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Notizen: In this article we derive an expression for the angular distribution of spin-detected electrons emitted in the Auger decay of a vacancy created by photoabsorption in a molecule belonging to one of the 32 point groups. The geometrical factor in the final expression is identical to the one recently obtained by us for angle- and spin-resolved photoelectron spectroscopy of freely rotating, unpolarized polyatomics by using a modified definition of the angular momentum transferred from the ionizing radiation to the outgoing electron. The "reduced'' amplitude in the present case contains, of course, both the Auger decay and photoionization matrix elements. The results derived herein, therefore, mean that identical geometrical analysis is applicable to spin-resolved Auger electron as well as photoelectron spectroscopies of molecules. We, in particular, show that the degree of spin-polarization of Auger electrons emitted following photoabsorption in C∞v and D∞h linear molecules can be completely characterized by four independent parameters. The procedure developed herein is used to predict those molecular vacancies whose Auger decay will give rise to anisotropic angular distribution provided spin of the ejected electron is also observed. The degree of spin polarization of Auger electrons in this case is completely determined by a single parameter, say αa, and does not depend upon the state of polarization of the absorbed photon. In the end, αa is predicted for some of the possible Auger transitions which may follow photoionization in 2a1 orbital of CCl4, SiCl4, and GeCl4.

Notizen: We have, in this paper, derived expressions for the partial photocurrent produced by ionization in the electric dipole approximation in an orbital of an oriented polyatomic molecule. The cross-section formulas, which are integrated over all directions of ejection of the photoelectron but differential with respect to the direction of the fixed molecular axis, are obtained in their simplest possible forms by taking full account of the transformation properties of the point symmetry group of the target and are thus applicable to photoionization in any oriented molecule belonging to one of the 32 point groups. The theory, as an example, has been applied to photoionization in a1 orbital of those oriented nonlinear systems whose point symmetry group is Td. This application shows that the singly differential, detection-integrated partial cross section for ionization by unpolarized, linearly or circularly polarized light in a1 orbital of a fixed Td molecule is (i) independent of the direction of its axis and (ii) equal to that averaged over all orientations of the target in space. Both conclusions are in agreement with recent experimental measurements on photoionization in 6a21 orbital of fixed CCl4. These results, in turn, are shown to mean that the variations with respect to the orientation of a molecule in space, found in theoretical calculations of photoelectron angular distribution for ionization in a1 valence orbitals of some of the Td targets, are due completely to the terms which stem from freezing both the molecular axis and the photoelectron detector in space. These terms completely vanish on integrating over all directions of propagation of the photoelectron, resulting in a current which is isotropic with respect to the orientation of the molecular axis in space. In such cases, it is therefore necessary to study the angular distribution of electrons ejected by photoionization in oriented molecules in order to obtain cross sections which will change with the direction of the target axis.

Notizen: In this paper we report theoretical studies of angle-resolved photoelectron spectroscopy (ARPES) and of circular dichroism in photoelectron angular distribution (CDAD) for ionization in molecules oriented in a single ||JKJMJ〉 rotational eigenstate. These processes have been investigated also as two of the possible alternatives to photodissociation to determine orientational distribution function of rotationally state selected, oriented molecules. Expressions are derived which can be used to calculate ARPES and CDAD for such molecular species from ab initio methods or to analyze these experimentally observed spectra for extracting information about the degree of orientation of the molecular framework. These formulas are put in their simplest possible forms using the transformation properties of the molecular point group to their full advantage. The ionization amplitude is thus shown to decompose into a sum of transitions each involving the final state wave function belonging to an irreducible representation of the point group of the target molecule. It is found that, similar to the case of photodissociation, one can determine the rotational quantum number J purely from experimental photoionization data.Expressions developed herein are used to study ARPES and CDAD for ionization in a1 orbital of those rotationally state selected and oriented spherical top molecules which transform according to the Td point symmetry group. In this case, the detection-integrated cross section, singly differential in molecular orientation, is found to be independent of the photoionization dynamics and directly gives the molecular orientational function. The other ARPES and CDAD formulas are shown to depend upon the dynamics through the integrated partial cross section σ¯, the angularly asymmetry parameter β¯, the phase shift of the continuum waves representing the photoelectron, and the phase of the dipole transition amplitudes. The formulation presented in this paper sets a methodology for the analysis of measurements and calculation of the photoelectron spectra in rotationally state selected and oriented molecules in general, spherical top Td molecules in particular. It is applied, as an example, to photoionization in 6a21 orbital of oriented CCl4 in a pure ||JKJMJ〉 rotational state. We find, among other things, that the photoelectron angular distributions change significantly when either or both of the directions of molecular orientation and of polarization of ionizing radiation vary from parallel to perpendicular to the quantization axis.

Notizen: A recently developed theory for angular distribution of electrons ejected by interaction of light with nonlinear molecules held fixed in space has been used to study ionization in a1 orbital of those systems which transform like the Td point symmetry group. Expressions for photoelectron angular distributions in the dipole approximation with the electric vector in the radiation beam both perpendicular and parallel to the molecular axis are derived. The properties of the two formulas, which are found to have completely different structures, have been studied. These expressions are shown to depend not only on all those quantities [i.e., the partial integrated cross-section σ¯, the asymmetry parameter β¯, and the polar angle θ of the propagation vector k (k,θ,φ) of the ejected electron] which are present in photoionization of an unoriented molecule, but involve in certain cases also the azimuthal angle φ, phase shifts of the continuum waves representing the outgoing electron, and the phase of the dipole transition amplitudes. Such fixed-molecule photoelectron angular distributions will therefore provide more stringent tests of theoretical models and probes of photoionization dynamics than the hitherto performed gas phase experiments on randomly oriented targets. They can also be used to identify the orientation of a molecule and/or geometry of a chemisorption site. The formulation presented here sets a frame work for the analysis of measurements and the calculations of spectra in those Td molecules which are fixed in space. We have applied it, as an example, to ionization in 4a1, 6a1, and 7a1 orbitals of oriented CF4, CCl4, and SiCl4, respectively. Without doing any dynamical calculations, using instead the experimentally measured values of σ¯ and β¯ as a function of the photon wavelength, the variations in the angular distributions with respect to the energy of the ejected electron as well as to the angles (θ,φ) and to the phases (which are treated as parameters) involved have been studied in detail. These distributions are found to have very rich and complicated structures arising from the spectral, angular, and/or phase variations of the angular momentum compositionof the photocurrent.

Notizen: This paper introduces a theory to interpret future experiments to simultaneously observe angular distribution of spin-resolved Auger and photoelectrons from a molecule belonging to one of the 32 point groups. The Auger electrons are emitted in the decay of the vacancy created by photoionization. We show that the desired correlation can be completely characterized by 12 parameters which are coefficients of trigonometric functions of the spherical angles of spin quantization directions of two outgoing electrons. The expressions for the parameters themselves, although reduced to the simplest possible forms by using the symmetry properties of the molecular point group to maximum advantage, depend upon bipolar harmonics involving the propagation directions of the Auger and photoelectrons. The angular and spin correlation function thus obtained is completely general and can be readily specialized to any experimental geometry used to observe the ejected electrons. In particular, it is found that for a linear experimental arrangement with spins oriented longitudinally to the respective propagation vectors of the two electrons moving out in opposite directions, the parameters become geometry independent with their number reducing to three, which are now coefficients of the first three Legendre polynomials. Correlation between the spin-quantization directions of Auger and photoelectrons is, on the other hand, described by six parameters which do not depend upon the experimental arrangement. Directional correlation between the two outgoing electrons has also been studied without observing their spins. These angular and/or spin correlation functions are shown to take particularly simpler forms for Auger and photoelectrons emitted from linear molecules. We have applied the procedures developed in this paper to study directional correlation between photoelectrons from 2a1 orbital in a Td molecule and the Auger electrons emitted in the decay of the consequent vacancy.

Notizen: This paper develops theoretical expressions to study angular distribution and spin polarization of those Auger electrons which are emitted in the decay of a vacancy created by the absorption of a photon in a rotating linear molecule. Identical expressions except, of course, for different decay amplitudes, in both the Hund's coupling schemes (a) and (b), are obtained for the differential Auger current emitted in the transition J→Jf measured by an electron spectrometer sensitive to spin detection. The structure of these angular distributions is exactly the same as that of the spin-resolved photoelectrons from unoriented atoms and molecules. The present paper thus puts the angle- and spin-resolved Auger and photoelectron spectroscopies on the same footing wherein identical geometrical and kinematical analysis is applicable. The four parameters needed to completely characterize such distributions depend, in the present case, on rotational orientation and/or alignment of the photoexcited molecule, in addition to its Auger decay amplitudes. The use of parity-adapted molecular states separates the Auger spectra into even and odd partial wave components of the ejected electron continuum in both of the coupling schemes. Our analysis shows that the integrated Auger current is spin resolved provided it is produced in the decay of oriented vacancies. We further find that Auger electrons which leave the molecular ion in Jf=0 state may have nonzero degree of spin polarization if they follow absorption of only circularly polarized light. In this case, both the angular distribution and spin polarization of emitted electrons become totally independent of Auger dynamics. Thus, angle- and spin-resolved Auger electron spectroscopy can be used to produce polarized electrons, to determine rotational orientation and alignment of linear molecules, to study their structure and dynamics, and to prepare ions of such molecules in selective ro-vibronic states.

Notizen: The structure of electric double layer at a metal/electrolyte interface is studied here using a density functional approach for the metallic electrons as well as the ions of the electrolyte. The metal is represented by a jellium and the electrolyte is modeled as an ensemble of charged hard sphere ions. The minimization of the total energy which includes the interaction of metallic electrons with the electrolyte ions yields the electron and the ion density distribution at the interface. The calculated interfacial capacitance compares quite well with the reported experimental results. © 1995 American Institute of Physics.

Notizen: A nonlocal density-functional theory of inhomogeneous ionic fluids proposed by us recently [J. Chem. Phys. 100, 5219 (1994)] for symmetric electrolytes is extended to study the structure of electric double layer for a charge-asymmetric (2:1) situation involving hard sphere ions of equal diameter with a continuum or neutral hard sphere model for the solvent. The hard sphere contributions to the excess free energy density and its derivatives for the inhomogeneous system are evaluated nonperturbatively through a position-dependent effective weighted density, which is also used to obtain the corresponding ionic contributions through a second-order functional Taylor expansion. The calculated results for the continuum solvent model show reasonably good agreement with the available simulation results, while the layering effect due to hard sphere exclusion and the charge inversion phenomena are some of the interesting consequences arising from the molecular nature of the solvent.

Notizen: The density functional theory of inhomogeneous classical neutral fluids is extended to study the structure of electric double layer using the restricted primitive model as well as the nonprimitive three-component molecular solvent model. The formalism is based on a weighted density approach where the hard-sphere contributions to the excess free energy density and the one-particle correlation function are evaluated nonperturbatively using a position-dependent effective density while the corresponding ionic part is obtained through a second-order functional Taylor expansion around this effective density. The calculated results for the density profiles of the ions and the mean electrostatic potential are in good agreement with the available simulation results for the continuum solvent primitive model. The corresponding results for the nonprimitive molecular solvent model provide insight into the layering effect due to hard-sphere exclusion and the charge inversion phenomena.

Notizen: A detailed theoretical framework is developed for studying sequential emission of a photoelectron and an Auger electron from a rotating linear molecule with information on momenta and spin-polarization of the departing particles. Identical expressions, except, of course, for different dynamical amplitudes, in both the Hund's coupling schemes (a) and (b) are obtained for the three different correlation functions considered in this paper. The use of the parity adapted wave functions for the molecular states involved results in, among other things, the presence of only a finite number of harmonics for each of the directions included in the correlation function. Several specific photon-propagation, electron-detection configurations are suggested for which the general correlation functions derived herein become particularly simple. The correlation between the Auger and the photoelectrons is shown to become, under specific conditions, completely isotropic for all bound molecular orbitals, whatever may be their symmetries, from which pair of electrons comes out. This analysis is independent of any dynamical calculations which can be performed in a hierarchy of approximations beginning from semiempirical phenomenological models to sophisticated ab initio methods. © 1995 American Institute of Physics.