Singular solutions and the S matrix in the interference theory of molecular shape resonances. I. General formulation and computational methods

Migal, Yu. F.

doi:10.1088/0953-4075/26/17/010

Cited by 17 publications

(4 citation statements)

References 6 publications

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“…Within this model the whole aggregate of factors, influencing position and form of the maxima of the one-electron origin, amounts to parameters describing the arrangement of atoms and characteristics of the intratomic potentials. For calculating S-matrix poles we use an equation in these poles obtained in Migal (1993) within the MT approach…”

Section: Methodsmentioning

confidence: 99%

“…Under such conditions, as we restrict the amount of data only by energies and widths of peaks, it is convenient to use a formalism based on analysis of poles of the S matrix for many-centre systems (Migal, 1993). Within this formalism it is not assumed to employ other quantities besides energies and widths of maxima, and it is balanced in amounts of input and output information.…”

Section: Problemmentioning

confidence: 99%

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Determination of parameters of valence states by using XANES

Migal

Kovaleva

2001

J Synchrotron Radiat

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A new approach for the parametrization of valence states of atoms in molecules and solids, facilitating the deciphering of experimental XANES spectra, is proposed. It is shown that energies and halfwidths of XANES maxima of the one-electron origin depend mainly on the arrangement of atoms and energies and mean radii of atomic valence states. Just these quantities having distinct physical meaning must be determined above all from experiment. A procedure for such a determination is developed. Values of energies and mean radii of the nitrogen and oxygen atoms in some molecules are obtained. Keywords: XANES, valence states ProblemOur aim is to investigate valence states of separate atoms in manyatom systems. Such systems can be molecules, free or adsorbed, solid clusters and so on. This problem is a part of the more general question which we try to examine (Migal, 1994): what information about objects under consideration is contained in XANES and how to extract this information.Analysing XANES we choose peaks of the one-electron origin. As usual such peaks are the most distinctive details of spectra. They correspond to the transition of the photoelectron to both unoccupied collective states of the discrete spectrum and so called shape resonances. The latter are one-electron quasi-stationary states with small positive energies. We consider only such peaks which correspond to states localized or quasi-localized within many-atom systems (i.e., the Rydberg series is excepted). Position and form of these peaks essentially depend on arrangements and types of atoms, magnetic microstructure, the presence and nature of defects, the distribution of electric charge, etc. This fact allows us, in principle, to obtain structure information by analysing characteristics of the peaks. However, unfortunately, general methods for extracting this information are still not developed.Before considering concrete questions about atomic valence states we would like to make three general remarks. Firstly, an amount of information coded in XANES is essentially greater than in EXAFS. It is caused by the fact that in the case of XANES the photoelectron, moving through a many-atom system with a comparatively small speed, interacts with the system for much longer time than in the case of EXAFS. Due to that, by using XANES it is possible to obtain, along with geometric parameters of the system, also parameters of the potential V(r) describing the interaction between the photoelectron and the system. Secondly, since position and form of peaks in XANES depend on a lot of factors, in order to extract information from XANES one must solve a many-parameter inverse problem. In a number of works, where for deciphering structure information from XANES

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Section: Methodsmentioning

confidence: 99%

Section: Problemmentioning

confidence: 99%

Determination of parameters of valence states by using XANES

Migal

Kovaleva

2001

J Synchrotron Radiat

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“…where E j is the energy of the j-th experimental maximum, G j is its halfwidth, and S j is the j-th pole of the S matrix for a model with a MT potential [9]. Let us choose the potential within atomic spheres in the form [10]…”

Section: Scheme Of Inverse Problem Solutionmentioning

confidence: 99%

“…The scheme is based on the S-matrix pole equation within the muffin-tin (MT) approach [9] (details are described below). The scheme was tested by the determina-tion of geometric parameters of the free molecules SO 2 , N 2 , NO 2 and CH 3 NO 2 .…”

Section: Introductionmentioning

confidence: 99%