In-plane Vibrational Modes Research Articles

The laser photoelectron spectrum of gas phase aniline

An effusive molecular beam of aniline vapor has been two-step ionized by irradiating it with the output from a frequency doubled dye laser. Photoelectrons ejected while exciting several different vibronic levels of its 1B2 electronic state have been kinetic energy analyzed. In all cases ions are found to be generated in their ground electronic state. Their vibrational state distribution is strongly wavelength dependent and differs remarkably from that obtained in conventional single photon photoelectron spectroscopy. The energies of several in-plane vibrational modes of aniline cations have been measured. In contrast with the ground electronic state of the neutral molecule, the ground state of the ion and 1B2 excited electronic state of the neutral molecule both appear to be nearly planar.

Mode specificity in the unimolecular dissociation of formaldehyde (H2CO→H2+CO), a two-mode model

The reaction path (the minimum energy path in mass-weighted Cartesian coordinates) and all the coupling functions which fully characterize the reaction path Hamiltonian of Miller, Handy, and Adams [J. Chem. Phys. 72, 99 (1980)], have been calculated for the unimolecular dissociation of formaldehyde (H2CO→H2+CO) in its ground electronic state. The reaction coordinate and the four other in-plane vibrational modes are strongly coupled to each other, but the out-of-plane vibration is coupled directly only to the reaction coordinate. Calculations of the type of Waite and Miller [J. Chem. Phys. 73, 3713 (1980); 74, 3910 (1981)] for the state-specific unimolecular rate constants are carried out for a two-mode model consisting of the reaction coordinate and the out-of-plane vibration, and one observes a significant degree of mode specificity; i.e., the unimolecular rate constant for a given metastable state is not a smooth function of the energy of the state. It is suggested that this mode specificity may persist in the complete six-mode system.

A normal mode analysis of free base porphin

The in-plane vibrational modes of free base porphin have been calculated. The results are compared to high resolution single-site fluorescence spectra and a tentative assignment of some experimental i.r. vibrational frequencies is made. The importance of the peripheral hydrogen atoms in vibronic analyses of porphins is discussed.

An intuitive approach to group representation theory

The purpose of this article is to outline a nonrigorous and highly intuitive introductory approach to the sort of group representation theory used in molecular and solid state physics. We examine the real three-space spanned by orthonormal polar basis vectors {‖i〉, i=1,2,3}; first it is shown that the familiar block diagonal ’’rotation matrix’’ is simply the {‖i〉} representation of the geometric transformation operator ?φ which causes a counterclockwise rotation of any three-space polar vector by the angle φ about the ‖3〉 axis. By applying this argument to the group of symmetry operators of the ammonia molecule, it becomes self-evident that the two irreducible representations obtainable from the {‖i〉} representation of C3v correspond to subspaces of real-space invariant relative to the six operators of that group. And the basis vectors which span these invariant subspaces (and which produce the corresponding irreducible representations) have clearly defined symmetry (A1 and E) properties under the operations of C3v. This idea is further illustrated in consideration of the representation produced by the in-plane normal modes of vibration of the three hydrogen atoms in ammonia. Finally, it is shown that the approach can readily be extended into function space.

In-plane normal vibrations of 1,2,5-oxa-, thia- and selena-diazoles, 1,3,4-oxa- and thia-diazoles and 1,2,3,4-thiatriazoles

In-plane vibration modes of 1,2,5- and 1,3,4-oxa- and thia-diazoles, and 1,2,5-selenadiazole have been assigned on the basis of detailed normal coordinate analysis employing data on several deuterated species. In-plane vibration frequencies of two 1,2,3,4-thiatriazole derivatives have been calculated and compared with observed values.

Theoretical Calculations of the Raman Intensities by the Vibronic Method. II. The In-plane Vibrations of Ethylene

Abstract The values of the transition moment of Raman scattering have been calculated according to the formula derived from the vibronic method. The calculations have been performed for the in-plane vibrational modes of ethylene determined by three different sets of force constants. The electronic wave functions were calculated by the CNDO/2-CI method. From the relative Raman intensities of three A1g-vibrations of ethylene in the respective cases, it was found that the Raman intensities are sensitive to the vibrational modes. Also, the Raman intensities of ethylene were calculated by the polarizability method in order to compare the results with those obtained from the vibronic method. From the results of these calculations, the conclusions of the previous work have been confirmed.

Theory of the Transport Properties in Graphite

The electrical conductivity, the magnetoresistance, the Hall coefficient and the thermoelectric power of single crystal graphite are theoretically calculated as functions of the temperature and magnetic field intensity in the region where lattice scattering is dominant. The values of the electron-phonon coupling constants which fit the theory to the experimental results best are: D 1 =16.2 eV and D 2 =3.73 eV. Here D 1 and D 2 denote the coupling constants related with the in-plane vibration (mode 1) and the out-of-plane vibration (mode 2) respectively. The field and temperature dependence of the magnetoresistance is in qualitative agreement with the measurements by Soule, while the calculated Hall coefficient has the opposite signs to the experimental results. These discrepancies may be closely related with the neglect of the trigonal symmetry of the bands (γ 3 ). The thermoelectric power calculated is positive and increases monotonously with increasing temperature, but there is no available data to be c...