Core ionized/excited states

In earlier papers [6-8] we have proposed a procedure for evaluating core ioniza-tion/excitation chemical shifts in molecules from computed core ionization/excitation energies for the relevant isolated atom in neutral and valence-ionized states and from computed charge transfer relative to this atom within the molecule. The atomic calculations involved relaxation, possibly correlation and, when appropriate, relativity and other effects, while in the molecule one could use any approximate method (possibly involving effective core potentials) yielding reliable charges. 

The active space used for both systems in these calculations is sufficiently large to incorporate important core-core, core-valence, and valence-valence electron correlation, and hence should be capable of providing a reliable estimate of Wj- In addition to the P,T-odd interaction constant Wd, we also compute ground to excited state transition energies, the ionization potential, dipole moment (pe), ground state equilibrium bond length and vibrational frequency (ov) for the YbF and pe for the BaF molecule. 

The ionized atom that remains after the removal of the core hole electron is in a highly excited state and will rapidly relax back to a lower energy state by one of two routes, namely X-ray fluorescence (Section 5.1.2) or by transferring the energy to an electron in another orbit, which, if it has sufficient energy, will be ejected into the vacuum as Auger emission. An example of the latter process is illustrated in Figure 5.29. 

Lastly, we mention one more excitation mechanism that has been observed in molecules. It is well-established that following strong field ionization in atoms and molecules, under certain conditions, the ionized electron can be driven back to the ion core where it can recombine to produce high-harmonic radiation, induce further ionization, or experience inelastic scattering. However, there is also the possibility of collisional excitation. Such excitation was observed in [43] in N2 and O2. In both molecules, one electron is tunnel ionized by the strong laser field. When the electron rescatters with the ion core, it can collisionally ionize and excite the molecular ion, creating either N + or Ol+ in an excited state. When the double ion dissociates, its initial state can... 

The X-ray photoelectron spectrum of the core ionization of an atom in a molecule consists of peaks and bands corresponding to transitions to various excited states. None of these transitions corresponds to the formation of the Koopmans theorem frozen-orbital ionic state, which is a completely hypothetical state. However, the center of gravity of the various peaks and bands lies at the energy corresponding... 

The selection rules appropriate for a shake-up transition are of the monopole type2, 76. The intensity of a shake-up peak depends on the overlap integral between the lower state molecular orbital from which the electron is excited (in the neutral molecule) and the upper state molecular orbital to which the electron is excited (in the core-ionized molecule). Consequently one expects transitions of the type au au, ag " ag> 7T nu, and irg - ng with g u and u - g transitions forbidden. 

The first transition would be expected to be of higher energy than the second from simple atomic charge considerations. Because the two atoms are of equal abundance, the two peaks have essentially equal intensities. Unfortunately, the observation of two XPS peaks does not rule out the possibility of delocalized valence electrons in the ground state. Two transitions are expected even in that case because of polarization of the excited state by the core ionization 123 The ground state of a delocalized mixed valence compound can be crudely represented by the formula M-M, where the intermediate position of the dot indicates that the odd valence electron is equally shared by the two metal atoms. The two XPS transitions can then be represented as follows,... 

Excitation to the repulsive electronic state may also involve a multi-electron process. For example, creation of a core hole on a metal atom in an oxide may lead to an interatomic Auger transition which ultimately results in a positive oxygen ion which desorbs because it is now in a strongly repulsive Madelung well. Knotek and Feibelman have reported results which they interpret in this manner. Core ionization in the adsorbed molecule can also lead to an Auger process which leads to desorption. 

The distribution of primary excited and ionized states produced directly by the primary ion inside the core of the track can be found knowing the probability P0m(b). If n is the concentration of molecules in the ground state, the distribution of molecules in the mth excited state over the distance from the axis of the track is described by the function... 

Figure 13 shows a pictorial view of the final-state radial wave functions relevant to core transitions in a molecule. Core transitions take place in an effective molecular potential seen by the excited photoelectron. Whereas for E < E0, that is, below the continuum threshold (where E0 is the energy of the core ionization potential), discrete transitions occur to the unoccupied valence states, photoelectrons excited in the photoionization process with... 

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