Multielectron excitation

Multielectron excitations in rare-earth compounds revealed by xray dichroism. Phys. Rev. B 46 3155 (1992). 

The 3d levels in lanthanides are far removed from 4f levels and the overlap of these two levels if any is very small. As a result, multiplet structure in the 3d region is not expected. Although this is the case, XPS of some lanthanide compounds, particularly elements from lanthanum to neodymium, exhibit splitting in the bands apart from the doublet due to spin-orbit interaction. This type of structure is shown in Figs. 9.10, 9.11 and 9.12. These splittings are known as satellites and originate from multielectronic excitations. In general,... 

A corresponding example in a simple molecular system would be the multielectron excitation of Li2 la la 2a S+, where three or four of the electrons in the subshells could be excited to relatively low-lying states labeled... 

Briefly, XANES is associated with the excitation process of a core electron to bound and quasibound states, where the bound states interacting with the continuum are located below the ionization threshold (vacuum level) and the quasibound states interacting with the continuum are located above or near the threshold. Thus, XANES contains information about the electronic state of the x-ray absorbing atom and the local surrounding structure. However, as stated above, unhke EXAES, since the excitation process essentially involves multielectron and multiple scattering interactions, interpretation of XANES data is substantially more complicated than that of EXAFS data. 

The eight- and twelve-electron reductions of CO2 to methane and ethylene, are very exciting results for two reasons. First, these results demonstrate that complex multielectron reductions are possible. Second, they illustrate the close relationship that exists between reactions observed for discrete molecular complexes and reactions observed on metal surfaces. 

Above room temperature, the mobile 3 d electrons are well described by a random mixture of Fel" and FeB ions with the mobile electrons diffusing from iron to iron, some being thermally excited to FeA ions, but the motional enthalpy on the B sites is AH < kT. As the temperature is lowered through Tc, the Seebeck coefficient shows the influence of a change in mobile-electron spin degeneracy, and at room temperature the Seebeck coefficient is enhanced by correlated multielectron jumps that provide a mobile electron access to all its nearest neighbors. The electron-hopping time xi, = coi = 10" s... 

As the energy of the excited states and the redox levels of each metal-polypyridine unit depend on metal and ligands in a predictable way, the simultaneous presence of different metals in a dendritic structures gives rise to intramolecular energy transfer processes as well to different redox patterns with multielectron processes. In particular, the tetranuclear [Os(2,3-dpp)3 (2,3-dpp)Ru(bpy)2 3]8+ (OsRu3) shown in Fig. 5.3 has been designed to achieve an efficient antenna effect. This species can also be considered a first-generation mixed-metal dendrimers.31... 

Some of the more interesting and valuable redox processes are multielectron in nature, suggesting the utility of coupling a two- or many-electron event into an excited state process. The study of the excited state photochemistry and photophysics of binuclear and polynuclear (cluster) molecules is thus becoming of importance, and two-electron reactions are being identified. 

The fact that excited states of these complexes are not generally quenched by water or acid in solution suggests that barriers for the electron-transfer process render it too slow to compete with excited state decay. The redox chemistry of water is in fact complicated because transformations between stable forms (H20 - H2 + 1/2 02) involve multielectron steps. On the other hand, the one-electron reduction of H+ to H and the one-electron oxidation of H20 to H+ + OH require much more energy than that available to the excited complex103). In order to circumvent these difficulties, one can devise cycles in which the excited state undergoes a simple electron transfer reaction to yield a reduced or oxidized quencher which is able to react with water. For example, one could take into con-... 

The greater the number of functions 4 J, belonging to the orthonormal set, the more completely and in more detail the spectrum of the /(-decay-induced excitations of a molecule can be calculated. Consequently, the method for calculating the wave functions of the daughter ion must be such that at a reasonable volume of calculation we would be able to construct a sufficiently large number of multielectron wave functions of excited states. The Hartree Fock method allows one to construct the wave functions of excited states as the combinations of determinants symmetrized in a certain way. Within this method the excitation is considered to be a transition of an electron from an occupied Hartree-Fock molecular orbital into a vacant one. 

Thus, as an MO basis for constructing the multielectron wave functions of configurations given by Eq. (33), we will use the Hartree-Fock MO for the occupied one-electron states and the Huzinaga MO [Eq. (34)] for the excited ones. An advantage of the Huzinaga MOs is the simplicity of the way they are obtained, since Eq. (34) is an equation with constant coefficients and one does not have to use the iteration method. Moreover, when one uses the Huzinaga... 

The model that is outlined above is generated from a one-electron Hamiltonian and is only an approximation to the tme wavefimction for a multielectron system. As suggested earlier, other components may be added as a linear combination to the wavefimction that has just been derived. There are many techniques used to alter the original trial wavefimction. One of these is frequently used to improve wavefimctions for many types of quantum mechanical systems. Typically a small amount of an excited-state wavefimction is included with the minimal basis trial fimction. This process is called configuration interaction (Cl) because the new trial function is a combination of two molecular electron configurations. For example, in the H2+ system a new trial fimction can take the form... 

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