Tully Model-III (Branching Probability)

This tutorial demonstrates how to calculate the branching probability in the Tully model III with the RPSH method for a range of k-values (initial momentum).

Follow the steps below to perform the simulation.

Prepare Base Input File

Create a base input parameter file base_param.in that specifies the system model parameters. This file serves as the template for all k values.

#tully model-III input parameter
model     tully3
ncore     1
nbeads    8
.
.
pinit     pval
acckval   yes
.
.
.
finish

Note

Ensure that acckval  yes in base_param.in to obtain the branching probability results at each k value.

Run Simulation

Run the provided branching job script job_script_branching.sh.

$ sh job-script-branching.sh

This script will:

  • Create the required number of run* directories based on the k values.

  • Submit and run the simulations inHPC cluster.

  • After all simulations are completed, the script automatically collects the outputs from all directories and combines them.

The final result is pot_branch_all.out for the specified k values.

Note

Make sure to modify the range and increment of k in job_script_branching.sh to match the desired initial momentum values, e.g.:

kmin=5   #minimum k-value
kmax=20  #maximum k-value
dk=0.5   #increment of k

Plot Branching Probability

Use any visualization tool to plot the branching probability results.

The output file pop_branch_all.out has the following structure:

  • First column: k values (initial momentum)

  • Second column: Transmission probability in state 1

  • Third column: Transmission probability in state 2

  • Fourth column: Reflection probability in state 1

  • Fifth column: Reflection probability in state 2

Gnuplot script plot-branch.gnu looks like:

#!/usr/bin/gnuplot
set terminal pdf size 4in,3in enhanced color font 'Helvetica,16'
set border lw 2.5
set tics scale 1.2
set output 'fig-tully3-branch.pdf'
set key  samplen 1.0 spacing 1.3 font "Helvetica, 14"
set multiplot layout 1,1
set xlabel 'k (a.u.)'
set ylabel 'P(k)'
set mytics 2
set ytics 0.2
set xtics 5
set yr[0:1]
ps=0.7
plot 'pop_branch_all.out' u 1:2 w lp lc 2 lw 2 dt 2 pt 7 ps ps t'T1',\
     'pop_branch_all.out' u 1:3 w lp lc 6 lw 2 dt 2 pt 7 ps ps t'T2',\
     'pop_branch_all.out' u 1:4 w lp lc 7 lw 2 dt 2 pt 7 ps ps t'R1',\
     'pop_branch_all.out' u 1:5 w lp lc 4 lw 2 dt 2 pt 7 ps ps t'R2'
Branching probability

Fig. 3 Branching probabilities as a function of the initial k for Tully Model III using RPSH method.