3. Results 39
3.3. MD Simulation of H scattering from Au(111) with Various Conditions
3.3.7. The Inuence of Changes in Electron Density
The coupling of electronic degrees of freedom to nuclear ones is taken into account by means of LDFA (see section 2.5) in this work. The friction coecient used in the resulting Langevin equa-tions is related to the background electron density (Eq. 2.30). In the derivation of this formula some approximations were employed. Here, I investigated how the electronically nonadiabatic adsorption dynamics are inuenced by changes in the background electron density, perhaps of-fering a possible explanation on the divergences to the experimental results (see chapter,4). I followed four dierent approaches:
In the rst case, I lower the electron background density to electron density from ab initio simulations (see section 3.2 and Fig. 3.48). To this end, I multiplied the background electron density the H atom experiences throughout the trajectory by a factor of 2/3. Fig. 3.48 shows how the reduction of the electron background density of EMT (blue) by a factor of 2/3 (green) reproduces the electron density from the GGA-DFT calculations (grey) [22] for the top-site.
Fig. 3.49(a), (b) shows the comparison of the ELD resulting from the unmodied background electron density (black) to the ELDs resulting from the modications of the background electron density. The consequence of lowing the background electron by 2/3 (green) is that the peak and shoulder of the (total and dierential) ELD shift to slightly lower energy losses. The scattering and adsorption dynamics (see Tab. 3.30, (1)) change slightly towards more scattering and less adsorption while the percentage of multibounce events increases, in accordance with the slightly (due to the shift of the rst peak) longer tail of the ELD (Tab. 3.31, (1)). The shift between the two ELDs is however not large (Tab. 3.32, (1)), indicating that a small modication to the electron density is of little consequence.
For the second case, I assume that the background electron density can be described by an analytic expression given by a logistic equation
n(z) = 0.25
1 + exp [6.0(z−1.7)], (3.5)
wherezis the H atom distance normal to the surface. The coecients in Eq. (3.5) are chosen such that the electron density decays at the surface in agreement with the EMT background electron density. It assumes a constant value within the slab and a constant one outside (Fig. 3.50). The total energy loss distribution obtained when applying Eq. (3.5) (Fig 3.49(a), red) to calculate
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-6 -4 -2 0 2 4 6 0.0
0.2 0.4 0.6 0.8 1.0
z(Å) Density(Å-3 )
Figure 3.48.: The EMT background electron density (blue) of an H atom and the one reduced by2/3 (green) compared to the density of the GGA-DFT calculations (grey) for the top-site.
the background electron density peaks at higher energy loss and its form changes signicantly compared to the total ELD calculated with the unmodied background electron density (black) in that the shoulder resulting from double-bounce events grows more pronounced and a new shoulder appears at high energy losses resulting from a large overlap between the total energy loss distribution of double- and multibounce events. The sticking and ad/absorption behavior changes slightly towards less scattering and more sticking (Tab. 3.30) and the ratio of bounce events is more evenly split up (Tab. 3.31). The dierential energy loss distribution at specular scattering (Fig 3.49(b), red) is likewise shifted to higher energy losses and shows a slightly fuller tail. The angular distribution in [10¯1]-direction is only insignicantly changed; what changes
Table 3.30.: Outcomes (in %) resulting from H atom collision with a Au(111) surface for nonadiabatic simulations for modications to the background electron density. The incidence conditions are Einc = 3.33eV, θinc = 45◦ along the [10¯1] surface direction, with a relaxed surface structure and6×6×6 slab at 300 K, number of simulated trajectories: 106.
Scattering Surface Subsurface Transmission
Modication Adsorption Absorption
none 55 23 21 1
(1) 59 20 21 1
(2) 51 27 22 0
(3) 55 23 21 1
(4) 82 4 6 8
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
Eloss(eV)
A.U.
(a)
0.0 0.5 1.0 1.5 2.0 2.5 3.0
Eloss(eV) (b)
-1.0 -0.5 0.0 0.5 1.0 r sin(θ)
75°
60°
45°
30° 0° 15°
-15°
-30° -45°
-60°
-75°
(c)
Figure 3.49.: (a) Total energy loss distribution of nonadiabatic calculation for dierent modications to the electron density. (b) dierential energy loss distribution at specular scattering angle. The dashed line indicates the position of the peak of the dierential energy loss distribution resulting from the unmodied EMT electron density (black). (c) Angular distributions along the [10¯1]-direction, negative θ correspond to backwards scattering.
Unmodied background electron density (black), constant density in surface (red), elec-tron density reduced by factor of2/3(green), density increased at repulsive walls (navy) and electronic friction post facto (yellow).
are to be observed are more likely to be caused by noise than any fundamental dierence due to the modication of the background electron density (Fig. 3.49(c), red). It is almost surprising that such a large modication in electron density does not result in a more signicant change in the ELDs. It is an indication that the region of electron density the H atom moves in or scatters at sees no great variations and that the H atom does not come close enough to the atom cores to experience regions of very high electron density.
The latter point is especially emphasized (case 3) when the background electron density is increased when the H atom comes close to the Au atoms. In this way, while an atom would
116
-6 -4 -2 0 2 4 0.0
0.2 0.4 0.6 0.8 1.0
z (Å) Density(Å-3 )
Figure 3.50.: The EMT background electron density (blue) of an H atom and the one given by Eq. (3.5) (red), for the top-site.
experience higher electron density in a direct collision with the Au atoms, an atom ad- or absorbed to the surface experiences the same background electron density as directed by the EMT-parameters. To achieve this modication, the background electron density is multiplied by a factor w, dependent on the distancerH,Au between H and Au atom (Fig. 3.51):
w(r) = 2 3
1
1 + exp [15.0 (rH,Au−1.0)]+ 1 (3.6) This modication results in no change between in the total ELD (see overlap of black and
Table 3.31.: Outcomes (%) of scattering for scattering events resulting from H atom collision with a Au(111) surface for nonadiabatic simulations for modications to the background electron density. The Surface-column refers to trajectories wherein H atoms scattered from 1st layer of the surface. The Roman numerals refer to the lowest subsurface to which pene-tration occurred. The incidence conditions areEinc = 3.33eV,θinc = 45◦ along the[10¯1]
surface direction, 300 K and6×6×6 cell, number of simulated trajectories: 106.
bounce events penetrating bounces
Modication single double multi surface I II III >III
None 23 34 43 82 17 1 0 0
(1) 22 32 46 81 18 1 0 0
(2) 25 35 40 83 16 1 0 0
(3) 23 33 43 81 17 1 0 0
(4) 17 25 59 64 23 8 3 2
Table 3.32.: Energy loss in % of incidence energy for various outcomes resulting from H atom collision with a Au(111) surface for nonadiabatic for modications to the background electron density. The mean and maximum energy loss are shown for total and dierential ELD at 300 K for106 trajectories. Due to the low signal-to-noise level, the values at specular scattering (θout = 45◦ φout= 60◦ ([10¯1])) are shown with less signicant gures.
Total θout= 45◦ φout= 60◦ Modication Mean Peak Mean Peak
none 35.3 14.0 37 14
(1) 32.3 13.1 38 13
(2) 37.1 18.2 34 10
(3) 35.3 15.8 37 14
(4) 74.8 14.0 68 13
navy curves in Fig. 3.49(a)), nor in the dierential energy loss distribution at specular scat-tering (Fig. 3.49(b)) and very little in the angular distribution for scatscat-tering in [10¯1]-direction (Fig. 3.49(c)). This means that regions of high electron density, where a friction coecient could be expected to be of larger impact, are either not sampled during a trajectory or play a very insignicant roll for energy losses.
Posteriori (4) electronic friction post-facto as described by Kroes and coworkers [3, 4] where the energy loss to electron hole pair is estimated by Eq. (3.4). The velocities, positions and elec-tron densities are taken from the adiabatic MD simulations. The total energy loss distribution
-6 -4 -2 0 2 4
0.0 0.5 1.0 1.5 2.0 2.5 3.0
z(Å) Density(Å-3 )
Figure 3.51.: The EMT background electron density of an H atom (blue) and the modied one dened by Eq. (3.6) (navy) for the top-site.
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(Fig, 3.49(a), yellow) exhibits some similarities with total ELDs at lowered temperature (e.g.
40 K, see section 3.3.2), apart from the fact that the tail of the distribution stretches to very high energy loss values (above 10 eV) which, given an incidence energy of 3.33 eV appears rather unphysical. The structure of the ELD has little to do with the structure of the ELD from direct nonadiabatic simulations at 300 K, but both peak in the same region of energy loss. Kroes and coworkers [3] found that the rst peak is due to penetrative collisions and that the non-penetrative collision exhibit an eight times higher average energy loss in the nonadiabatic case compared to the adiabatic case. This is much larger than the factor of three dierence in mean energy loss I nd for the comparison of the total energy loss distribution for the nonadiabatic and adiabatic case. Accordingly, Kroes and coworkers estimate from comparison with AIMDEF simulations that the energy transfer to ehp predicted by AIMDEFp should overestimate the energy transfer from direction inclusion of energy loss to ehp by ∼20%. Here, I nd that the post-facto approach overestimates the mean energy loss to ehp by a factor of 1.8. From both the form of the total ELD and the dierential energy loss distribution at specular scattering, it is clear that the post facto approach cannot serve to replace the on-the-y simulation of energy loss due to electron hole pair excitation.
In summary, I found that large modication of background electron densities have no dramatic inuence on the simulation results. These are interesting ndings for they suggest that the approach taken by Blanco-Rey et al. [19] during their AIMD simulations including electronic friction to calculate the friction coecient from the electron densities of an undistorted slab is indeed a reasonable approximation. Furthermore, if only a general impression of the energy loss to electron hole pairs is needed, the calculation of a friction coecient from the local electron density is not necessary; a well-adjusted constant friction coecient will also give reasonable ideas.
Most of all, however, that such grave changes in the electron density only aect the outcome of the trajectory to a minor extend, makes it seem unlikely that treating the friction coecient as a tensor would lead to much dierent results.