Crystalline cohomology and GL(2, ℚ)

This paper applies recent advances in crystalline cohomology to the classical case of open elliptic modular curves. In so doing control is gained over the action of inertia in the Galois representations attached to modular forms. Our aim is to study the modular Galois representations attached to automorphic forms modp of weightk≥2. We generalize to higher weightk several results which were previously accessible only in the case of weight 2 where jacobian varieties can be invoked. Additionally we reconsider Gross’s theorem on companion forms in a crystalline context. Partially supported by NSF grant DMS 90-02744. Partially supported by NSA grant MDA904-90-H-4020 and by a PSC-CUNY grant.     

On Atkin-Lehner Quotients of Curves

We study the erednik–Drinfeld p-adic uniformization ofcertain Atkin–Lehner quotients of Shimura curves overQ. We use it to determine over which local fields they haverational points and divisors of a given degree. Using a criterionof Poonen and Stoll, we show that the Shafarevich–Tategroup of their jacobians is not of square order for infinitelymany cases. 1991 Mathematics Subject Classification 11G18, 11G20,14G20, 14G35, 14H40.     

CHARACTERISTICS OF THE CHEMILUMINESCENCE FROM THE BLOOD PLASMA OF A NORMAL HUMAN POPULATION

Oxygen-dependent chemiluminescence was detected from human blood plasma. The intensity of the chemiluminescence increased about three-fold under oxygenation and decreased almost to the background (zero) level under a nitrogen atmosphere. The blood plasma from a sample (n = 100) of donors was tested to determine the variability of several properties of the chemiluminescence in a normal population. No statistically significant difference in blood plasma chemiluminescence between genders was found, but there was a slight increase in luminescence intensity with age. However, the results were found to be dependent on a number of other factors, such as diet, smoking and the length of time between the donor's last meal and the sampling of the blood. Some of the trends in the results coincide with similar trends in the plasma lipoprotein levels and thus support the suggestion that the chemiluminescence arises from the decomposition of lipid hydroperoxides. These factors must all, therefore, be taken into account when using chemiluminescence as an indicator of illness.     

On the extent of intramolecular hydrogen bonding in gas-phase and hydrated 1,2-ethanediol

We investigate the quantum dynamical nature of hydrogen bonding in 1,2-ethanediol and monohydrated 1,2-ethanediol using different levels of ab initio theory. Global full-dimensional potential energy surfaces were constructed from PW91/cc-pVDZ, B3LYP/cc-pVDZ, and MP2/cc-pVDZ ab initio data for gas-phase and monohydrated 1,2-ethanediol, using a modified Shepard interpolation scheme. Zero-point energies and nuclear vibrational wave functions were calculated on these surfaces using the quantum diffusion Monte Carlo algorithm. The nature of intra- and intermolecular hydrogen bonding in these molecules was investigated by considering a ground-state nuclear vibrational wavefunction with reduced complete nuclear permutation and inversion (CNPI) symmetry. Separate wavefunction histograms were determined from the ground-state nuclear vibrational wavefunction by projection into bondlength coordinates. The O-H and O-O wavefunction histograms and vibrationally averaged distances were then used to probe the extent of intra- and intermolecular hydrogen bonding. From these data, we conclude that gas-phase ethanediol may possess a weak hydrogen bond, with a relatively short O-O distance but no detectable proton delocalization. Monohydrated ethanediol was found to exhibit no intramolecular hydrogen bonding but instead possessed two intermolecular hydrogen bonds, indicated by both shortening of the O-O distance and significant proton delocalization. The degree of proton delocalization and shortening of the vibrationally averaged O-O distance was found to be dependent on the ab initio method used to generate the potential energy surface (PES) data set.     

Comparison of two genres for linear scaling in density functional theory: purification and density matrix minimization methods

Two classes of linear-scaling methods to replace diagonalization of the one-particle Hamiltonian matrix in density functional theory are compared to each other. Purification takes a density matrix with the correct eigenfunctions and corrects the occupation numbers; density matrix minimization takes a density matrix with correct occupation numbers and corrects the eigenfunctions by rotating the orbitals. Computational comparisons are performed through modification of the MondoSCF program on water clusters and the protein endothelin. A purification scheme and a density matrix minimization scheme, based on the 1,2-contracted Schrodinger equation [D. A. Mazziotti, J. Chem. Phys. 115, 8305 (2001)] are implemented in large systems.     

With regard to the hydrogen bonding in complexes of pyridylureas, less is more. a role for shape complementarity and CH...O interactions?

A pyridylurea.tetraazaanthracenedione complex with three hydrogen bonds is more stable than an analogous complex with four hydrogen bonds. An X-ray analysis and modeling suggests a steric mismatch destabilizing the latter and a CH...O contact enhancing the stability of the former.     

Ruthenium-catalyzed [2 + 2] cycloadditions between bicyclic alkenes and alkynyl halides

Ru-catalyzed [2 + 2] cycloadditions between norbornadiene and alkynyl halides were found to occur in moderate to good yields (32-89%). The presence of the halide moiety greatly enhances the reactivity of the alkyne component in the cycloaddition and can be transformed into a variety of products that are difficult or impossible to obtain via direct cycloaddition. [reaction: see text]     

Calculation of the photodetachment cross sections of the HCN- and HNC- dipole-bound anions as described by a one-electron Drude model

The Drude model for treating the interaction of excess electrons with polar molecules is extended to calculate continuum functions and to evaluate photodetachment cross sections. The approach is applied to calculate the cross sections for photodetachment of dipole-bound electrons from HCN(-) and HNC(-). In addition, an adiabatic model separating the angular and radial degrees of freedom of the excess electron is introduced and shown to account in a qualitative manner for the cross sections.     

AB Initio study of the ground state anions of LiF,NaF, BeO and MgO

We report the results of ab initio calculations on LiF, NaF, BeO, MgO and their anions. Our vertical electron affinities of BeO and LiF are 2.10 and 0.31 eV, respectively. Our BeO electron affinity is 0.33 eV larger and our LiF electron affinity 0.11 eV smaller than the corresponding values of Jordan et al. We also predict stable anions of NaF and MgO, the calculated vertical electron affinities being 0.42 and 2.64 eV, respectively. The variation with bond length of the dipole moments and the Koopmans' theorem and Hartree-Fock estimates of the electron affinities is studied.     

Binding of an electron to a molecular dipole: BeF

Results of extended-basis SCF calculations indicate that BeF may exist as a metastable species. Comparison of results obtained from SCF calculations on neutral BeF₂ with those of BeF shows that the orbital occupied by the electron of BeF is well approximated by the lowest unoccupied molecular orbital of neutral BeF₂.