Dissociation and Recombination of D2 on
Cu(111): Ab Initio Molecular Dynamics
Calculations and Improved Analysis of
Desorption Experiments
Francesco Nattino1, 1, Alessandro Genova1, 2 , Marieke Guijt1, Alberto S. Muzas2,
Cristina Díaz2, Daniel J. Auerbach1, 3 and Geert-Jan Kroes1
1
Leiden Institute of Chemistry, Leiden University, Gorlaeus Laboratories, P.O. Box
9502, 2300 RA Leiden, The Netherlands.
2
Departamento de Química Módulo 13, Universitad Autónoma de Madrid, 28049
Madrid, Spain
3
1
Max Planck Institute for Biophysical Chemistry, Göttingen, Germany
Electronic mail: f.nattino@chem.leidenuniv.nl
Present address: Department of Chemistry, Rutgers University, Newark, NJ 07102,
USA
2
Supplemental text.
Table SI reports the geometries and the heights of the barriers present in our SRPDFT PES for high symmetry impact sites. Table SII reports fitting parameters and 2
values for reaction probabilities computed with the BOSS model. The fitted curves
are plotted in Figure S1. The observation of a ν parameter which is close to zero for
all the examined states shows that the non-symmetric (GMP) form of the LGS
expression better fits the BOSS data than the symmetric (TANH) limit of the LGS
form. Both the FPC expression and the LGS expressions perform better than the ERF
expression in fitting the data (lower 2). Table SIII reports fitting parameters and 2
values for AIMD initial-state-selected reaction probabilities (plotted in Figure S2).
For the (v=0, J=4) initial state, we show the ERF and LGS fits of the 5 lower collision
energy points and the fits that also include the highest collision energy point.
Considering all the investigated initial states, the LGS form produces better fits than
the ERF form for the AIMD data, as is the case for the BOSS results. In Figure S3
AIMD fits are constrained to have the same saturation values as the corresponding
BOSS fits. In most cases the AIMD curves are slightly broader than the BOSS ones
(except for v=0, J=4) and are slightly shifted to lower energies, as in the fits without
constraints. Table SIV reports fitting parameters and 2 values for the experimental
time-of-flight (TOF) spectra. Note that lower χ2 values are obtained with the LGS
form, in particular for the v=0 rotational states. Figure S4 shows W parameters from
ERF fits of all the available desorption TOF spectra. The W values do not change
significantly if the new expression of the TOF signal is employed. In Figure S5 we
plot the parameters obtained from LGS fits of all the available desorption TOF
spectra. Note that E0¢ first increases with J (up to J=4-5) and then decreases, while the
ν parameter is close to 0 (GMP form) for v=0 and it increases with v until ν =1
(TANH form) for v=2. The W, W1 and W2 parameters, as defined in Eqs. 6-8, have
been computed for the experimental LGS reaction probability curves and are shown
in Figure S6. While the LGS curves have similar width in the low energy portion
(similar W1 values across states), the broadening of the high energy portion differs
substantially across vibrational states. In Figure S7 the sticking probability measured
in adsorption experiments is compared to the curves obtained from the initial state
selected reaction probability curves from desorption experiments, on a linear scale.
Note that the sticking probability curve measured with seeded beams at the highest
nozzle temperature (2100 K) is much better described in the high energy range than
was achieved previously with the ERF fits.
Supplemental Material
Configuration
bth
ttb
fcc, φ=0°
t2f, φ=0°
r (Å)
1.032
1.397
1.588
1.270
Z (Å)
1.164
1.386
1.270
1.270
Eb (eV)
0.628
0.891
1.013
0.770
Table SI. Barrier heights and barrier geometries for some configurations in the SRPDFT PES1, 2. The configurations are bridge-to-hollow (bth), top-to-bridge (ttb), above
the fcc site (fcc), and above the site midway between a top and fcc site (t2f).
State
v=0, J=0
Function
ERF
LGS
FPC
v=0, J=2
ERF
LGS
FPC
v=0, J=4
ERF
LGS
FPC
v=0, J=6
ERF
LGS
FPC
v=0, J=11
ERF
LGS
FPC
v=1, J=2
ERF
LGS
FPC
v=1, J=6
ERF
LGS
FPC
v=2, J=2
ERF
LGS
FPC
A
0.549
0.662
1.000
0.503
0.598
0.699
0.534
0.642
1.000
0.520
0.604
0.896
0.594
0.718
0.691
0.672
0.712
0.777
0.711
0.752
0.808
0.754
0.782
0.869
E’0
0.808
0.792
0.723
0.776
0.756
0.635
0.762
0.741
0.653
0.750
0.728
0.639
0.714
0.691
0.481
0.562
0.517
0.518
0.537
0.495
0.476
0.381
0.328
0.261
W’
0.122
0.113
0.077
0.143
0.128
0.066
0.160
0.144
0.099
0.124
0.114
0.064
0.187
0.171
0.066
0.154
0.119
0.177
0.149
0.118
0.180
0.178
0.130
0.080
ν
3.69 10-7
4.85 10-7
1.64 10-7
7.96 10-7
3.10 10-7
1.15 10-7
1.13 10-7
7.24 10-7
-
E”0
0.914
0.832
0.911
0.875
0.746
0.395
0.406
0.248
W”
0.228
0.144
0.292
0.206
0.123
0.018
0.035
0.287
χ2
546.459
69.560
5.963
1093.929
226.596
7.208
1014.269
144.116
3.331
2858.227
585.047
7.756
1611.941
265.116
34.501
6179.267
2099.695
62.617
5510.366
977.690
70.940
6301.884
1626.766
78.902
Table SII. Fit parameters corresponding to the BOSS reaction probability curves
plotted in Figure S1. E’0 (E”0) and W’ (W”) parameters are in eV.
State
v=0, J=0
# Data Function
A
5
ERF
0.673
LGS
0.833
v=0, J=2
5
ERF
0.587
LGS
0.737
v=0, J=4
6
ERF
0.638
LGS
0.669
v=0, J=6
5
ERF
0.617
LGS
0.745
v=0, J=11
5
ERF
0.734
LGS
0.917
v=1, J=2
5
ERF
0.596
LGS
0.665
v=1, J=6
5
ERF
0.655
LGS
0.753
v=2, J=2
5
ERF
0.662
LGS
0.713
E’0
0.853
0.832
0.775
0.761
0.790
0.773
0.793
0.770
0.746
0.726
0.511
0.475
0.522
0.493
0.326
0.293
W’
0.209
0.193
0.192
0.180
0.192
0.110
0.204
0.174
0.265
0.235
0.159
0.130
0.175
0.140
0.177
0.124
ν
χ2
10.673
-7
2.04 10
4.055
6.275
-7
1.70 10
3.327
7.331
0.434
5.037
2.427
-7
3.79 10
0.886
1.405
-5
1.25 10
0.111
11.912
-7
5.67 10
2.435
7.356
0.002
2.707
2.202
0.116
0.088
Table SIII. Fit parameters corresponding to the AIMD reaction probability curves
plotted in Figure S2. E’0 and W’ parameters are in eV.
State
v=0, J=0
Dataset Function E’0
DS0609A
ERF
0.660
LGS
0.713
v=0, J=2 DS0609E
ERF
0.696
LGS
0.785
v=0, J=4 DS0608D
ERF
0.760
LGS
0.853
v=0, J=6 DS0606E
ERF
0.724
LGS
0.757
v=0, J=11 DS0607A
ERF
0.617
LGS
0.705
v=1, J=2 DS0620E
ERF
0.468
LGS
0.454
v=1, J=6 DS0620C
ERF
0.483
LGS
0.462
v=2, J=2 DS0624D
ERF
0.266
LGS
0.258
W’
ν
0.171
0.186
0.050
0.182
0.229 3.67 10-7
0.199
0.230
0.055
0.176
0.162
0.136
0.180
0.228 1.35 10-5
0.169
0.096
0.461
0.178
0.094
0.518
0.145
0.057
1.000
χ2
1.166 1010
5.471 109
2.647 109
5.759 108
1.130 109
4.744 108
8.276 108
5.626 108
4.297 1011
3.875 1011
1.750 1012
1.358 1012
2.317 1012
1.917 1012
1.724 1014
1.493 1014
Table SIV. Fit parameters corresponding to the curves plotted in Figure 6 obtained in
a specific experiment, as indicated by the name of the corresponding data set. E’0 and
W’ parameters are in eV.
0.9
0.6
Fit LGS
Fit ERF
Fit FPC
BOSS
0.3
v=0, J=0
v=0, J=2
v=0, J=4
v=0, J=6
v=0, J=11
v=1, J=2
v=1, J=6
v=2, J=2
0.0
Reaction Probability
0.6
0.3
0.0
0.6
0.3
0.0
0.6
0.3
0.0
0.0
0.3
0.6
0.9
1.2 0.0 0.3 0.6
Collision Energy / eV
0.9
1.2
1.5
Figure S1. BOSS reaction probabilities (blue symbols) are plotted as a function of the
collision energy for some representative initial states. ERF, LGS and FPC fits of the
BOSS data are plotted as green, black and violet solid lines, respectively.
0.9
0.6
Fit LGS
Fit ERF
AIMD
0.3
v=0, J=0
v=0, J=2
v=0, J=4
v=0, J=6
v=0, J=11
v=1, J=2
v=1, J=6
v=2, J=2
0.0
Reaction Probability
0.6
0.3
0.0
0.6
0.3
0.0
0.6
0.3
0.0
0.0
0.3
0.6
0.9
1.2 0.0 0.3 0.6
Collision Energy / eV
0.9
1.2
1.5
Figure S2. AIMD reaction probabilities (red symbols) are plotted as a function of the
collision energy for some representative states. ERF and LGS fits of the AIMD data
are plotted as green and black lines, respectively. For (v=0,J=4), also the ERF and
LGS fits of the 5 lowest collision energy points are plotted as dashed lines (see text,
Section III.B).
0.9
0.6
AIMD
BOSS
LGS Fit
LGS Fit
0.3
v=0, J=0
v=0, J=2
v=0, J=4
v=0, J=6
v=0, J=11
v=1, J=2
v=1, J=6
v=2, J=2
0.0
Reaction Probability
0.6
0.3
0.0
0.6
0.3
0.0
0.6
0.3
0.0
0.0
0.3
0.6
0.9
1.2 0.0 0.3 0.6
Collision Energy / eV
0.9
1.2
1.5
Figure S3. BOSS and AIMD reaction probabilities (blue x and red +, respectively) are
plotted as a function of the collision energy for some representative initial states; the
solid lines are LGS fits of the probabilities. The fits of the AIMD data have been
constrained to have the same saturation values as the BOSS fits.
0.28
v=0
v=1
v=2
JCP 1993 (v = 0)
JCP 1993 (v = 1)
JCP 1993 (v = 2)
0.26
0.24
0.22
W / eV
0.20
0.18
0.16
0.14
0.12
0.10
0.08
0
2
4
6
8 10 12 14
J
Figure S4. W parameters obtained from ERF fits of all the available desorption TOF
spectra are plotted as a function of the initial rotational state J. Green, violet and blue
symbols correspond to v=0, 1 and 2 initial vibrational states, respectively. Solid
curves represent average of the v=0,1, 2 data, while dashed lines are average of the
data from Ref.3. Line colors are as for the symbols.
Figure S5. Parameters obtained from LGS fits of all the available desorption TOF
spectra are plotted as a function of the initial rotational state J. Green squares, violet
circles and blue triangles correspond to v=0, 1 and 2 initial vibrational states,
respectively. Solid curves in the E’0 plot represent quadratic fits of the v=0,1, 2 data
(colors as for the symbols).
0.6
W
A
W1
B
Width parameters / eV
0.5
W2
C
v=0
v=1
v=2
0.4
0.3
0.2
0.1
0
0
2
4
6
8 10 12 14 0
J
2
4
6
8 10 12 14 0
J
2
4
6
8 10 12 14
J
Figure S6. W, W1 and W2 parameters computed for the experimental LGS reaction
probability curves are plotted as a function of the initial rotational state J. Green
squares, violet circles and blue triangles correspond to v=0, 1 and 2 initial vibrational
states, respectively.
0.4
2100 K
S0
0.3
0.2
0.1
Pure Beams
0.3
0.4
0.5
0.6
0.7
<En> / eV
0.8
Figure S7. The sticking probability measured in molecular beam experiments is
shown as a function of the average collision energy using a linear scale (only
probabilities larger than 1%). Seeded beam results corresponding to specific nozzle
temperatures are plotted as circles, pure beam results using crosses. The results of our
fits are plotted as solid lines. Dashed lines are from the previous fit (Ref.3).
References
1
C. Díaz, E. Pijper, R. A. Olsen, H. F. Busnengo, D. J. Auerbach, and G. J. Kroes,
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2
C. Díaz, R. A. Olsen, D. J. Auerbach, and G. J. Kroes, Phys. Chem. Chem. Phys. 12,
6499 (2010).
3
H. A. Michelsen, C. T. Rettner, D. J. Auerbach, and R. N. Zare, J. Chem. Phys. 98,
8294 (1993).