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. [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 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
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]
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).

AtomDepQuality

Type:	Non-standard block
Description:	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

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.