Line Position Fitting

This is the preferred method of determining constants from an experimental spectrum, and can be used when lines are reasonably well resolved. Where this is not the case it may be possible to do contour fitting, but note that this may not give good results.

The procedure described here works best using a mouse; it is possible with a trackpad or other pointing device, but a little fiddly. Where right click is required, mac users will probably want to use Ctrl+Normal Click which is equivalent to right click for a single button mouse or trackpad.

Overlay the experimental spectrum over the PGOPHER simulation. Note that for the process described here, peaks in the experimental spectrum should be pointing upwards, rather than downwards as is sometimes used for absorption spectra. If the experimental spectrum is plotted separately you can right click on the experimental spectrum and select invert or otherwise select Overlays, Invert from the main menu.

Drag the simulation and/or manually adjust the constants so that you can match at least some peaks between the two spectra. The assignment process works best if you start with low J transitions near the band origin. To adjust constants open the constants window which allows typing in values or adjusting them with the mouse.

Right click on a peak that can be assigned to a peak in the experimental spectrum. 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 as above. 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

. Note you can adjust that the settings controlling the number of peak displayed and assigned from the Line List Options Window.)

Measure the corresponding peak in the experimental spectrum by dragging the across the peak with the right mouse button. (Press 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 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.
You can remove the markers from the simulation from the Overlays menu - select "Delete Last Peak" or "Clear All Peaks" as required.

Provided Auto is selected in the line list window, the "Position" column in the line window of the selected rows will change to that of the experimental peak and the “Std Dev” will be set to 1 to indicate a measured, rather than a calculated frequency. (If Auto is off press the Assign button to do this manually.)

Repeat steps 3 to 6 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 misassigned 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.

It is easy to misassign peaks, and wrongly assigned peaks can distort the fit quite badly. 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.

Given a reasonable number of assigned peaks you can perform a fit. 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. Notes:

You can change between "no" to "yes" by clicking on the cell, or simply enter "y" or "n".
It is important to float a small number of parameters to start with - say only the most significant ones such as the origin, spin orbit coupling constant, A, (if appropriate) and rotational constant, B.

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 (unless you have AutoReplot turned off, in which case you will need to press the "Simulate" button).
If you used an offset on the simulated spectrum you will probably need to reset the offset to zero after the first fit.

If the results look reasonable, then press "Fit" 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 window will step constants back one fit cycle for each press

If you go too far, the Redo Fit button in the log window will step the constants forward one fit cycle.
To correct assignments, see step 9.

Complete the fit by repeating from step 3, adding more peaks to the line list and floating more parameters.

A complete report on the fit can be obtained from the Log window:

Clear the log window with the clear button
Press the "fit" button in the line list window
In the log window the copy button: will copy the report to the clipboard, or alternatively use the save as button to save the log to a file.

The contents of the line list window are normally saved to, and loaded from, the .pgo file, though it is more flexible to save the assignments to a separate file. See the next section for how to do this.

Common Problems

You can't float more parameters than you have observations. (The program will handle the case when you have equal numbers.)

You can only float parameters which depend on the observations you have given; if they do not, or there is very little information available, the constants and their errors will become very large. PGOPHER now uses singular value decomposition which can often detect this sort of problem, and indicate the problematic combinations of parameters in the log window; this is controlled by SVDThresh. A "Singular Matrix" error message can also arise from this sort of issue.

The error message "Overflow in Boltzmann for...". This often simply reflects a problem with the assignments or floating too many parameters - use "Undo Fit" and adjust as above. It can reflect a deeper problem with the calculation, and is discussed in more detail under J Range and Partition Functions; possible quick fixes include setting IntensityUnits to "Arbitrary" while fitting or limiting the J range of the simulation as described in Determining Colours and J ranges. ("Arbitrary" is not recommended for general use, as it can give very misleading relative intensities in simulations.)

If the fit does not converge, or converges slowly, it is worth checking and adjusting the increment, the step size used for working out the numerical derivatives which are used in the fitting process. A good guide for the increment for a parameter is the standard deviation of the parameter; the Fix button in the constants window allows all the step sizes to be set to a fraction that you choose of the standard deviation. The numerical derivatives can be checked by selecting Check Derivatives from the pop-up menu provided from the down arrow button

next to the fit button. All the values in the "Deriv Diff" column should be much less than 1.

Line lists in separate files

It is normally more flexible to work with assigned lines in an external file for larger fits as only limited editing is possible in the line list window. External files are text files, normally with a .lin or .obs extension, and will accept a wide variety of directives and formats in addition to the line list as displayed in the line window. Directives allow more control over the fit; for example, a "stop" directive will cause the rest of the file to be ignored, allowing fits to part of the data, and a "Units" directive allows the units to be set for the following lines allowing, say, data from microwave and infra-red spectra to be combined. For more details see Combined and Multi-State Fits and the Line List Input File Format. A custom text editor, the Tabslave Editor, is distributed with PGOPHER which has been specially designed for editing these files. See Fitting example - the A-X transition in C3 for a worked example in line position fitting involving two overlapping transitions, which demonstrates the process, and why it might be useful. The procedure below describes how to generate a basic version of the file from the line list window.

To set the file:

Either:

Press

and select "Save to File" to save the current line list to a file. Any of the formats presented will work in simple cases; see the discussion in Multiple State Fitting example - the A-X transition in C3 for more information on the possibilities. Use "Branch" or "Simple" format for straightforward applications.

or (to set a previously generated file):

Go to the log window(View, Log).
Press the button and browse to the file (or where you would like the file to be created). This will put the file name in the observations file name window. (The file name should typically end in .lin or .obs).
Press the Edit Button . If the file does not exist you will be asked if you want to create it. If the Slave Editor is set up correctly, this should start.

To add observations to the file:

Use "More, Copy Branch Table", "More, Copy Simple Format" or the copy button(

in the line list window)to put your assignments onto the clipboard. These produce different text formats, and one of the first two is likely to be easier to work with.

Paste the assignments into your observations (.lin) file, and save it.

To use this file, rather than lines in the line position window:

Use the Fit Button

in the log window, rather than the line list window. If the Slave Editor is in use, then the contents of all slave editors are saved before starting the fit. Note that if a slave editor is unable to save a file that has been modified then the fit will not start and the slave window will come to the front or flash.

Assignments are best added to the external file by copying and pasting from the line list window.