I performed adiabatic and nonadiabatic MD simulations for H in interaction with Au(111) with propagation times of 120 fs or 1 ps and a time step of 0.1 fs using the MD_tian program.
This package has been developed over the last years in our research group and was written by Dr. Alexander Kandratsenka, Prof. Dr. Daniel J. Auerbach and myself. It encompasses the tting procedure and MD-simulation procedure, including an implementation of the analytic expressions for the EMT forces (see attachment B).
The Au slab was equilibrated over 5 ps by assigning velocities from the Maxwell-Boltzmann distribution corresponding to a given temperature to the Au atoms. After that, the simulation was continued for another 100 ps and the Au atom congurations and velocities sampled every 100 fs. Each trajectory randomly assumes one of these 1000 congurations and velocities at the start of the trajectory to make sure that I sampled a wide variety of Au congurations for
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each temperature. For a 6×6×6 slab the atoms of the lowest three levels were xed to their ideal lattice positions to simulate the bulk structure and keep the slab stationary during the simulations, and for a6×6×4 slab only the atoms of the lowest layers were xed to their ideal lattice positions.
For MD simulations of H in interaction with Au(111), I have classied the outcomes into four classes: (1) scattered if the H atom at the end of the propagation time is further away than 5 Å from the surface, (2) adsorbed if the H atom is above the rst layer of Au atoms of the slab but closer than 3 Å, (3) absorbed if the H atom remains within the slab and (4) transmitted if the H atom has passed through the slab at the end of the propagation time, that is, nds itself below the Au atoms of the bottom layer of the slab. H atoms belonging to the last case are estimated to continue deeper into the bulk and to make no contribution to the scattered H atoms. If the H atom nds itself inside the slab, I class its position according to the layer it nds itself in. For this, I use the perfect fcc structure. In the perfect fcc-structure, the Au atoms of the surface are centered atz= 0Å; any H atom that nds itself abovez= 0Å (and below 3 Å) I consider as being on the surface. Likewise, any H atom that nds itself betweenz= 0Å and the atoms of the rst subsurface layer centered atz=−a0/√
3 I consider as being absorbed in the rst subsurface interlayer space (sublayer), &c. I am conscious that this division is only a rough one, especially when the Au atoms nd themselves in thermal motion or the slab relaxes from its perfect fcc-structure. However, any other classication would be vastly more complicated. I therefore chose a very simple model to classify the position in z-coordinate of the H atoms, it being easily reproducible and readily understood.
Furthermore, I classied the trajectories of scattered H atoms into how many collision the H atoms experience with the surface. This I did by monitoring the embedding electronic density of a H atom in each step. If it underwent a maximum between the present and the two previous steps and an background electron density>0.25Å−3, I consider the H atom to have experienced a bounce, for the closer an H atom approaches an Au atom, the higher the electron density it will experience, peaking at the closest point to an Au atom. I discriminate between three types of bounce events: one (single-bounce events), two (double-bounce events) or more (multibounce events) collisions with a surface atom. Of course, as any classication based on a threshold, the classication given here is not entirely accurate, but I expect it to be reasonable enough.
In each section of chapter 3.3, I show three tables containing information about scattering and sticking probabilities as well as the peak and mean energy loss of the total and dierential energy loss distributions (ELDs) belonging to dierent scattering conditions. For the dierential energy loss distributions, I give a lesser number of signicant gures to account for the fact that these distributions usually have a low signal-to-noise ratio which makes it dicult to assign the peak position. Wherever the peak position for a dierential energy loss distribution at a specic scattering angle is given, it should therefore be treated with caution. Here, `total energy
loss distribution' is to be understood as that energy loss distribution that is obtained when the contribution of all scattering trajectories is considered. In contrast, `dierential energy loss distribution' refers to the ELD that is obtained when only trajectories are considered in which the H atoms leave the surface under specic scattering angles. This nomenclature has been chosen analogous to total and dierential cross section. If ELD is mentioned without preceding adjective (outside chapter 4), the description applies to both dierential and total energy loss distribution.
All energy loss distributions shown here are of the scattering ux. To construct them, unless otherwise noted, I took a binning interval of 10 meV. To obtain the dierential energy loss distributions for dierent scattering angles, I selected all the trajectories where the H atoms scattered within5◦to the vector along the selected scattering direction. By that I mean that for observing scattering for θout= 45◦ along the [10¯1]-direction, I dened a vector pointing in this direction and selected all trajectories where the H atom had a scattering velocity vector within 5◦ as contributing to this dierential energy loss distribution. This scheme can be imagined as a disk of respective radius that is part of the spherical surface centered at the coordinate origin, thereby mimicking the hole of a detector that scans for scattering H atoms at a constant distance to the surface. I adopted this scheme to obtain dierential energy loss distributions for individual scattering angles that were constructed in a manner that follows the experimental procedure as closely as I could devise.
For the total angular distributions, where double counting would have a serious inuence on the shape of the distribution, I got the better of this drawback by employing a dierent selection scheme: I created a grid inθout andφout, ranging from θout= 0◦ toθout= 90◦ with∆θout= 10◦ and from φout = 0◦ to φout = 90◦ with∆φout = 10◦ and binned the returning trajectories with this grid according to their exit angle. I corrected the number of counts in each interval by a factor of 1/sin(θout) to account for the shrinking of the binning surface with shrinking polar angle.
Furthermore, I constructed angular distributions selected after their azimuth angle, that is, not overall angular distribution but such along certain surface direction. To circumvent the problem of shrinking binning intervals or double-counting, I employed the following scheme:
a cross section of a sphere that corresponds to the desired azimuth angle is created. The H atoms that scatter within 90±3◦ to the vector normal to that cross section are considered as contributing to the in-plane angular distribution.
The adiabatic energy loss can be estimated by means of the Baule limit which can be repre-sented in terms of the projectile-surface mass ratio µ=m/M:
∆Ead= 4µ
(1 +µ)2Einc (2.58)
The simulated annealing for the investigations of the surface reconstruction of Au(111) was
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performed using the Langevin Dynamics as a thermostat. A higher friction coecient of η ≈ 3·10−3fs−1 was assumed. This makes the annealing simulations more eective and decreases the simulation time.