Roland Lefebvre

Calculation of the Electron Spin Resonance Line Shape of Randomly Oriented Molecules in a Triplet State. I. The Δm=2 Transition with a Constant Linewidth

The electron spin resonance line shape for the Δm=2 transition of randomly oriented aromatic molecules in a triplet state is analyzed. This is an extension of the treatment of van der Waals and de Groot to molecules having less than ternary symmetry. In the present paper the spectrum of a molecule is approximated by a Gaussian function of constant width and the electron g tensor is assumed to be isotropic. The various stages of the calculation have been fitted into a computer program, using as input data the principal values of the electron spin‐spin coupling tensor. The calculations show that a characteristic structure may be present in the spectrum. The experimental spectra of naphthalene and its deuterated homologue present in effect enough of this structure to make it possible to determine the absolute values of the two constants characterizing the electron spin—spin interaction.

Use of Computer Programs in the Interpretation of Electron Paramagnetic Resonance Spectra of Dilute Radicals in Amorphous Solid Samples. I. High‐Field Treatment. X‐Band Spectra of π‐Electron Unconjugated Hydrocarbon Radicals

The successive stages of the calculation of a high‐field electron paramagnetic resonance line shape for a radical dilute in a polycrystalline or glassy sample from the parameters of its spin Hamiltonian have been fitted into a computer program. We have considered the general case where there may be a 32 tensor, anisotropic hyperfine couplings, and satellite lines arising from nuclei of any spin up to 32 and approximated the component line shape by a Gaussian function of constant width. Possible uses of such a program are: (1) determining the line shapes associated with some model radicals and establishing approximate rules to facilitate the interpretation of experimental spectra; (2) checking the validity of an assignment of tensors made on the basis of some plausible structure for a species under investigation; and (3) finding the parameters which make the best fit to an observed spectrum. Applications to some π‐electron hydrocarbon radicals are presented, and the possibilities offered by such calculatio...

Calculation of the Electron Spin Resonance Line Shape of Randomly Oriented Molecules in a Triplet State. II. Correlation of the Spectrum with the Zero‐Field Splittings. Introduction of an Orientation‐Dependent Linewidth

The structure in the electron‐spin‐resonance spectrum of randomly oriented molecules in a triplet state is due to resonance fields stationary with respect to a change in the molecular orientation. This is the basis for the derivation of the electron spin—spin coupling constants from such spectra. In this paper we investigate this structure with the help of a computer program which generalizes the one described in Part I to deal with the so‐called Δm=2 spectra. Some rules are derived for the interpretation of spectra. We then examine the possibility of including in such calculations the anisotropy of the electron g tensor and some dependence on the orientation of the linewidth. For the canonical orientations, the linewidth in a variable‐magnetic‐field experiment is shown not to depend on the microwave quantum.

The wavefunction of the complex coordinate method

We show for a model system previously studied by Moiseyev et al. (1978, Molec. Phys., 36, 1613) how, with a basis of sufficient flexibility, the wave-function of the complex coordinate method can approach the function which can be directly obtained from a numerical integration of the wave equation with a complex coordinate and a complex energy. Diagrams of the complex wavefunction are used to visualize its behaviour in the short and long range regions, and the attenuation (localization) produced by the rotation.

Resonance Raman scattering by a predissociative state: A study of nonadiabatic effects

A coupled equation approach is used to study the excitation profiles of the resonant Raman scattering of a predissociative electronic state in a diatomic molecule. The method allows one to calculate also the photopredissociation cross section so that a comparison between the two processes can be made. Calculations are presented for a realistic system, the scattering from the predissociated B 3Π0+ state of IBr.

Coupled equations applied to the photodissociation of linear triatomics: A test of approximate schemes for calculating the line shape and the effect of final states interactions

Coupled equations are used to obtain the line shape and the final probability distribution of linear triatomic molecules undergoing photodissociation. These calculatins provide a test for some current approximations made in the evaluation of the one‐dimensional nuclear overlap integrals needed for the bound‐free couplings. The linearization of the repulsive potential yiels a line shape of correct position and width, although with a somewhate reduced area. The uniform Airy approximation is superior at most energies but may fail at some energy within the line shape. This behavior can be related to a small difference in slopes of the potentials at a crossing point. A study has also been made of the half‐collision formalism which relates the probability distribution for the vibrational states of the diatomic fragment to bound–free couplings and matrix elements of the transition operator on the repulsive surface. It is found that this procedure underestimates the rearrangement of probabilities resulting from f...

Electron Spin Resonance Line Shape of a Polycrystalline CH Radical

A formula is derived for the electron spin resonance line shape of a polycrystalline sample containing the CH π‐electron radical. The assumption is made in this derivation that the spectrum of the radical in a specific orientation is made up of Gaussians. The line shapes are calculated at the X, K, and J bands, and shown to be rather different for a sufficiently small component line width.

Continuum resonance Raman scattering of light by diatomic molecules. I. The role of radiative crossings between the potentials of the dressed molecule

Usual scattering theory only provides a formal result for continuum resonance Raman scattering amplitudes, leaving the task of evaluating numerically these amplitudes. We look instead, in the case of a diatomic molecule, for a system of coupled equations patterned after those of molecular collision theory which can provide them directly (i.e., numerically). These equations emphasize the role of radiative crossings between the potential curves of the dressed molecule (molecule in its initial electronic state with the incoming photon, in its intermediate state with no photon, in its final state with the outgoing photon). The channels involve the potentials of the dressed molecule plus two artificial entrance and exit channels coupled in such a way as to yield the Raman scattering amplitudes through the analysis of one of the elements of the scattering matrix. Electronic transition moments depending on the internuclear distance are easily introduced into the formalism. In order to test the numerical accuracy...

Continuum resonance Raman scattering of light by diatomic molecules. II. Theoretical study of the Q branches of Δn=1 profiles of molecular bromine

The methods developed in Part I for the calculation of continuum resonance Raman scattering amplitudes are applied to the calculation of the Q branches of the Δn=1 profiles of Br2 which have been measured by Baierl and Kiefer [J. Raman Spectrosc. 3, 353 (1975)]. The experimental conditions being such as to imply many initial and final rovibrational states, we first of all study the effect of rotation on the scattering amplitudes. It is observed that while the amplitudes may vary substantially with the rotational number of the initial state, almost no effect is introduced by taking into account the changes in rotational quantum numbers which accompany transitions between different electronic states. This is useful to derive an efficient formula for the scattering cross section. The profiles are then calculated with the potentials available for the 1Π1u and B (3Π+0u) excited states which, as shown by previous workers, interfere strongly in producing the spectra. These calculations make it possible to examin...

Determination of tunneling rates in bound systems using the complex coordinate method

Up to now tunneling rates in bound systems have been obtained primarily by semiclassical or wave packet calculations. A new accurate quantum time‐independent method is presented. Those irregular eigenfunctions of bound systems which diverge asymptotically, but upon complex scaling of coordinates X→X exp(iΘ) become square integrable functions and are associated with complex eigenvalues are found to describe barrier penetration processes. The imaginary part of each of the complex eigenvalues of the complex scaled Hamiltonian contains the tunneling decay rate provided that the Balslev–Combes rotation angle is large enough. The appearance of a critical value Θc as the rotational angle Θ is varied, at which a sharp transition from a real energy spectrum of the bound system to a complex eigenvalue spectrum is an indication of an exponential decay through the potential barrier. Tunneling in multiple barrier problems is important in several areas of physics and chemistry, including isomerization reactions, Joseph...