Wavefunc

Contents

Introduction

This application demonstrates the form of the wave functions for the first ten vibrational levels (numbered 0-9) of a two atom harmonic oscillator. The wavefunctions for up to three different vibrational levels can be overplotted for comparison. Instead of the wave functions, you can instead elect to plot the square of the wave functions, which can be taken as being equivalent to the probability of finding the system in that particular state.

In electronic spectroscopy, the intensity of vibrational component bands in an electronic transition is proportional to the overlap of the wave functions of the initial and final state. The third option gives a simple demonstration of this, in that the squares of the wave functions for two vibrational levels, and the overlap are plotted. Since the equilibrium bond extensions are often different in the two electronic states, there is also the option to offset the equilibrium position for the second vibrational level.

Users are reminded that real molecules are not harmonic oscillators, but the general principles demonstrated here are equally valid for the anharmonic oscillator.

Installation

Simply drag and drop the Wavefunc application into the directory of your choice.

Usage

The application can be started from within the desktop by double clicking on the !WaveFunc icon in a directory viewer, when it will be installed on the iconbar.

On clicking with SELECT on the iconbar icon, the input window will be opened, into which you can enter your chosen parameters. When you are satisfied with your parameters, you may then plot the graph, which can show for comparison the wave functions for up to three different vibrational levels (in the range 0 - 9).

The input window

At the top are three buttons used to select the type of graph to be plotted (wave function, wave function squared, or a demonstration of the Franck-Condon overlap).

Below these are three writable fields into which you can enter the vibrational levels to be plotted. If you only wish to compare two levels, then simply leave the third level blank. There are also bump arrows that may be used to set the levels. Since a blank entry is valid, meaning Don't plot this level, then if you use the down adjuster when the field is showing 0, the field is cleared. Conversely, clicking the up adjuster when the field is blank will place 0 into the field. You can use any value in the range 0 - 9 for the vibrational levels.

Franck-Condon overlap
If you have chosen to plot the Franck-Condon overlap then the third vibrational level will be shaded and unavailable, and the r_e offset will now be available. This is used to shift the equilibrium position of one vibrational level with respect to the other. This allows one to simulate situations in e.g. an electronic transition where the equilibrium bond lengths in the two electronic states are different (a common occurence).

The Plot button will display a graph using the parameters entered, while the Clear button will clear all the values.

The graph window

The graph (an example is shown on the right) is a simple plot of the function selected, with up to three lines overlaid, corresponding to the three vibrational levels, or two levels and the Franck-Condon overlap.

The graph window menu

This has only three items.

To MultiPlot

This option will bypass the "Save as" dialogue, and attempt to load the current graph directly into !MultiPlot. If !MultiPlot is not running, then WaveFunc will complain. Depending on the settings in 'Choices', the data exported will either be added to the graph that !MultiPlot is currently displaying or a new graph will be created. See the help notes for !Multiplot for further information on the display of multiple graphs. Transfer to MultiPlot will allow much more customisation of the appearance of the graph, perhaps for presentation purposes.

Save as

This allows, via a submenu, two ways to save the graph by drag and drop, either as a CSV file, or as a MultiPlot file.

Help...

Opens the HTML help files (which you are currently viewing) in a browser.

The iconbar menu

Info

Following the submenu arrow raises a standard information window, including the version number and date of issue. This is the information that should be quoted in any communication regarding the application. The information window also contains a button labelled Web site. Clicking this button will attempt to connect to the download site, launching a browser if necessary, where the latest version should be available.

Help...

Opens the HTML help files (which you are currently viewing) in a browser.

Choices...

This allows certain aspects of the graph to be set. The outline font and font size used to label the graph may be set. The colour of the lines plotted on the graph may be chosen from the standard desktop colours. The line segments controls how closely the lines plotted approximate to a curve (plotted as a number of straight line segments). The maximum allowed is 200.

Finally, you can choose how the data is passed to Multiplot. It can be sent either as lines or as points. Finally, if Multiplot is showing a graph, you can choose whether to add the new data to it, or create a new graph.

Set will apply the settings to the current session, while Save will apply the settings and store them so they are reloaded when !WaveFunc is run on a subsequent occasion.

Quit

This simply terminates !WaveFunc and removes the icon from the iconbar.

Contact

All communication about WaveFunc should be directed to Chris Johnson (Email:chris@chris-johnson.org.uk). Suggestions for new features are always welcome.

Web sites

Chris Johnson's web site is at http://www.chris-johnson.org.uk/index.html, with his RISC OS software at http://www.chris-johnson.org.uk/software/index.html.

MultiPlot can be downloaded from there if you do not already have it.