FORTRAT DIAGRAM PDF

Vulrajas This is, in effect, a better approximation to the Morse potential near the potential minimum. This media file is uncategorized. Each line in a vibrational progression will show P- and R- branches. The analysis of vibronic spectra of diatomic molecules provides information concerning both the ground electronic state and the excited electronic state. The vibronic spectra of diatomic molecules in the gas phase also show rotational fine structure. This is true even when the molecule has a zero dipole moment and therefore has no vibration-rotation infrared spectrum or pure rotational microwave spectrum.

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This section walks through the typical steps that might be used for working on a spectrum. The file N2Onu2. Adding a microwave spectrum. Using and fitting to an external JPL line list Fitting to data from multiple sources More advanced fitting - hot bands Band contour Fits Adding custom parameters - the "other" hot band Using HITRAN data Steps 1 to 3 provide a basic introduction, with the following sections introducing more advanced features.

The spectrum provided is at a particularly high resolution spectrum 0. The high resolution arises as the spectrum was taken on the far IR beam line of the Canadian Light Source and was provided by Brant Billinghurst; the file size has actually been reduced by a factor of 4 by averaging over 0. To view selected parts of the spectrum, select the required portion with the mouse and press the zoom to selected button. The other key controls are: Simulate Spectrum Compress plot to show all lines — use this if no spectrum is visible or you are lost Pan plot left or right Compress Plot Expand plot Cycle through various plot styles.

The spectrum shows the the classic P, Q and R branch structure associated with a perpendicular band of a linear molecule: To simulate this, select "File", "New", Linear Molecule". To start with we will just look at the P and R branches and ignore the Q branch the strong central feature.

Saving Files This would be a good point to start saving files. Note that, when saving, the experimental overlay and simulation parameters are saved in separate files. Later on it will contain some assignments. Manual Adjustment of Parameters To adjust the constants the program uses select "View", "Constants" which brings up the Constants Window. The most obvious thing to adjust is the band origin approximately the band centre to place the band in about the right place.

Press the simulate button to update the simulation and use the zoom to selected button to just display the band of interest.

The next obvious thing to adjust is the band type - the default spectrum is missing the central Q branch. This will introduce the Q branch to the spectrum: The strong central Q branch has adjusted the scale so that the features to the left and right almost disappear. This is an artefact of the default parameters, which make the unrealistic assumption that the rotational constants are the same in both states. To investigate try making small adjustments to the B value in the upper state underneath the Origin.

Mouse Adjustment of Parameters This is a good application of the mouse adjust function — right click on B and select Turn on Mouse Adjust, after which the mouse wheel will step the rotational constant.

You can click on different parameters to switch the adjustment to these; the "active" parameter is shown in bold. Hitting "Esc" stops the process and resets the value; using the menu will also stop the process but leave the adjusted value.

This mode can be confusing if left on, so remember to turn it off before the next stage. Assigning and Fitting the Spectrum Estimating the Rotational Constant To improve the simulation requires more precise values of the rotational constants, B, for the upper and lower states. We could legitimately obtain these from the literature or ab initio calculations of the geometry, but for the purposes of the current exercise we will determine them from the spectrum.

Try improving the simulation by manually adjusting B for the upper and lower states. As a tip, the two rotational constants should be about equal, though not exactly to avoid issues with the central Q branch. This dual adjustment is best not done with the mouse adjustment function. The aim of this step is to be able to adjust the simulation until you can make a reasonable guess for the assignments of the lines, i.

This is best started with the low J lines around the band origin. In the current case, setting rotational constants to about 0. Possible assignments are indicated in blue. Line Position Assigning The next step is produce a list of experimental line positions and the quantum numbers for the transition.

When following the steps below, expect to have to make some corrections; the program is designed to make mistakes easy to detect and correct. Right click on one of the peaks in the simulated lower spectrum that you think you can assign. A Line List Window will appear: You will normally want to arrange the windows so that the simulation and the line list do not overlap. Selecting View, Arrange Windows from the main menu may help. All the lines close to the mouse within a few pixels on the screen will be shown selected, which will often catch more than one rotational transition.

The intensity of the individual transitions shown under Strength is normally enough to indicate if you have a sensible selection of lines. The next step will ignore the weaker lines, or you can adjust the selected lines with the mouse.

You can delete the unwanted transitions by selecting the required rows with the mouse and pressing the delete button,. Measure the corresponding peak in the experimental spectrum by dragging the across the peak with the right mouse button. Press and hold with the right mouse button to the left of the peak, drag the mouse to the right of the peak, and release. The peak position will be determined from the spectrum and a marker indicating the determined position will be displayed.

Note: The exact positions you click and release on in the experimental spectrum is not important, provided you do not include any other peak in the range. For closely spaced peaks you may need to try more than once, possibly expanding the scale. If Auto is off press the Assign button to do this manually.

Repeat steps 1 to 4 to assign a few more peaks. To check that you have the correct assignments, press the "Test" button. The program will read and plot your assignments: The observed and calculated values are joined with lines above the experimental spectrum. The upper end of the line is the experimental frequency, and the lower end is the calculated frequency.

When the fit is perfect, these will appear as small vertical tick marks. At this stage the lines will probably be sloping, but it is normally obvious if you have miss-assigned something.

Positioning the mouse over the top of one of the marks will show the number in the line list of the assignment in the status bar below the simulation. Right click on the mark to show the row containing the experimental line position in the line list window.

If you enter the assignments indicated in the picture above, the "Test" button should give a picture like this: It is easy to miss-assign peaks, and wrongly assigned peaks can distort the subsequent fit quite badly An error might give a plot such as: To correct an assignment, select the corresponding rows s with the mouse and either: Delete those rows with the delete button Re-measure the peaks as in step 5 by dragging across the peak with the right mouse button.

Manually edit the values in the grid. You can temporarily remove an observation by setting the "Std Dev" to zero. Note that the assignments are saved in the. Line Position Fitting Given a reasonable number of assigned peaks you can perform a fit. At this stage only a few assignments are needed, and the fitting process will start by only trying to determine correspondingly few parameters.

Select the parameters you want to float by going to the constants window View, Constants and set "Float" to "yes" by each of the parameters you want to float, by clicking on "no". At this stage appropriate constants to float are the upper and lower state rotational constants, B and the origin of the upper state. Click Fit in the line list window.

A list of observed and calculated transition frequencies, the average overall error, new values for the constants and estimates for their uncertainties and a correlation matrix will be displayed in the log window View, Log though this will normally show automatically.

You will normally want to arrange your desktop so that the simulation, line list and log windows do not overlap. For more details on the values displayed, see the documentation for the log window. A plot of the residuals before the fit will be shown in the residuals window. This is normally shown automatically, or use View, Residuals. The main window will show an updated simulation. If the results look reasonable, then press the "Fit" button in the line list window, not the log window repeatedly until the error converges.

Note that the residuals and calculated positions displayed are the values before the fit, rather than after. If the fit does not look good, the Undo Fit button in the log or line list window; this will step constants back one fit cycle for each press. Use this and consider: If you floated too many or the wrong parameters toggle float as in step 2 and try again If you have some miss-assignments, see the previous section for correcting them. If you are uncertain about some transitions - perhaps they have poor signal to noise, or are blends of more than one line - consider increasing the estimated relative error of the peak.

This is the "Std Dev" column; the defaut is 1, but values of are sensible for less clear lines. Zero or negative values exclude the peak from the fit entirely. Complete the fit by measuring up all the P and R branch lines, or at least a reasonable selection of them.

For further refinements of the fit the residuals window is most useful. With all the P and R branch lines in it should look something like this: Note the choice of x axis made here the drop down in the top middle.

The default is observation number, but the J has been chosen for the plot above. There is clearly a systematic trend in the residuals - perhaps the centrifugal distortion constant, D, should be floated?

Floating both the upper and lower state D does indeed improve the fit, but reveals a couple of lines are fitting particularly poorly: This is with my measurements - yours may well look different. For best results the plot should be on quite an expanded scale - if "Show Transition" has just been used the expand plot button will expand the plot about the transition of interest. With the transition indicated with the arrow above, the plot looks something like this: It is clear from the top mark that I have been careless in measuring this particular transition.

To remeasure, right click on the transition in the residuals window again, but this time select "Edit Point". This selects the transition in the line list window, and it can be measured again by right clicking and dragging on the experimental spectrum. Repeating this for the any other poorly fitting transitions and re-fitting should yield a random set of residuals, which is a sign of a good fit: The file at this stage is available as N2Ostage2.

At this stage you could also consider trying to determine H, but the residuals plot suggests it will not be determined, and indeed floating the upper and lower state H does not reduce the overall error, and the estimated errors in H are larger than the values determined.

Try fits with and without. Tools for understanding the spectrum Various tools are available to understand the simulated spectrum and the underlying pattern of energy levels. Right clicking on an individual line will give the quantum numbers associated with the line or the strongest lines close to where you click if there is more than one.

The information is expressed in more than one way; on the left hand side are the quantum numbers always used internally, with extra information on the right hand side. For a complete list see the line list window documentation. The Fortrat Diagram The overall pattern can also be understood by turning on the Fortrat plot with the Fortrat button.

The resulting plot has the same horizontal axis as the main plot, but J as the vertical axis. This allows individual branches to be picked out.

A symbol is plotted for each transition, and the size of the symbol proportional to the intensity: The Q Branch To finish the fit, we need to fit the central Q branch also.

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