Hybrid range-separated hybrids

Further, there are asymptotically corrected XC kernels available, and other variants (for instance kernels based on current-density functionals, or for range-separated hybrid functionals) with varying degrees of improvements over adiabatic LDA, GGA, or commonly used hybrid DFT XC kernels [45]. The approximations in the XC response kernel, in the XC potential used to determine the unperturbed MOs, and the size of the one-particle basis set, are the main factors that determine the quality of the solutions obtained from (13), and thus the accuracy of the calculated molecular response properties. Beyond these factors, the quality of the... 

The discussion of the range-separated hybrids is similar. The four functionals have a similar behavior for the barriers heights, their MAEs having a deep minimum (around 3.5 kcal/mol) for values in the interval [0.3-0.5] (Fig. 1.4). 

Fig. 1.4 MAEs in the barrier heights of the DBH24 dataset (in kcal/mol) of the range-separated hybrids based on the S-RC, PBE-TCA, PBE-RevTCA, and ModPBE-RevTCA functionals. The results are given in function of the range-separation parameter Full line S-RC. Long-dashed line PBE-TCA. Dotted line PBE-RevTCA. Short-dashed line ModPBE-RevTCA...

Table 1.2 MAEs (in kcal/mol) in atomization energies, barrier heights, and noncovalent binding energies of the range-separated hybrids based on various local or semi-local functionals. The value of the range-separation parameter co for each case is also reported. The MAEs of the original local or semi-local functionals are given in parenthesis...

Range-separated hybrid functional, 223 Reaction centre (RC), 230—231 Reactive oxygen species, 121 Reversible intramolecular reaction with intermolecular counterpart, 2, 3f Reversible peroxyl radical formation,... 

F. Aquino, N. Govind, J. Autschbach. Scalar Relativistic Computations of Nudear Magnetic Shielding and -Shifts with the Zeroth-Qrder Regular Approximation and Range-Separated Hybrid Density Functionals. /. Chem. Theory Comput., 7 (2011) 3278-3292. 

Refaely-Abramson S, Sharifzadeh S, Govind N, Autschbach J, Neaton JB, Baer R, Kronik L (2012) Quasiparticle spectra from a nonempirical optimally tuned range-separated hybrid density functional. Phys Rev Lett 109 226405... 

Baer R, Livshits E, Salzner U (2010) Tuned range-separated hybrids in density functional theory. Annu Rev Phys Chem 61 85... 

Refaely-Abramson S, BaerR, Kronik L (2011) Fundamental and excitation gaps in molecules of relevance for organic photovoltaics from an optimally tuned range-separated hybrid functional. Phys Rev B 84 075144... 

RSHXLDA (range-separated hybrid with LDA exchange separation parameter (n = 0.40 a.u. as proposed for solids )... 

Four different Fock/Kohn-Sham operators have been applied to obtain the orbitals, which are subsequently localized by the standard Foster-Boys procedure. In addition to the local/semi-local functionals LDA and PBE, the range-separated hybrid RSHLDA [37, 56] with a range-separation parameter of /r = 0.5 a.u. as well as the standard restricted Hartree-Fock (RHF) method were used. The notations LDA[M] and LDA[0] refer to the procedure applied to obtain the matrix elanents either by the matrix algebra [M] or by the operator algebra [O] method. All calculations were done with the aug-cc-pVTZ basis set, using the MOLPRO quantum chemical program package [57]. The matrix elements were obtained by the MATROP facility of MOLPRO [57] the Cg coefficients were calculated by Mathematica. 

Gerber, I. C., 8c Angyan, J. G. (2007). London dispersion forces by range-separated hybrid density functional with second order perturbational corrections The case of rare gas complexes. Journal of Chemical Physics, 126, 044103. 

R. Baer, E. Livshits, and U. Salzner, Annu. Rev. Phys. Ghent., 61, 85-109 (2010). Tuned Range-Separated Hybrids in Density Functional Theory. 

T. M. Henderson, B. G. Janesko,and G. E. Scuseria,/. Ghem. Phys., 128,194105 1-9 (2008). Generalized Gradient Approximation Model Exchange Holes for Range-Separated Hybrids. 

Aquino F, Govind N and Autschbach J 2011 Scalar relativistic computations of nuclear magnetic shielding and g-shifts with the zeroth-order regnlar approximation and range-separated hybrid density functionals. J. Chem. Theory Comput. 7, 3278-3292. 

Finally, we consider the range-separated global hybrids. In this case, there are two parameters to be optimized, ao and co. The results we have obtained by the hybrid based on the PBE-TCA functional are shown in Figs. 1.7, 1.8, and 1.9. In... 

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