Nanosurf Lab

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==== The geometry ====

First of all we need the “*.bas” file of the tip and sample geometry
(separately). We can use the Jmol to view the “*.xyz” file. Tip should have tip
apex at 0.0 0.0 xy position.
We have even to prepare the “Fdata” of given properties of elements of tip
and sample we will use.
For followings we should run the fireball to relax these structures. If you
are using new FIREBALL input format, set up followings at the “fireball.in” file:

__&OPTION__ part

‐ basisfile = <filename> \\
‐ lvsfile = <filename> \\
‐ kptpreference = <filename> \\
‐ nstepf = 1 \\

Than you have the “CHARGES” of both the systems tip and sample

 \\



==== The files we need ====


We need several files before we can simulate the STM scanning for both
tip and sample. For sample it is “Atomo_i” and "struc.inp files", hopping file
“tip_sample_i_j.inp” (“interaction_i_j.dat”), “tip_e_str.inp” and “tip_g_str.inp” with
the densities and geometry of the tip.

 \\

=== II.I. Atomo_i, struc.inp ===

Once we have the “CHARGES” we can produce the "Atomo_i" files by the
FIREBALL. “CHARGES” file has to be at the same directory when you are running
the FIREBALL. To the “fireball.in” we will write:

__&OPTION__ part

‐ nstepf = 1 \\
‐ ifixcharge = 1 \\

__&OUTPUT__ part

‐ iwrtatom = 1

Than you obtained “Atomo_i” files and the “struc.inp” file, which should be
modified to work properly when you run the STM simulation. How to do that:
The “struc.inp” file contains some information about the sample:

1                                 !number. of atoms in unit cell \\
1                                 !initial and final atom which is contributing to the tunneling current \\
12                                ! number maximum of neighbours \\
//!! you have to modify this upper part//

0.000000 0.000000 0.000000 1      ! coordinates and type of each atom \\
. \\
. \\
. \\

//!! Next part (up to the lattice vectors) must be added// \\
4                                 !number of orbitals in each type of atom (in a row) \\
2                                 !number of shells of each atom type (in a row) \\
0 1                               !l of each shell type atom=1 (each atom type in a row) \\
16                                !nkprl: no. of k's in one row (nk=nkprl2), =0 read a samplek.kpts file \\
1 1                               !index_cell1, index_cell2 (ncell = (2*index_cell1+1)*(2*index_cell1+1) \\

0.866025 , 0.5 , 0.               !Horizontal lattice vector (x‐axis) \\
0.866025 , ‐0.5 , 0.              !Horizontal lattice vector (y‐axis) \\
//!! We have to delete the last row of Lattice vector//

The fixing the "nkprl" value to 0 and using the fireball k-points (with the
opposite to complete the Brouilloin) is strongly reccomended.
The "index_cell1" and "index_cell2" are relative to the number of cells we
need in each direction x and y to avoid the border problems. The product of them
gives us number of repetition unit which influence is involved to the
computation.

 \\

=== II.II. tip_sample_i_j.inp file ===


In our approximation, we use a dimer formed by one kind of atom from
the tip and another kind from the sample. We have to generate a
"tip_sample_i_j.inp" (or "interaction_i_j.dat") for each pair of kinds. As we want
interactions for bigger distances than we have in a crystal relaxation, we need to
generate these wave-functions by the **BEGIN** with a cut‐off radius of about 10‐15 au.
When we have the wave‐functions we generate the interactions (Fdata) with
**CREATE**. After that, we run with **FIREBALL** the dimer, mentioned before, for
several distances (normally from 2 au to 20 or 30 au). To obtain the hoppings in
the STM format we need (“fireball.in”):

__&OPTION__ part \\

‐ ifixcharges = 1 \\
‐ nstepf = 1 \\ 

__&OUTPUT__ part \\

‐ iwrthop = 1

To do this, we can use the script “run_hops.com” which is necessary to
modify in dependence what output format you expect (read the “README” file of
this script).

== II.II.I. The “run_hops.com” script: ==

#!/bin/bash \\
#mv -f interactions.dat interactions.dat.old \\
echo 1 > lockfile \\
tipo1="`cat lista`" \\
for i in $tipo1; \\ 
do \\
tipo2="`cat lockfile`" \\
if [ $tipo2 == "2" ]; \\ 
then \\
echo 1 > lockfile\\
name2="`echo $i`"; \\
sed "s/AAAAAAA/$name2/g" tip_sample_aux >> interactions.dat; \\
echo $i \\
else \\
echo 2 > lockfile \\
name1="`echo $i`"; \\
sed "s/AAAAAAA/$name1/g" model.bas > tmp.bas; \\
./fireball.k.x > out_tmp; \\
fi \\
done \\
cat header.dat > interaction_X_Y.dat \\
cat interactions.dat >> interaction_X_Y.dat \\
rm -f lockfile \\
rm -f inter_aux.dat \\
rm -f tip_sample_aux

== II.II.II. The “README” file: ==

a short description how to generate hopping data \\
files we need: \\
fireball.in \\
model.bas \\
lista \\
header.dat \\

=======A. edit: \\
CHARGES \\
model.bas \\

=======B. edit run_hops.com \\
If you need the **fireball output format**, than to the
"interactions.dat" you have to write
the inter_aux.dat \\
If you need the **STM code output format**, than to the
"interactions.dat" you have to write
the tip_sample_aux. \\

The difference is amount of some writen informations at
the header of interaction (hopping) file, number of interactions and even the length units. For
STM format it is a.u. when for the fireball format it is Angstroms.

=======C. launch \\
./run_hop.com \\

=======D. modify header of interacti_X_Y.dat file \\
!*Interactions for W(spd)-C(sp) using FIREBALL program*! \\
57 !number of distances \\
2.00000 30.00000 !dist_min, dist_max \\
10 !number of interactions \\

//In the case you choose the STM output format, don't forget
to remove duplicate (symmetric) interactions
from the "interactions_X_Y.inp" file. You have to write there
even the line of 3 more numbers (2 3 10)
which gives us the number of the shells of the tip and
sample respectively.//

!*Interactions for W(spd)-C(sp) using FIREBALL program*! \\
57 !number of distances \\
2.00000 30.00000 !dist_min, dist_max \\
2 3 10 !number of shells of the tip, of the
sample, number of interactions \\

//If we put the hoppings for all the distances in a file, we will have the basis
for the "tip_sample_i_j.inp" (or "interaction_i_j.dat") files (see the example in the **STM**
code). Then we have to complete the file with the parameters for the long
distances approximation.// \\
Look at the header:

!*Interactions for W‐Tid using FIREBALL program*! \\
57 \\
2.000000 30.00000 \\
3 3 14 \\
0 0 0 ‐21.0000 1.0000 0.5738 1 1 14.5000 \\
0 1 0 95.0000 1.0000 0.5738 1 1 16.5000 \\
. \\
. \\
. \\
where 57 is the number of distance steps, from 2 au to 30 ua. 3 and 3 are
the number of shells for each kind of atom on the tip and the sample respectively.
14 is the total number of interactions for each distance. Finally, the 14 next rows
are related with the long‐range approximation. 0,0,0 means orbital s (0)in the tip
and orbital s (0) in the sample and an interaction sigma (0). Orbitals p will be 1
and d 2, the interaction pi will be 1 and delta 2. \\
For long distances, we do the parallel planes approximation using
the expression: \\
 
A.e<sup>-W.r</sup>

The "A" (4th value in the row) is the independent value we
have to find. "α" (5th value) depends on the orbitals you have in the hoppings, the
expression used is: α=l1+l2+1, but sometimes it could be changed depending on
the fix conditions. The "W" (6th) is related with the work function of the
materials in the hopping: 

W = ((ω<sub>T</sub> + ω<sub>S</sub>) / 2)<sup>1/2</sup>

where ω’s are the work function for
each kind of atom. There is no function as **BEGIN** or **CREATE** to calculate these
long‐distance parameters, but there is a tool in the **XEO** program made by Daniel
Gonzalez. Here you have to change by hand the values of "A" till you “see” (with the
eyes) a coincidence in the value and the derivative. Finally, let’s mention that the
7th and 8th values in the row are related with the simple basis or double basis
case. When you have a double basis you need an extra parameter to differentiate
from the simple basis orbital. \\
The last value is the cut‐off radius.

Here you can download : \\ 
========================. \\
="run_hops.com" script  \\
="README" file \\
========================.

\\

=== II.III. tip_g_str.inp ===

Last thing which we have to do is to write the “tip_g_str.inp” file. This file
contains the geometrical structure of the tip. The xyz atom coordinates should be
written there at the same order as we used for the “tip_e_str.inp” file, with the
apex atom at first position. The file could looks like this: \\

1 5 ! natoms_tip_contributing, natoms_tip \\
0.000000 0.000000 0.400000 1 9 ! x, y, z, atomic type, # of orbitals \\
1.590800 1.590800 1.590800 1 9 ! x, y, z, atomic type, # of orbitals \\
1.590800 ‐1.59080 1.59080 1 9 ! x, y, z, atomic type, # of orbitals \\
‐1.590800 1.59080 1.59080 1 9 ! x, y, z, atomic type, # of orbitals \\
‐1.590800 ‐1.59080 1.59080 1 9 ! x, y, z, atomic type, # of orbitals \\
3 ! number of shells in each type of atom \\
0 1 2 ! l for each shell in atom type=1 \\
‐2.0 4.0 81 ! energy initial, range and steps in dos file \\

// But be carefull, the energy in the STM code is related to the Fermi level. When Fermi level is -2 eV from FIREBALL in the "tip_g_str.inp" in it's last line the first value has to be 0.0 (energy initial - Fermi level)//
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