Exchange-correlation potential excited states

The quality of the TD-DFT results is determined by the quality of the KS molecular orbitals and the orbital energies for the occupied and virtual states. These in turn depend on the exchange-correlation potential. In particular, excitations to Rydberg and valence states are sensitive to the behavior of the exchange-correlation potential in the asymptotic region. If the exchange-correla-... 

To perform excited-state calculations, one has to approximate the exchange-correlation potential. Local self-interaction-free approximate exchange-correlation potentials have been proposed for this purpose [73]. We can try to construct these functionals as orbital-dependent functionals. There are different exchange-correlation functionals for the different excited states, and we suppose that the difference between the excited-state functionals can be adequately modeled through the occupation numbers (i.e., the electron configuration). Both the OPM and the KLI methods have been generalized for degenerate excited states [37,40]. 

In section 2 the theory of ensembles is reviewed. Section 3 summarizes the parameter-free theory of G par[ll]. The self-consistently determined ensemble a parameters of the ensemble Xa potential are presented. In section 4 spin-polarized calculations using several ground-state exchange-correlation potentials are discussed. In section 5 the w dependence of the ensemble a parameters is studied. It is emphasized that the excitation energy can not generally be calculated as a difference of the one-electron energies. The additional term should also be determined. Section 6 presents accurate... 

First excitation energies determined from ground-state exchange-correlation potentials... 

Table II presents the first excitation energies obtained from spin- polarized calculations [24]. As ground-state exchange-correlation potentials were used the extra term in Eq.(20) does not appear. This is, certainly, one of the reasons for the difference between the calculated and the experimental excitation energies. There is a definite improvement comparing with the nonspin-polarized results [13]. Still, in most cases the calculated excitation energies are highly overestimated. The results provided by the different local density approximations are quite close to each other. The best one seems to be the Gunnarson-Lundqvist-Wilkins approximation. (In non-spin-polarized case the Perdew-Zunger parametrization gives results closest to the experimental data[30].)...

In the present paper, first we investigate the photoionization cross sections for atomic orbitals calculated with different scaling parameters of exchange-correlation potential, and for those of different oxidation states, namely different charge densities. We discuss the effect of the variation of the spatial extension of the atomic orbital on the photoionization cross section. Next we make LCAO (linear combination of atomic orbitals) molecular orbital (MO) calculations for some compounds by the SCF DV-Xa method with flexible basis functions including the excited atomic orbitals. We calculate theoretical photoelectron spectrum using the atomic orbital components of MO levels and the photoionization cross sections evaluated for the flexible atomic orbitals used in the SCF MO calculation. The difference between the present result and that calculated with the photoionizaion cross section previously reported is discussed. 

TTie accuracy of excitation energies is typically -0.5 eV for valence states, but Rydberg states, where the electron is excited into a diffuse orbital, can be in error by several eV. This problem has the same physical reason as the anion problem above, and can be solved by using corrections for the asymptotic behaviour of the exchange-correlation potential. Such Asymptotic Corrected (AC) functionals display much improved predictions for response properties. 

The development of accurate calculations for the excited states involved in XANES spectroscopy closely mirrors developments in ground-state calculations in molecules and solids. There are, however, several important differences, such as the necessity of a core-hole potential, the core-hole lifetime and final-state photoelectron lifetime effects, possible multi-channel effects, and the energy dependence of the exchange-correlation potential, which complicate the physical model but which may in principle be dealt with, although work continues in all of these areas. 

---