# 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
AtomDepQuality # Non-standard block. See details.
...
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).
AtomDepQuality
Type: Non-standard block One can define a different fit-set quality for each atom. The syntax for this free block is ‘iAtom quality’, where iAtom is the index of the atom in input order.

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.