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 [Auto | VeryBasic | Basic | Normal | Good | VeryGood | Excellent]
   FitSetQuality [Auto | VeryBasic | Basic | Normal | Good | VeryGood | Excellent | FromBasisProducts]
   DependencyThreshold float
   QualityPerRegion
      Quality [VeryBasic | Basic | Normal | Good | VeryGood | Excellent]
      Region string
   End
End
RIHartreeFock
Type

Block

Description

Quality
Type

Multiple Choice

Default value

Auto

Options

[Auto, VeryBasic, Basic, Normal, Good, VeryGood, Excellent]

Description

Numerical accuracy of the RI procedure. If ‘Auto’, the quality specified in the ‘NumericalQuality’ will be used.

FitSetQuality
Type

Multiple Choice

Default value

Auto

Options

[Auto, VeryBasic, Basic, Normal, Good, VeryGood, Excellent, FromBasisProducts]

Description

The quality of auxiliary fit set employed in the RI scheme. If ‘Auto’, the value of the RIHartreeFock Quality option will be used. Normal quality is generally sufficient for basis sets up to and including TZ2P. For larger basis sets (or for benchmarking purposes) a VeryGood fit set is recommended. Note that the FitSetQuality heavily influences the computational cost of the calculation.

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 you obtain unphysically large bond energy in an Hybrid calculation, or an unphysically low correlation energy in an RPA, MP2, or double hybrid calculation, you might try setting the DependencyThreshold to a larger value (e.g. 3.0E-3) Note, that in GW calculations and GW-BSE calculations the default for this key is 5.0e-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.