35.11 DF-LMP2-F12 calculations with local approximations

Local variants of the DF-MP2-F12 and CCSD(T)-F12 methods are invoked by the
commands `DF-LMP2-F12`, `DF-LCCSD-F12`, `DF-LCCSD(T)-F12` with ansatz 3*A(LOC) [for DF-LCCSD-F12 fixed amplitudes are used, i.e.,
the default is 3*A(LOC,FIX)]. These calculations are performed
with a different program than non-local calculations.
The (LOC) option implies that the LMP2 calculation with domain approximations is performed, and by default a local projector
as first described in
H.-J. Werner, J. Chem. Phys. **129**, 101103 (2008) is used [see also
T. B. Adler, F. R. Manby, and H.-J. Werner, J. Chem. Phys. **130**, 054106 (2009);
T. B. Adler and H.-J. Werner, J. Chem. Phys. **130**, 241101 (2009);
T. B. Adler and H.-H. Werner, J. Chem. Phys. **135**, 144117 (2011)]

This yields very similar restults as the corresponding canonical methods at much lower cost
^{3}and the method can be applied to quite large molecules.

Special options for these local variants are (local RI works only with ansatz 3*A):

`PAIRS`- Specifies which pairs to be treated by R12 or F12

(`STRONG|CLOSE|WEAK|ALL`; pairs up to the given level are included). The default is`ALL`. Note that even with`ALL`very distant pairs are neglected if these are neglected in the LMP2 as well. `USEVRT`- If zero, the form of the projector is used, and local RI approximations apply to and . If set to 1, the form of the projector is used; any local RI approximation then applies only to the RI contribution .
`USEPAO`- If
`USEPAO=1`use pair-specific local projectors instead of . This is the default if either the ansatz contains '(LOC)' or if domain approximations are made in the LMP2 (i.e.,`DOMSEL<1`is explicitly specified). Otherwise the default is`USEPAO=0`.`USEPAO=1`automatically implies`USEVRT=1`, i.e. local RI approximations only affect the RI contributions . Furthermore, if`USEPAO=1`is specified and`DOMSEL`is not given, default domains are assumed in the LMP2. If`USEPAO=0`, full domains (`DOMSEL=1`) will be used. `FULLAO`- if
`USEVRT=0`and`FULLAO=1`, local RI approximations only apply to the RI contributions . This should give the same results as`USEVRT=1`(only applies if`USEPAO=0`). `DEBUG`- Parameter for debug print
`LOCFIT_F12`- If set to one, use local fitting. Default is no local fitting (
`LOCFIT_F12=0`) `LOCFIT_R12`- Alias for
`LOCFIT_F12`. Local fitting is not recommended in R12 calculations. `FITDOM`- Determine how the base fitting domains are determined (only applies if
`LOCFIT_F12=1`):

0: Fitdomains based on united operator domains;

1: Fitdomains based in orbital domains (default);

2: Fitdomains based on united pair domains using strong pairs;

3: Fitdomains based on united pair domains using strong, close and weak pairs. Note: This is the only option implemented in the DF-LMP2 program. Therefore, the DF-LMP2 and DF-LMP2-F12 programs might give slightly different results if default values are used. `RDOMAUX`- Distance criterion for density fitting domain extensions in case of local fitting. The default depends on
`FITDOM`. `IDOMAUX`- Connectivity criterion for density fitting domain extensions in case of local fitting.
`RAODOM`- Distance criterion for RI domain extensions. Zero means full RI basis (default).
If
`USEPAO=1`or`USEVRT=1`or`FULLAO=1`a value of 5 bohr is recommended. In other cases the local RI domains must be very large (`RAODOM>12`) and the use of local RI approximations is not recommended. `IAODOM`- Connectivity criterion for RI domain extensions. Zero means full RI basis (default).
Values greater or equal to 2 should lead to sufficiently accurate results, provided the local projector (
`USEPAO=1`) is used. `THRAO`- Screening threshold for coulomb integrals in the AO or RI basis.
`THRAOF12`- Screening threshold for F12 integrals.
`THRMO`- Screening threshold for half transformed integrals.
`THRPROD`- Product screening threshold in the first half transformation.
`NOMP2`- If set to 1, only the F12 calculation is performed, and the LMP2 is skipped. This is sometimes useful if full domains are used, since the iterative LMP2 then causes a big overhead and needs a lot of memory. It is then more efficient to do the a DF-MP2 calculation separately and compute the total energy as the sum of the DF-MP2 energy and the F12 energy
`PROJF`- Values greater than 0 invoke the local projector.
`PROJF=1`project vv parts only (this is formally the most accurate case but only possible with the canonical program [`ANSATZ=3*A(FIX,NOX)`],`PROJF=2`project vv and vo parts (default). This is unavoidable if the local program is used [`ANSATZ=3*A(LOC)`]. `MODOMC`- If , core contributions are neglected in the projector. This is a necessary approximation in order to
compute the LCCSD-F12 coupling terms efficiently (implementation not yet finished). Setting
`MODOMC=0`avoids the approximation. Note that the results in J. Chem. Phys.**135**, 144117 (2011) have been obtained using`MODOMC=0`.

Further options for density fitting are described in section 15, and further options to choose the ansatz in section 35.7.

Typical inputs for calculations with local approximations are:

!parameters for local density fitting: DFIT,LOCFIT_F12=1,FITDOM_MP2=1,IDOMAUX_MP2=3,DSCREEN=1 !LMP2-F12(loc) with local RI: {DF-LMP2-F12,ANSATZ=3*A(LOC),DOMSEL=0.985,RAODOM=5,PAIRS=WEAK}

This would perform a local MP2 with a Boughton-Pulay domain completeness criterion of 0.985.
In the F12 part, distant pairs are not included (`PAIRS=WEAK`) and the local projector is used (`USEPAO=1`, default).
Local density fitting and local RI approximations are used.

A corresponding non-local calculation (still using localized orbitals and the diagonal ansatz) would be

{DF-LMP2-F12,ANSATZ=3*A(LOC),DOMSEL=1.0,USEVRT=1,NOMP2=1} ecorr_F12=ef12 {DF-MP2} ecorr_MP2=energy-energr !mp2 correlation energy ecorr_MP2_F12=ecorr_MP2+ecorr_F12 !total correlation energy

Note: The use of local DF and RI domains is still experimental and should be use with care!

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