Chemical Science
Edge Article
so pseudopotentials33 and a revised Perdew–Burke–Ernzerhof
The frequency calculations of adsorbed CO molecules were
exchange–correlation functional (RPBE)34,35 based on the conducted using the DMol3 code.38 These calculations involved
generalised gradient approximation. The plane wave basis set the RPBE functional, a double-numeric quality basis set with
was truncated at a kinetic energy of 370 eV. A Fermi smearing of polarization functions (DNP, comparable to Gaussian 6-
0.1 eV was utilised. The reciprocal space wasꢁs1ampled using 311G**)39 associated with a real-space cut-off of 4.2 A, DFT semi-
˚
a k-point mesh with a typical spacing of 0.04 A generated by core pseudopotential core treatment40 and Fermi smearing of
˚
the Monkhorst–Pack scheme.36 Convergence criteria comprised 0.1 eV. The SCF convergence was accelerated using the iterative
(a) a self-consistent eld (SCF) tolerance of 1.0 ꢂ 10ꢁ6 eV per scheme proposed by Kresse and Furthmuller. The partial
41
¨
atom, (b) an energy tolerance of 1.0 ꢂ 10ꢁ5 eV per atom, (c) Hessian matrix, including C and O atoms, was computed to
a maximum force tolerance of 0.05 eV Aꢁ1, and (d) a maximum evaluate the harmonic frequencies of the adsorbed CO. All
˚
displacement tolerance of 1.0 ꢂ 10ꢁ3 A for structural optimi- computed harmonic frequencies were scaled by an empirical
˚
zation and energy calculation. Atomic coordinates were fully factor of 1.0386, which corresponds to the ratio between the
relaxed, whereas lattice constants were xed. Surface energies of experimental42 and computed values for gas-phase CO
bimetallic plane were calculated using eqn (2):
(2143 cmꢁ1/2063.4 cmꢁ1).
1
g ¼ lim
½ES ꢁ NEBꢃ;
(2)
n/N
Acknowledgements
2A
where EB is the energy of bulk unit cell, A is the surface area, n
is the number of layers and N is the number of unit cells in the
slab. These surface energies typically converged within 6–8
atomic layers. When a cutting plane generates two unequiv-
This work was supported by JSPS KAKENHI Grant Number
26820350. We deeply thank the Center for Advanced Materials
Analysis Tokyo Institute of Technology for aid with TEM
observation.
ꢀ
alent facets as observed for the (100) and (111) planes of Pm3m
(CsCl-type) structures, the Rh-terminated (or Rh-rich) plane
was chosen as an active surface for hydrogenation. The
surface energies of such planes were estimated using
a procedure reported elsewhere.10,37 For the geometry opti-
mization of adsorbed CO, (2 ꢂ 2) structures were considered
for all Rh-based bimetallic surfaces, so that CO coverage on
Rh was #1/4. Slabs were modelled typically with 4-atomic-
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Chem. Sci.
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