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Exchange-Correlation Functionals Available

The following exchange-correlation functionals are available:

For EXX and LHF, see Chapter 16

In detail, the functional library consists of:

Additionally, for all four modules (dscf, grad, ridft, and rdgrad) following hybrid functionals are available (a mixture of Hartree-Fock exchange with DFT exchange-correlation functionals):

Additionally the Double-Hydbrid Functional B2-PLYP can be used for single point energy calculations. Note that one has to run an MP2 calculation after the DFT step to get the correct B2-PLYP energy!

B2-PLYP is a so-called double-hybrid density functional (DHDF)[62] that uses in addition to a non-local exchange contribution (as in conventional hybrid-GGAs) also a non-local perturbation correction for the correlation part. Note the following options/restrictions in the present version of this method:

The non-local perturbation correction to the correlation contribution is given by second-order perturbation theory. The idea is rooted in the ab initio Kohn-Sham perturbation theory (KS-PT2) by Görling and Levy[63,64]. The mixing is described by two empirical parameters ax and ac in the following manner:

EXC(DHDF) = (1 - ax)EX(GGA) + axEX(HF)     (6.6)
+ (1 - ac)EC(GGA) + acEC(KS - PT2),      

where EX(GGA) is the energy of a conventional exchange functional and EC(GGA) is the energy of a correlation functional. EX(HF) is the Hartree-Fock exchange of the occupied Kohn-Sham orbitals and EC(KS - PT2) is a Møller-Plesset like perturbation correction term based on the KS orbitals:

EC(KS - PT2) = $\displaystyle {\frac{{1}}{{2}}}$$\displaystyle \sum_{{ia}}^{}$$\displaystyle \sum_{{jb}}^{}$$\displaystyle {\frac{{(ia\vert jb)[(ia\vert jb)-(ib\vert ja)]}}{{e_i+e_j-e_a-e_b}}}$. (6.7)

The method is self-consistent only with respect to the first three terms in Eq. 6.6, i.e., first a SCF using a conventional hybrid-GGA is performed first. Based on these orbitals EC(KS - PT2) is evaluated afterwards and added to the total energy.

For B2-PLYP, B88 exchange[53] and LYP correlation[54] are used with the parameters ax = 0.53 and ac = 0.27 . Due to the relatively large Fock-exchange fraction, self-interaction error related problems are alleviated in B2-PLYP while unwanted side effects of this (reduced account of static correlation) are damped or eliminated by the PT2 term.

1.2

How to use B2-PLYP:


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Next: Restricted Open-Shell Hartree-Fock Up: Hartree-Fock and DFT Calculations Previous: Background Theory   Contents   Index
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