# DFT calculations

See also Geometry optimization section.

### General recommendations about molecular DFT calculations (Ragnar Bjornsson)

For GGA calculations (functionals like PBE, BP86, TPSS), use of the RI-J approximation is generally recommended and is the default in ORCA. An auxiliary basis set is required and one should make sure that a reliable one is specified (using def2-XVP basis set and the accompanying def2/J auxiliary basis set makes this easy, see Basis sets).

For hybrid GGA or hybrid meta-GGA calculations, use of the RI-JK or RIJCOSX approximations can speed things up considerably. Note though that it is your responsibility to control monitor the error introduced by these approximations (see Numerical accuracy and RI and auxiliary basis sets).

Use a dispersion correction. Grimme’s DFT-D3 method includes dispersion in DFT calculations free of charge and is generally recommended. D3 keyword. See also the new DFT-D4 method.

For organic or maingroup molecules, we recommend using the best performing functionals according to large benchmarking studies like the GMTKN30 or GMTKN55. Of the GGA functionals this includes functionals like BP86, BPBE, TPSS etc. in combination with DFT-D3 dispersion corrections (which is often crucial for reliable energies). Hybrid functionals generally give much improved energies and the best performing hybrid-GGA functionals for the GMTKN30 database are B3PW91, PW6B95 and M06-2X. Note that while the popular functional B3LYP has a good record for satisfactory molecular geometries it is actually not the best method for reliable organic and main-group energies or properties. Thus single-point energy calculations on B3LYP geometries with other functionals may give more reliable results. Studies indicate that PBE0 with a triple-zeta basis set (or Grimme's PBEh-3c method) could be an even better choice for geometries.

Note that double hybrid functionals have emerged as the most reliable group of DFT functionals for energies of organic and maingroup molecules as well for some closed-shell transition metal chemistry (note: typically not well-behaved for open-shell 3d metal-containing compounds!) and they are the clear winners in Grimme's GMTKN30 study as well in the MOR41 metal-organic chemistry study . While more expensive, double hybrid calculations can be run very efficiently in ORCA. See the double hybrid page. Double hybrid geometry optimizations are more expensive though (due to the expensive MP2+DFT gradient) and usually not worth the effort unless you require really accurate geometries.

For transition metal compounds things are bit different. BP86 and TPSS/TPSSh functionals show excellent performance for first-row transition metal geometries while PBE0 is recommended as you go down the periodic table (see studies by Bühl et al. for 1st-row, 2nd-row, 3rd-row complexes) while single-point calculations with hybrid functionals (such as TPSSh, B3LYP or PBE0) can give more reliable energies or molecular properties of transition metal compounds. Unfortunately, performance is very system-dependent and DFT functionals often fail to describe the static correlation present in open-shell transition metal compounds. The covalency of metal-ligand or even metal-metal bonds is strongly affected by the amount of Hartree-Fock exchange in the functional. GGA functionals may overestimate the covalency of bonds while hybrid functionals with HF exchange of say, 30 % or higher, will give too ionic bonds. Metal-metal bonds are often better described by GGA functionals than hybrid functionals.

DFT calculations on heavy elements can either use an all-electron relativistic approach or effective core potentials (ECPs). ECPs are selected automatically in ORCA 4.0 (see ECP page). If your molecule contains an element heavier than Kr (i.e. second TM row and below, iodine etc.) then it is often recommended to use either a relativistic approximation (such as ZORA or DKH2, see Relativistic approximations) or to replace the core electrons of that element with an effective core potential (see ECP page). Note that while ECPs are very common in the literature, ZORA/DKH2 calculations will give you much more accurate results while being only slightly more costly (for molecules with many heavy elements though, ECP calculations should be more efficient).

### List of popular GGA, meta-GGA and hybrid functionals available in ORCA. See ORCA Manual for a full list (see Double hybrid page for a list of double hybrids)

Note: Minnesota functionals such as M06-L, M06 and M06-2X are known to be more sensitive to the integration grid than other functionals. This means that use of these functionals often necessitates increasing the integration grid in ORCA (defgrid3 is probably a safe choice) for reliable numbers with these functionals. See Numerical precision for more information about integration grids.

### GGA and meta-GGA calculations

GGA and meta-GGA (non-hybrid) calculations run typically much faster than hybrid calculations and so if the accuracy is sufficient, this GGA-DFT is typically the fastest useful DFT you can do. Calculation using the popular BP86 functional using the RI-J approximation (default) and the def2-TZVP basis set and the def2/J auxiliary basis set. RI-J is a strongly recommended and is by default on.

! RI BP86 def2-TZVP def2/J

Calculation using the popular BP86 functional WITHOUT the RI-J approximation (not recommended as this will be considerably slower).

! BP86 def2-TZVP NORI

### Hybrid GGA/hybrid meta-GGA functional calculations in ORCA (see manual for a complete list of functionals)

Hybrid GGA/ hybrid meta-GGA calculations without any any RI approximations used to be the default in ORCA version 2-4. This is no longer the case as the RIJCOSX approximation has become much more reliable. See below. To request a hybrid-DFT calculation without any approximation made to the Coulomb or Exchange integrals (not recommended as it is slow) you must add the !NORI keyword.

! B3LYP def2-TZVP NORI

Use of the B3LYP hybrid functional:

There are multiple B3LYP definitions used in the literature. This is the B3LYP version as implemented in ORCA and Turbomole:

! B3LYP def2-TZVP

This is the B3LYP version as implemented in the Gaussian code (different LDA correlation functional):

! B3LYP/G def2-TZVP

### Hybrid-GGA calculations using RIJK, RIJCOSX or RIJONX approximations

Single-point B3LYP calculation using the RIJCOSX approximation (this is the default since ORCA 5.0). Becomes faster than RI-JK for medium to large molecules. Uses a J auxiliary basis set for Coulomb integrals and numerical COSX integration for the Exchange integrals (Default COSX grid chosen automatically). Gradients are available. Generally recommended.

! B3LYP RIJCOSX def2-TZVP def2/J

Single-point B3LYP calculation using the RIJK approximation. Very fast and reliable for small molecules. Uses a single JK auxiliary basis set for Coulomb and Exchange RI integrals (def2/JK). Gradients are available.

! B3LYP RIJK def2-TZVP def2/JK

Single-point B3LYP calculation using the RIJONX (also called RIJDX) approximation. This uses the RI-J approximation for Coulomb integrals but a standard treatment of the Exchange integrals is performed. Gradients are availab.e.

! B3LYP RIJONX def2-TZVP def2/J

Range-separated hybrid DFT calculations

Range-separated hybrid DFT calculations

Calculations using range-separated hybrids can be performed in ORCA by simply selecting the keyword for the range-separated functional (see table above). Analytical gradients or frequencies are available.

! wB97X def2-TZVP def2/J RIJCOSX

It is also possible to modify the parameters of the existing range-separated hybrid forms:

%method

RangeSepEXX True

RangeSepMu 0.25

RangeSepScal 0.7

ACM 0.2, 0.1, 1.0

end

See manual for more details.

### Dispersion corrections for DFT

The recommended dispersion correction in ORCA is to use Grimme’s DFT-D3 approach which can be selected by a simple keyword in ORCA: D3ZERO or D3BJ which selects the DFT-D3 method with the original damping function (D3ZERO) or by the newer recommended Becke-Johnson damping (D3BJ).

B3LYP-D3 with the original damping:

! B3LYP D3ZERO def2-TZVP

B3LYP-D3BJ, with Becke-Johnson damping (recommended):

! B3LYP D3BJ def2-TZVP

B3LYP-D4:

! B3LYP D4 def2-TZVP

Many functionals can use the dispersion correction out of the box, by combining the functional and dispersion keywords and the recommended scaling factors for that functional will be used. Unsupported functionals can still be corrected but then the scaling factors need to be provided manually

Nonlocal correlation functionals can also be used and nowadays there are even gradients available. See ORCA manual for more details.

! B3LYP NL def2-TZVP

### Speeding up SCF convergence using RI-JK or RIJCOSX and then turning the approximation off.

Sometimes one may want to minimize numerical errors, for example for accurate molecular property calculations, yet take advantage of RI-J/RIJCOSX/RI-JK. Therefore it may be desirable to converge a computationally expensive SCF using RIJK or RIJCOSX to save time and then reconverge without the approximation. This can be done in a single input file as shown below (RIJCOSX can be substituted for RI-JK below).

! B3LYP RIJCOSX def2-TZVP def2/J xyzfile

%base "rijcosx"

*xyz 0 1

coordinates

*

$new_job

! NORI B3LYP def2-TZVP MOREAD

%base "normal"

%moinp "rijcosx.gbw"

*xyzfile 0 1

Modifying the HF exchange of hybrid functionals

Modifying the HF exchange of hybrid functionals

Occasionally it may be of interest to modify the HF exchange percentage in hybrid functionals. The following input changes the HF exchange percentage of B3LYP from 20 % (default) to 15 %.

Note that due to the presence of both GGA exchange and LDA exchange in hybrid functionals, modifying these parameters requires some knowledge. See chapter 9.2.2 for more information.

! B3LYP def2-TZVP

%method

ScalHFX = 0.15

end

Non self-consistent DFT calculation using other orbitals

Non self-consistent DFT calculation using other orbitals

It is possible to perform a non-iterative DFT calculation using orbitals from another source. This idea has e.g. seen some use in computing electron affinities of molecules where non-iterative DFT calculations using HF orbitals yields improved results due to reduced self-interaction errors.

!HF def2-TZVP xyzfile

%base "hf"

* xyz 0 1

coordinates

*

$new_job

! BP86 def2-TZVP def2/J MOREAD

%base "dft"

%moinp "hf.gbw"

%scf

maxiter 1

Dampfac 1.0

end

* xyzfile 0 1

### Finite-temperature fractional occupation DFT (smearing)

Introduces a temperature that applies a Fermi-like occupation number smearing over all the orbitals of the system. This is used in FOD analysis. Makes the energy dependent on the temperature. See ORCA manual for more details. Not available with SOSCF or CNVRico SCF procedures. Make sure to have these turned off.

! BP def2-SVP def2/J smear NOSOSCF

%scf

smeartemp 5000 # Smearing temperature. Default is 5000 K.

end