Probe particle model code is supposed to simulate AFM ( and to some extent STM and inelastic-STM) images obtained with tip modified by an atom or small molecule (such as Xe, CO, CH4, H2). In all cases the actual particle (atom or molecule) is replaced by a spherical model particle and classical potential (Lenard-Jones) is used for description of Pauli repulsion and Van der Waals attraction.

New code is written in C/Python and can operate in framework of Lennard-Jones forces as well as electrostatic forces, if necessary.

Older documentation

The documentation is for “Master” branch, that can be downloaded from http://github.com/ProkopHapala/ProbeParticleModel/ or by running:

git clone http://github.com/ProkopHapala/ProbeParticleModel/

in your terminal.

It should be working for developers “dev” branch, too.

It can be downloaded from http://github.com/ProkopHapala/ProbeParticleModel/tree/dev or simply from terminal by running this commands:

git clone http://github.com/ProkopHapala/ProbeParticleModel/
cd ProbeParticleModel
git checkout dev

python-2.7; python-2.7-numpy(-1.8); gcc(-4.8); python-2.7-matplotlib(-1.3) - for plotting of figures;

module add python27-modules-intel
module add scipy-0.17.1-py2.7.10

And don't forget to add:

import matplotlib as mpl;  mpl.use('Agg');

on the 3rd line of plot_results.py, if it is not allready in the script and if you want to use it on a cluster. This makes it run without Xserver (e.g. on supercomputer) # see http://stackoverflow.com/questions/4931376/generating-matplotlib-graphs-without-a-running-x-server

DFT inputs

The geometry of the sample can be read from *.bas or *.xyz files, which has to have xyz extension! Here we show part of the geometry file from example attached to the model:

71

C       0.165   0.165   0.165   -0.0132352941
C       2.2987  1.39372 0.16643 -0.0132352941
C       4.4293  2.62743 0.16468 -0.0132352941
C       6.56208 3.85683 0.16431 -0.0132352941
C       8.69719 5.08888 0.16545 -0.0132352941
...

Which is in format:

Number of atoms optional line Symbol/or/Z-of-element x y z charge-optional

The Lennard-Jones (L-J) potential needed for calculations can be created by running:

python PATH_TO_YOUR_PROBE_PARTICLE_MODEL/generateLJFF.py -i YOUR_INPUT_FILE.xyz

If charges are also in the input file add “-q” flag to create electrostatic field.

Optionally, the geometry can be also read from *.xsf or *.cube file, too. The command for creation of L-J force field then looks like:

python PATH_TO_YOUR_PROBE_PARTICLE_MODEL/generateLJFF.py -i YOUR_INPUT_FILE.xsf

or

python PATH_TO_YOUR_PROBE_PARTICLE_MODEL/generateLJFF.py -i YOUR_INPUT_FILE.cube

x, y and z components of L-J forces are stored in LJFF_x.xsf, LJFF_y.xsf and LJFF_z.xsf files, respectively. These files that can be viewed e.g. via XCrySDen (http://www.xcrysden.org/) or VESTA (http://jp-minerals.org/vesta/en/).

If an electrostatic Hartree potential is obtained from some DFT calculations, it can be read *.xsf or *.cube files. The electrostatic force field is created by running:

python PATH_TO_YOUR_PROBE_PARTICLE_MODEL/generateElFF.py -i YOUR_INPUT_FILE

If default parameters are used, than you have monopole represented by an Gaussian cloud of charge with its FWHM of 0.7 Ǎ. The monopole can be changed to non-tilting dipoles or quadrupoles by adding flag: -t type, where type ∈ {s,px,py,pz,dx2,dy2,dz2,dxy,dxz,dyz}; s stands for monopole (default), p for dipoles, d for quadrupoles. The FWHM of the Gaussian cloud can be changed by adding flag: -s FWHM.

This files contains all important information about the scan and informations for creation of important forcefields. Here we show an example of it:

probeType       8                               # atom type of ProbeParticle (to choose L-J potential ),e.g. 8 for CO, 54 for Xe  
tip            'dz2'                            # For calculations with electrostatics only - multipole of the PP {'dz2' is the most popular now fo CO}, charge cloud is not tilting  #
sigma           0.71                            # For calculations with electrostatics only - FWHM of the gaussian charge cloud {0.7 or 0.71 are standarts}  #
charge         -0.05                            # For calculations with electrostatics only: if 0.00 then ElFF is not even read - effective charge of probe particle [e] {for multipoles the real moment is q*sigma - dipole - or q*sigma**2 - quadrupole} {for CO 'dz2' we typically use -0.30 - -0.05}  #
stiffness       0.20 0.20 20.00                 # [N/m] harmonic spring potential (x,y,R) components, x,y is bending stiffness, R particle-tip bond-length stiffness, {for CO we typically use 0.24 0.24 20.00}
r0Probe         0.0 0.0  3.00                   # [Å] equilibirum position of probe particle (x,y,R) components, R is bond length {3.00 for CO mostly these days}, x,y introduce tip asymmetry
PBC             True                            # Periodic boundary conditions ? [ True/False ]
gridN           240 240 200                     # Grid division around each cell axis; Not necessary - if it is not here a 0.1 division is applied
gridA   23.10994667   0.000000      0.000000    # lattice vector of the cell; If geometry is read from .xsf or .cube
gridB   11.55497333  20.01380089    0.000000    # !!!! If geometry is read from *.xyz, but electrostatics from .xsf or .cube than gridN and gridA/B/C has
gridC    0.000000     0.000000    20.000000     # to be in agreement with the harteee potential. Also the shift vector in the cube file has to be 0.0 0.0 0.0 !!!! 
scanMin     00.0   00.0    10.0                 # start of scanning (x,y,z) (z should be something like: the highest atom of the sample + R + 2.5)
scanMax     30.0   22.0    15.0                 # end of scanning (x,y,z)
scanStep    0.1   0.1    0.10                   # steps of scan (dx, dy, dz)
Amplitude       1.0                             # [Å] oscillation amplitude for conversion Fz->df

If you want to make a scan for different probe, you have to change the probeType in params.ini and to recompute L-J forces.

The number of grid divisions in *.xsf files is enlarged by one in each direction. Therefore, gridN have to be numbers of cubicles in *.xsf file reduced by one, if geometry is read from *.xyz, but electrostatics from .xsf

With having L-J and electrostatic forces made by generating scripts, you can try to run an AFM scan via:

python PATH_TO_YOUR_PROBE_PARTICLE_MODEL/relaxed_scan.py

which run the scan with charge Q and lateral stiffness K written in params.ini. Please note, that electrostatic forces are necessary only if Q ≠ 0.0. The result - Fz force acting on the tip – is saved in Q?.??K?.?? directory as an OutFz.xsf file. The df results for constant height scans can be plotted by:

python PATH_TO_YOUR_PROBE_PARTICLE_MODEL/plot_results.py  --df

that plot results for oscillation written in params.ini. The results - df_???.png maps for each tip height - are in directory: Q?.??K?.??/Amp?.??

optionally WSxM files for each height can be written by putting flag - -WSxM behind the plotting command. Outputs are df_???.xyz files with WSxM head and x y df data. If - -save_df flag is applied the df data are stored in df.xsf file. Flag - -atoms used simultaneously with - -df puts positions of atoms of the sample saved in input_plot.xyz into df_???.png. The flag - -bonds ads into the maps also lines connecting close-by atoms.

If a flag - -pos is applied for both commands (scanning & plotting) than xy positions of the relaxing Probe Particle (PP) are shown in xy_???.png as a red dots, while the gray scale on the background maps represent z position of the PP (brighter - higher).

Examples of df simulation is already in the downloaded/cloned repository in folder examples/. You should try to run these examples before going to your own stuff, in order to see that the code is working on your machine.

A scan with different charge (Q) and/or lateral stiffness (K) than those written in params.ini can be calculated via running (be aware, that for Q ≠ 0.0, you need to have precalculated electrostatic forces):

python PATH_TO_YOUR_PROBE_PARTICLE_MODEL/relaxed_scan.py -q (Q) -k (K)

It will create a new folder Q?.??K?.??/ where will be stored the results from the new run. A df map for wanted oscillation amplitude (A) can be then created by:

python PATH_TO_YOUR_PROBE_PARTICLE_MODEL/plot_results.py --df -q (Q) -k (K) -a (A)

The results will be saved in subfolder Amp?.??/.

Also scans over ranges of (Q),(K) and (A) can be done, via:

python PATH_TO_YOUR_PROBE_PARTICLE_MODEL/relaxed_scan.py --krange min max nK  --qrange min max nQ

python PATH_TO_YOUR_PROBE_PARTICLE_MODEL/plot_results.py --df --krange min max nK  --qrange min max nQ --arange min max nA

Prokop Hapala, Georgy Kichin, Christian Wagner, F. Stefan Tautz, Ruslan Temirov, and Pavel Jelínek, Mechanism of high-resolution STM/AFM imaging with functionalized tips, Phys. Rev. B 90, 085421 – http://journals.aps.org/prb/abstract/10.1103/PhysRevB.90.085421

Prokop Hapala, Ruslan Temirov, F. Stefan Tautz, and Pavel Jelínek, Origin of High-Resolution IETS-STM Images of Organic Molecules with Functionalized Tips, Phys. Rev. Lett. 113, 226101 – http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.113.226101