Theoretical Study of Formamide Tautomers—A Discussion of Enol-Keto Isomerizations and Their Corresponding Energies

In order to gain insight into the formamide molecule, seven tautomers and twelve transition states are found after being modeled by the density function theory of Becke's three-parameter hybride (B3LYP) type and ab initio Möller–Plesset second-order perturbation (MP2)-type methods. The isomerization phenomena between enol-keto tautomers and transition states via internal rotation or the proton transfer process are surveyed. A localized analysis is also introduced to ascertain the bond character caused by the delocalization of electrons, which will force the formamide tautomers to become planar. The trans effect in the molecule increases molecular stability.     

Subunit rotation models activation of serotonin 5-HT<Subscript>3AB</Subscript> receptors by agonists

The N-terminal extracellular regions of heterooligomeric 3AB-type human 5-hydroxytryptamine receptors (5-HT3ABR) were modelled based on the crystal structure of snail acetylcholine binding protein AChBP. Stepwise rotation of subunit A by 5 degrees was performed between -10 degrees and 15 degrees to mimic agonist binding and receptor activation. Anticlockwise rotation reduced the size of the binding cavity in interface AB and reorganised the network of hydrogen bonds along the interface. AB subunit dimers with different rotations were applied for docking of ligands with different efficacies: 5-HT, m-chlorophenylbiguanide, SR 57227, quinolinyl piperazine and lerisetron derivatives. All ligands were docked into the dimer with -10 degrees rotation representing ligand-free, open binding cavities similarly, without pharmacological discrimination. Their ammonium ions were in hydrogen bonding distance to the backbone carbonyl of W183. Anticlockwise rotation and contraction of the binding cavity led to distinctive docking interactions of agonists with E129 and cation-pi interactions of their ammonium ions. Side chains of several further amino acids participating in docking (Y143, Y153, Y234 and E236) are in agreement with the effects of point mutations in the binding loops. Our model postulates that 5-HT binds to W183 in a hydrophobic cleft as well as to E236 in a hydrophilic vestibule. Then it elicits anticlockwise rotation to draw in loop C via pi-cation-pi interactions of its ammonium ion with W183 and Y234. Finally, closure of the binding cavity might end in rebinding of 5-HT to E129 in the hydrophilic vestibule.     

Fourier Invariant Partially Approximating Subalgebras of the Irrational Rotation C*-Algebra

For a dense G-set of parameters, the irrational rotation algebrais shown to contain infinitely many C*-subalgebras satisfyingthe following properties. Each subalgebra is isomorphic to adirect sum of two matrix algebras of the same (perfect square)dimension; the Fourier transform maps each summand onto theother; the corresponding unit projection is approximately central;the compressions of the canonical generators of the irrationalrotation algebra are approximately contained in the subalgebra.2000 Mathematics Subject Classification 46L80, 46L40, 46L35.     

A rotation-torsion-vibration treatment with three-dimensional internal coordinate approach and additional FTIR spectral assignments for the CH3-bending fundamentals of methanol

A theoretical model has been developed to account for certain features of both newly observed and previously reported CH₃-bending subbands between 1450 and 1570 cm⁻¹ in the high-resolution Fourier transform infrared spectrum of CH₃OH [Can. J. Phys. 79 (2001) 435]. The features include (i) an apparent inversion of the rotationless E-A torsional splitting with respect to the ground state, i.e., the A state located above the E state, (ii) a pronounced upward slope in the K-reduced torsion-vibration energy pattern for the subband origins, and (iii) unexpected A₁/A₂ inversion of the K=2A and K=3AJ-rotational levels that led to ambiguity in identifying the vibrational mode as or . The model is an effective internal coordinate Hamiltonian constructed in G₆ molecular symmetry with the CH₃-bends coupled to each other and to torsion and including a- and γ-type Coriolis coupling. With this model, 33 out of 36 experimental upper-state K-term values for newly assigned , and ν₁₀ subbands plus previous ν₄ subbands have together been fitted successfully, employing 9 adjustable parameters and 17 fixed parameters to give a standard deviation of 0.14 cm⁻¹. The P_γ Coriolis term appears to be the leading cause of the upward shift in the K-reduced energies. When J-dependence is introduced via a rotational Hamiltonian including b- and c-type Coriolis terms in addition to molecular asymmetry, the observed A₁/A₂ inversion of the K=2A and 3A rotational levels can also be reproduced. Predictions using the fitted K-rotation-torsion-vibration Hamiltonian show an interesting Coriolis-induced crossover and mixing of the ν₅ and ν₁₀ torsion-vibration energy patterns. These predictions played a role in identifying two of the new ν₅ subbands in the crossing region, thereby helping to validate the model.     

Microwave Spectra of o-Fluorotoluene and Its 13C Isotopic Species: Methyl Internal Rotation and Molecular Structure

The rotational spectra of o-fluorotoluene and its seven ¹³C isotopic species were recorded in the frequency range from 4 to 20 GHz with employment of pulsed molecular beam Fourier-transform microwave (MB-FTMW) spectrometers. The analysis of the spectra in the two lowest states of methyl internal rotation (torsional ground state, A and E species) was based on a asymmetric frame-rigid symmetric top Hamiltonian with inclusion of centrifugal distortion terms, yielding structural rotational constants, as well as the threefold barrier V ₃ to internal rotation and the angle(a,i) between the principal moment of inertia a axis and the internal rotor axis i. The rotational constants of all eight isotopomeres were used to derive the seven ¹³C r _s coordinates of the molecule.     

Calculation of Two-Center Nuclear Attraction Integrals over Integer and Noninteger n-Slater Type Orbitals in Nonlined-Up Coordinate Systems

Two-center nuclear attraction integrals over Slater type orbitals with integer and noninteger principal quantum numbers in nonlined up coordinate systems have been calculated by means of formulas in our previous work (T. Özdoan and M. Orbay, Int. J. Quant. Chem. 87 (2002) 15). The computer results for integer case are in best agreement with the prior literature. On the other hand, the results for noninteger case are not compared with the literature due to the scarcity of the literature, but also compared with the limit of integer case and good agreements are obtained. The proposed algorithm for the calculation of two-center nuclear attraction integrals over Slater type orbitals with noninteger principal quantum numbers in nonlined-up coordinate systems permits to avoid the interpolation procedure used to overcome the difficulty introduced by the presence of noninteger principal quantum numbers. Finally, numerical aspects of the presented formulae are analyzed under wide range of quantum numbers, orbital exponents and internuclear distances.     

On Certain Extensions of a Rotation Invariant Markov Process

Let (X _t ,P ^x ) be a rotation invariant (RI) Feller process on R ^d {0}, d2. We study certain type of strong Markov extensions of (X _t ,P ^x ) to R ^d . It turns out that that the unique (RI) extension always exists and is of that type. We give a kind of quasi-ergodicy condition (E) under which the (RI) extension is the only extension of that type. A class of processes fulfilling (E) is also characterized.     

Muon Spin Rotation and Relaxation Experiments on Thin Films

The recent development at the Paul Scherrer Institute of a beam of low energy muons allows depth dependent muon spin rotation and relaxation investigations in thin samples, multilayers and near surface regions (low energy SR, LE-SR). After a brief overview of the LE-SR method, some representative experiments performed with this technique will be presented. The first direct determination of the field profile just below the surface of a high-temperature superconductor in the Meissner phase illustrates the power and sensitivity of low energy muons as near-surface probe and is an example of general application to depth profiling of magnetic fields. The evolution of the flux line lattice distribution across the surface of a YBa₂Cu₃O₇ film in the vortex phase has been investigated by implanting muons on both sides of a normal-superconducting boundary. A determination of the relaxation time and energy barrier to thermal activation in iron nanoclusters, embedded in a silver thin film matrix (500nm), demonstrates the use of slow muons to measure the properties of samples that cannot be made thick enough for the use of conventional SR. Other experiments investigated the magnetic properties of thin Cr(001) layers at thicknesses above and below the collapse of the spin density wave.     

Petrov Types of Slowly Rotating Fluid Balls

Circularly rotating axisymmetric perfect fluid space-times are investigated to second order in the small angular velocity. The conditions of various special Petrov types are solved in a comoving tetrad formalism. A number of theorems are stated on the possible Petrov types of various fluid models. It is shown that Petrov type II solutions must reduce to the de Sitter spacetime in the static limit. Two space-times with a physically satisfactory energy-momentum tensor are investigated in detail. For the rotating incompressible fluid, it is proven that the Petrov type cannot be D. The equation of the rotation function can be solved for the Tolman type IV fluid in terms of quadratures. It is also shown that the rotating version of the Tolman IV space-time cannot be Petrov type D.