Coriolis effects in symmetric top spectra /

The "x-y Coriolis Coupling Theory" as presented by Dilauro and Mills (1966) is reformulated and extended to the determination of Raman intensities. Theoretical Raman and Infrared spectra are computed in order to understand the effects due to this coupling in both types of spectra. Both the Infrared and Raman spectra obtained indicate very real effects due to Coriolis coupling. In some of the cases chosen the computed spectra are grossly different from the normal spectra where coupling is absent. Such large effects can greatly impede the interpretation of experimental results. Theoretical spectra therefore aids in the interpretation of experimental results, as is clearly demonstrated in the results of this work.

Large amplitude motions in the S1 state of formic acid /

A detailed theoretical investigation of the large amplitude motions in the S, excited electronic state of formic acid (HCOOH) was done. This study focussed on the the S, «- So electronic band system of formic acid (HCOOH). The torsion and wagging large amplitude motions of the S, were considered in detail. The potential surfaces were simulated using RHF/UHF ab-initio calculations for the two electronic states. The energy levels were evaluated by the variational method using free rotor basis functions for the torsional coordinates and harmonic oscillator basis functions for the wagging coordinates. The simulated spectrum was compared to the slit-jet-cooled fluorescence excitation spectrum allowing for the assignment of several vibronic bands. A rotational analysis of certain bands predicted that the individual bands are a mixture of rotational a, b and c-type components.The electronically allowed transition results in the c-type or Franck-Condon band and the electronically forbidden, but vibronically allowed transition creates the a/b-type or Herzberg-Teller components. The inversion splitting between these two band types differs for each band. The analysis was able to predict the ratio of the a, b and c-type components of each band.

Towards the enantioselective synthesis of lycoricidine alkaloids /

Two efficient, regio- and stereo controlled synthetic approaches to the synthesis of racemic analogs of pancratistatin have been accomplished and they serve as the model systems for the total synthesis of optically active 7-deoxy-pancratistatin. In the Diels-Alder approach, an efficient [4+2] cycloaddition of 3,4-methylenedioxyco- nitrostyrene with Danishefsky's diene to selectively form an exo-nitro adduct has been developed as the key step in the construction of the C-ring of the target molecule. In the Michael addition approach, the key step was a conjugate addition of an organic zinc-cuprate to the 3,4-methylenedioxy-(B-nitrostyrene, followed by a diastereocontroUed closure to form the cyclohexane C-ring of the target molecule via an intramolecular nitro-aldol cyclization on a neutral alumina surface. A chair-like transition state for such a cyclization has been established and such a chelation controlled transition state can be useful in the prediction of diastereoselectivity in other related 6-exo-trig nitroaldol reactions. Cyclization of the above products fi^om both approaches by using a Bischler-Napieralski type reaction afforded two lycoricidine derivatives 38 and 50 in good yields. The initial results from the above modeling studies as well as the analysis of the synthetic strategy were directed to a chiral pool approach to the total synthesis of optically active 7-deoxy-pancratistatin. Selective monsilylation and iodination of Ltartaric acid provided a chiral precursor for the proposed key Michael transformation. The outlook for the total synthesis of 7-deoxy-pancratistatin by this approach is very promising.A concise synthesis of novel designed, optically pure, Cz-symmetrical disulfonylamide chiral ligands starting from L-tartaric acid has also been achieved. This sequence employs the metallation of indole followed by Sfj2 replacement of a dimesylate as the key step. The activity for this Cz-symmetric chiral disulfonamide ligand in the catalytic enantioselective reaction has been confirmed by nucleophilic addition to benzaldehyde in the disulfonamide-Ti (0-i-Pr)4-diethylzinc system with a 48% yield and a 33% e.e. value. Such a ligand tethered with a suitable metal complex should be also applicable towards the total synthesis of 7-deoxy-pancratistatin.

Using stimulus equivalence to teach monetary skills to school-age children with autism

The present study evaluated the use of stimulus equivalence in teaching monetary skills to school aged children with autism. An AB within-subject design with periodic probes was used. At pretest, three participants demonstrated relation DA, an auditory-visual relation (matching dictated coin values to printed coin prices). Using a three-choice match-to-sample procedure, with a multi-component intervention package, these participants were taught two trained relations, BA (matching coins to printed prices) and CA (matching coin combinations to printed prices). Two participants achieved positive tests of equivalence, and the third participant demonstrated emergent performances with a symmetric and transitive relation. In addition, two participants were able to show generalization of learned skills with a parent, in a second naturalistic setting. The present research replicates and extends the results of previous studies by demonstrating that stimulus equivalence can be used to teach an adaptive skill to children with autism.

Fluorescence spectra and ab initio theoretical studies of HCOOH /

A fluorescence excitation spectrum of formic acid monomer (HCOOH) , has been recorded in the 278-246 nm region and has been attributed to an n >7r* electron promotion in the anti conformer. The S^< S^ electronic origins of the HCOOH/HCOOD/DCOOH/DCOOD isotopomers were assigned to weak bands observed at 37431.5/37461.5/37445.5/37479.3 cm'''. From a band contour analysis of the 0°^ band of HCOOH, the rotational constants for the excited state were estimated: A'=1.8619, B'=0.4073, and C'=0.3730 cm'\ Four vibrational modes, 1/3(0=0), j/^(0-C=0) , J/g(C-H^^^) and i/,(0-H^yJ were observed in the spectrum. The activity of the antisymmetric aldehyde wagging and hydroxyl torsional modes in forming progressions is central to the analysis, leading to the conclusion that the two hydrogens are distorted from the molecular plane, 0-C=0, in the upper S. state. Ab initio calculations were performed at the 6-3 IG* SCF level using the Gaussian 86 system of programs to aid in the vibrational assignments. The computations show that the potential surface which describes the low frequency OH torsion (twisting motion) and the CH wagging (molecular inversion) motions is complex in the S^ excited electronic state. The OH and CH bonds were calculated to be twisted with respect to the 0-C=0 molecular frame by 63.66 and 4 5.76 degrees, respectively. The calculations predicted the existence of the second (syn) rotamer which is 338 cm'^ above the equilibrium configuration with OH and CH angles displaced from the plane by 47.91 and 41.32 degrees.

Extracting Ramachandran torsional angle distributions from 2D NMR data using Tikhonov regularization /

Solid state nuclear magnetic resonance (NMR) spectroscopy is a powerful technique for studying structural and dynamical properties of disordered and partially ordered materials, such as glasses, polymers, liquid crystals, and biological materials. In particular, twodimensional( 2D) NMR methods such as ^^C-^^C correlation spectroscopy under the magicangle- spinning (MAS) conditions have been used to measure structural constraints on the secondary structure of proteins and polypeptides. Amyloid fibrils implicated in a broad class of diseases such as Alzheimer's are known to contain a particular repeating structural motif, called a /5-sheet. However, the details of such structures are poorly understood, primarily because the structural constraints extracted from the 2D NMR data in the form of the so-called Ramachandran (backbone torsion) angle distributions, g{^,'4)), are strongly model-dependent. Inverse theory methods are used to extract Ramachandran angle distributions from a set of 2D MAS and constant-time double-quantum-filtered dipolar recoupling (CTDQFD) data. This is a vastly underdetermined problem, and the stability of the inverse mapping is problematic. Tikhonov regularization is a well-known method of improving the stability of the inverse; in this work it is extended to use a new regularization functional based on the Laplacian rather than on the norm of the function itself. In this way, one makes use of the inherently two-dimensional nature of the underlying Ramachandran maps. In addition, a modification of the existing numerical procedure is performed, as appropriate for an underdetermined inverse problem. Stability of the algorithm with respect to the signal-to-noise (S/N) ratio is examined using a simulated data set. The results show excellent convergence to the true angle distribution function g{(j),ii) for the S/N ratio above 100.

Investigation of molecular polarizabilities and derivatives in halomethanes

The research undertaken was to obtain absolute Raman intensities for the symmetric stretching vibrations of the methyl halides, CH3X with (X=F, CI, Br), by experiment and theory. The intensities were experimentally measured using the Ar+ ion gas laser as excitation source, a Spex 14018 double monochromator and a RCA C-31034 photomultiplier tube as detector. These intensities arise from changes in the derivative of the polarizability (8 a'), with respect to vibration along a normal coordinate (8qi). It was intended that these derivatives obtained with respect to normal coordinates would be converted to derivatives with respect to internal coordinates, for a quantitative comparison with theory. Theoretical numerical polarizability derivatives for the stretching vibrations are obtained using the following procedure. A vibration was simulated in the molecule by increasi.ng and decreasing the respective bond by the amount ±o.oosA for the C-H bonds and ±o.oIA for the C-X (X=F, CI, Br) bond. The derivative was obtained by taking the difference in the polarizability for the equilibrium geometry and the geometry when a particular bond is changed. This difference, when divided by the amount of change in each bond and the number of bonds present results in the derivative of the polarizability with respect to internal coordinate i.e., !1u/!1r. These derivatives were obtained by two methods: I} ab initio molecular orbital calculation and 2} theory of atoms in molecules (AIM) analysis. Due to errors in the experimental setup only a qualitative analysis of the results was undertaken relative to the theory. Theoretically it is predicted that the symmetric carbonhalogen stretch vibrations are more intense than the respective carbon-hydrogen stretch, but only for the methyl chloride and bromide. The carbon fluorine stretch is less intense than the carbon-hydrogen stretch, a fact which is attributed to the small size and high electronegativity of the fluorine atom. The experimental observations are seen to agree qualitatively with the theory results. It is hoped that when the experiment is repeated, a quantitative comparison can be made. The analysis by the theory of atoms in molecules, along with providing polarizabilities and polarizability derivatives, gives additional information outlined below. The theory provides a pictorial description of the main factors contributing to the molecular polarizability and polarizability derivative. These contributions are from the charge transfer and atomic dipole terms i.e., transfer of charge from one atom to another and the reorganization of atomic electronic charge distribution due to presence of an electric field. The linear relationship between polarizability and molecular volume was also observed.

Molecular mechanics calculations of tin-bis (triphenylphosphine oxide) complexes

The capability of molecular mechanics for modeling the wide distribution of bond angles and bond lengths characteristic of coordination complexes was investigatecl. This was the preliminary step for future modeling of solvent extraction. Several tin-phosphine oxide COrnI)le:){es were selected as the test groUl) for t.he d,esired range of geometry they eX!libi ted as \-vell as the ligands they cOD.tained r Wllich were c\f interest in connection with solvation. A variety of adjustments were made to Allinger's M:M2 force·-field ill order to inl.prove its performance in the treatment of these systems. A set of u,nique force constants was introduced for' those terms representing the metal ligand bond lengths, bond angles, and, torsion angles. These were significantly smaller than trad.itionallY used. with organic compounds. The ~1orse poteIlt.ial energ'Y function was incorporated for the M-X l')ond lE~ngths and the cosine harmonic potential erlerg-y function was invoked for the MOP bond angle. These functions were found to accomodate the wide distribution of observed values better than the traditional harmonic approximations~ Crystal packing influences on the MOP angle were explored thr"ollgh ttle inclusion of the isolated molecule withil1 a shell cc)ntaini11g tl1e nearest neigl1'bors duri.rlg energy rninimization experiments~ This was found to further improve the fit of the MOP angle.

Solid state NMR chemical shifts as an alternative to diffraction data in the determination of SIC polytypic structures

Silicon carbide, which has many polytypic modifications of a very simple and very symmetric structure, is an excellent model system for exploring, the relationship between chemical shift, long-range dipolar shielding, and crystal structure in network solids. A simple McConnell equation treatment of bond anisotropy effects in a poly type predicts chemical shifts for silicon and carbon sites which agree well with the experiment, provided that contributions from bonds up to 100 A are included in the calculation. The calculated chemical shifts depend on three factors: the layer stacking sequence, electrical centre of gravity, and the spacings between silicon and carbon layers. The assignment of peaks to lattice sites is proved possible for three polytypes (6H, 15R, and 3C). The fact that the calculated chemical shifts are very sensitive to layer spacings provides us a potential way to detennine and refine a crystal structure. In this work, the layer spacings of 6H SiC have been calculated and are within X-ray standard deviations. Under this premise, the layer spacings of 15R have been detennined. 29Si and 13C single crystal nmr studies of 6H SiC polytype indicate that all silicons and carbons are magnetically anisotropic. The relationship between a magnetic shielding tensor component and layer spacings has been derived. The comparisons between experimental and semi-empirical chemical shielding tensor components indicate that the paramagnetic shielding of silicon should be included in the single crystal chemical shift calculation.

An analysis of the methyl rotation dynamics in the So (x' A) and T (a A) states of thioacetaldehyde from Pyrolysis jet spectra /

Jet-cooled, laser-induced phosphorescence excitation spectra (LIP) of thioacetaldehyde CH3CHS, CH3CDS, CD3CHS and CD3CDS have been observed over the region 15800 - 17300 cm"^ in a continuous pyrolysis jet. The vibronic band structure of the singlet-triplet n -* n* transition were attributed to the strong coupling of the methyl torsion and aldehydic hydrogen wagging modes . The vibronic peaks have been assigned in terms of two upper electronic state (T^) vibrations; the methyl torsion mode v^g, and the aldehydic hydrogen wagging mode v^^. The electronic origin O^a^ is unequivocally assigned as follows: CH3CHS (16294.9 cm"'' ), CH3CDS (16360.9 cm"'' ), CD3CHS (16299.7 cm"^ ), and CD3CDS (16367.2 cm"'' ). To obtain structural and dynamical information about the two electronic states, potential surfaces V(e,a) for the 6 (methyl torsion) and a (hydrogen wagging) motions were generated by ab initio quantum mechanical calculations with a 6-3 IG* basis in which the structural parameters were fully relaxed. The kinetic energy coefficients BQ(a,e) , B^(a,G) , and the cross coupling term B^(a,e) , were accurately represented as functions of the two active coordinates, a and 9. The calculations reveal that the molecule adopts an eclipsed conformation for the lower Sq electronic state (a=0°,e=0"') with a barrier height to internal rotation of 541.5 cm"^ which is to be compared to 549.8 cm"^ obtained from the microwave experiment. The conformation of the upper T^ electronic state was found to be staggered (a=24 . 68° ,e=-45. 66° ) . The saddle point in the path traced out by the aldehyde wagging motion was calculated to be 175 cm"^ above the equilibrium configuration. The corresponding maxima in the path taken by methyl torsion was found to be 322 cm'\ The small amplitude normal vibrational modes were also calculated to aid in the assignment of the spectra. Torsional-wagging energy manifolds for the two states were derived from the Hamiltonian H(a,e) which was solved variationally using an extended two dimensional Fourier expansion as a basis set. A torsionalinversion band spectrum was derived from the calculated energy levels and Franck-Condon factors, and was compared with the experimental supersonic-jet spectra. Most of the anomalies which were associated with the interpretation of the observed spectrum could be accounted for by the band profiles derived from ab initio SCF calculations. A model describing the jet spectra was derived by scaling the ab initio potential functions. The global least squares fitting generates a triplet state potential which has a minimum at (a=22.38° ,e=-41.08°) . The flatter potential in the scaled model yielded excellent agreement between the observed and calculated frequency intervals.

Generating finite integral relation algebras

Relation algebras and categories of relations in particular have proven to be extremely useful as a fundamental tool in mathematics and computer science. Since relation algebras are Boolean algebras with some well-behaved operations, every such algebra provides an atom structure, i.e., a relational structure on its set of atoms. In the case of complete and atomic structure (e.g. finite algebras), the original algebra can be recovered from its atom structure by using the complex algebra construction. This gives a representation of relation algebras as the complex algebra of a certain relational structure. This property is of particular interest because storing the atom structure requires less space than the entire algebra. In this thesis I want to introduce and implement three structures representing atom structures of integral heterogeneous relation algebras, i.e., categorical versions of relation algebras. The first structure will simply embed a homogeneous atom structure of a relation algebra into the heterogeneous context. The second structure is obtained by splitting all symmetric idempotent relations. This new algebra is in almost all cases an heterogeneous structure having more objects than the original one. Finally, I will define two different union operations to combine two algebras into a single one.

Market reactions to changes in the Nasdaq-100 Index membership

We examine stock market reactions around the Nasdaq-100 Index reconstitutions. We find a symmetric and transitory price response accompanied by a significant increase in trading volume on the effective date. Firms added to the Nasdaq-100 Index experience significant increases in institutional ownership, the number of market makers, and the number of shareholders. In contrast, firms removed from the index show significant decreases in the number of institutional shareholders. Additions to the Nasdaq-100 Index also show significant increases in four liquidity measures, whereas deletions demonstrate significant decreases in two liquidity measures. These changes in liquidity are related to the abnormal return on the announcement day. Taken together, the results suggest support for the price pressure, liquidity, and investor awareness hypotheses.

Region Connection Calculus: Composition Tables and Constraint Satisfaction Problems

Qualitative spatial reasoning (QSR) is an important field of AI that deals with qualitative aspects of spatial entities. Regions and their relationships are described in qualitative terms instead of numerical values. This approach models human based reasoning about such entities closer than other approaches. Any relationships between regions that we encounter in our daily life situations are normally formulated in natural language. For example, one can outline one's room plan to an expert by indicating which rooms should be connected to each other. Mereotopology as an area of QSR combines mereology, topology and algebraic methods. As mereotopology plays an important role in region based theories of space, our focus is on one of the most widely referenced formalisms for QSR, the region connection calculus (RCC). RCC is a first order theory based on a primitive connectedness relation, which is a binary symmetric relation satisfying some additional properties. By using this relation we can define a set of basic binary relations which have the property of being jointly exhaustive and pairwise disjoint (JEPD), which means that between any two spatial entities exactly one of the basic relations hold. Basic reasoning can now be done by using the composition operation on relations whose results are stored in a composition table. Relation algebras (RAs) have become a main entity for spatial reasoning in the area of QSR. These algebras are based on equational reasoning which can be used to derive further relations between regions in a certain situation. Any of those algebras describe the relation between regions up to a certain degree of detail. In this thesis we will use the method of splitting atoms in a RA in order to reproduce known algebras such as RCC15 and RCC25 systematically and to generate new algebras, and hence a more detailed description of regions, beyond RCC25.

The Cenozoic Gonyaulacacean Dinoflagellate Genera Operculodinium Wall, 1967 and Protoceratium Bergh, 1881 and Their Phylogenetic Relationships

The palynology of Ocean Drilling Program Site 1007, leeward of the present Bahamas Bank, provides insights into upper Oligocene–lower Pleistocene dinoflagellate cyst associations in the tropical Americas. These associations are reviewed along with the sedimentary paleoenvironment to provide context for a morphological study of the cystdefined dinoflagellate Operculodinium bahamense and its comparison with the thecadefined dinoflagellate Protoceratium reticulatum which produces a cyst assignable to the cyst-defined genus Operculodinium. Detailed reconstructions of the tabulation in both species reveal strong similarities, having a sexiform hyposomal tabulation and L-type or modified L-type ventral organization. Protoceratium reticulatum has dextral torsion of the hypotheca, requiring assignation of the genus to the subfamily Cribroperidinioideae, whereas Operculodinium bahamense has neutral torsion requiring assignation to the subfamily Leptodinioideae. Results either imply polyphyletic origins for the genus Operculodinium or that combinations of ventral organization and torsion cannot always be applied rigidly to subdivide the family Gonyaulacaceae.