Alexandre Tkatchenko and Matthias Scheffler
An accurate description of van der Waals (vdW) forces remains a grand challenge for current electronic structure theories. At present, only high-level quantum-chemical methods [e.g. coupled cluster with single, double and perturbative triple excita tions, CCSD(T)] can attain a consistently accurate description of vdW interactions. Unfortunately, CCSD(T) is limited to rather small systems due to its high com putational cost and steep O(N7) scaling with system size. In contrast, all popular local-density or gradient corrected exchange-correlation (xc) functionals of density-functional theory (DFT) and the Hartree-Fock (HF) approximation fail to describe the vdW attraction. Even on average more accurate Møller-Plesset second-order perturbation theory frequently yields unsatisfactory results.
One of the efficient approaches to describe vdW interactions is the summation of appropriately damped interatomic C6R−6terms, inspired by the asymptotic disper sion energy expansion between two spherical atoms. The main shortcoming of this approach is that it contains many empirical parameters (at least two per every atom type in a molecule) and does not take into account the changes in the C6 coefficients due to different chemical environments of an atom. In order to improve the accuracy and transferability of the C6R−6 approach, we have developed a method to obtain all the parameters (C6 coefficients and vdW radii) self-consistently from the molec ular ground-state electron density . We achieve a mean absolute error of 5.5% for the C6 coefficients when compared to reference experimental data – a signi?cant improvement over existing methods based on ground-state and even excited state wavefunctions. Furthermore, our dynamic de?nition of the vdW radius of an atom in a molecule turns out to be crucial to describe vdW and hydrogen-bonded systems on equal footing.
We present applications of our approach for correcting both DFT  and MP2  calculations for a range of systems bounded by hydrogen bonding, electrostatics and dispersion. Both DFT+vdW and MP2+ΔvdW perform remarkably well when com pared to CCSD(T) binding energies, with the latter showing a mean absolute error of just 3 meV from the reference data. While PBE+vdW provides a good geome try, for the energetics and electronic structure such efficient geometry optimization should (in some cases) be followed by a PBE-hydrid+vdW calculation .
 A. Tkatchenko and M. Scheffler, PRL 102, 073005 (2009).
 A. Tkatchenko, R. A. DiStasio Jr., M. Head-Gordon, M. Scheffler, JCP 131, 094106 (2009).
 N. Marom, A. Tkatchenko, M. Scheffler, L. Kronik, submitted.
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