# Keesom and Debye forces in DFT

Do van der Waals corrected DFT functionals include Keesom and Deby corrections too or just London dispersion? Because when I look at these methods in detail, I see that there is just an attempt to correct London dispersion correction and no mention to the remaining two (Deby and Keesom) van der Waals correction. What is the reason? If there is just London dispersion correction, then why are they called van der Waals corrections?

Another question that I could not find an answer to is: Are Keesom and Deby forces already included in semilocal and local density functionals compared to long-range London dispersion interactions?

• +1 Welcome to Matter Modelling SE! I am not an expert on DFT, but my guess is that Keesom and Debye forces are accounted for in local DFT because they are kind of static polarization/electrostatic effects. Dispersion is not included because it is modelled by charge transfer, which cannot be done by local/semilocal functionals. Jun 21 at 13:42
• @ShoubhikRMaiti Dispersion is a long-range correlation effect, arising from the double excitation \Psi_{ij}^{ab}, where the orbitals i and a are localized on one molecule and j and b are localized on the other molecule. There is a dipole-dipole Coulomb interaction between the occupied-virtual pairs (ia) and (jb), which explains the long-rangedness of the dispersion interaction. But the excitations i->a and j->b are both local, so there is no charge transfer, thus dispersion is not modeled by charge transfer. Jun 22 at 10:01
• @ShoubhikRMaiti Charge transfer is described by the single excitations \Psi_i^b, where i and b are far apart. They cannot be reliably described by TDDFT when local and semilocal functionals are used (although they can be described by SCF), which is due to the DFT exchange being short-ranged. This is also a famous pitfall of many functionals, but a different one than the pitfall of describing dispersion, the latter of which being due to the DFT correlation being short-ranged. Jun 22 at 10:05
• @wzkchem5 I see, thanks. I didn't know about the single vs double excitation difference. Jun 22 at 11:49

For the London dispersion term, things are wholly different. The London interaction is a long-range correlation interaction that decays like $$1/R^6$$. By contrast, all local and semilocal functionals, as their name suggests, have a correlation contribution that decays at least exponentially. It is because of this reason that they cannot describe the London dispersion term adequately. Within the semilocal framework, one can parameterize the functional such that it describes the London interaction when the molecules are not very far apart (e.g. the M06 and M06-2X functionals), but as the molecules become progressively far from each other, any parameterization must eventually fail and underestimate the London interaction, because the exponential decay is bound to kick in. Thus, the simplest physically correct way to restore the London interaction is to introduce diatomic attraction potentials with built-in $$1/R^6$$ behavior, which is exactly the approach used by DFT-D. More robust but costly alternatives (such as the VV10 correction) also exist.