Hartree–Fock RI

The Hartree-Fock exchange matrix is calculated through a procedure known as Resolution of the Identity (RI). The implementation of the RI scheme in BAND is loosely based on work by Ren et al. [1]. For more information on hybrid functionals in BAND, see the XC section.

Technical aspects of the RI scheme can be tweaked in the RIHartreeFock block:

RIHartreeFock
   Quality [VeryBasic | Basic | Normal | Good | VeryGood | Excellent]
   FitSetQuality [VeryBasic | Basic | Normal | Good | VeryGood | Excellent]
   DependencyThreshold float
   QualityPerRegion
      Quality [VeryBasic | Basic | Normal | Good | VeryGood | Excellent]
      Region string
   End
End
RIHartreeFock
Type:Block
Description:The Hartree-Fock exchange matrix is calculated through a procedure known as Resolution of the Identity (RI). Here you can tweak various parameters of the procedure.
Quality
Type:Multiple Choice
Default value:Normal
Options:[VeryBasic, Basic, Normal, Good, VeryGood, Excellent]
GUI name:RI Hartree-Fock
Description:Accuracy of numerical integration and thresholds of the RI procedure.
FitSetQuality
Type:Multiple Choice
Default value:Normal
Options:[VeryBasic, Basic, Normal, Good, VeryGood, Excellent]
Description:The auxiliary fit set employed in the RI scheme. This is an important aspect of the procedure, significantly affecting both accuracy and computation time. For SZ and DZ basis set a ‘basic’ FitSetQuality will suffice. For ‘DZP’ and ‘TZP’ a normal quality is recommended. For larger basis set, use either ‘normal’ or better FitSetQuality.
DependencyThreshold
Type:Float
Default value:0.001
Description:To improve numerical stability, almost linearly-dependent combination of basis functions are removed from the Hartree-Fock exchange matrix. If the SCF does not converge or you obtain unphysically large bond energy in an Hybrid calculation, you might try setting the DependencyThreshold to a larger value (e.g. 3.0E-3).
QualityPerRegion
Type:Block
Recurring:True
Description:Sets the fit-set quality for all atoms in a region. If specified, this overwrites the globally set quality.
Quality
Type:Multiple Choice
Options:[VeryBasic, Basic, Normal, Good, VeryGood, Excellent]
Description:This region’s quality of the auxiliary fit set employed in the RI scheme.
Region
Type:String
Description:The identifier of the region for which to set the quality.

For efficiency and numerical stability reasons, it is advisable to include:

SoftConfinement
  Quality Basic
End

See the Confinement of basis functions section for more info.

Notes: for periodic systems it is only possible to use short-range hybrid functionals (e.g. HSE06) and all-electron basis sets.

Note

  • In AMS2019.3 the fit set for FitSetQuality Good has been improved.

References

[1]X. Ren, P. Rinke, V. Blum, J. Wieferink, A. Tkatchenko, A. Sanfilippo, K. Reuter and M. Scheffler, Resolution-of-identity approach to Hartree–Fock, hybrid density functionals, RPA, MP2 and GW with numeric atom-centered orbital basis functions, New J. Phys. 14 053020.