Hybrid functionals global

Recently, Heyd et al. [262] used the screening of 1/m to adapt global hybrid functionals to calculations of periodic systems with small band gaps. Such an adaptation is necessary because direct evaluation of exact exchange in periodic systems with metallic character is prohibitively expensive, rendering conventional hybrids utterly impractical for many solids. Heyd et al. start with rewriting the one-parameter global hybrid functional of Eq. (187) as... 

An independent line of thought also revives our interest in energy densities. The standard global hybrid functionals [2] mix a large constant fraction of a semilocal (LDA, GGA, or meta-GGA) exchange energy with a complementary... 

This section explains how to use the LCOE to global hybrid functionals and assesses their performance regarding orbital energies. Numerical assessments on ionization potentials (IPs) and concluding remarks are also given. 

We describe two procedures of how to construct the OS global hybrid functionals using Eq. (14.61) the determination of OS parameters and estimation of orbital energies. 

Figures 14.1 illustrate the 01s and Sis orbital energies with respect to FON electrons. A similar tendency is observed for the Ols and Sis orbitals As the number of electrons increases, orbital energies of HFx -F DFTc functional decrease and those of the conventional DFT XC functionals increase. In contrast to HOMO, the dependences of DFTc functionals for HFx -F DFTc are smaller than those for the conventional XC functionals. The curves of the OS global hybrid functionals with appropriate a,- determined through the LCOE are approximately flat for Ols and Sis. The OS parameters aois, sis are approximately 0.57,0.71, which are slightly larger than those of CV-B3LYP, determined by numerical assessment for core excitations [50-52].

In order to assess the performance of the OS global hybrid functionals from a different point of view, we also compare the orbital energies and IPs of valence and core orbitals for OCS molecule in a sense of Koopmans theorem. IPs obtained by the OS hybrid functionals are shown in Table 14.16. The deviations from experimental IPs [53] and values of a, are shown in parentheses and square brackets, respectively. For HOMO, the OS global hybrid functionals provide comparatively similar IPs 11.45,10.99, 11.18, and 11.17 eV for SVWN5, BLYP, PBE, and TPSS functionals, and the corresponding deviations are at most 0.25 eV. The OS hybrid functionals also reproduce Ols and Sis IPs within the deviation of 2.5 eV for the LDA, GGA, and meta-GGA functionals, though the accurate estimation of large IPs is rather difficult. 

Table 14.16 OCS IPs (eV) by OS global hybrid functionals of SVWN5, BLYP, PBE, and TPSS functionals and Oj determined for the OS in eV...

The above assessment reveals that the LCOE improves FON dependence and estimation of IPs significantly for all global hybrid functionals, which bases S VWN5, BLYP, PBE, and TPSS XC functionals and an added HFx term. Finally, let us compare the results of the OS functional based on LC-BLYP. For core orbitals, the global hybrid-based OS functionals basically perform slightly better than the OS functional of LC-BLYP does, although the obtained a, values are relatively different. For valence orbitals, all OS functionals provide MAEs less than 0.5 eV. The MAE of the conventional LC-BLYP is the smallest among all functionals, which is consistent with the previous reports [100, 101]. The overall MAEs of the OS functional of LC-BLYP are comparable to those of the LDA, GGA, and meta-GGA functionals. 

We have constructed and assessed the OS global hybrid functionals satisfying the LCOE for core and valence orbitals. As was reported for LC hybrid functionals [53], the LCOE drastically reduces the FON dependence and enables accurate estimates... 

The valence s OS HFx portions obtained for global hybrid functionals are significantly larger than those for LC hybrid functionals [53], although the core s ones are similar to those of LC hybrid functionals. The effect of HFx has been discussed theoretically and numerically from various points of view. 

For these complexes, we examined the following exchange-correlation (XC) functionals (i) GGA functional, BLYP [38, 39] (ii) four global hybrid functionals,... 

The structures of B -Bjj cations shown in Figure 29.1 were taken from the Ref. [7], in which they were considered as the most stable structures previously reported in the literature. They were reoptimized using hybrid density functional method known in the literature as B3LYP [67-69] with the 6-311 +G basis set [70-72] as implemented in Gaussian 03 program [73]. There is no guarantee that all the considered structures here are indeed global minimum structures. 

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