Numerical precision

The user is always responsible for the numerical precision you get from whatever quantum chemistry code you use. Below are some helpful keywords and recommendations to deal with numerical precision.

ORCA5 Note: Numerical robustness was a major improvement of ORCA 5.0. New, much more accurate integration grids are available (both DFT and COSX) and the defaults are generally trustworthy settings.

SCF Convergence tolerance

The default SCF convergence criteria in ORCA for single-point calculations is given by the keyword NormalSCF(see below). This may not always be a reliable setting for energies, molecular properties, geometry optimizations etc. When geometry optimizations are performed, the default SCF convergence is automatically changed from NormalSCF to TightSCF to reduce noise in the gradients. Shown below are recommended keywords for changing SCF convergence (Note that Energy change is not the only convergence tolerance changed by the keyword, see ORCA output file or ORCA SCF Keyword Reference and Good Practice (requires ORCA Forum Login ). Only rarely does one need to go beyond the TightSCF setting, but for some sensitive molecular properties this may be the case.

! SloppySCF => Energy change 3.0e-05 au

! LooseSCF => Energy change 1.0e-05 au

! NormalSCF => Energy change 1.0e-06 au. Default for single-point calculations.

! StrongSCF => Energy change 3.0e-07 au

! TightSCF => Energy change 1.0e-08 au. Default for geometry optimizations.

! VeryTightSCF => Energy change 1.0e-09 au

! ExtremeSCF => Energy change 1.0e-14 au

DFT integration grid

Learning how to handle numerical errors due to the the integration grid is important for reliable use of any DFT program.

In ORCA 5.0 things have dramatically changed for the better as there are now 3 primary keywords that control the overall accuracy of the DFT grid (and the COSX grid at the same time) for all possible ORCA calculations that use a grid (SCF, CP-SCF, TDDFT etc.).

These settings are:

! defgrid1

! defgrid2 (default).

! defgrid3

These 3 grids have been completely re-optimized by machine-learning techniques and should be more robust than previous defaults (or old grid-keyword-combos like "Grid4 FinalGrid5").

The default DFT Grid setting in ORCA is specified by defgrid2 and has been chosen to be numerically robust and is much more accurate than the previous default grid. defgrid1 is closer in quality and size to the older defaults (but more robust for heavier elements than the default in older ORCA versions). It is only recommended to use this setting however, if the accuracy has been carefully checked. defgrid3 is a much denser grid and might be useful in rare cases where defgrid2 is insufficient.

General recommendation: stick with defgrid2

To see the effect of the grid settings on the electron density one can look at the integrated number of electrons which should closely match the actual number. The SCF output for a 10-electron system might look like this:

DFT components:
N(Alpha) : 4.999999629595 electrons
N(Beta) : 4.999999629595 electrons
N(Total) : 9.999999259189 electrons

If the integrated number is not close to the real number of electrons (above it is close enough) then the integration grid was probably not large enough.

If one wants to manually specify grids (rare!), the most important ones are the selection of the angular grid (e.g. LebedevXXX) and the radial grid (IntAcc parameter).

In some rare cases it may be desirable to increase the radial grid (IntAcc) only on certain atoms. This may be useful for molecular properties of transition metal complexes (where the metal is the most important atom) or for atoms that are particularly sensitive to grid effects (heavy atoms like iodine). Note: this is likely to no longer be required in ORCA 5.0

!
%method
SpecialGridAtoms 26 # (26 is here the atomic number for iron)
SpecialGridIntAcc 7
end

*xyz 0 2
Fe 0.0 0.0 0.0
Cl 0.0 0.0 1.0
*

Accuracy of the RI-J, RIJCOSX, RI-JK and RI-MP2 approximations

See RI and auxiliary basis sets

Accuracy of the COSX grid in RIJCOSX calculations

The accuracy of the RIJCOSX approximation will on one hand depend on the size (and contraction) of the auxiliary basis set for the RI-J part which can be controlled by increasing the size of the auxiliary basis set (see RI and auxiliary basis sets), and on the other hand, the size of the COSX grid.

In ORCA5, the COSX grid is controlled by the same defgrid keywords that control the DFT grids (though the grids are different):

These settings are:

! defgrid1

! defgrid2 (default).

! defgrid3

If the default COSX grid (see below) is not accurate enough, the COSX grid can be increased by trying !defgrid3.

RIJCOSX when using large and/or diffuse basis sets (probably outdated information)

When diffuse functions are used (often to describe anions reliably) or very large basis sets are used, the default COSX grid settings (or even the GridXn keywords above) have in the past, sometimes resulted in SCF divergence or even a very inaccurate energy or geometry due to numerical noise (was a larger problem in earlier ORCA versions before ORCA 5.0). In such cases was is recommended to try changing the COSX grid settings to a steeper increase in the radial grid in the %method block. Note that increasing the COSX grid a lot may result in such expensive numerical integration that the RIJCOSX approximation no longer gives any benefit (might even make it slower than the analytical calculation) so this requires some care (see below).

Keywords in %method block:

IntaccX R1, R2, R3

R1 is the radial grid used for the initial iterations (should be small). R2 is used for most iterations while R3 is used for the final energy and gradient evaluations.

GridX A1, A2, A3

A1 is the angular grid used for the initial iterations (should be small). A2 is used for most iterations while A3 is used for the final energy and gradient evaluations.

end

Below are some recommended grid settings that have been successfully used to remove COSX numerical noise when using diffuse and/or large basis sets:

It is unclear how useful this strategy is in ORCA 5.

Small increase in grid:

! B3LYP def2-TZVP def2/J RIJCOSX D3BJ TIGHTSCF

%method
IntaccX 4.01,4.01,4.34 # Changing the 3 radial grids
GridX 1,1,2 # Changing the 3 angular grids
end

Medium increase in grid:

! B3LYP def2-TZVP def2/J RIJCOSX D3BJ TIGHTSCF
%method
IntAccX 4.34,4.34,4.67
GridX 2,2,2
end

Large increase in grid:

! B3LYP def2-TZVP def2/J RIJCOSX D3BJ TIGHTSCF
%method
IntAccX 5,5,5
GridX 3,3,4
end