Core excited states

From a theoretical point of view XES furthermore provides a very strong basis for the evaluation of methods for population analysis, i.e., the decomposition of the molecular orbitals into atomic contributions [10]. Many different schemes subdividing the charge density into contributions assigned to respective atoms have been proposed, but the lack of means to directly measure the atomic populations in different orbitals has made all techniques somewhat arbitrary and a matter of taste. Due to the strongly localized character of the intermediate core-excited state, however, in combination with the direct dependence of the XES transition probability on the amount of local -population (assuming a Is core hole), XES provides a very sensitive tool to directly measure this atomic population. In all, we have an atom-specific tool, which can be used to address important questions regarding... 

Due to the intermediate core-excited state in the XES spectroscopic process, there are additional selection rules for molecules with an inversion center which allows one to distinguish the symmetry of both the occupied and unoccupied orbitals [41]. Due to the two-step character of the XES measurements with initial absorption (excitation) and subsequent emission (de-excitation) steps, we find selection rules for molecules with inversion symmetry that require the same characteristics of initial and final states. New states below the Eermi level can then be identified and attributed to the population of the n orbital through the back-donation process while above the Fermi level the presence of states of 7i-character confirm the 7i-donation process [40, 42]. 

In Figure 4 we show the transmission spectrum of benzene at higher energies. The lowest feature Is the second "shape" resonance ( B2g). Above this lie several smaller features which must correspond primarily to core-excited states. Detailed studies of the decay channels of these resonances have not yet been carried out, although some Information is available. The vertical arrows in Figure 4 indicate the energies at which maxima occur in the excitation functions for Vi of the ground electronic state of ben-... 

Abstract This chapter discusses descriptions of core-ionized and core-excited states by density functional theory (DFT) and by time-dependent density functional theory (TDDFT). The core orbitals are analyzed by evaluating core-excitation energies computed by DFT and TDDFT their orbital energies are found to contain significantly larger self-interaction errors in comparison with those of valence orbitals. The analysis justifies the inclusion of Hartree-Fock exchange (HFx), capable of reducing self-interactions, and motivates construction of hybrid functional with appropriate HFx portions for core and valence orbitals. The determination of the HFx portions based on a first-principle approach is also explored and numerically assessed. 

Description of Core-Ionized and Core-Excited States by Density... 

The transition matrix elements in the two processes are different dipole (PES) vs. Coulomb-type (for the decay process in RPE), and each has its own molecular dynamics. These different matrix elements and the involvement of an intermediate, core-excited state in RPE often result in altered intensity ratios of the spectral features [28,29] and a different relative population of vibrational states [28]. Since core excitations are site-specific for different elements or chemically shifted atoms [30], with well-defined and separated absorption edges, RPE may supply information on the local electronic structure [31-33]. 

Contacts, 19-2-19-3, 19-6-19-10, 19-17, 19-19, 19-23-19-24, 19-29, 19-31, 19-39 Contour length, 9-24, 9-25-9-26 Conventional thin films, 7-20 Cooperativity, 18-7-18-8 Coplanarity, 9-23 Copolymerization, 8-13-8-14 Copolymers, 20-13, 20-22, 20-34-20-44 Core-excited states, 21-7 Corrosion, 18-6-18-7, 18-29 Cotton effect, 3-9-3-12 Coulomb blockade transport, 16-15-16-18 Coulomb-blockade (CB), 16-15-16-18, 16-21 Critical regime, 16-5, 16-9 Crossed metallic SWNT, 16-11 Cross-linking, 7-32, 7-34-7-35, 8-12-8-13, 8-34-8-38, 9-17, 9-18... 

The problem is worse when one considers atoms involving several valence electrons. If one wants to obtain the information relative to a double-zeta valence basis set of the C atom, it will be necessary, in principle, to find states of the type ls 2p and also ls 3p if 2p and 3p are the RHF AOs in the basis set, the latter (ls 3p ) determinant will certainly be higher in energy than core excited states of the type (ls2s 2p ), which will act as intruder states. The definition of the target space will then be quite difficult, since for some basis sets it will be difficult to discriminate between the eigenstates of the problems which keep a frozen core from those which are core excited. 

Regarding core-excited states most of them are still unidentified. Only for core-excited Be, which was studied in detail by R0dbro et could a... 

Loos PE, Assfeld X (2007) Core-ionized and core-excited states of macromolecules. Int J Quantum Chem 107 2243-2252... 

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