Q-Chem 5.1 User’s Manual

5.8 Empirical Corrections for Basis Set Superposition Error

This section describes DFT-C,[Witte et al.(2017b)Witte, Neaton, and Head-Gordon] an empirical correction for basis set superposition error (BSSE) in DFT calculations that is an adaptation of Grimme’s geometrical counterpoise (gCP) correction.[Kruse and Grimme(2012)] Unlike the traditional Boys-Bernardi counterpoise correction (Section 8.8),[Boys and Bernardi(1970)] 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

  \begin{equation} E_{\text {DFT-C}} = \sigma \sum ^{\text {atoms}}_ A c_ A \sum ^{\text {atoms}}_{B\neq A} g_{AB^\ast }^{\text {DFT-C}}(R_{AB}) \; h_{AB^\ast }(\{ A, B, \ldots \} ) \end{equation}   (5.54)

where $g_{AB^\ast }^{\text {DFT-C}}$ is a damped, pairwise BSSE correction,

  \begin{equation} g_{AB^\ast }^{\text {DFT-C}}(R_{AB}) = d(R_{AB}) \; f_{AB^\ast }^{\text {DFT-C}}(R_{AB}) + \bigl [1-d(R_{AB})\bigr ] f_{AB^\ast }^{\text {DFT-C}}(R_{\text {cov},AB}) \; . \end{equation}   (5.55)

The quantity

  \begin{equation} f_{AB^\ast }^{\text {DFT-C}}(R_{AB}) = c_{AB} \exp \bigl (-\alpha _{AB} R_{AB}^2 + \beta _{AB} R_{AB}\bigr ) \end{equation}   (5.56)

is the undamped pairwise BSSE and

  \begin{equation} d(R_{AB}) = \frac{1}{1+k_{1,AB}(R_{AB}/R_{0,AB})^{-k_{2,AB}}} \end{equation}   (5.57)

is a damping function. The quantity $h_{AB^\ast }(\{ A,B,...\} )$ is a many-body correction to the two-body BSSE correction, given by

  \begin{equation} \label{3b} h_{AB^\ast }(\{ A,B,...\} ) = \left[ 1 + \sum _{C\neq A,B} \frac{N_{C}^{\text {virt}}}{N_{B}^{\text {virt}}} \operatorname {terfc}\left(R_{AC},R_{AB}\right) \operatorname {terfc}\left(R_{BC},R_{AB}\right) \right]^{-1} \end{equation}   (5.58)

where

  \begin{equation} \label{terfc} \operatorname {terfc}( x,y) = 1 - \frac{1}{2}\big [\ensuremath{\mathrm{erf}}(x+y) + \ensuremath{\mathrm{erf}}(x-y)\bigr ] \; . \end{equation}   (5.59)

The parameters $c^{}_ A$, $c^{}_{AB}$, $\alpha ^{}_{AB}$, and $\beta ^{}_{AB}$ are basis-set-dependent, and the overall scaling parameter $\sigma $ 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 $rem variable DFT_C; to invoke the DFT-C method, simply add this to your input: 

DFT_C    TRUE

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

Example 5.54  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.

$molecule
   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
$end

$rem
   JOBTYPE            opt
   BASIS              def2-SVPD
   METHOD             b97m-v
   DFT_C              true
$end

DFT_C

Controls whether the DFT-C empirical BSSE correction should be added.


TYPE:

LOGICAL


DEFAULT:

FALSE


OPTIONS:

FALSE

(or 0) Do not apply the DFT-C correction

TRUE

(or 1) Apply the DFT-C correction


RECOMMENDATION:

NONE