Hole Excited States

The proper theoretical study of core-hole excited states has been one of the most challenging problems in molecular quantum mechanics. The difficulty stems from the fact that these states lie above the continuum part of the spectra, and their attainment as high-energy roots in an ordinary configuration interaction calculation is impossible [46]. However, core-hole excited states play an important role in the identification of chemical species by X-ray based spectroscopic techniques. Additionally, there are many interesting effects that are particular to this region of the spectra and their study are the object of active research [47]. 

When a given symmetric molecule contains indistinguishable nuclei, the associated core-hole spectra present extra complications. At the monoconfigurational level, symmetry broken localized ROHF solutions have 

Transition energies for inner-shell excitation of the C02 molecule 

It must be noted that the experiments did not resolve the bands of the quasidegenerate states and the theoretical calculation is essential to get some understanding of the processes involved. The sum of the calculated optical 

A similar theoretical study was undertaken for the core-hole states for the ethylene molecule [52], There are two identical carbon atoms and the molecule has D2h symmetry. The localized core-hole states have C2v symmetry and the direct product C2v Cs recovers properly the full symmetry of the system. The results for transition energies and optical oscillator strengths agree well with those available in the literature. 

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M. Rosina and M. V. Mihailovic, The determination of the particle—hole excited states by using the variational approach to the ground state two-body density matrix, in International Conference on Properties of Nuclear States, Montreal 1969, Les Presses de I Universite de Montreal, 1969. 

Th. Mercouris, Y. Komninos, C.A. Nicolaides, Time-resolved hyperfast processes of strongly correlated electrons during the coherent excitation and decay of multiply excited and inner-hole excited states, Phys. Rev. A 76 (3) (2007) 033417. 

Good examples are the core hole excited states of homonuclear molecules. When one electron is removed from a core orbital, the original Dooh symmetry is lowered to C v The D h group can be decomposed into two CooV components related by a C, or Cs operation, so it is fair to consider that the core-hole excited states are described by resonance between the two structures. The adiabatic subsystems have, by definition, zero overlap in the real space. Their interaction is defined only in complex space through the explicit overlap between the many-electron states. 

The following picture is emerging from this research. Core electron excited states have finite lifetimes and unique characters. The electronic and chemical relaxations are coupled and depend upon the atomic and electronic structure of the molecule, the atomic site of the core hole, and the configuration of the core hole excited state. Experiments leading to an understanding of these dependences are just beginning to be done. 

The decay of a core hole excited state is dominated by autoionization or Auger processes for the light elements of the periodic table. The contribution from x-ray fluorescence is small, amounting to less than 1% for carbon and reaching 10% for argon. For the first series of the periodic table, the lifetime of a core hole excited state is about 10 femtoseconds, corresponding to an Auger transition rate of around lO Vsec. In special cases discussed in Section IV.A, a molecule in a core hole excited state may dissociate prior to... 

Studies have demonstrated that the electronic relaxation depends upon the location of the core hole site and the configuration of the core hole excited state. The important feature is that the core hole is localized on a specific atom and this localization is projected onto the valence electrons in the decay process. Molecular Auger spectra thus present a view of molecular electronic structure from the perspective of particular atoms in a molecule. The spectra therefore can serve to identify particular molecules and functional groups, to distinguish between localized and delocalized bonding, and to measure orbital atomic populations for various atoms in a molecule (Rye and Houston 1984). This localization and the projection onto the valence... 

Fluorescence in the visible and ultraviolet regions of the spectrum provides a convenient means for detecting decay produts, both neutral and ionic, produced in excited electronic states. Fluorescence spectra with resolved rotational and vibrational structure provide information about the energy spacing between electronic states, about the structure and bonding properties of these states, and about the populations of rotational and vibrational levels, which can characterize the populating mechanisms associated with decay of the core hole excited state. The production of the doubly charged molecular cation by decay of the core hole is of particular interest because little is known about the properties of these ions and because the fluorescence decay... 

Autoionization spectra resulting from specific resonances can be obtained by electron-electron coincidence measurements (Haak et al. 1984 Ungier and Thomas 1983, 1984, 1985). To associate a fr.rgmentation pattern with a particular core hole excited state and a particular autoionization or Auger decay channel, a double-coincidence experiment must be done using electron impact excitation. The energy of the scattered electron must be determined, the energy of the emitted electron must be detennined, and the ions produced in coincidence with these two events must be determined. The difficulties inherent in these kinds of experiments have been aptly summarized by Hitchcock (1989), If you can do it by photons, don t waste your time with electron-coincidence techniques. ... 

As has been described, the creation and relaxation of a core hole excited state involving shake-up, shake-off, and single and multiple electron autoionization and Auger decay, generally leaves the system with two or more holes in bonding orbitals, which essentially means that bond has disappeared and often the system is left on a repulsive potential curve. The importance of such multiple-electron excited states has been discussed for bond rupture and desorption for covalently bonded species (Ramaker 1983a, b,c Madey et al. 1981 Jaeger et al. 1982 Treichler et al. 1985). 

While much effort has been expended on understanding the Auger spectra of molecules, only a few autoionization spectra of core hole excited states have been obtained and analyzed. A detailed understanding of the electronic relaxation must be developed because this is essential to understanding the subsequent chemistry that occurs. 

It is clear that the chemical reactions induced by core electron excitation are atom-specific. They generally depend upon the atomic site of the core hole and the electronic configuration of the core hole excited state. In this sense, the chemistry is selective. The chemistry can be selected by tuning the photon energy to produce particular core hole excited states. In another... 

In all XNCD measured so far, it has been found that the predominant contribution to X-ray optical activity is from the E1-E2 mechanism. The reason for this is that the El-Ml contribution depends on the possibility of a significant magnetic dipole transition probability and this is strongly forbidden in core excitations due to the radial orthogonality of core with valence and continuum states. This orthogonality is partially removed due to relaxation of the core-hole excited state, but this is not very effective and in the cases studied so far there is no definite evidence of pseudoscalar XNCD. 

It would be instructive to illustrate the use of these rules. As a first example let us consider the core-hole excited states of homonuclear diatomic molecules. When one electron is removed from the core orbital, the original Da,h symmetry of the wavefunction is lowered to Coov This situation is depicted in the figure below where only the Is core electrons are represented. According to the rules in table 2, the Dooh group can be decomposed into two C v components related by a Ci or Cs operation. The two C >v structures (a) and (b) below ... 

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