Hybrid functionals local

Figure 4.9 Total and projected density of states forthe hydroxylated (top) and reduced (bottom) TiOjfl 1 0) surface, calculated using the B3LYP hybrid functional. The Ti3+ states are localized on (a) the Ti ion between the two bridging OH groups, Tilton (d) the Ti ion nearest to the oxygen vacancy, Tij (b), (c) on a five-...

A substantial improvement in the theoretical modeling of this substrate, able to overcome the drawbacks of both former approaches (standard GGA and localized atomic basis set B3LYP) is the implementation of the HSE03 [36] hybrid functionals in a plane-wave formalism. 

Aside from the well-known LDA (local density approximation (26, 27) BLYP (Becke-Lee-Yang-Parr (28, 29)) and B3LYP (29, 30) functionals, we considered the more recent B97-1 functional (which is a reparametrization (31) of Becke s 1997 hybrid functional), the B97-2 functional (32) (a variation of B97-1 which includes a kinetic energy density term), and the HCTH-407 (33) functional of Boese and Handy (arguably the best GGA functional in existence at the time of writing). The rationale behind the Wlc (Weizmann-1 cheap) approach is extensively discussed elsewhere. (34,35) For the sake of self-containedness of the paper, we briefly summarize the steps involved for the specific system discussed here ... 

All of the calculations described here use local functionals that do not include exact exchange. The best choice of functional for calculating MCD spectra is still an open question. In our experience, the MCD parameters produced with different local functionals do not vary much (83). The exception to this rule is functionals that are asymptotically correct. Asymptotically correct functionals tend to give excitation energies that differ from those produced by standard local functionals, particularly for Rydberg and charge-transfer transitions. The MCD parameters produced by asymptotically correct functionals tend to follow a similar pattern when compared with results of other local functionals. A few studies have considered hybrid functionals (42,43). This work found that hybrid functionals were superior in some applications. More work in this area is needed. 

For a short exposition of the evolution from the local-density approximation to the local-spin-density approximation and gradient-corrected and hybrid functionals, see Levine IN (2000) Quantum chemistry, 5th edn. Prentice Flail, Upper Saddle River, NJ, pp 581-592... 

TDDFRT/TDHF mixture coefficients, as well as the composition of the approximate vxca, depend on the hybrid scheme used. Applications of the TDDFRT/TDHF approach with the hybrid functionals, such as the hybrid Becke s three-parameter functional [55] and the gradient correction of Perdew, along with his 1981 local correlation functional [45], B3P86, the Lee-Yang-Parr nonlocal correlation functional [56], B3LYP, or the Perdew-Burke-Erzenrhof (PBE) [57, 58] hybrid functional, PBEO [59], will be discussed below. 

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