Welcome to Wave_Function_Propagation’s documentation!¶

Contents:

WaveFunctionPropagation

Welcome to the very first Manual for the wave function propagtaion module¶

This manual will describe the methodology a user should apply
when using this module. Only then he/she can benefit the best
from what this module can do.

Brief introduction to the module structure¶

The module contains several sub-modules, each one of them
has different functionality that contributes to the upper goal
which is the wave-function propagation.

Here is a short list of module’s sub-modules:

Stage_1.py

Stage_2.py

Locpot_class.py

Help_function_library_yair.py

Structure_vis.py

Main_execution.py

In the following sections, each one of the sub-modules will be described with more details about its capabilities and its role in the bigger work-flow of the wave-function propagation module

Stage_1¶

Stage_1 sub-module was built mainly for performing grid-density
convergence
and for calculating and determining the initial parameters of the
initial wave-function
of an electron occupying the bottom of the conduction band. In this
part, we have to supply the algorithm with the initial total energy of
the electron \(E_0\) in units of Joule.

The user also has to supply the standard deviation, \(\sigma\) , of the gaussian wave-function. The electron initial wave-function is of the form of gaussians wave-packet that centered at \(z_0\). This is the initial position where the most likelihood to find the electron at the initial conditions.

The beginning of operating the complete wave-function propagation the module will always be with extracting the relevant parameters of the initial wave-function.

If the grid-density convergence-test was also required to be taken by the user, it would be performed at that point, at the Stage_1 sub-module calling.

To sum up this section:¶

Stage_1: The importance of extracting the necessary parameters for the electron wave-function such as: \(E_0\), grid-density, \(\sigma\).

These parameters will be given as input for the next step of the algorithm with no dependence whether the grid-density convergence test was held or not. Performing the Convergence test for the grid density. Usually, it will be preferable to converge the simplest system we have. Namely, if we can apply the convergence test to one of the bulk-material systems, it will end with a cheaper computational cost. – All kinds of systems should be undergone a grid-density convergence test: an interface system, slabs (with or without a vacuum), and continuous bulk materials. – None of the changes that will be performed at this level will affect the next steps in the algorithm. It just passes the crucial parameters for the next steps.

Stage_2¶

Stage_2 sub-module may be considered the core and the most
essential part of the entire project. It holds all the practice and logic
of the propagation procedure.
At this level, all the user’s decisions regarding his system have to
be accounted for. The user has to tell the program what kind of system
he has or where the position it should refer to as a reference point
for many types of calculations.
In Stage_2, the user also defines all the operations he would like to
perform. Whether to extend the Locpot vector and in what way to do
so. In addition, there are several functions included in this
sub-module that aim to calculate the necessary quantities and properties
of the system: cumulative probability through the reference point and
even transmission coefficient at that point.
Eventually, this sub-module proposes other two convergence tests that
are:

System size

It stands for achieving the converged system’s length in which the transmission coefficient difference between two consecutive iterations does not surpass 0.01. In addition, it demands energy conservation, thus two successive iterations yield initial total energies that do not deviate in more than 0.01 eV.

Time step convergence test

It stands for achieving the converged time step, dt. It should be a trade-off between accuracy, animation time length, and computer resource cost. For accuracy, we would like it to be the smallest as far as it can be. However, for too small a time step, the animation of the simulation would not display any change since each frame represents negligible changes that cannot be observed. In addition, too small dt’s would end up with an enormous amount of frames and memory for storage.

The importance reflected in the written above should be taken into consideration by the user. This convergence test module is not completed perfectly. Each user has different motives and standards, and reaching convergence can be defined in various ways. Therefore, The user should examine the final dt resulting from this sub-module function and decide if it satisfies his/her demands

Some more capabilities of Stage_2:

Stage_2: > - It enables the elongation of the local potential vector of any form of system. > - It allows to apply of all the parameters describing the wave-function that are found in Stage_1 in the new local potential interface system. > - It allows to propagate the wave-function in time across our system by applying the split-step method. > - It offers the option of creating the simulation animation. > - It can calculate the cumulative probability through the interface position or any other specified reference position. > - System size and time step convergence tests.

Using the Gui for executing some operations¶

First, what it requires to be installed to use: > - python 3.7 and above > - installed packages and modules:

>> - Anaconda

environment: >> - Pymatgen >> - PySimpleGUI

How it looks like :

https://user-images.githubusercontent.com/89647386/167392844-0ce0c6de-7b1e-4a62-b14f-297ef7e56dcf.png

Work-flow: > - Loading the locpot file. If you have an interface, you can load the bulk-materials locpots too. > - Define your system. Do you have an interface? Do you refer to a specific range within your local potential (in cases of vacuum or any slabs form). Pay attention that choosing this will result in popping up another window to supply the range. (It will pop-up after submitting the entire form). > - The next step is choosing whether or not to perform any type of convergence test. Please notice that if you decide not to perform any convergence test, you will be asked to provide the initial conditions manually after submitting the entire form. > - Providing initial parameters for initializing the wave function. > - Choosing the central axis that all the calculations will be referenced. The default is z. > - Last but not least, you can choose what operations you would like to do.