FOD analysis

Stefan Grimme and coworkers have come up a static electron correlation diagnostic that is easy to use and reveals the nature of the static electron correlation as well. The diagnostic is based on fractional occupation DFT or finite temperature DFT and is called fractional occupation number weighted electron density (FOD).
Information is available in the ORCA manual and in the original article: see paper by Grimme. A later article discusses FOD analysis as a tool for selecting active spaces in CASSCF calculations

FOD analysis is easy to carry out in ORCA and requires only a DFT calculation.

Simple FOD example

The simplest way of doing FOD analysis is to just use the FOD keyword (no other settings) for your molecule.

This enables the default FOD-theory level (TPSS/def2-TZVP with a smearing temperature of 5000 K) which works well for most cases.

Here a FOD calculation on para-benzyne is performed:

! FOD

*xyz 0 1
C 0.0000000 1.2077612 0.7161013
C 0.0000000 0.0000000 1.3596219
C 0.0000000 -1.2077612 0.7161013
C 0.0000000 -1.2077612 -0.7161013
C 0.0000000 0.0000000 -1.3596219
C 0.0000000 1.2077612 -0.7161013
H 0.0000000 2.1606260 1.2276695
H 0.0000000 -2.1606260 1.2276695
H 0.0000000 -2.1606260 -1.2276695
H 0.0000000 2.1606260 -1.2276695
*

Once the SCF converges, the following output can be seen:

9 -230.7579768346 0.000000076533 0.00018805 0.00000543 0.0001382 0.0000
10 -230.7579769281 -0.000000093540 0.00005320 0.00000159 0.0000392 0.0000
**** Energy Check signals convergence ****
Fermi smearing:E(HOMO(Eh)) = -0.196582 MUE = -0.175341 gap= 1.089 eV
N_FOD = 0.938222

The FOD number (N_FOD) already indicates static electron correlation but it is even more useful to visualize the fractional occupation density.

In ORCA 4.0, ORCA always gives a filename.scfp_fod file when smearing is enabled. This file that contains the fractional occupation density can be plotted like other densities using the orca_plot tool.

orca_plot filename.gbw -i

Then select the type of plot (1), electron density (2), default name (n = no), give the name of the FOD file, e.g. filename.scfp_fod, grid resolution wanted (4 and then a number e.g. 80; 80 may be fine, 120 for high-quality plots but may take a long time), the outputfile format (5) and choose 7 for Cube file format and then 10 to generate the plot. Open the Cube file in a program like Chemcraft/Avogadro, use the recommended contour value of 0.005 e/Bohr³ to visualize these FOD plots.

The FOD plot above (plotted with Chemcraft) indicates a significant and delocalized FOD. Multiconfigurational methods should be used to study this molecule and any single-reference result (HF, DFT, MP2, CC should be regarded with suspicion)

FOD analysis with different functional

If a different functional is used then this needs to be defined in the simple inputline and also note that the Smeartemp should then be changed (from the default 5000K), depending on the amount of HF exchange in the functional.

! UKS B3LYP def2-TZVP tightscf
%scf
smeartemp 9000
end

*xyz 0 1
C 0.0000000 1.2077612 0.7161013
C 0.0000000 0.0000000 1.3596219
C 0.0000000 -1.2077612 0.7161013
C 0.0000000 -1.2077612 -0.7161013
C 0.0000000 0.0000000 -1.3596219
C 0.0000000 1.2077612 -0.7161013
H 0.0000000 2.1606260 1.2276695
H 0.0000000 -2.1606260 1.2276695
H 0.0000000 -2.1606260 -1.2276695
H 0.0000000 2.1606260 -1.2276695
*