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33.3 DFT-SAPT

It is of crucial importance to account for the intramolecular correlation effects of the individual SAPT terms since Hartree-Fock theory often yields poor first- and second-order electrostatic properties. While this can be done using many-body perturbation theory [1] (in a double perturbation theory ansatz) a more efficient way is to use static and time-dependent DFT theory. This variant of SAPT, termed as DFT-SAPT [2-6], has in contrast to Hartree-Fock-SAPT the appealing feature that the polarisation terms ( $E_\mathrm{pol}^{(1)}$, $E_\mathrm{ind}^{(2)}$, $E_\mathrm{disp}^{(2)}$) are potentially exact, i.e. they come out exactly if the exact exchange-correlation (xc) potential and the exact (frequency-dependent) xc response kernel of the monomers were known. On the other hand, this does not hold for the exchange terms since Kohn-Sham theory can at best give a good approximation to the exact density matrix of a many-body system. It has been shown [6] that this is indeed the the case and therefore DFT-SAPT has the potential to produce highly accurate interaction energies comparable to high-level supermolecular many-body perturbation or coupled cluster theory. However, in order to achieve this accuracy, it is of crucial importance to correct the wrong asymptotic behaviour of the xc potential in current DFT functionals [3-5]. This can be done by using e.g.:

{ks,lda; asymp,<shift>}

which activates the gradient-regulated asymptotic correction approach of Grüning et al. (J. Chem. Phys. 114, 652 (2001)) for the respective monomer calculation. The user has to supply a shift parameter ( $\Delta_\mathrm{xc}$) for the bulk potential which should approximate the difference between the HOMO energy ( $\varepsilon_\mathrm{HOMO}$) obtained from the respective standard Kohn-Sham calculation and the (negative) ionisation potential of the monomer ($\mathrm{IP}$):

$$\Delta_\mathrm{xc}=\varepsilon_\mathrm{HOMO}-(-\mathrm{IP})$$ (61)

This method accounts for the derivative discontinuity of the exact xc-potential and that is missing in approximate ones. Note that this needs to be done only once for each system. (See also section 33.7.2 for an explicit example).

Concerning the more technical parameters in the DFT monomer calculations it is recommended to use lower convergence thresholds and larger intergration grids compared to standard Kohn-Sham calculations.

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