Exploring the random phase approximation: Application to CO adsorbed on Cu(111)

The adsorption of CO on the Cu(111) surface is investigated in the random phase approximation (RPA) as formulated within the adiabatic connection fluctuation-dissipation theorem. The RPA adsorption energy is obtained by adding a “local exchange-correlation correction” that is extrapolated from cluster calculations of increasing size, to the Perdew-Burke-Ernzerhof (PBE) value for the extended system. In comparison to density-functional theory calculations with the generalized gradient functionals PBE and AM05 and the hybrid functionals PBE0 and HSE03, we find a hierarchy of improved performance from AM05/PBE to PBE0/HSE03, and from PBE0/HSE03 to RPA, both in terms of the absolute adsorption energy as well as the adsorption-energy difference between the atop and the hollow fcc sites. In particular, the very weak atop site preference at the PBE0/HSE03 level is further stabilized by about 0.2 eV in the RPA. The mechanism behind this improvement is analyzed in terms of the $GW$ density of states that gives a spectral representation en par with the RPA formalism for the total energy.

Figure 1

(Color online) The adsorption-energy differences of four different functionals: AM05, PBE0, HSE03, and RPA@PBE0 with respect to PBE for the atop and the hollow fcc sites. The PBE0/HSE03 values in the periodic limit are from Ref. 27.

Figure 2

(Color online) The site-preference energy corrections given by AM05, PBE0, HSE, and RPA@PBE0, with respect to PBE.

Figure 3

(Color online) Orbital-energy levels of a free CO molecule and density of states from LDA (black dashed lines), PBE (blue dashed lines) and PBE0 (red dashed lines): orbital-energy levels [panel (a)]—experimental values are marked by blue circles—DOS projected on the CO orbitals of the $\text{CO}/{\text{Cu}}_{16}$ cluster with CO adsorbed on the top site [panel (b)] and fcc hollow site [panel (c)] and DOS projected on the Cu orbitals on the top site [panel (d)] and hollow site [panel (e)]. The gray shaded region corresponds to the $G_0{W}_0@\text{PBE}0$ results shown in red in Fig. 4.

Figure 4

(Color online) same as Fig. 3 but with $G_0{W}_0@\text{LDA}$ (black solid line), $G_0{W}_0@\text{PBE}$ (blue solid line), and $G_0{W}_0@\text{PBE}0$ (red solid region).