Adsorption of cobalt on graphene: Electron correlation effects from a quantum chemical perspective

In this work, we investigate the adsorption of a single cobalt atom (Co) on graphene by means of the complete active space self-consistent field approach, additionally corrected by the second-order perturbation theory. The local structure of graphene is modeled by a planar hydrocarbon cluster (C${}_{24}$H${}_{12}$). Systematic treatment of the electron correlations and the possibility to study excited states allow us to reproduce the potential energy curves for different electronic configurations of Co. We find that upon approaching the surface, the ground-state configuration of Co undergoes several transitions, giving rise to two stable states. The first corresponds to the physisorption of the adatom in the high-spin $3d^{7}4s^2$ ($S=3/2$) configuration, while the second results from the chemical bonding formed by strong orbital hybridization, leading to the low-spin $3d^9$ ($S=1/2$) state. Due to the instability of the $3d^9$ configuration, the adsorption energy of Co is small in both cases and does not exceed 0.35 eV. We analyze the obtained results in terms of a simple model Hamiltonian that involves Coulomb repulsion ($U$) and exchange coupling ($J$) parameters for the 3$d$ shell of Co, which we estimate from first-principles calculations. We show that while the exchange interaction remains constant upon adsorption ($\simeq 1.1$ eV), the Coulomb repulsion significantly reduces for decreasing distances (from 5.3 to $2.6\pm 0.2$ eV). The screening of $U$ favors higher occupations of the 3$d$ shell and thus is largely responsible for the interconfigurational transitions of Co. Finally, we discuss the limitations of the approaches that are based on density functional theory with respect to transition metal atoms on graphene, and we conclude that a proper account of the electron correlations is crucial for the description of adsorption in such systems.

Figure 1

Schematic representation of cobalt supported on a coronene molecule used in this work as an approximant to the local structure of graphene.

Figure 2

The set of orbitals included in the active space within the CASSCF approach (in the form of natural orbitals). The symmetry of the orbitals is shown in parentheses.

Figure 3

Potential energy curves for different electronic configurations of Co on graphene. Zero energy corresponds to the ground-state energy of the noninteracting system.

Figure 4

Isosurfaces of the natural orbitals associated with the hybridized $d_{E_2}$ (adatom) and ${\pi }_{ab}^{*}$ (surface) orbitals. The numbers correspond to the natural orbital occupation numbers.

Figure 5

(a) Potential energy curves for different orbital occupations of Co in the 3$d^9$ configuration; (b) energy differences between nonequivalent 3$d$-orbital levels of Co (the effective crystal-field splitting parameters) calculated as functions of the adatom-surface separation (see text for details). The splitting of the energy levels is shown schematically inside the lower panel.

Figure 6

Electron-electron interaction parameters for Co on graphene as a function of distance: exchange couplings ($J_{s\text{−}d}$ and $J_{d\text{−}d}$) and intraorbital Coulomb repulsion ($U_{d\text{−}d}$). The latter is shown for different splitting parameters ${\Delta }_{ij}$ (see text for details). ${\delta }_{s\text{−}\pi }^{\text{HF}}$ quantifies the Pauli repulsion between the 4$s$ (Co) and ${\pi }_b$ (surface) orbitals.[68] The dashed lines mark the most favorable electronic configuration of Co for a given range of distances (in accordance with potential energy curves given by Fig. 3).