2.2 Models
For the CO/Cu(100) system, to mimic the 0.1 monolayer coverage situation of the
experiment from Ref. [3], a periodic grid of 3 Wigner-Seitz (WS) cells was used.
This grid would correspond in a 2D situation to having 1 molecule in a (3 × 3)
surface cell, i.e. a coverage of 1/9 ≈ 0.1. In each cell, it was sufficient to retain
24 eigenvalues for the temperature of 190 K, as this choice yields converged
calculations.
To evaluate Eq. (4), we test the following 1D models for the diffusion motion
along the 100
h
i direction, i.e. the x coordinate of the carbon atom position parallel
to the substrate, which links two top sites via a bridge site.
Model 1 The potential V(x) is given by the formula
VðxÞ ¼ V 2 sin px=L
ð
Þ
2
ð5Þ
where V 2 ¼ 100 hc cm
À1
% 12:4 meV is the diffusion barrier of this
model and L = 255.6 pm was defined above as the bulk Cu-Cu nearest
neighbor distance.
Model 2 The potential V(x) is given by the formula
VðxÞ ¼
X
k¼4;6;8
V k sin px=L
ð
Þ
k
ð6Þ
where V 4 % 656, V 6 % À1; 203, and V 8 % 1; 003 hc cm
À1 . This form fits
excellently the relaxed potential over the bridge site from [6, Fig. 8b
therein]. The barrier height from [6] is 465 hc cm
À1 , whereas Eq. (6)
yields 456 hc cm
À1
% 56:5 meV:
Model 3 The potential V(x) is given by the same formula as in Eq. (6), but with
parameter values V 4 % 381; V 6 % À698; and V 8 % 582 hc cm
À1 . This
form describes the first “adiabatic channel” for the diffusion, in which
the variation of the zero point energy was included approximately from
the variation of the harmonic zero point energies between the top and
bridge sites as calculated in [6]. The barrier for this potential is
270 hc cm
À1
% 33:5 meV
Figure 1 shows plots of the model potentials.
For the H/Pd(111) system, the analytical potential energy surface derived originally in [5] for the H 2 /Pd(111) system was first modified such as to describe a
single hydrogen atom adsorbed on the palladium substrate. To achieve this, all
hydrogen-hydrogen two-body terms, as well as the hydrogen-palladium-hydrogen
three-body terms in the PES defined in [5] were zeroed, and the function definition
180
T. Firmino et al.
For the CO/Cu(100) system, to mimic the 0.1 monolayer coverage situation of the
experiment from Ref. [3], a periodic grid of 3 Wigner-Seitz (WS) cells was used.
This grid would correspond in a 2D situation to having 1 molecule in a (3 × 3)
surface cell, i.e. a coverage of 1/9 ≈ 0.1. In each cell, it was sufficient to retain
24 eigenvalues for the temperature of 190 K, as this choice yields converged
calculations.
To evaluate Eq. (4), we test the following 1D models for the diffusion motion
along the 100
h
i direction, i.e. the x coordinate of the carbon atom position parallel
to the substrate, which links two top sites via a bridge site.
Model 1 The potential V(x) is given by the formula
VðxÞ ¼ V 2 sin px=L
ð
Þ
2
ð5Þ
where V 2 ¼ 100 hc cm
À1
% 12:4 meV is the diffusion barrier of this
model and L = 255.6 pm was defined above as the bulk Cu-Cu nearest
neighbor distance.
Model 2 The potential V(x) is given by the formula
VðxÞ ¼
X
k¼4;6;8
V k sin px=L
ð
Þ
k
ð6Þ
where V 4 % 656, V 6 % À1; 203, and V 8 % 1; 003 hc cm
À1 . This form fits
excellently the relaxed potential over the bridge site from [6, Fig. 8b
therein]. The barrier height from [6] is 465 hc cm
À1 , whereas Eq. (6)
yields 456 hc cm
À1
% 56:5 meV:
Model 3 The potential V(x) is given by the same formula as in Eq. (6), but with
parameter values V 4 % 381; V 6 % À698; and V 8 % 582 hc cm
À1 . This
form describes the first “adiabatic channel” for the diffusion, in which
the variation of the zero point energy was included approximately from
the variation of the harmonic zero point energies between the top and
bridge sites as calculated in [6]. The barrier for this potential is
270 hc cm
À1
% 33:5 meV
Figure 1 shows plots of the model potentials.
For the H/Pd(111) system, the analytical potential energy surface derived originally in [5] for the H 2 /Pd(111) system was first modified such as to describe a
single hydrogen atom adsorbed on the palladium substrate. To achieve this, all
hydrogen-hydrogen two-body terms, as well as the hydrogen-palladium-hydrogen
three-body terms in the PES defined in [5] were zeroed, and the function definition
180
T. Firmino et al.