Exchange-correlation potential excitation energy

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-... 

Table 9.1 presents excitation energies for a few atoms and ions. Calculations were performed with the generalized KLI approximation [69,74], For comparison, experimental data and the results obtained with the local-spin-density (LSD) exchange-correlation potential [75] are shown. The KLI method contains only the exchange. 

As was mentioned above, in KS-TDDFT the effects of electron exchange and Coulomb correlation are incorporated in the exchange-correlation potential vxaJ and kernel fxl- While the potential determines the KS orbitals (j)ia and the zero-order TDDFRT estimate (35) for excitation energies, the kernel determines the change of vxca with Eqs. 21, 22, 24. Though both vxca and are well defined in the theory, their exact explicit form as functionals of the density is not known. Rather accurate vxca potentials can be constructed numerically from the ab initio densities p for atoms [35-38] and molecules [39-42]. However, this requires tedious correlated ab initio calculations, usually with some type of configuration interaction (Cl) method. Therefore, approximations to vxcn and are to be used in TDDFT. 

We did not look at other properties, but it is worthwhile to mention the work performed by Casida et al. with the time dependent DFT formalism for the determination of polarizabilities and excitation energies within the linear response approach, both properties being very sensitive to the large r behavior of the exchange-correlation potential [78]. They made use of the VLB functional and obtained a strong improvement of the polarizabilities over the LDA, although they observed also an overcorrection of LDA vs experiment [82]. 

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].)...

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. 

In more recent work, Schipper et al. presented a new exchange-correlation potential that was constructed to give a correct asymptotic behaviour (as in the potential of van Leeuwen and Baerends ) and also an accurate description in the regions closer to the nuclei. The resulting potential (SAOP, for Statistical Average of different model Orbital Potentials) became orbital dependent and was subsequently tested on some small molecular systems for which both excitation energies and polarizabiUties and hyperpolarizabihty were calculated. It was indeed found that an improved agreement with experimental results was obtained. 

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