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 [55] 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 [56]. 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 https://repo.ctcc.no/projects/xcfun/wiki

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) [59].
- 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) [62].
- 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 [57,58,60,64].
- The Tao, Perdew, Staroverov, and Scuseria functional (Slater–Dirac, TPSS exchange and Perdew-Wang (1992) and TPSS correlation functionals) [57,58, 60,65].

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):

- 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,
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 program.
- The 1996 hybrid functional of Perdew, Burke, and Ernzerhof, with the
form,
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,
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 energy!

B2-PLYP is a so-called double-hybrid density functional (DHDF) [70] 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 RIMP2/RICC2 modules).
- 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,
s
_{6}(B2-PLYP)=0.55).

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 a_{x} and a_{c} in the following manner:

| (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 E_{C}(KS - PT2) is evaluated afterwards and added to the total
energy.

For B2-PLYP, B88 exchange [61] and LYP correlation [62] are used with the parameters
a_{x} = 0.53 and a_{c} = 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.

How to use B2-PLYP:

- during preparation of your input with DEFINE select b2-plyp in the DFT menu.
- 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