Density fitting

Density fitting can be used to approximate the integrals in spin restricted Hartree-Fock (HF), density functional theory (KS), second-order Møller-Plesset perturbation theory (MP2 and RMP2), explicitly correlated MP2 (MP2-F12), all levels of closed-shell local correlation methods (LCC2, LMP2-LMP4, LQCISD(T), LCCSD(T)), as well as for CASSCF and CASPT2 methods. Density fitting is invoked by adding the prefix DF- to the command name, e.g. DF-HF, DF-KS, DF-MP2 and so on. Gradients are available for DF-HF, DF-KS, DF-MP2, DF-LMP2, DF-CASSCF, and DF-CASPT2. Symmetry is implemented for energy calculations (without gradients) for DF-RHF, DF-RKS,DF-UHF, DF-UKS DF-RMP2,DF-RMP2-F12, DF-CASSCF|DF-MULTI, DF-CASPT2|DF-RS2, and DF-RS2C, but for DF-MP2, DF-CCSD (and variants) as well as for local methods symmetry is not implemented and automatically turned off.

By default, a fitting basis set will be chosen automatically that corresponds to the current orbital basis set and is appropriate for the method. For instance, if the orbital basis set is VTZ, the default fitting basis is VTZ/JKFIT for DF-HF or DF-KS, and VTZ/MP2FIT for DF-MP2. Other fitting basis sets from the library can be chosen using the DF_BASIS option, e.g.

BASIS=VTZ             !use VTZ orbital basis
DF-HF,DF_BASIS=VQZ    !use VQZ/JKFIT fitting basis
DF-MP2,DF_BASIS=VQZ   !use VQZ/MP2FIT fitting basis

The program then chooses automatically the set which is appropriate for the method. Optionally, the basis type can be appended to the basis name and then this supercedes the default, e.g.

DF-HF,DF_BASIS=VQZ/JKFIT    !use VQZ/JKFIT fitting basis

Orbital basis sets can be chosen using type ORBITAL (but this is not recommended normally!). Contraction/uncontraction can be forced appending (CONTRACT) or (UNCONTRACT) to the basis name, e.g.
DF_BASIS=AVQZ(UNCONTRACT)/ORBITAL.
If other options are given in parenthesis, these can be separeted by commas, e.g.
DF_BASIS=AVQZ(f/d,UNCONTRACT)/ORBITAL.
Alternative forms, which should work as well, are
DF_BASIS=AVQZ(f/d)(UNCONTRACT)/ORBITAL
or
DF_BASIS=AVQZ(f/d)/ORBITAL(UNCONTRACT).
Note that the CONTRACT/UNCONTRACT option cannot be used with basis set names previously defined in a basis block (see below).

Alternatively, fitting basis sets can be defined in a preceding basis block (see basis input), and then be refered to with their set names, e.g.,

DF-HF, DF_BASIS=MYJKBASIS
DF-MP2, DF_BASIS=MYMP2BASIS

where MYJKBASIS and MYMP2BASIS are sets defined in a basis block. In this case it is the responsibility of the user to ensure that the basis set is appropriate for the method.

Further options, as fully described in section options for density fitting, can be added on the command line. In this case they are valid only for the current command. Alternatively, the options can be specifed on a separate DFIT directive. If this is given within a command block, the options are used only for the current program; this is entirely equivalent to the case that the options are specified on the command line. However, if a DFIT (or GDFIT) directive is given outside of a command block, the specified options are used globally in all subsequent density fitting calculations in the same run.

The options specified on a global DFIT directive are also passed down to procedures. However, if a DFIT is given within a procedure, the corresponding options are used only in the same procedure and procedures called from it. When the procedure terminates, the options from the previous level are recovered.

The options described in this section have sensible default values and usually do not have to be given. Many options described below have alias names. These can be obtained using

HELP,CFIT,ALIASES.

  • BASIS Basis set for fitting (Default: set corresponding to the orbital basis)
  • BASIS_COUL Basis set for Coulomb fitting (default BASIS)
  • BASIS_EXCH Basis set for exchange fitting (default BASIS)
  • BASIS_MP2 Fitting basis set for DF-MP2 (default BASIS)
  • BASIS_CCSD Fitting basis set for DF-LCCSD (default BASIS)
  • THRAO Threshold for neglecting contracted 3-index integrals in the AO basis (default 1.d-8).
  • THRMO Threshold for neglecting half-transformed 3-index integrals (default 1.d-8).
  • THRSW Threshold for Schwarz screening (default 1.d-5).
  • THROV Threshold for neglecting 2-index integrals in the AO (default 1.d-10.
  • THRPROD Product screening threshold for first half transformation (default 1.d-8).

Analogous thresholds for specfic programs can be set by appending the above keywords by the following specifications

  • _SCF Coulomb and exchange fitting in DF-HF/DF-KS
  • _COUL Coulomb fitting in DF-HF/DF-KS
  • _EXCH Exchange fitting in DF-HF/DF-KS
  • _CPHF Coulomb and exchange fitting in CPHF
  • _SCFGRD Coulomb and exchange fitting in DF-HF/DF-KS gradients

The default values are the same as for the general thresholds.

Further thresholds:

  • THR2HLF Threshold for second-half transformation in exchange fitting (default THRAO_SCF)
  • THRASM_SCF Threshold for local assembly of exchange matrix (default THRAO_SCF)
  • THRAO_FOCK Threshold for Coulomb fitting in DF-KS

(default MIN(THRAO_SCF*1.d-2,1.d-12))

Local fitting as described in H.-J. Werner, F. R. Manby, and P. J. Knowles, J. Chem. Phys. 118, 8149 (2003), Polly, H.-J. Werner, F. R. Manby, and Peter J. Knowles, Mol. Phys. 102, 2311 (2004), and M. Schütz, H.-J. Werner, R. Lindh and F. R. Manby, J. Chem. Phys. 121, 737 (2004) can be activated by setting LOCFIT=1. By default, local fitting is disabled, because under certain circumstances it can lead to unacceptable errors. For instance, local fitting must not be used in counter-poise calculations, since the lack of fitting functions at the dummy atoms can lead to wrong results.

Local fitting can be restricted to certain programs, using the following options:

  • LOCFIT If positive, use local fitting in all programs in which it is available (default 0).
  • LOCFIT_SCF If positive, use local fitting in SCF (default LOCFIT)
  • LOCFIT_MP2 If positive, use local fitting in DF-LMP2; 1: use orbital domains; 2: use pair domains (default LOCFIT)
  • LOCFIT_F12 If positive, use local fitting in DF-LMP2-F12 (default LOCFIT)
  • LOCFIT_CCSD If positive, use local fitting in DF-LCCSD (default LOCFIT)
  • LOCFIT_2EXT If positive, use local fitting in LCCSD 2ext transformation (default LOCFIT_CCSD)
  • LOCFIT_3EXT If positive, use local fitting in LCCSD 3ext transformation (default LOCFIT_CCSD)
  • LOCFIT_4EXT If positive, use local fitting in LCCSD 4ext transformation (default LOCFIT_CCSD)
  • LOCFIT_CPHF If positive, use local fitting in CPHF (default LOCFIT)
  • LOCFIT_SCFGRD If positive, use local fitting in gradient calculations (default LOCFIT)
  • LOCORB If positive, use localized orbitals in DF-HF (default 1)
  • LOCTRA If positive, use local screening in first half transformation (default LOCFIT).
  • DSCREEN If positive, enable density screening in LMP2 (default 0)
  • KSCREEN If positive, enable fit-basis Schwarz screening in LMP2 (default depends on LOCTRA).

The following options can be used to modify the domains used in local fitting. These parameters only have an effect if LOCFIT=1. The local fitting domains are determined in two steps: first primary orbital domains are determined. In the LMP2 and LCCSD programs, the primary orbital domains are the same as used for excitation domains and determined by the Boughton-Pulay procedure, as described in Sect. PAO-based local correlation treatments. Depending on the value of FITDOM_MP2 or FITDOM_CCSD for LMP2 and LCCSD, respectively, either the orbital domains are used directly or united pair domains are generated. In DF-HF the primary orbital domains include all basis functions at atoms which have Löwdin charges greater or equal to THRCHG_SCF. In the second step the primary fitting domains are extended using either distance criteria (RDOMAUX, in bohr) or bond connectivity criteria (IDOMAUX). IDOMAUX=1 means to include all functions at atoms wich are at most one bond distant from the primary domains. By default, distance criteria are used. However, if IDOMAUX.ge.0, the distance criteria are ignored and connectivity is used.

  • THRCHG_SCF Parameter to select the primary orbital domains in local exchange fitting (default 0.1). All atoms are included which have Löwdin charges greater than this value. The primary domains are extended according to RDOMAUX_SCF or IDOMAUX_SCF.
  • FITDOM_MP2 Parameter to select primary fitting domains in LMP2 transformation (default 3). 1: use orbital domains; 2: use united orbital domains of strong pairs; 3: use united orbital domains of strong and weak pairs (default 3). The primary domains are extended according to RDOMAUX_MP2 or IDOMAUX_MP2
  • FITDOM_CCSD Similar to FITDOM_MP2 but used for LCCSD 2-ext transformation.
  • RDOMAUX_SCF Distance criterion for fitting domain extension in SCF (default 5.0)
  • IDOMAUX_SCF Connectivity criterion for fitting domain extension in SCF (default 0)
  • RDOMAUX_CORE Distance criterion for core orbital fitting domain extension in SCF (default RDOMAUX_SCF).
  • IDOMAUX_CORE Connectivity criterion for core orbital fitting domain extension in SCF (default IDOMAUX_SCF).
  • RDOMSCF_START Distance criterion for fitting domain extension in the initial SCF iterations (default 3.0).
  • IDOMSCF_START Connectivity criterion for fitting domain extension in the initial SCF iterations (default 1).
  • RDOMSCF_FINAL Distance criterion for fitting domain extension in the final SCF iterations (default RDOMAUX_SCF).
  • IDOMSCF_FINAL Connectivity criterion for fitting domain extension in the final SCF iterations (default IDOMAUX_SCF).
  • RDOMAUX_MP2 Distance criterion for fitting domain extension in LMP2. The default value depends on FITDOM_MP2
  • IDOMAUX_MP2 Connectivity criterion for fitting domain extension in LMP2. The default value depends on FITDOM_MP2
  • RDOMAUX_CCSD Distance criterion for fitting domain extension in LCCSD. The default value depends on FITDOM_CCSD).
  • IDOMAUX_CCSD Connectivity criterion for fitting domain extension in LCCSD. The default value depends on FITDOM_CCSD.
  • RDOMAUX_CPHF Distance criterion for fitting domain extension in CPHF (default 3.0).
  • RDOMAUX_SCFGRD Distance criterion for fitting domain extension in gradients (default 5.0).
  • SCSGRD Switches the DF-LMP2 analytic gradient to Grimmes SCS scaled MP2 energy functional (default 0).

There is a rather large number of parameters. Many of these should normally not be changed, and therefore only a subset is described here. A full list can be obtained using

HELP,CFIT