3. Results 39
3.2. Fit
3.2.2. Comparison of dierent ts
As already mentioned in section 3.2, obtaining a parametrization that has both a low rms error value and ts the constraints is far from trivial. To obtain parametrizations that t the con-straints better than the EMT-JAWK presented here, I tried several strategies. I tested how the t depended on the input data set belonging to the 3D-grid; rst I checked if the number of symmetry sites included redundant sites which did not appear to be the case as the t does not improve with exclusion of the symmetry sites but tends to worsen. Second, I tested how the t depended on excluding the minima in potential energy from the 3D-grid input data set. I did this because I noticed during previous ts that the better the minima are represented, the lower is the shear modulus and the higher is the H-Au bond energy. Indeed, the more points with a low potential energy were excluded, the better the representation of physical properties of the Au became. Surprisingly, the rms error to all AIMD trajectories did not worsen but remained around 160 meV. However, if only the potential energy walls around the atom cores were tted, the shear modulus became too high and the H-Au bond too weak. Increasing the energy cut-o to include higher values in potential energy up to 25eV compared to 20eV for the t resulting in the EMT-JAWK parametrization also improved the representation of the physical properties
0.0 0.5 1.0 1.5 2.0 2.5 3.0
0.0 0.2 0.4 0.6 0.8 1.0
E
loss(eV)
Probability Density ( 1 / eV )
Figure 3.10.: Total energy loss distribution of nonadiabatic MD-simulations using EMT-JAWK (black) and EMT-mJS (purple).
50
0.0 0.5
top bridge
- 6 - 4 - 2 0 2 4 6
z (Å)
0.0
-3Density ( Å ) 0.5
hcp
- 6 - 4 - 2 0 2 4 6 fcc
Figure 3.11.: Background electron density for four high symmetry sites as a function of the H atom distance to the Au surfacezfor the ts 894 (purple), 921 (red) and EMT-JAWK (thick, black), and the electron density obtained from DFT (thick, grey).
of Au and the H-Au bond energy, most likely by virtue of reducing the weight on the points representing the structure of the minima.
There are two further constraints which I would suggest for future tting processes. First, Jacobsen et al. [2] write in their description of the EMT that only δmetal/ηmetal 1 is the acceptable range forδmetal. Furthermore, the background electron density that results from the t should be monitored to avoid too high or too low values. While the rst case is most likely caused by a too low s0,H, I was not able to establish a straightforward relation between the parameters that could explain very large background electron densities, since the relation of the parameters that give rise to the background electron density is rather complex (see Eq. (2.30).
Although the electron density that can be obtained with DFT-GGA functionals diers from the background electron density obtained from EMT by not including the feedback caused by the presence of the H atom, it still can be used as an indication of whether the background electron density obtained from a t is reasonable: if the background electron density is (i) much higher in the space between the Au atoms or (ii) much lower around the atom cores than the electron density from DFT calculations, the t should be discarded. As shown in the two examples presented below, case (i) leads to almost complete sticking to the surface. Case (ii) leads to unphysical behavior: the H atom may not see an increase in electron density upon approaching the Au atoms.
Table 3.5.: Values of various physical properties for bulk Au calculated with the dierent ts compared to the literature values. ζ is the energy of the H-Au bond.
Fit 894 Fit 921 Fit 1138 Fit 1226 Fit 1288 Lit.
rms error to
AIMD (meV) 170 160 150 160 160
C11 (GPa) 205.0 198.8 200.0 201.8 202.4 201.6 [125]
C12 (GPa) 162.0 158.6 158.0 157.1 156.8 169.7 [125]
C44 (GPa) 43.05 40.21 42.1 44.75 45.6 45.4 [125]
Bulk modulus (GPa) 172 172 172 172 172 173 [234]
ζ (eV) 2.8 2.9 3.0 3.1 3.1 3.0 [229]
Tstable (K) 1250 1150 1100 1150 1050 1337 [235]
While trying to optimize the tting procedure, I obtained a large number of ts of which several full the physical constraints I have chosen for EMT-JAWK. Here, I give a comparison between ve dierent ts that all have an rms error below 185 meV and otherwise full the physical constraints described in the previous section. I identify the parametrizations by their t number and chose ts 894 and 921 (see Tab. 3.5) to point out that for both of them the physical constraints appear to be met, but the background electron density takes too large or too low values (see Fig. 3.11, purple and red, respectively); for both t 894 and t 921δmetal/ηmetal >1, too.
I obtained several other EMT parametrizations (Tab 3.5, ts 1138, 1226 and 1288) displaying low rms errors, good agreement with the elastic moduli andζ (see Tab. 3.5). I consider all three of them as examples for potential candidates for a PES that reproduce the bulk properties of Au better than EMT-JAWK and could be used if the EMT-JAWK should turn out unsatisfactory in future. The dierence between the last three ts is in their respective input data sets: for t 1138, I used a single bounce trajectory as input data set from the AIMD trajectories. For t 1226, I allowed the inclusion of all points in the input data set that had a potential energy below 25 eV instead of 20 eV as a maximal energy cut-o, and for t 1288 I excluded the 240 points with the lowest potential energy values of the 3D-grid input data. The values of the parameters to the ts are listed in Tab. 3.6.
To test how the dierent parametrizations inuence the H atom scattering I performed elec-tronically adiabatic and nonadiabatic molecular dynamics simulations. The incidence conditions for all simulations were: Einc= 3.33eV,θinc = 45◦ along the [10¯1]surface direction, T = 300K and 6×6×6 slab (105 trajectories). Tab. 3.7 shows a comparison of the various outcomes of the simulations for the dierent ts. For the electronically adiabatic case (given in parenthesis), all ts display much the same results. For the nonadiabatic case, the dierences between
EMT-52
JAWK, t 1138, 1226 and 1288 are almost negligible, whereas for t 894, all H atoms stick to the surface and t 921 brings many more H atoms to adsorb to the surface than to subsurface regions.
A comparison of the total energy loss distributions shows great similarity for the electronically adiabatic case (Fig. 3.12(a)). In the electronically nonadiabatic case, t 894 does not appear as, according to Tab. 3.7, no H atoms scatter if interaction with electron hole pairs is included. The
Table 3.6.: Fit Parameters dening H-Au EMT PESs.
η2 (Å−1) n0 (Å−3) ε0 (eV) λ(Å−1) V0 (eV) κ (Å−1) s0 (Å) Fit 894
Au 3.485 0.064 -3.8 [2] 4.233 0.378 2.7531 1.642
H 5.404 0.408 -2.371 [23] 8.036 0.244 9.752 0.674
Fit 921
Au 3.308 0.061 -3.8 [2] 4.182 0.391 2.629 1.642
H 1.235 0.184 -2.371 [23] 1.741 0.335 3.287 0.480
Fit 1138
Au 3.200 0.047 -3.8 [2] 4.182 0.460 3.630 1.642
H 4.320 0.181 -2.371 [23] 7.133 0.229 7.588 0.680 [23]
Fit 1226
Au 3.096 0.051 -3.8 [2] 4.182 1.114 4.898 1.642
H 4.692 0.167 -2.371 [23] 7.855 0.359 8.322 0.680 [23]
Fit 1288
Au 3.101 0.051 -3.8 [2] 4.182 1.193 4.948 1.642
H 4.787 0.167 -2.371 [23] 7.940 0.364 8.496 0.680 [23]
0.0 0.5 1.0 1.5
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5
Eloss(eV)
ProbabilityDensity(1/eV) (a)
0.0 0.5 1.0 1.5 2.0 2.5 3.0
0.0 0.2 0.4 0.6
Eloss(eV)
ProbabilityDensity(1/eV)
(b)
Figure 3.12.: Total energy loss distribution for (a) adiabatic and (b) nonadiabatic scattering for the ts 894 (purple), 921 (red), 1138 (blue), 1226 (dark green) and 1288 (dark yellow) and EMT-JAWK (black, dashed).
Table 3.7.: Various outcomes (in %) resulting from H atom collision with a Au(111) surface for nonadia-batic and adianonadia-batic (in parenthesis) simulations using various ts. The incidence conditions areEinc= 3.33eV,θinc= 45◦along the[10¯1]surface direction,T = 300K, a6×6×6slab and number of trajectories105.
Surface Subsurface
conditions Scattering adsorption absorption Transmission
EMT-JAWK 55 (82) 23 (4) 22 (6) 0 (8)
Fit 894 0 (82) 93 (4) 6 (6) 0 (9)
Fit 921 57 (82) 32 (6) 10 (4) 1 (7)
Fit 1138 54 (81) 23 (4) 23 (7) 0 (8)
Fit 1226 52 (80) 22 (4) 25 (7) 0 (8)
Fit 1288 52 (80) 22 (4) 26 (8) 1 (8)
reason for this behavior becomes evident from Fig. 3.11: the background electron density for t 894 (purple) is so high that the friction coecient in Eq. (2.53) becomes so large that the H atoms lose much of their initial energy and stick to the surface.
The total energy loss distribution in case of t 921 (Fig 3.12(b), red) is shifted to higher energy values compared to the other ts. In view of the much lower background electron density (Fig. 3.11, red), this is surprising, but it might be caused by dierent scattering due to the H atoms being able to come closer to the Au atoms which is made possible by the less steep rise in electron density close to the Au atoms. However, as the repulsive interaction with the atomic cores should be caused by electron-electron repulsion between the electron of the H atom and those of the Au atom, the lack of increasing electron density upon getting closer to an Au atom is clearly wrong. This failing can most likely be attributed to the too low value of the s0,H-parameter (see Tab. 3.6).
For the ts 1138, 1226, 1288 and the one resulting in EMT-JAWK the total energy loss distributions for both the adiabatic (Fig. 3.12(a)) and nonadiabatic (Fig. 3.12(b)) case agree well, as do their respective electron densities (Fig 3.13). The scattering probabilities show only very small dierences. The percentage of single bounces in all scattering trajectories is also very similar, lying between25−26%, as is that of the double-bounces (34−36%) and multibounces (39−43%). The percentage of penetrating trajectories varies between20−24%.
A comparison of the dierential energy loss distributions for all four ts in specular scattering angle (see Fig. 3.14) shows that all ts give rise to the same DELD. It appears therefore that the translational energy loss for the adiabatic and nonadiabatic case as well as the sticking behaviour is not much inuenced by the choice of the parameter set if all constraints are met (including the additional ones mentioned in this section).
54
0.0 0.5
top bridge
- 6 - 4 - 2 0 2 4 6
z (Å)
0.0
-3Density ( Å ) 0.5
hcp
- 6 - 4 - 2 0 2 4 6 fcc
Figure 3.13.: Background electron densities for four high symmetry sites as a function of the H atom distance to the Au-surface for the ts 1138 (blue), 1226 (dark green), 1288 (dark yellow) and t 1 (black, thick).
0.0 0.5 1.0 1.5 2.0 2.5 3.0
0.0 0.2 0.4 0.6 0.8 1.0
E
loss(eV)
Probability Density ( 1 / eV )
Figure 3.14.: Dierential energy loss distribution for ts EMT-JAWK (black), 1138 (blue), 1126 (dark green) and 1188 (dark yellow) for specular scattering extracted from 106 simulated tra-jectories.