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, Science 326, 832 (2009). 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).