ALBERT

Notes: We report a new mechanism for intramolecular vibrational redistribution (IVR) in CF3CHFI which couples the CH chromophore vibrations through a strong Fermi resonance to the formal CF stretching normal mode (a heavy atom frame mode) involving the trans F-atom across the CC bond. The analysis is made possible by comparing spectroscopic results with extensive ab initio calculations of the vibrational fundamental and overtone spectra in the range extending to 12 000 cm−1. Potential energy and electric dipole moment hypersurfaces are calculated ab initio by second order Møller–Plesset perturbation theory (MP2) on a grid involving the CH stretching, two CH bending modes and one high frequency CF stretching normal mode. The potentials are scaled to obtain agreement between the experimental spectrum and the theoretical spectrum calculated by a discrete variable representation technique on this grid. Both spectra are then analyzed in terms of three-dimensional (3D) and four-dimensional (4D) effective vibrational Hamiltonians including Fermi- and Darling–Dennison-type resonances between the CH stretching mode and the CH bending modes and the CF stretching mode. The interaction between the CH modes and the CF mode is clearly visible in the experimental and calculated (4D) spectra. The effective Fermi resonance coupling constants [ksff′(similar, equals)(40±10) cm−1 and ksaf′(similar, equals)(55±10) cm−1] coupling the CH and CF mode subspaces are of about the same magnitude as the intra-CH chromophore Fermi resonances (ksaa′(similar, equals)56 cm−1 and ksbb′(similar, equals)42 cm−1, coupling CH stretching mode "s" with the two CH bending modes "a" and "b"). The chiral, pseudo-Cs symmetry breaking coupling (ksab′(similar, equals)11 cm−1) is complemented by an equally strong coupling through the CF mode (ksfb′(similar, equals)15 cm−1). It is demonstrated that low order perturbation theoretical analysis using potential constants from a polynomial expansion to represent effective coupling constants gives inadequate results with discrepancies ranging about from factors of 2–5. Time dependent population and wave packet analysis shows essentially complete IVR among the CH chromophore modes within about 100 fs, the 3D and 4D evolutions being similar up to about that time. At longer times of about 250 fs, there is substantial excitation of the CF stretching mode (with initial pure CH stretching excitation). The 4D treatment is then essential for a correct description of the dynamics. © 2000 American Institute of Physics.

Notes: The dependence of structural parameters and force constants for Cu–Se, Ga–Se, and In–Se bonds on compositional deviations in CuIn0.5Ga0.5Se2 have been studied. The composition gradient along the ingot was obtained by a single fusion at 1150 °C of the components and subsequent slow cooling in a still ampoule placed in a vertical furnace. All along the sample, a single chalcopyrite phase is present and its composition along its length was found by energy dispersive analysis of x-ray measurements on slices. Unit cell parameters, anion displacement, and Cu occupation fraction in its sublattice were analyzed by x-ray powder diffraction and Rietveld refinement methods. The anion displacement found is a function of the Cu defect in its sublattice. The existence of associated defects, i.e., two Cu vacancies and one Ga in Cu site, [2V(Cu)+GaCu], is proposed to explain the Cu defect in its sublattice and the changes in lattice parameters. This leads to the existence of BIII vacancies (BIII=In+Ga), and interstitial Cu up to 8 at. % that also cause changes in the structural parameters. Infrared reflectance measurements led to the imaginary dielectric constant determination which, fitted to a Lorentz function, permitted to obtain atomic vibration modes. Using the model of Neumann for chalcopyrites, the values of force constants for Cu–Se, Ga–Se, and In–Se bonds were computed. These appear to increase when the occupation of each sublattice increases. © 2000 American Institute of Physics.

Notes: Three different methods to quantize the spherically symmetric sector of electromagnetism are presented: First, it is shown that this sector is equivalent to Abelian BF-theory in four spacetime dimensions with suitable boundary conditions. This theory, in turn, is quantized by both a reduced phase space quantization and a spin network quantization. Finally, the outcome is compared with the results obtained in the recently proposed general quantum symmetry reduction scheme. In the magnetically uncharged sector, where all three approaches apply, they all lead to the same quantum theory. © 2000 American Institute of Physics.

Notes: The group theoretical quantization scheme is reconsidered by means of elementary systems. Already the quantization of a particle on a circle shows that the standard procedure has to be supplemented by an additional condition on the admissibility of group actions. A systematic strategy for finding admissible group actions for particular subbundles of cotangent spaces is developed, two-dimensional prototypes of which are T*R+ and S=S1×R+ (interpreted as restrictions of T*R and T*S1 to positive coordinate and momentum, respectively). In this framework (and under an additional, natural condition) an SO↑(1,2)-action on S results as the unique admissible group action. Furthermore, for symplectic manifolds which are (specific) parts of phase spaces with known quantum theory a simple "projection method" of quantization is formulated. For T*R+ and S equivalent results to those of more established (but more involved) quantization schemes are obtained. The approach may be of interest, e.g., in attempts to quantize gravity theories where demanding nondegenerate metrics of a fixed signature imposes similar constraints. © 2000 American Institute of Physics.

Notes: The appearance of avoided crossings among energy levels as a system parameter is varied is signaled by the presence of square-root branch points in the complex parameter-plane. Even hidden crossings, which are so gradual as to be difficult to resolve experimentally, can be uncovered by the knowledge of the locations of these branch points. As shown in this paper, there are two different analytic structures that feature square-root branch points and give rise to avoided crossings in energy. Either may be present in an actual quantum-mechanical problem. This poses special problems in perturbation theory since the analytic structure of the energy is not readily apparent from the perturbation series, and yet the analytic structure must be known beforehand if the perturbation series is to be summed to high accuracy. Determining which analytic structure is present from the perturbation series is illustrated here with the example of a dimensional perturbation treatment of the diamagnetic hydrogen problem. The branch point trajectories for this system in the complex plane of the perturbation parameter δ (related to the magnetic quantum number and the dimensionality) as the magnetic field strength is varied are also examined. It is shown how the trajectories of the two branch-point pairs as the magnetic field strength varies are a natural consequence of the particular analytic structure the energy manifests in the complex δ-plane. There is no need to invoke any additional analytic structures as a function of the field strength parameter. © 2000 American Institute of Physics.

Notes: Monte Carlo simulations of a model for the stripping of (square root of)3×(square root of)3 R30° alkanethiol lattices from terraces and steps of a (111) metal face in aqueous solutions are presented. In the model the stripping probability of an adsorbed alkanethiolate molecule depends on the applied potential, on intermolecular forces that stabilize the alkanethiol layer, and on the presence of substrate defects. Stabilizing intermolecular forces are also responsible for alkanethiolate aggregate formation during the stripping process. Snapshots and voltammograms derived from the model reproduce experimental STM images and electrochemical data for alkanethiol stripping from the Au(111) surface. © 2002 American Institute of Physics.

Notes: The quantum theory of stress is developed within the atoms in molecules (AIM) framework. The complete local stress field is introduced and integrated within atomic basins, and it is shown that the kinetic term gives rise to the atomic virial theorem. The role of the potential part of the stress field in the AIM theory is discussed, and its necessary consideration in order to define atomic pressures presented. These atomic pressures are shown to tend to the thermodynamic limit as the size of the system grows. A link between the AIM theory and the theory of electronic separability has also been found. A set of simple examples illustrates our results. © 2002 American Institute of Physics.

Notes: A simple algebraic model is used to show that Hirshfeld surfaces in condensed phases may be understood as approximations to the interatomic surfaces of the theory of atoms in molecules. The conditions under which this similarity is valid are explored, and both kinds of surfaces are calculated in the LiF and CS2 crystals to illustrate the main results. The link between Hirshfeld and interatomic surfaces provides a physical ground to understand the usage of the former to visualize intermolecular interactions. © 2002 American Institute of Physics.

Notes: The Raman spectra of P4 and P2 molecules have been studied in nitrogen, argon, krypton, and xenon matrices at 15 K. The vibrational frequencies of the P4 molecule are up to 14 cm−1 higher than the experimental gas phase data. This apparent blue-shift is not caused by matrix effects but rather due to an underestimation of the fundamentals in the gas phase as a course of the elevated temperatures. The observed frequencies confirm a recent theoretical prediction on the basis of high-level calculations. From the observed frequencies of the P4 molecule a general valence force field was calculated. © 2002 American Institute of Physics.

Notes: A new approach to the analysis of the internal phonons of tris(quinolin-8-olato) aluminum(III) is presented, which enlightens the role played by the ligands in determining the vibrational properties of the organometallic compound and evidences the importance of the contributions arising from the coupling terms among the three quinolinato fragments. An accurate exam of the normal modes of the meridianal isomer evidences the role of the interactions among the fragments in the vibrational dynamics of the ground state. Due to the special attention paid to the quinolinato fragments, a preliminary investigation on the vibrational properties of 8-hydroxyquinoline, taken as a model fragment, was also performed. The vibrational properties of the polymorph species β of the organometallic molecule were obtained refining the calculated frequencies, the dipole moment derivative matrix, and the polarizability derivative tensor derived by the hybrid density functional B3LYP/6-31G* comparing with the frequencies and intensities recorded by the infrared and the Raman spectroscopies performed on a polycrystalline sample. One thus obtains the most accurate intramolecular force constants up to date for the meridianal isomer in a crystalline phase. © 2002 American Institute of Physics.