Electronic excitation between complementary orbitals

Let us first choose u = 0, i.e., ng = The optimal obtained from Eq. (1) with such a choice for equals the complementary density Ua = only if the potential t)f (r) disappears (or it is constant). Indeed, if = 0, the effective potentials in either the Kohn-Sham equations for the total system or in Eq. (1) (for the chosen s) are the same. As a consequence, (pu and y>2s are eigenvectors of either equations and their eigenvalues are ordered in the same way. The lowest eigenvalue corresponds to (pu, whereas the y>2s is the solution which corresponds to the excited state of the reference system of non-interacting electrons. Therefore, the ground-state orbital obtained from Eq. (1) is also the square root of the target density - b (modulo the phase factor). The Aufbau principle is not violated. It is worthwhile to notice that despite the fact that the overlap between two orbital densities and = 2y>2s is non-zero, = 0 (or constant). The... 

Although the occupied orbitals are of main importance, since they are directly involved in the formation of the chemical bond, the unoccupied states also provide complementary information. In X-ray absorption spectroscopy (XAS), often denoted Near Edge X-ray Absorption Fine Structure (NEXAFS), we excite a core electron to the empty states above the Fermi level [3,4,13]. There is a close connection between XES and XAS where the former gives information on the occupied orbitals while the latter relates to the character and symmetry of the unoccupied levels. Both are governed by the dipole selection rule and the localized character of the core orbitals allows a simple atom-specific projection of the electronic structure the major difference is in the final states. In XAS the empty electronic states are probed... 

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