A(SLq(2)) at Roots of Unity is a Free Module over A(SL(2))

It is shown that when q is a primitive root of unity of order not equal to 2 mod 4, A(SL_q(2)) is a free module of finite rank over the coordinate ring of the classical group SL(2). An explicit set of generators is provided.     

Matrix-isolation FT-IR study and theoretical calculations of the vibrational, tautomeric and H-bonding properties of hypoxanthine

The neutral compound hypoxanthine is investigated using the technique of matrix-isolation FT-IR spectroscopy combined with density functional theory (DFT) and ab initio methods. Two theoretical methods (RHF and DFT/B3-LYP) are compared for vibrational frequency prediction, and four methods (RHF//RHF, MP2//RHF, DFT//DFT and MP2//DFT) for prediction of the relative energies of the tautomers and the interaction energies of the complexes. All the possible tautomeric forms have been considered theoretically, and the results indicate that two oxo forms (O17 and O19) and one hydroxy form (H9-r1) are the three most stable forms. The experimental FT-IR spectra are consistent with this prediction, and nearly all the characteristic spectral features of these forms have been identified in the spectrum. A theoretical study of the H-bonded complexes of these three tautomers with water is also performed. Several structures have been found for each form and the results demonstrate that the closed complexes with two H-bonds are the most stable systems due to the H-bond cooperative effect.     

Electron affinities,gas phase acidities,and potential energy curves: Benzene

The experimental electron affinities of benzene, E_a(Bz), 0.4 to ?4.8 eV, are evaluated. Multiple negative ion states are proposed to account for different electron affinities. The semi‐empirical procedure known as “configuration interaction or unrestricted orbitals to relate experimental quantities to self‐consistent field values by estimating electron correlation” (CURES‐EC) has several advantages: (i) supports multiple E_a(Bz), (ii) supports the E_a(phenyl) and the D(C? H,Bz), (iii) supports the gas phase acidity of benzene from the latter, (iv) predicts the singlet–triplet split for the phenyl anion of 1.2(2) eV, and (v) predicts the existence of an excited quartet state of the benzene anion with an E_a(Bz), ?2.5(2) eV. Nine ionic Morse curves are calculated from CURES‐EC properties and experimental data. These are compared with quantum mechanical crossing “c” potentials obtained using a subroutine in commercial software and ab initio and density functional theory (DFT) procedures. Curves are calculated for the proposed quartet state of the benzene anion. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

MPWB1K calculations of stepwise encapsulations: Lix@C60

Computations are carried out on Li@C₆₀, Li₂@C₆₀ and Li₃@C₆₀ with the newly introduced MPWB1K density functional. The computed equilibrium thermodynamics shows that Li₂@C₆₀ is at least by two orders of magnitude less populated than Li@C₆₀ when the saturated Li vapor is considered while for Li₃@C₆₀ it is at least four orders of magnitude compared to Li@C₆₀. The evaluations correspond to the available experimental findings.     

Strong Connections and Chern–Connes Pairing¶in the Hopf–Galois Theory

We reformulate the concept of connection on a Hopf–Galois extension B⊆P in order to apply it in computing the Chern–Connes pairing between the cyclic cohomology HC ^{2 n} (B) and K ₀ (B). This reformulation allows us to show that a Hopf–Galois extension admitting a strong connection is projective and left faithfully flat. It also enables us to conclude that a strong connection is a Cuntz–Quillen-type bimodule connection. To exemplify the theory, we construct a strong connection (super Dirac monopole) to find out the Chern–Connes pairing for the super line bundles associated to a super Hopf fibration. Received: 8 March 2000 / Accepted: 5 January 2001     

Electromagnetic field in a slab of photonic crystal by BPM

The finite-difference vector beam propagation method is used to simulate propagation of Gaussian light beam in a finite slab of photonic crystal. A possibility to control light flow by the change of symmetry and polarisation of the incident light beam is demonstrated.     

Extended floating spherical Gaussian basis sets for molecules. Alternative correlating orbitals for molecular energy calculations

A procedure previously described for representing large basis SCF results in terms of a smaller floating spherical Gaussian orbital (FSGO) basis set is generalized to apply to the virtual orbitals from the SCF calculation. This provides a method for systematically reducing the dimensions of the virtual space or replacing the virtual orbitals with a simpler, compact basis set. The method is illustrated by application to Lill.     

Vibrational softening of diatomic molecules

An analysis of a model molecular oscillator is presented: a vibrating diatomic molecule carrying N ₀ electrons. The energy derivatives over the number of electron (N) and the deformation (Q), ∂ ⁿ /∂N ⁿ and ∂ ⁿ /∂Q ⁿ have been analyzed up to second order (n=2), including the appropriate mixed derivatives. The effect of coupling between distortion of the electron density induced by ΔN and the vibrational deformation of the molecule has been studied. Anharmonicity of the oscillator has been shown to be a possible result of that coupling; new relations between the parameters characterizing the anharmonicity of the oscillator and the energy derivatives at density functional theory level have been obtained. Ab initio calculations for a set of diatomic molecules have been performed, yielding values for all the derivatives discussed and demonstrating the effect of coupling with vibrations. Received: 1 June 2000 / Accepted: 20 October 2000 / Published online: 21 March 2001