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Surface and solid state analysis tools
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.. |angst|  unicode:: U+0212B .. ANGSTROM SIGN
.. |infin|  unicode:: U+0221E .. INFINITY
.. |simeq|  unicode:: U+02243 .. ASYMPTOTICALLY EQUAL TO
.. |sigma|  unicode:: U+003C3 .. GREEK SMALL LETTER SIGMA
.. |Delta|  unicode:: U+00394 .. GREEK CAPITAL LETTER DELTA
.. |mu|     unicode:: U+003BC .. GREEK SMALL LETTER MU
.. |beta|   unicode:: U+003B2 .. GREEK SMALL LETTER BETA
.. |pi|     unicode:: U+003C0 .. GREEK SMALL LETTER PI
.. |alpha|  unicode:: U+003B1 .. GREEK SMALL LETTER ALPHA
.. |nu|     unicode:: U+003BD .. GREEK SMALL LETTER NU
.. |deg|    unicode:: U+000B0 .. DEGREE SIGN

Band diagrams
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Band diagrams are usefull analysis tools. Read  `Al_band.py`_ and try to understand what i does, then use it to construct the band diagram of bulk Al and Si. Compare the Si band diagram to band diagram below (adapted from Cohen and Chelikowsky: "Electronic Structure and Optical Properties of Semiconductors" Solid-State Sciences 75, Springer-Verlag 1988). How does this correspond to the DOS calculation in Exercise 3. 

.. _Al_band.py : attachment: Al111.py

.. figure:: Si_banddiagram.gif
   :width: 350
   :align: center




Wannier Orbitals
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Transforming the planewave basis into a maximal localized Wannier orbital basis set offer an opportunity to interpret the Kohn Sham orbitals as molecular orbitals. We have cheated a little bit and prepared some .nc files for small and medium molecules so that you only have to concentrate on the wannier analysis of the molecules. The wannier functions is created using `Wannier.py`_ .

* Benzene: `Benzene.nc`_

* Pyridine: `Pyridine.nc`_

* Thiophene: `Thiophene.nc`_ 

* H2O : use your own .nc file from exercise 3

* CO : use your own .nc file from exercise 3

Choose a medium sized molecule and determine the number of occupied orbitals. Create the Wannier Functions of your molecule with the number of orbitals equal to the number of occupied orbitals. Is the molecular orbitals well described? What could you do to improve on the description of the molecular orbitals? How does the localization depend on the number of wannier orbitals? Try to find all the molecular orbitals in your molecule?

.. _Wannier.py : attachment: Wannier2.py

.. _Benzene.nc : attachment: Benzene.nc

.. _Pyridine.nc : attachment: Pyridine.nc

.. _Thiophene.nc : attachment: Thiophene.nc

STM simulations
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Scanning Tunneling Microscopy (STM) is a widely used experimental technique. STM maps out a convolution of the geometric and electronic structure of a given surface and it is often difficult if not impossiple to intrepret STM images without the aid of theoretical tools. We will use VMD to plot our simulations of STM images. Start by setting up an Al 100 FCC surface with 2 layers, calculate the adsorption energy of H at high symmetry sites.  Use  `STM_VMD.py`_ to simulate the the clean FCC 100 surface and then go on to the surfaces with H adsorbed. Can STM see the H atoms on the surface, what do the atoms look like in the simulations? Can STM see the difference between the different adsorption sites? What kind of aproach what you take if you had experiemtal data that you needed to interpret?  

.. _STM_VMD.py : attachment: STM_VMD.py