Core ionization

Table 28 Core Ionization and Shake-up Energies (eV) for Some Heterocycles (73M130102)...

When experimental results are later introduced, it will be seen that the significance of the final-state scattering in PECO measurements is confirmed by the observation that for C li core ionizations, which must therefore proceed from an initial orbital that is achiral by virtue of its localized spherical symmetry, there is no suggestion that the dichroism is attenuated. The sense of the chirality of the molecular frame in these cases can only come from final-state continuum electron scattering off the chiral potential. Generally then, the induced continuum phase shifts are expected to be of paramount importance in quantifying the observed dichroism. 

C ionization from the carbonyl group, and the HOMO ionization of the carbonyl oxygen lone pair were included, with similar conclusions. In Fig. 10 the results for the C=0 core ionization are summarized, with the stmcture of each derivative being indicated at the top of the figure. 

In an effort to better understand the differences observed upon substitution in carvone possible changes in valence electron density produced by inductive effects, and so on, were investigated [38, 52]. A particularly pertinent way to probe for this in the case of core ionizations is by examining shifts in the core electron-binding energies (CEBEs). These respond directly to increase or decrease in valence electron density at the relevant site. The CEBEs were therefore calculated for the C=0 C 1 orbital, and also the asymmetric carbon atom, using Chong s AEa s method [75-77] with a relativistic correction [78]. 

Auger electrons and X-rays are formed in the relaxation of core-ionized atoms, as discussed in the sections on AES and XPS. 

In the early 1980s, one of the authors of this chapter began to study argon matrix isolation of radical cations235 by applying the radiolytic techniques elaborated by Hamill and Shida. A central factor was the addition of an electron scavenger to the matrix which was expected to increase the yield of radical cations and the selectivity of the method. For practical reasons, X-rays replaced y-rays as a radiolytic source and argon was chosen as a matrix material because of its substantial cross section for interaction with keV photons (which presumably effect resonant core ionization of Ar). Due to the temporal separation of the process of matrix isolation of the neutral molecules and their ionization, it was possible to obtain difference spectra which show exclusively the bands of the radical cations. 

We have tacitly assumed that the photoemission event occurs sufficiently slowly to ensure that the escaping electron feels the relaxation of the core-ionized atom. This is what we call the adiabatic limit. All relaxation effects on the energetic ground state of the core-ionized atom are accounted for in the kinetic energy of the photoelectron (but not the decay via Auger or fluorescence processes to a ground state ion, which occurs on a slower time scale). At the other extreme, the sudden limit , the photoelectron is emitted immediately after the absorption of the photon before the core-ionized atom relaxes. This is often accompanied by shake-up, shake-off and plasmon loss processes, which give additional peaks in the spectrum. 

The lifetime of the core-ionized atom is measured from the moment it emits a photoelectron until it decays by Auger processes or X-ray fluorescence. As the number of decay possibilities for an ion with a core hole in a deep level (e.g. the 3s level) is greater than that for an ion with a core hole in a shallow level (e.g. the 3d level), a 3s peak is broader than a 3d peak. 

A core-ionized atom has two possibilities to lower its energy, namely Auger decay and X-ray fluorescence (described in more detail in Chapter 7). The Auger yields for processes following core hole creation in the K and L shell are sketched in Fig. 3.25 (right). Obviously, Auger processes are the dominant decay mode in light elements. 

In kinetic emission, at higher kinetic energy above a certain threshold energy the impact of an ion can cause the emission of an electron from an inner shell. The core-ionized atom may subsequently decay by an Auger decay, which leads to the emission of another electron. 

The interaction of an electron with an atom gives rise to two types of X-rays characteristic emission lines and bremsstrahlung. The atom emits element-characteristic X-rays when the incident electron ejects a bound electron from an atomic orbital. The core-ionized atom is highly unstable and has two possibilities for decay X-ray fluorescence and Auger decay. The first is the basis for electron microprobe analysis, and the second is the basis of Auger electron spectroscopy, discussed in Chapter 3. 

The heats of formation of CH4 and e are well known, but we cannot directly obtain the heat of formation of CH4 from ordinary thermodynamic data. However, we can do this if we apply the so-called equivalent cores approximation6 n> 2a 24 According to this approximation, the hypothetical process in which an electron is transferred from the nucleus of a core-ionized atom to the core hole has an energy which is independent of the chemical environment of the core-ionized atom. For example, in the case of carbon Is holes in CH4 and CO2, it is assumed that the following reactions have the same energy. 

For such core replacement reactions the ordinary isotopic distributions of the elements can be assumed. It is assumed that the energy of any reaction like (4a) or (4b) is a constant, Ac. Note that if we add reactions as follows, (3a) + (4a) and (3b) + (4b), we eliminate the core-ionized species ... 

In the general case of a molecule M(Z) containing an atom of atomic number Z which undergoes core ionization,... 

Obviously for each type of core ionization (C Is, 0 Is, P 2p, etc.), there is a different value of Az- Carbon Is binding energies and the corresponding calculated Ac values for some gaseous carbon compounds are given in Table 2. It can be seen that the various Ac values are fairly constant ... 

Application of the equivalent cores method to solid compounds is slightly more complicated, requires additional assumptions, and is therefore less accurate than the application to gaseous compounds. However, fairly good correlations have been obtained for solid compounds of boron, carbon, nitrogen, and iodine20. The correlations were restricted, because of the nature of the assumptions involved, to molecular compounds or to compounds in which the core-ionized atoms are in anions. 

The electronic relaxation energy associated with the core ionization of a molecule can be divided into two parts54) ... 

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. 

As a first, trivial, example of the application of the overlap criterion, let us consider the possibility of a shake-up peak associated with the C Is ionization of the terminal carbon atom in nitroethane and the v - v transition of the nitro group in that molecule. In this case the core ionization occurs in a region of the... 

The core ionization of an atom stabilizes all the valence electrons in the atom. Depending on whether the electronic transition shifts electron density to or from an atom, the energy separation for a shake-up peak of that atom will be less than or greater than the energy of the neutral molecule ionization81. As an illustration of these effects, let us consider the shake-up spectra of formamide, H2NCH082. The principal transitions involved are the vl - n3 and 7r2 - 7r3 transitions. The tTj... 

X-Ray photoelectric ionization is believed to take place in a time interval of about 10-18 s. Therefore separate XPS peaks are possible for atoms if the lifetime of the asymmetric electronic state is greater than about 10 18 s, whether or not the atoms are structurally equivalent. We may represent the ground state of a localized mixed valence compound (involving two metal atoms differing in oxidation state by one unit) by the following formula, where the dot represents the extra valence electron M—M. The two possible XPS transitions can then be represented as follows, where the asterisk indicates core ionization,... 

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,... 

Another approach of this kind uses the approximate Brueckner orbitals from a so-called Brueckner doubles, coupled-cluster calculation [39, 40]. Methods of this kind are distinguished by their versatility and have been applied to valence ionization energies of closed-shell molecules, electron detachment energies of highly correlated anions, core ionization... 

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