5 Density Functional Theory

5.8 Empirical Corrections for Basis Set Superposition Error

(May 16, 2021)

This section describes DFT-C, 1193 Witte J., Neaton J. B., Head-Gordon M.
J. Chem. Phys.
(2017), 146, pp. 234105.
an empirical correction for basis set superposition error (BSSE) in DFT calculations that is an adaptation of Grimme’s geometrical counterpoise (gCP) correction. 579 Kruse H., Grimme S.
J. Chem. Phys.
(2012), 136, pp. 154101.
Unlike the traditional Boys-Bernardi counterpoise correction (Section 8.9), 122 Boys S. F., Bernardi F.
Mol. Phys.
(1970), 19, pp. 553.
the cost of the DFT-C correction is essentially zero (on the scale of a DFT calculation), and the latter provides an estimate of both inter- and intramolecular BSSE. The form of this correction is

EDFT-C=σAatomscABAatomsgABDFT-C(RAB)hAB({A,B,}) (5.54)

where gABDFT-C is a damped, pairwise BSSE correction,

gABDFT-C(RAB)=d(RAB)fABDFT-C(RAB)+[1-d(RAB)]fABDFT-C(Rcov,AB). (5.55)

The quantity

fABDFT-C(RAB)=cABexp(-αABRAB2+βABRAB) (5.56)

is the undamped pairwise BSSE and

d(RAB)=11+k1,AB(RAB/R0,AB)-k2,AB (5.57)

is a damping function. The quantity hAB({A,B,}) is a many-body correction to the two-body BSSE correction, given by

hAB({A,B,})=[1+CA,BNCvirtNBvirtterfc(RAC,RAB)terfc(RBC,RAB)]-1 (5.58)


terfc(x,y)=1-12[erf(x+y)+erf(x-y)]. (5.59)

The parameters cA, cAB, αAB, and βAB are basis-set-dependent, and the overall scaling parameter σ is loosely method-dependent. All of these parameters are set internally based on the method and basis $rem specifications.

Note:  Currently, only the def2-SVPD basis set is supported for use with DFT-C.

The DFT-C correction is governed by the following $rem variable:

       Controls whether the DFT-C empirical BSSE correction should be added.
       FALSE (or 0) Do not apply the DFT-C correction TRUE (or 1) Apply the DFT-C correction

The DFT-C method can be applied to any local, GGA, or meta-GGA density functional, as in the following example.

Example 5.15  Geometry optimization of the methane dimer using B97M-V-C/def2-SVPD, i.e., the B97M-V functional with the DFT-C BSSE correction in the def2-SVPD basis set.

   0 1
   C   0.000000  -0.000140   1.859161
   H  -0.888551   0.513060   1.494685
   H   0.888551   0.513060   1.494685
   H   0.000000  -1.026339   1.494868
   H   0.000000   0.000089   2.948284
   C   0.000000   0.000140  -1.859161
   H   0.000000  -0.000089  -2.948284
   H  -0.888551  -0.513060  -1.494685
   H   0.888551  -0.513060  -1.494685
   H   0.000000   1.026339  -1.494868

   JOBTYPE            opt
   BASIS              def2-SVPD
   METHOD             b97m-v
   DFT_C              true

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