(395am) Why DFT Fails in Describing Adsorption of Open-Shell Systems? A Combined Multiconfigurational and Model Hamiltonian Study of Cobalt On Graphene

Why
DFT fails in describing adsorption of open-shell systems? A combined
multiconfigurational and model Hamiltonian study of cobalt adsorption
on graphene

In
contrast to molecular closed-shell adsorbates or light monovalent
impurities, theoretical investigation of adsorption of transition
metal (TM) compounds is more challenging due to the presence of
strong electron correlations. The results of the commonly used
density functional therory (DFT) are usually controversial and
strongly depend on the parametrization of the exchange-correlation
functional. Motivated by the deficiency of the DFT in the description
of TM adsorption on semimetallic surfaces, we present a scheme that
can be used for their systematic investigation. As a test case we
investigate the adsorption of Co adatom on graphene.

As
a first step in this study, we
apply the multiconfigurational complete active space self-consistent
field formalism (CASSCF) in order
to take into account the effects of electron correlations in a
systematic way. By
using this method it is possible to obtain accurate potential energy
(PE) curves for different electronic states of a TM atom as well as
binding energies. In Fig.1 three most important PE curves for the
Co/graphene system are shown. The total adsorption energy curve of
the TM atom is not typical for the adsorption of closed-shell
adsorbates. Upon approaching the surface, the ground-state electronic
structure undergoes several transitions, giving rise to two stable
states: 3d⁷4s²
(high-spin) and 3d⁹4s⁰
(low-spin). In both cases the adsorption is weak (E_ads
<
0.35 eV) in contrast to the strong binding, predicted by DFT studies
(1-2 eV) [1].

In
order to more deeply understand the adsorption of Co on graphene, we
map the CASSCF results onto a mean-field model. To this end, we
consider a simple Hamiltonian:

where
the first term describes the one-electron contribution, while the
rest part corresponds to electron-electron interactions. The
parameters U_i,
U'_ij,
and J_ij
determine intraorbital and interorbital Coulomb interactions as well
as interorbital exchange interaction (Hund's rule coupling),
respectively. The
energies obtained at the CASSCF level for different electronic
configurations allow us to extract information on the magnitude of
these parameters.

In
Fig.2 we show the calculated electron-electron interaction parameters
as functions of the Co--graphene distance. The exchange coupling
parameters J_sd
and J_dd
are almost constant and do not change over the entire range of
distances. In contrast, the Coulomb repulsion U_dd
significantly decreases as the atom comes closer to the surface. From
the correspondence between the U_dd
parameter and the particular electronic configurations of Co, it can
be concluded that the interconfigurational transitions in the
adsorption of Co on graphene are attributed to the reduction of the
Coulomb repulsion in the Co 3d
shell.

In
the regime of small U
our results, with respect to the Co state (3d⁹s⁰),
are similar to that obtained by
DFT using the standard LDA (GGA) functional [1,2]. On the other hand,
the results of intermediate U
(3d⁸s¹)
are comparable with the GGA+U
[3] or hybrid functional calculations [4]. Being significantly
dependent of U,
the DFT results are applicable only to a certain range of adsorption
distances, whereas the total adsorption energy curve cannot be
described without external parameters. Inability to describe the
total potential energy curves for TM atoms on graphene within the DFT
scheme leads to difficulties in determination of binding energies.
Another point that prevents DFT from giving accurate binding energies
is the lack of non-local dispersion interactions in standard
exchange-correlation functionals. With the present approach these
problems can be widely overcome.

References
[1]
C. Cao et
al.,
Phys. Rev. B 81
(2010) 205424.
[2]
K.T. Chan et
al.,
Phys. Rev. B 83
(2011) 035405.
[3]
T.O. Wehling et
al.,
Phys. Rev. B 81
(2010) 115427.
[4]
D. Jacob et
al.,
Phys. Rev. B 82
(2010) 085423.

Figures

Fig.
1. Potential energy curves obtained for different electronic
configurations of Co on graphene.


Fig.
2. Electron-electron interaction parameters for Co on graphene as a
function of distance.