Energy

Rotational distribution


Rotational distribution

Clicking Adjust on the iconbar icon, or choosing Rotation... from the iconbar icon menu will open the rotational energy distribution dialogue. This allows the calculation of the rotational level populations of gas phase molecules. The intensities of the absorption lines in the pure rotation spectrum are also simulated.

The rotational energy dialogue is shown below.

There are five writable fields to enter the details of the molecule of interest. The molecular name will be used in the title bar of the graph window when it opens (see below). The masses of the two atoms should be entered in amu. The bond length should be in pm, and the temperature in kelvin.

There is a popup menu button which allows the auto-entry of some example molecular data into the writable fields. These can be adjusted before plotting the graph if so desired.

This part of the program simulates the pure rotational spectrum of a diatomic molecule from data entered by the user. The elementary treatment of the relative intensities of absorption from the various energy levels assumes dependence only on the relative populations of the rotational energy levels. The relative population of rotational energy level J is given by the expression

The rotational constant B is calculated from the data entered and the relative populations of the rotational energy levels (J) are displayed as a bargraph in the lower part of the graph window. In the elementary treatment of the relative intensities of absorption, it is assumed that they depend only on the relative populations of rotational energy levels given by the above expression. However, this does not give good agreement with experiment because of the neglect of a number of factors. Better agreement with experiment is obtained if the relative intensities of absorption from the Jth level are calculated from the equation

where IJ is the relative intensity, and C is a constant.

The program plots a bargraph of the relative intensities as calculated from the second equation in the upper part of the graph window. The difference in the results given by the two expressions is shown as a plot of intensity against rotational energy level J.

The upper bars are calculated using the more accurate expression; the lower bars are derived from the simple expression. The value of J shown is for the rotational level from which absorption occurs.

An example graph is shown below.

Remember that homonuclear diatomic molecules cannot have a dipole moment, and would not therefore show any absorption corresponding to a pure rotational spectrum.

By default, the program does not show an intensity graph when the masses of the two atoms are the same. Only the relative populations of the rotational levels are displayed. However, the test can be overridden if you wish to see the hypothetical intensities. This is set by selecting the option button at the bottom of the dialogue.


At the bottom of the dialogue are three action buttons.

Close

Pressing Close will close the dialogue. If a bargraph is already showing this will also be closed. Any data in the writable fields will be retained for when/if the dialogue is reopened.

Clear

Pressing Clear will simply remove any data that has been entered in to the writable fields, leaving a blank dialogue, ready for the entry of new data.

Graph

Pressing Graph will open a new window showing the details entered in the dialogue in bargraph form. The lower bargraph will show the relative populations of the various rotational levels in the molecule, plotted against J value, while the upper bargraph will show the calculated intensities of the lines in the rotational absorption spectrum, as described above.


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Energy is © Chris Johnson, 2021
Email:chris@chris-johnson.org.uk