====== Calculation of surface energies of Au ======

In this exercise, we will build three small slabs based on the following figures; the cell is an **orthorombic** cell with repetition along z.

{{:exercises:2015_ethz_mmm:lect2_surf.001.jpg?nolink&400|}}

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{{:exercises:2015_ethz_mmm:lect2_surf.002.jpg?400|}}

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{{:exercises:2015_ethz_mmm:lect2_surf.003.jpg?400|}}

Figure out what is (in nearest neighbor units) the length of the three vectors Lx, Ly, Lz for the three high-symmetry surfaces.

{{ screen_shot_2014-03-07_at_8.47.53_am.png?direct |}}

Take the above table as reference for the orders of magnitude of surface energies. 
  * Download all the necessary files for computing the surface energies of all 3 high symmetry faces of gold from  from the wiki: {{exercise_3.2.zip|exercise_3.2.zip}} (**all inputs are commented**) in your home directory and unzip it:
<code bash>
you@eulerX ~$ wget http://www.cp2k.org/_media/exercises:2015_ethz_mmm:exercise_3.2.zip
you@eulerX ~$ unzip exercises:2015_ethz_mmm:exercise_3.2.zip
you@eulerX ~$ cd exercise_3.2
</code>
In principle all reconstructed phases should be with a lower surface energy, but this EAM potential fails for some of them.
The input files are:
  - 100_bulk.inp for determining the energy per atom in the bulk
  - 100_unr.inp for the bulk termination (100)
  - 100_rec.inp for the hexagonally reconstructed (100)
  - 110_unr.inp for the (110) bulk termination
  - 110_rec.inp for the (2x1) reconstruction
  - 111.inp for the unreconstructed (111).

Before, however, to be able to run the cp2k program, we need to build the **xyz** files for all cases. 
First, we build the slabs, using this chain of commands (**First assignment**). 
Use for the following:
<note important>
  - (100) surface: use (in first neighbor units) LX LY LZ = ????????  ????????  1.4142135 ; NX NY NZ = 4 5 5 
  - (110) surface: use (in first neighbor units) LX LY LZ = ????????  ????????  1.0000000 ; NX NY NZ = 6 4 5
  - (111) surface: use (in first neighbor units) LX LY LZ = ????????  ????????  2.4494897 ; NX NY NZ = 4 3 3 
  - Find the correct values of lx ly for the three cases. 
  - use ** D = 2.885 ** (correct value for gold)
</note>

Example:
<code>
you@eulerxx $ m_lattice LX LY LZ NX NY NZ < 100.unit | m_xyzrescale D | m_xyzrefold 1 1 1 | m_xyzcenter 1 1 1 | m_xyzsort  > 100_unr.xyz
you@eulerxx $ m_lattice LX LY LZ NX NY NZ < 110.unit | m_xyzrescale D | m_xyzrefold 1 1 1 | m_xyzcenter 1 1 1 | m_xyzsort  > 110_unr.xyz
you@eulerxx $ m_lattice LX LY LZ NX NY NZ < 111.unit | m_xyzrescale D | m_xyzrefold 1 1 1 | m_xyzcenter 1 1 1 | m_xyzsort  > 111_unr.xyz
</code>

<note important>For the bulk case, simply copy 100_unr.xyz into 100_bulk.xyz</note>
Substitute the LX LY LZ (but **ADD SOME VACUUM IN THE Z DIRECTION**) in the **ABC** section of the *inp files.
Check with vmd that the cell is ok.
Run the cp2k code as 

<code bash>
you@eulerxx $ bsub cp2k.popt -i 100_unr.inp -o 100_unr.out
you@eulerxx $ bsub cp2k.popt -i 110_unr.inp -o 110_unr.out
you@eulerxx $ bsub cp2k.popt -i 111_unr.inp -o 111_unr.out
</code>

The compute_surf* scripts give an idea how to compute the surface energies.

In the next step, we work also with 2 reconstructed surfaces: the 110_rec.xyz and the 100_rec.xyz.


<code bash>
you@eulerxx $ bsub cp2k.popt -i 100_rec.inp -o 100_rec.out
you@eulerxx $ bsub cp2k.popt -i 110_rec.inp -o 110_rec.out
</code>
<note tip>
Assignments:

  - Mark surface energies and relaxations of the first 2-3 top layers (use vmd or editor)
  - Try to color the surfaces in vmd in a way that makes the height evident (ask the assistant) and produce snapshots (render)
  - Comment on the (2x1) reconstruction: what do you see?
  - Copy the 110_unr.xyz into a new file 110_my_rec.xyz 
  - Edit the file and remove one line each two on the two surfaces
  - Check that the result is the same as in 110_rec.xyz
  - Plot the same slabs, but adding periodic images in vmd: remember pbc set { a b c 90 90 90 }.
</note>
<note important>Hint: you can save a configuration file in vmd and reuse it for a new sample! Ask the assistant!</note>