# 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 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 Normal [VeryBasic, Basic, Normal, Good, VeryGood, Excellent] RI Hartree-Fock Accuracy of numerical integration and thresholds of the RI procedure.
FitSetQuality
Type: Multiple Choice Normal [VeryBasic, Basic, Normal, Good, VeryGood, Excellent] 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 0.001 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 True Sets the fit-set quality for all atoms in a region. If specified, this overwrites the globally set quality.
Quality
Type: Multiple Choice [VeryBasic, Basic, Normal, Good, VeryGood, Excellent] This region’s quality of the auxiliary fit set employed in the RI scheme.
Region
Type: String 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


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