Popular Kohn-Sham density functionals strongly overestimate many-body interactions in van der Waals systems

We find spuriously large repulsive many-body contributions to binding energies of rare gas systems for the first three rungs of “Jacob’s Ladder” within Kohn-Sham density functional theory. While the description of van der Waals dimers is consistently improved by the pairwise London $C_6/R^6$ correction, inclusion of a corresponding three-body Axilrod-Teller $C_9/R^9$ term only increases the repulsive error. Our conclusions based on extensive solid state and molecular electronic structure calculations are particularly relevant for condensed phase van der Waals systems.

Figure 1

(Color online) Left: two-body energy as function of interatomic distance for ${\text{Ar}}_2$ with various functionals and CCSD(T) (Ref. 55). Dashed lines correspond to the $C_6$ corrected functionals. Right: three-body energies as a function of interatomic distance for the equilateral triangular ${\text{Ar}}_3$. CCSD(T), MP2, and HF have been taken from Ref. 56.

Figure 2

(Color online) Electron density difference isosurface plots for ${\text{Ar}}_3$ at $3\text{Å}$ equilateral distance—roughly the distance at which the three-body energy of ${\text{Ar}}_3$ is maximal for LDA (see Fig. 1). Blue/dark gray represents depletion, red/gray represents creation of density. (a) Trimer density difference between CCSD, using the $Z$-vector method (Ref. 49) and LDA, $n_{\text{CCSD}}-n_{\text{LDA}}$, isovalue (1.0E-4 a.u.). (b) three-body LDA electron density, $n_{\left(3\right)}\left(\mathbf{r}\right)=n_{\text{trim}}\left(\mathbf{r}\right)-3n_{\left(2\right)}\left(\mathbf{r}\right)-3n_{\text{mon}}\left(\mathbf{r}\right)$. $n_{\left(2\right)}\left(\mathbf{r}\right)$ being the two-body electron density, $n_{\text{dim}}\left(\mathbf{r}\right)-2n_{\text{mon}}\left(\mathbf{r}\right)$. Isovalue (1.0E-5 a.u.).

Figure 3

(Color online) Left: Cohesive energies as a function of interatomic distance in the fcc crystal of Ar. The zero-point energy taken from Ref. 37 was removed from the experimental value (Ref. 61). DFT (solid) and $C_6+\text{DFT}$ (dashed) curves are displayed, together with the two-body-crystal curve (dotted) corresponding to CCSD(t) from Ref. 55. Right: Many-body curves corresponding to the difference between the cohesive energy (shown left) and the DFT two-body-crystal curves (not shown).

Figure 4

(Color online) Left: Interaction energies as a function of interatomic distance in the Ne and Kr dimer. Right: three-body energy curves as a function of the interatomic distance in the equilateral Ne and Kr trimer.