6.2 Exchange-Correlation Functionals Available
The following exchange-correlation functionals are available:
- LDAs: S-VWN, PWLDA
- GGAs: B-VWN, B-LYP, B-P, PBE
- MGGA: TPSS; M06 (using XCFun)
- hybrid functionals: BH-LYP, B3-LYP, PBE0, TPSSh; M06-2X (using XCfun)
- double–hybrid functional: B2-PLYP (energy calculations only!)
For EXX and LHF, see Chapter 18
The XCFun library (Arbitrary-Order Exchange-Correlation Functional Library) by Ulf
Ekström and co-workers has been included  and some of the functionals implemented
there can now be utilized. Among them are the empirically fitted MGGAs M06 and
M06-2X from the Truhlar group . XCFun functionals are available for energy, gradient,
vib. frequencies and TDDFT excited state energy calculations - with and without RI
approximation. For details and the license of XCFun please refer to its web site
In detail, the Turbomole own functional library consists of:
- The Slater–Dirac exchange functional only (S) [57,58].
- The 1980 correlation functional (functional V in the paper) of Vosko, Wilk,
and Nusair only (VWN) .
- A combination of the Slater–Dirac exchange and Vosko, Wilk, and Nusair 1980
(functional V) correlation functionals (S-VWN) [57–59].
- The S-VWN functional with VWN functional III in the paper. This is the same
functional form as available in the Gaussian program [57–59].
- A combination of the Slater–Dirac exchange and Perdew-Wang (1992)
correlation functionals [57,58,60].
- A combination of the Slater–Dirac exchange and Becke’s 1988 exchange
functionals (B88) [57,58,61].
- Lee, Yang, and Parr’s correlation functional (LYP) .
- The B-LYP exchange-correlation functional (B88 exchange and LYP
correlation functionals) [57,58,61,62].
- The B-VWN exchange-correlation functional (B88 exchange and VWN (V)
correlation functionals) [57–59,61].
- The B-P86 exchange-correlation functional (B88 exchange, VWN(V) and
Perdew’s 1986 correlation functionals) [57–59,61,63].
- The Perdew, Burke, and Ernzerhof (PBE) exchange-correlation functional
- The Tao, Perdew, Staroverov, and Scuseria functional (Slater–Dirac, TPSS
exchange and Perdew-Wang (1992) and TPSS correlation functionals) [57,58,
Additionally, for all four modules (dscf, grad, ridft, and rdgrad) following
hybrid functionals are available (a mixture of Hartree–Fock exchange with DFT
- The BH-LYP exchange-correlation functional (Becke’s half-and-half exchange
in a combination with the LYP correlation functional) [57,58,61,62,66].
- The B3-LYP exchange-correlation functional (Becke’s three-parameter
functional) with the form,
where HF denotes the Hartree-Fock exchange [57,58,61,62,67].
|0.8S + 0.72B88 + 0.2HF + 0.19V WN(V ) + 0.81LY P || ||(6.3) |
- The B3-LYP exchange-correlation functional with VWN functional V in
the paper. This is the same functional form as available in the Gaussian
- The 1996 hybrid functional of Perdew, Burke, and Ernzerhof, with the
where PBE(X) and PBE(C) are the Perdew–Burke–Ernzerhof exchange
and correlation functionals and PW is the Perdew–Wang correlation
|0.75(S + PBE(X)) + 0.25HF + PW + PBE(C) || ||(6.4) |
- The TPSSH exchange-correlation functional of Staroverov, Scuseria, Tao and Perdew
with the form,
where HF denotes the Hartree–Fock exchange [57,58,60,65,69].
|0.9(S + TPSS(X)) + 0.1HF + PW + TPSS(C) || ||(6.5) |
The Double-Hydbrid Functional B2-PLYP can be used for single point energy calculations.
Note, that one has to run a MP2 calculation after the DFT step to get the correct
B2-PLYP is a so-called double-hybrid density functional (DHDF)  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. In the following
options/restrictions of this method are given:
- single point calculations only (computed with the DSCF/RIDFT and
- UKS treatment for open-shell cases.
- can be combined with resolution-of-identity approximation for the SCF step
(RI-JK or RI-J option).
- can be combined with the dispersion correction (DFT-D 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 [71,72]. The mixing is described by
two empirical parameters ax and ac in the following manner: 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:
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
For B2-PLYP, B88 exchange  and LYP correlation  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
How to use B2-PLYP:
- during preparation of your input with DEFINE select b2-plyp in the DFT
- carry out a DSCF run. Prepare and run a RI-MP2 calculation with either RIMP2
or RICC2 program modules.
- the RI-MP2 program directly prints the B2PLYP energy if this functional has
been chosen before
Or use the b2plypprep script to setp up the calculation.
- define coord and basis set
- (optional: switch on ri or rijk and define jbasis or jkbasis)
- run b2plypprep
- run DSCF (or RIDFT) and RICC2