Excitation core/inner shell

The CCD, CCSD, CCSD(T), and CCSDT methods are size consistent but not variational. Analytic gradients are available for these methods. Often, the frozen-core (FC) approximation is used in CC calculations. Here, excitations of inner-shell electrons are omitted. 

The interpretation of experimental results based on the one electron picture also raises fundamental questions. It has been shown that the low energy elementary excitations in metals can be described as quasi-particles. By making suitable many-body corrections one can convert the one electron states into quasi-particle states. For excitations from inner shells, which become possible when the excitation energy is high, the change of state of one electron is accompanied by a rearrangement of the states of many other electrons in the same core. This is a complicated many-body problem that can not be handled by the simple methods of band calculation. To what extent should one include many electron effects when an electron is excited from a deep band state remains an open question. 

In the following subsections electron excitation from inner-shell states will be considered in some detail we present first the basic principles inelastic electron scattering (sections 5.1-5.3), and discuss then possibilities of the EELS technique to determine the valence in rare earth systems by core level excitation (section 5.4). Frequently, comparison between electron impact and photon excitation will be made, and similarities and differences of the two excitation modes will be emphasised. 

HyperChem supports MP2 (second order Mpller-Plesset) correlation energy calculationsusing afe mi/io methods with anyavailable basis set. In order to save main memory and disk space, the HyperChem MP2 electron correlation calculation normally uses a so called frozen-core approximation, i.e. the inner shell (core) orbitals are omitted. A setting in CHEM.INI allows excitations from the core orbitals to be included if necessary (melted core). Only the single point calculation is available for this option. 

The calculations were performed using a double-zeta basis set with addition of a polarization function and lead to the results reported in Table 5. The notation used for each state is of typical hole-particle form, an asterisc being added to an orbital (or shell) containing a hole, a number (1) to one into which an electron is promoted. In the same Table we show also the frequently used Tetter symbolism in which K indicates an inner-shell hole, L a hole in the valence shell, and e represents an excited electron. The more commonly observed ionization processes in the Auger spectra of N2 are of the type K—LL (a normal process, core-hole state <-> double-hole state ) ... 

In addition, for thermochemical purposes we are primarily interested in the core-valence correlation, since we can reasonably expect the core-core contributions to largely cancel between the molecule and its constituent atoms. (The partitioning between core-core correlation -involving excitations only from inner-shell orbitals - and core-valence correlation - involving simultaneous excitations from valence and inner-shell orbitals - was first proposed by Bauschlicher, Langhoff, and Taylor [42]). 

Hitchcock, A. P., Urquhart, S. G., and Rightor, E. G. (1992). Inner shell spectroscopy of benz-aldehyde, terephthalaldehyde, ethylbenzoate, terephthaloyl chloride, and phosgene Models for core excitation of poly(ethylene terephthalate). J. Phys. Chem. 96,... 

In a typical EEL spectrum, the count rate Ia (area under the excitation edge after background subtraction, for element A) is a product of the incident electron current density, J0, the number of atoms Na of element A per unit area, and oa> the total ionization cross-section per atom for the excitation of the appropriate inner-shell by the incident electrons. However, to preserve good energy resolution, an aperture is placed after the specimen which limits scattering to angles less than P and hence only a fraction of the core loss signal Ia(P) is measured. Moreover, in most... 

The structural parameters and vibrational frequencies of three selected examples, namely, H2O, O2F2, and B2H6, are summarized in Tables 5.6.1 to 5.6.3, respectively. Experimental results are also included for easy comparison. In each table, the structural parameters are optimized at ten theoretical levels, ranging from the fairly routine HF/6-31G(d) to the relatively sophisticated QCISD(T)/6-31G(d). In passing, it is noted that, in the last six correlation methods employed, CISD(FC), CCSD(FC),..., QCISD(T)(FC), FC denotes the frozen core approximation. In this approximation, only the correlation energy associated with the valence electrons is calculated. In other words, excitations out of the inner shell (core) orbitals of the molecule are not considered. The basis of this approximation is that the most significant chemical changes occur in the valence orbitals and the core orbitals remain essentially intact. On... 

In electron correlation treatments, it is a common procedure to divide the orbital space into various subspaces orbitals with large binding energy (core), occupied orbitals with low-binding energy (valence), and unoccupied orbitals (virtual). One of the reasons for this subdivision is the possibility to freeze the core (i.e., to restrict excitations to the valence and virtual spaces). Consequently, all determinants in a configuration interaction (Cl) expansion share a set of frozen-core orbitals. For this approximation to be valid, one has to assume that excitation energies are not affected by correlation contributions of the inner shells. It is then sufficient to describe the interaction between core and valence electrons by some kind of mean-field expression. 

Inner shell absorption spectroscopy provides a map of unoccupied electronic states (or levels) and the electronic structures of conduction bands in the vicinity of the core-excited atom. The X-ray absorption spectroscopy (XAS) represents a fingerprint of the chemical state of the element. It provides useful means of nondestructive site-dependent chemical analysis of complex systems. Ultra-soft X-ray absorption (USXA) method is categorically interesting for chemical analysis of a variety of complex materials in battery industry, environmental science, and semiconductor industry. 

Inner-shell excitation of the Li-like ion core is the second mechanism to populate the doubly excited levels. For the three electron system, the cascade effect between doubly excited levels is negligible compared to dielectronic recombination. This is justified by the fact that for highly charged ions the states with higher n, n > 3, have large initial populations, so therefore the contribution due to the cascade is negligible. The emission of the satellite line is then ... 

The primary electron beam may also be inelastically scattered through interaction with electrons from surface atoms. In this case, the collision displaces core electrons from filled shells e.g, ns (K) or np (L)) the resulting atom is left as an energetic excited state, with a missing inner shell electron. Since the energies of these secondary electrons are sufficiently low, they must be released from atoms near the surface in order to be detected. Electrons ejected from further within the sample are reabsorbed by the material before they reach the surface. As we will see in the next section (re SEM), as the intensity of the electron beam increases, or the density of the sample decreases, information from underlying portions of the sample may be obtained. 

The main peaks in X-ray Photoelectron Spectroscopy (XPS) for molecules appear because of the photoionization of core electrons. In addition, satellite peaks on the high binding energy side of the main peak have often been observed. These peaks are generally referred to as shakeup satellite peaks. In the sudden approximation, the shakeup process which accompanies photoionization can be considered as a two-step process. First, a core electron is emitted as a photoelectron, creating an inner shell vacancy. In the next step, electron(s) in the same molecule transfer from valence orbital(s) to unoccupied orbital(s) with relaxation of orbital energies. It is important to study these satellites in order to understand the valence and excited states of molecules (1). 

A good example occurs in the alkali spectra the integrated oscillator strength evaluated over the optical range is approximately 1 for all alkalis. This proves that the other electrons (i.e. those in the core) hardly participate in the visible spectrum. If, however, observations are extended to very high excitation energies, one eventually breaks into deeper electronic shells (see chapter 7), and so a separate sum rule will apply for inner-shell excitation. For instance, we may expect an oscillator strength of 10 for excitation from a d, subshell. 

In X-ray spectra, when a deep core hole is excited, the excited shell occupies a very small volume and its spatial overlap with other core electrons is large, while with the orbital of the outer excited electron it is small. Under such conditions, the lifetime of the core vacancy becomes short one speaks of large core-level widths due to Auger broadening, which compete with autoionisation. This is why, in X-ray spectra near absorption edges due to inner-shell excitation, only the first few Rydberg members are observed. We return to this issue in section 11.2. 

Even within the independent electrom approximation, it is obvious that there must exist inner-shell excitation spectra, and that their energy must extend well above the first ionisation potential. This arises from the simple fact that one can choose which electron is excited it does not necessarily have to be the valence electron, and the inner electrons, being more strongly bound, require photons of higher energy to excite them. Since the valence electron extends furthest out from the atomic core, one is tempted to think that it is always the easiest electron to excite, both because it can more readily interact with an external field (higher transi-... 

Fig. 7.2. A typical inner-shell excitation spectrum the 3p spectrum of Ca. Note the wide doublet splitting between the two series limits due to the large spin-orbit interaction of the nearly-closed core, the prominent Rydberg series and the broad, asymmetric autoionising resonances (after J.-P. Connerade et aL [302]).

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