Simple STM images
In this exercise we will consider different termination of two polyantryl molecules that are an intermediate step for the formation of a long armchair nanoribbon. 10.1021/ja311099k.
We will show how a simple change in the termination (1 vs. 2 Hydrogens) changes the state structure completely.
bsub -n 16. Download, as usual, the files from the media manager: exercise-10.2.tar.gz. The 1h.1.5.inp file is commented).
Please use command module load cp2k/2.5.14075 , as well as module load python/2.7.9 to do this particular exercise.
1. Task: Running the job and looking at the orbitals
This time we will not optimize the structure. With an ENERGY run, we run with cp2k the job 1h.1.5.inp and 2h.1.5.inp. Here the number 1.5 represents the number of units of the original molecule in the gas phase.
The interesting part of the code is in the &PRINT section of &DFT :
&PRINT ! controls the printing of cubes for the generation of STM images. &STM ! set of sample bias ! negative for occupied states and positive for unoccupied states BIAS -2.0 -1.0 1.0 2.0 ! orbital symmetry of the tip ! The change in the tip symmetry can radically alter the contrast of the topographic ! image due to changes in tip-surface overlap TH_TORB S &END STM ! print molecular orbitals &MO_CUBES ! 10 occupied orbitals NHOMO 10 ! 10 unoccupied orbitals NLUMO 10 ! limit the size of cube files STRIDE 2 2 2 WRITE_CUBE T &END ! a cube file with eletrostatic potential generated by the total density (electrons+ions). &V_HARTREE_CUBE &END
There will be an output file with the unoccupied energy levels and the last “EIG” file with occupied energy levels. To plot the energy level diagram, copy and paste following lines into the python script eldplot.py. The file energy.dat contains energy eigenvalues (in a.u.) in one column from the output file and from the EIG file. The Fermi energy (Ef in a.u., is the energy of the highest occupied value) must be entered in the eldplot.py script. Use the command python eldplot.py to get the energy level diagram as a postscript image. (use gs to visualize it). Identify the occupied and unoccupied energy levels and name them. Feel free to change the png image names.
import matplotlib.pyplot as plt import numpy as np import scipy as spy import pylab as ply import argparse import sys # Open file f = open('energy.dat', 'r') lines = f.readlines() f.close() x1 =  y1 =  # Fermi energy Ef=0.0 for line in lines: p = map(float,line.split()) y1.append(float((p-Ef)*27.212)) for yv in y1: x = [0.2,0.8] y = [yv, yv] if yv <= 0: plt.plot(x,y,color='red') else: plt.plot(x,y,color='green') # add label to y-axis ply.ylabel("E - Ef [eV]") # set x and y range ply.xlim([0,1]) ply.ylim([-5,5]) # remove x-axis label plt.gca().xaxis.set_major_locator(plt.NullLocator()) # show plot #plt.show() # save plot in a eps file plt.savefig('ELD.eps')
An example of the energy level diagram is as follows,
- Draw the energy level diagram for the two molecules. What is the energy gap in the two cases? What are the differences?
- Look with vmd at the cube files corresponding to the most interesting levels (close to Fermi…). Comment on the distribution of the states.
2. Task: Producing a simple STM image
The section &STM shown above produces STM images at different bias (feel free to change), meaning, using the Tersoff-Hamann approximation, it integrates all the density of states with energies between Fermi energy and the Bias potential: this energy interval is involved in the tunnel current. The *STM* cube files are 3D maps of the integrated density of states. Imagine that we have a microscope with a feedback that can keep constant current between tip and sample, by changing the height of the tip on the surface. Since the current is proportional to the density of states, we move the tip on isosurfaces of our cubefile. The program stm.py allows to extract a 2D map of the height of a given isosurface.
Run the stm.py program in the following way: $ module load new cp2k $ module load python/2.7.9 $ export PYTHONPATH=/cluster/home/pshinde/ase:$PYTHONPATH $ export PATH=/cluster/home/pshinde/ase/tools:$PATH $ export PYTHONPATH=/cluster/home/pshinde/asetk-0.1-alpha:$PYTHONPATH $ export PATH=/cluster/home/pshinde/asetk-0.1-alpha/scripts:$PATH $ stm.py --stmcubes *STM*.cube --isovalues 1E-5 --plot | tee stm.out OR $ stm.py --stmcubes *STM*.cube --isovalues 1E-5 --plot --plotrange VALUE VALUE | tee stm.out where VALUE VALUE is the data range
For more options use command stm.py -h. The resulting .dat files contain the z profile (in angstrom) and may for example be plotted by gnuplot:
gnuplot set pm3d map set size square set xrange [...... set yrange [..... splot "mystm.dat" matrix using 2:1:3
Where instead of “mystm” you use an appropriate filename.
- In the output file of cp2k, the program tells you how many states have contributed to each STM image. Discuss the images that you see in the two cases.
- What makes the 1h* case particular with respect to the 2h*?
- Change the isosurface and look at the z-range. Discuss the changes in the range.
- Would you define the differences between 1h and 2h in the STM images as more of structural origin or electronic origin?