# Hartree–Fock RI scheme¶

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. [57]. For more information on hybrid functionals in BAND, see the XC section.

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

RIHartreeFock
Quality [basic|normal|good|verygood]
FitSetType [Mirko|ET6|ET7|ET8]
DependencyThreshold 1.0E-3
End

Quality
(Default: Normal) Set the numerical quality of some internal technical procedures, including numerical integration and linear scaling parameters.
FitSetType
(Default: Mirko) The auxiliary fit set employed in the RI scheme. ET8 is a fairly large fit set, and can be used for assessing the accuracy of the RI procedure.
DependencyThreshold
(Default: 1.0E-3) To improve numerical stability, almost linearly-dependent combination of basis functions are removed from the Hartree-Fock exchange matrix. If you obtain unphysical large bond energy in an Hybrid calculation, you might try setting the DependencyThreshold to a larger value (e.g. 3.0E-3).

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

SoftConfinement
Quality Basic
End