Gaussian expansions of orbital products for the evaluation of two-electron integrals

A method is described for evaluating multicenter integrals over contracted gaussian-type orbitals by the use of gaussian expansion of orbital products. The expansions are determined by the method of non-linear least squares with constraints. There is no restriction upon the symmetry of the orbital product and the method is applicable to all products arising from s, p and d-type orbitals. Results are given to indicate the accuracy of the method.     

Building mass spectrometers and a philosophy of research

Development of the techniques of ion kinetic energy spectrometry and mass-analyzed ion kinetic energy spectrometry is described. The extension of these concepts to the method of tandem mass spectrometry for direct mixture analysis is traced, and a rationale for the construction of hybrid mass spectrometers is presented. Collisions of polyatomic ions with surfaces are discussed as an outgrowth of gaseous collisions. An attempt is made to describe a philosophy of research that guided the construction of a dozen mass spectrometers and the exploration of organic ion chemistry in as many contexts.     

Linked porphyrin systems

Porphyrin monomers, 5-(monopyridyl)-10,15,20-(triphenyl)porphyrin ( 1 ), 5,10-(dipyridyl)-15,20-(diphenyl)-porphyrin ( 2 ), and 5,15-(dipyridyl)-10,20-{diphenyl)porphyrin ( 3 ), were linked by hydrocarbon chains to form a series of dimers, trimers and polymers. The 5-(monopyridyl)-10,15,20-(triphenyl)porphyrin monomers were linked by 2, 4, 6, 8 and 10 carbon chains through the alkylation of the pyridine nitrogens using the appropriate diiodoalkane to form positively charged linked dimers 4–8 . A trimer 12 was synthesized from two 5-(monopyridyl)-10,15,20-(triphenyl)porphyrin and one 5,10-(dipyridyl)-15,20-(diphenyl)porphyrin linked by a six carbon chain. Hydrocarbon linked (5,10-(dipyridyl)-15,20-(diphenyl)porphyrin)_n ( 13 ) and (5,15-(dipyridyl)-10,20-(diphenyl)porphyrin)_n ( 14 ) were also prepared.     

Intermolecular interactions in pi-stacked conjugated molecules. Synthesis,structure, and spectral characterization of alkyl bithiazole oligomers

Syntheses are reported of new 4,4'-dialkyl-2,2'-bithiazole oligomers that have alkenoxy side chains that are capable of easy conversion to oligomers with functionalized side chains, e.g., terminally substituted hydroxy chains. The crystal structures of two representative oligomers (4,4',4' ',4' "-tetra-(2-propenoxymethyl)-2,2',5',5' ',2' ',2' "-quaterthiazole (3P2) and 4,4',4' ',4' "-tetra-(3-hydroxypropyloxymethyl)-2,2',5',5' ',2' ',2' "-quaterthiazole (3H2)) were determined; 3P2 crystallizes in a pi-stacked motif with two molecules per unit cell, whereas 3H2 forms pi-stacks that are linked with hydrogen bonds to form infinite two-dimensional sheets with one molecule per unit cell. A comparison of the UV-vis spectra of the compounds in solution and in the solid state provides unequivocal evidence for the presence of a Davydov splitting, W(D) approximately 0.2 eV, in solid 3P2. The spectra are interpreted in the framework of molecular exciton theory to extract a value of the intermolecular transfer integral, J approximately 0.2 eV, for a total exciton bandwidth of ca. 0.8 eV. Monte Carlo calculations were used to determine the density of states of the exciton band and the absorption and emission line shapes of the 0 <-- 0 transition. It is suggested that the "three-humped" absorption profile typical of partially crystalline, regioregular polymers is the "optical signature" of pi-stacking.     

Simple method for the quantitative examination of extra column band broadening in microchromatographic systems

In recent years capillary chromatography has gained popularity for trace analyses. Most often UV or electrochemical detection is employed because the small peak volumes make post-column derivatization challenging. We have developed a simple method based on flow injection for determining contributions to peak broadening from post-column reactors. The only requirement for application of our methodology is that diffusion be in the Taylor regime so that radial concentration gradients are relaxed enabling mixing purely by diffusion.     

Evaluation of Electrospun PCL-PLGA for Sustained Delivery of Kartogenin

In this study, kartogenin was incorporated into an electrospun blend of polycaprolactone and poly(lactic-co-glycolic acid) (1:1) to determine the feasibility of this system for sustained drug delivery. Kartogenin is a small-molecule drug that could enhance the outcome of microfracture, a cartilage restoration procedure, by selectively stimulating chondrogenic differentiation of endogenous bone marrow mesenchymal stem cells. Experimental results showed that kartogenin did not affect the electrospinnability of the polymer blend, and it had negligible effects on fiber morphology and scaffold mechanical properties. The loading efficiency of kartogenin into electrospun membranes was nearly 100%, and no evidence of chemical reaction between kartogenin and the polymers was detected by Fourier transform infrared spectroscopy. Analysis of the released drug using high-performance liquid chromatography–photodiode array detection indicated an abundance of kartogenin and only a small amount of its major hydrolysis product. Kartogenin displayed a typical biphasic release profile, with approximately 30% being released within 24 h followed by a much slower, constant rate of release up to 28 days. Although additional development is needed to tune the release kinetics and address issues common to electrospun scaffolds (e.g., high fiber density), the results of this study demonstrated that a scaffold electrospun from biodegradable synthetic polymers is a suitable kartogenin delivery vehicle.     

A Diffusion Approximation for a Markovian Queue with Reneging

Consider a single-server queue with a Poisson arrival process and exponential processing times in which each customer independently reneges after an exponentially distributed amount of time. We establish that this system can be approximated by either a reflected Ornstein–Uhlenbeck process or a reflected affine diffusion when the arrival rate exceeds or is close to the processing rate and the reneging rate is close to 0. We further compare the quality of the steady-state distribution approximations suggested by each diffusion.     

How Focusing Phenomena in the Instructional Environment Support Individual Students' Generalizations

This article sets forth a way of connecting the classroom instructional environment with individual students' generalizations. To do so, we advance the notion of focusing phenomena, that is, regularities in the ways in which teachers, students, artifacts, and curricular materials act together to direct attention toward certain mathematical properties over others. The construct of focusing phenomena emerged from an empirical study conducted during a 5-week unit on slope and linear functions in a high school classroom using a reform curriculum. Qualitative evidence from interviews with 7 students revealed that students interpreted the m value in y = b + mx as a difference rather than a ratio as a result of counterproductive generalization afforded by focusing phenomena. Classroom analysis revealed 4 focusing phenomena, which regularly directed students' attention to various sets of differences rather than to the coordination of quantities.