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where the E(M
40
) and E(M) are the energies of optimized metal nanocluster
and of a single metal atom, respectively.
From the fully optimized geometries, we find that the shortest separa-
tion between a metal atom of the deposited metal cluster and the closest
carbon atom of the graphene layer for the graphene@M
40
complexes are
between 2.3 and 2.8 (see Table 1). Also as given in table 1, the rela-
tive stabilization energies are higher in magnitude for Pd, Ag, Pt clusters
embedded graphene complexes compared to the Au
40
cluster which clearly
indicates a relatively weak interaction between the Au nanoparticles and
the graphene in comparison to others. The relatively higher binding ener-
gies combining with smaller equilibrium distances of separation dictate that
all three (Pd, Ag, Pt) metal clusters do eventually adsorbed strongly on
the graphene surface, inducing local structural deformation. An analysis of
the Mulliken population suggests that there is an effective charge transfer
between the adsorbed metal cluster and graphene. For the Pd, Ag, and Pt
cluster deposition, the charge transfer occur from graphene to metal cluster
at their equilibrium distances of separation, while for Au nanoclusters the
direction of charge transfer is from metal cluster to graphene. It is also
clear from the table 1 that the extent of charge transfer for Pd, Ag, Pt
nanocluster is larger compared to that for the Au cluster with greater ex-
tent of charge transfer for Pd case, resulting in higher stabilization energy.
To understand this, we have computed the vertical as well as adiabatic
first ionization energy (I.E.) and electron anity (E.A.) of individual metal
clusters. Both the I. E. and E. A. values computed with the two differ-
ent strategies follow the similar trend and can be analyzed to understand
the extent of charge transfer. We find that the trend in extent of charge
transfer which determines the overall stabilization energy of the complexes
follow the same pattern in changes in either I. E. or E. A. of the metal clus-
ters belonging to a particular period in the periodic table. In contrast to
Pd, Ag, Pt clusters, the comparatively smaller magnitude of E. A. together
with relatively lower value of I. E. make the Au
40
cluster to act as weak
electron donor towards the graphene.
In order to understand the mechanism and the extent of charge trans-
fer, we have calculated the energy and difference in charge densities of
the composites by varying the distance between the ad metal nanoclus-
ters and the graphene. The interaction energy is found to change inversely
with the distance between metal cluster and graphene, clearly predicting
that such interactions are mainly due to Coulombic forces as already ob-
served for SWCNT interacting with Pt, Au nanoclusters
51
and for electron
