures analogous to benzene (C6H6) can be stabilized in the presence of lithium. The resulting planar Si6Li6 structure is both stable and aromatic, sharing many key characteristics with benzene. To facilitate possible synthesis and characterization of these species, routes of formation with high exothermicity are suggested and several spectral properties (including optical absorption, infrared, and Raman) are calculated.