Procedures Automatic Fitting <Prev Next>

Automatic Assignment and Fitting of the ν5 band of cis-1,2 Dichloroethene

This page provides a detailed walk through to accompany “Automatic and semi-automatic assignment and fitting of spectra with PGOPHER”, Colin M Western and Brant E Billinghurst, Physical Chemistry Chemical Physics. It describes the process of assigning and fitting a high resolution (0.001 cm−1) spectrum of the ν5 band of cis-1,2-dichloroethene at 168 cm−1, taken at a temperature of 207 K at the Canadian Light Source. It assumes some familiarity with the basic operation of PGOPHER, as in Walk-through of Simulating and Fitting a Simple Spectrum.  This walk through starts with nu5cooldeglitch.ovr; this file has been edited to remove some strong water absorptions and a baseline. The original file from the spectrometer is available from "High resolution spectra of cis- and trans- 1,2-dichloroethene",  Colin M Western and Brant E Billinghurst, University of Bristol Research Data Repository, doi:10.5523/bris.16lvnq33mt9ea24wclci640zhu.

A. Generating a line list from the experimental spectrum

The first step is to convert the spectrum to a list of line positions and intensities. This can be done with an external tool if required, but the internal tool is described here.

  1. Load original spectrum, nu5cooldeglitch.ovr.
  2. Right click on the overlay and select "Baseline and Peaks...". This brings up a window allowing a baseline algorithm to be chosen, and an automatic peak finder to be run. Tools for zooming and panning are available at the top of the window, and work in the same way as those on the main window. It contains many options, some of which are still under development.
  3. For this walk through we do not attempt to remove the baseline, and simply run a peak finder that looks for local maxima in the spectrum. To see this in action zoom in on a small region of the spectrum so that individual peaks can clearly be seen and ensure "Live Update" is selected. This should yield a display giving something like this in the top half of the window:

    The vertical blue lines indicate the peak positions, and the horizontal bars the peak height found. For this spectrum, which has multiple overlapping peaks "Area" unchecking area gives the best results. Adjusting the "Noise Multiplier" setting changes the threshold for keeping a peak, and larger values will only find the strongest peaks. Note that this also affects the descision as to whether two closely spaced peaks are considered as a single peak. For the current spectrum noise multiplier values values less than 1 probably produce too many spurious peaks at the edges, and values above 1.7 may be discarding too many peaks. For this walk-through we choose a value of 1.3.
  4. Press "Peak Find" to find all the peaks, and "Make New" to generate a line list that will show in the main window.
  5. The resulting line list is saved as nu5coolline.ovr. To save space the raw spectrum has been deleted, though for the later steps it can be helpful to have both spectra available, and peaks missed by the automatic peak finder can be measured manually if needed. (To load two overlays at once drag and drop both files onto the main window, or use "File, Load Overlay..." followed by "File, Add Overlay...".

B. C2H235Cl2

1. Rough Alignment.

The obvious starting point is with the most abundant species. An initial simulation is provided in 3535initial.pgo. This is a standard asymmetric top simulation set up as follows:

  1. Constants for both states were initially set to those determined by a microwave spectrum of the ground state (Leal et al, 1994).
  2. As this is a near prolate top, the rotational constants were converted to use Bbar = ½(B+C) and δ = BC, as the spectrum is relatively insensitive to the latter.
  3. A manual adjustment has been made to the origin, to centre the spectrum in the right place.

2. Setting up the initial search for K'a = 0 lines

Upper state Ka = 0 lines are chosen as a good starting point as these are likely to be among the stronger lines in the spectrum.

  1. For an initial search for K'a = 0 lines open the transitions window ("View", "Transitions") and select:
    1. Upper state Ka as 0
    2. Make sure "Filter" is checked and then select:
    3. "Change" as "<>", which hides the Q branch transitions. (This is probably not essential, but these lines are weaker so less likely to be assigned.)
  2. Pressing "All" in the transitions window will change the main plot to just show the selected lines. The resulting plot shows a regular pattern, much like the classic P and R branch combination of a linear molecule, which will therefore be described by two effective upper state parameters:
  3. When you are happy with the selection displayed click "Add". This will add entries to the line list window for all the transitions selected by the transitions window.
  4. For subsequent operations, it is helpful for these to be sorted by J. In the line list window, select "More", "Sort On", "Upper State".
  5. In the line list window, make sure "More, Advanced" is selected to make the advanced settings visible. Set "Accept" to the maximum error you expect for the "check" transitions - in this case try 0.001, approximately the line width.
  6. Bring up the auto fit window with "Overlays", "Autofit..."
  7. Set "Window" to the search window for the initial fits, i.e. how far each side of the initial line positions you want to search. This should reflect how far out you think the lines might be - try 1 cm−1 here, which is approximately the accuracy with with which the origin can be estimated.
  8. Select the upper state parameters to float in the constants window - in this case Bbar and Origin.
  9. Select a range of lines for the autofit process in the line list window. Two trial fit transitions are required (as we are trying to determine two parameters) and a number of check transitions. These should be lines that you are reasonably confident will be clear in the spectrum. In this case there are many possibilities so try:
    1. Select a range of J, say J' = 10-20 in the line list window by clicking and dragging.
    2. Mark these as check transitions by right clicking and selecting "Mark as Check". A bold C will appear in the "Std Dev" column, and open triangles will indicate their position in the main plot window.
    3. Mark the first and last transitions (pR1,9(9) and pR1,19(19)) as trial fit transitions by click on the individual lines, right clicking and selecting "Mark for Autofit". A bold F will appear in the "Std Dev" column, and filled triangles will indicate their position in the main plot window.
  10. The file at this stage is saved as 3535A.pgo.
  11. Press "Search" in the Auto Fit window. There will be a short delay (a couple of minutes) as the search is done. The file saved immediately after running the fit is available as 3535Aafter.pgo.

3. Using the automatic fit results

  1. When the search is complete, the best fits will be presented in the auto fit window, which lists:
    • nOK - the number of "check" transitions within the "Accept" window
    • Residual - the RMS observed - calculated for these "check" transitions.
    • SumI - the sum of observed intensity for these "check" transitions.
    • The values of the constants obtained for each fit.
    • Trial - The number of the trial. (This is typically only useful for debugging purposes.)
    • nDiff - the number of transitions different to the selected fit. This is only displayed if one of the fits is selected.
    Some additional information is shown in the log window.
  2. The MinCheck setting deserves special consideration, as it determines the trials displayed. The trials are sorted by nOK and then SumI, with the best fit at the top. If MinCheck is not zero this sort order is modified; the intent is that it can indicate how many check transitions are likely not to be found. If it is set to a positive value then the nOK is ignored for sorting, provided it is greater than or equal to MinCheck. A negative value has the same effect, but the threshold is the number of check transitions + MinCheck. The default of -1 implies trials with 0 or 1 unsatisfied check transitions are sorted together. MinCheck can be changed without re-running the autofit, and the displayed trials will update accordingly.
  3. To try out an individual fit, double click on that row. This will update the line list window with all the assignments made by that fit, and update the main plot with a simulation using these parameters. The standard residuals window will also appear with the obs-calc plotted for the assignments made. In the current case the default x axis is observation number, which is not the best choice, as most observations are not assigned. Try changing this to J in the drop down.
  4. To try a different one, double click on that row; all the assignments and parameters will be updated.
  5. The "Reset" button will discard the new assignments and reset the parameters.
The standard PGOPHER fit process can in principle now be used to refine the fit selected, but In the current case the line density is such that just looking at the simulations produced for each trial does not provide any useful discrimination, so a additional diagnostics are required.

3. The nearest lines window

The nearest lines window is invaluable in this case. Set it up as follows.

  1. Bring up this window from the line list window with "More", "Plot Nearest Lines".
  2. Set the "Y Range" to 0.01
At its simplest this window plots, for each line in the line list window, a point for each observed line within the given Y range of that line. If the simulation is perfect, than a clear horizontal line should appear along the centre zero line, together with a typically random set of points either side. An approximately correct simulation should show as curved lines in the spectrum. This plot is also updated when a trial is selected by double clicking. In the current case it very clearly distinguishes between a bad trials (obtained double clicking on the second row in the autofit window):

and a good trial (double click on the top row in the trial window), which shows a clear curve :

To obtain this exact plot "Dim Assigned" has been selected which plots the assigned points in grey. For this case we have been lucky, in that the top sorted trial is also the correct one. The plot indicates that not only are the 21 autofitted transitions well described by the constants selected, but also many of the other Ka = 0 transitions lie on a clear trend, if not necessarily exactly fitted. The file with this fit selected is saved as 3535B.pgo

Assignments can be made directly from this window as follows:
  1. To assign along the curved lines, click and drag with the mouse so that the diagonal line plotted lies along the line, right click and select "Assign On Diagonal":
  2. Repeat as required; if you make a mistake various "Clear Point..." actions are available by right clicking, and work in the same way as the residuals window. (The residuals window will be automatically updated, and it is also possible to fix problems there.)
  3. Press "Fit" in the line list window a couple of times to fit with the new set of assignments. It is clear an additional parameter is required, and in this case as the residuals are still curved, so float upper state BDelta.
  4. This improves the fit, but it is still curved, but so try floating upper state DJ. This gives an almost straight line, with an average residual much less that the line width, so it is probably not worth floating more parameters at this stage.
The file at this stage is saved as 3535C.pgo.

3. The combination differences filter

An additional check on the assignments is possible from the nearest lines window, which is to check for combination differences. This is engaged by checking "CD Filter", and selecting a non zero value in the box to the right. This makes use of the known lower state constants (provided "Upper" is checked) which implies that transition with an upper state in common have a known separation. The plotting algorithm then work as follows:

In the current case the "CD Filter" value needs to be quite small to be effective; something in the range of 1/3 of the line width or less looks good, and eliminates some potential candidates and confirms others. To limit the assignments to those confirmed by combination differences:
  1. Clear all the assignments in the line list window by clicking on the "Std Dev" column heading to select the entire column.
  2. Pressing the delete key to clear all the values.
  3. Press "Test" to refresh the nearest lines window.
  4. Reassign the transitions from the nearest lines window as above.
Refitting fives the file 3535D.pgo.

4. Adding K'a = 1 lines; filtering by state

At this stage we can try adding K'a = 1 lines:

  1. Use the transitions window as above to add K'a = 1 lines to the line list window.
  2. Press "Test" (in the line list window) to update the nearest lines window.
  3. Separating the lines by both J and Ka is useful here; try selecting "Ka+J/n" from the X drop down in the nearest lines window. The x value plotted is K'a+J'/99 in this case; the divisor is chosen to be the maximum J' plotted.
  4. The nearest lines window suggests at first glance that the K'a lines are in the approximately the right place, but zooming out a little indicates two sets of lines:
    These in fact correspond to two different symmetries. You can confirm this by changing the "Labels" drop down to "Symmetry" or, to give a clearer plot:
  5. Select "Filter" in the nearest lines window. If the transitions window is showing, then any selection set up will be applied to the nearest lines window. Here, we want to select by symmetry, and setting the upper state symmetry to O+ or O- will show one or other of the two curves above. This avoids assigning to the wrong class of lines, and is used extensively below.
  6. Both sets of Ka' = 1 lines can be assigned from the nearest lines window, and A determined from the upper state by fitting.
  7. DJK must also be floated to give a good fit. The file at this stage is saved as 3535E.pgo.

5. Completing the fit

Adding Ka' = 2 lines to the line list window as above indicates that these are also in approximately the right place. To speed things up it is worth adding all the lines to the line list window, and use filtering for selection. Try:
  1. In the transitions window, remove all selections, apart from the selection on strength and ΔJ.
  2. Press "Add" to add to add all the lines to the line list. (This adds about 14,000 lines.)
  3. Scrolling through the Ka' values indicates an offset steadily increasing with Ka'. Ka' = 10 looks clear, so try assigning those transitions.
  4. Add DK, deltaK and deltaJ to the fit, and refine the Ka' = 10 assignments.
  5. Repeat with, say, Ka' = 20, which is now showing a small error.
  6. Similarly, repeat with Ka' = 30.
  7. At this stage almost all the lines are in the right place, as shown by the nearest lines window if all filtering is removed:
    To obtain this plot the mark size has been reduced by right clicking on the plot, selecting "Mark Size..." and entering 50.
  8. This shows a mild systematic trend. All the lines near the centre can now be assigned. (Draw a box with the mouse, right click and select "Assign Points Inside". Note that if this corresponds to more than one assignment, the assignment closest to the centre of the box is taken.)
  9. Allowing the sextic centrifugal distortion constants to float removes the remaining systematic error, though phiJK does not seem to be determined.
  10. The simulated spectrum will now show some regions of good agreement, particularly if one of the sub-band heads is chosen:
  11. The other structure is examined below.
The file is saved as 3535F.pgo.The fit yields:
SVD fit: 8937 Observations,  16 Parameters (scaled)
Initial Average Error: 0.00015671996892265
Predicted New Error: 0.00015671996876619
Parameters:
# Old New Std Dev Change/Std Sens Summary Name
1 168.6726199347147 168.6726199356630 6.5669e-6 0.0001 9.79e-7 168.6726199(66) v5 v5 Origin
2 .3863882670187941 .3863882670284609 6.7265e-8 0.0001 3.11e-9 0.386388267(67) v5 v5 A
3 .07699632041933983 .07699632041453160 9.6864e-9 -0.0005 4.5e-10 0.0769963204(97) v5 v5 BBar
4 .01539541616148179 .01539541611604062 2.7760e-8 -0.0016 2.04e-9 0.015395416(28) v5 v5 BDelta
5 1.41648688475879e-6 1.41648685071010e-6 1.503e-10 -0.0002 4.7e-12 1.41649(15)e-6 v5 v5 DK
6 -3.6503095283262e-7 -3.6503087978723e-7 4.834e-11 0.0015 1.6e-12 -3.65031(48)e-7 v5 v5 DJK
7 4.66951341054434e-8 4.66951203872055e-8 4.906e-12 -0.0028 9.9e-14 4.66951(49)e-8 v5 v5 DJ
8 1.01758348183677e-7 1.01757477339539e-7 2.132e-10 -0.0041 9.3e-12 1.0176(21)e-7 v5 v5 deltaK
9 1.15898493061178e-8 1.15898422607635e-8 3.259e-12 -0.0022 9.1e-14 1.15898(33)e-8 v5 v5 deltaJ
10 2.4676894426514e-11 2.4676709534607e-11 1.336e-13 -0.0014 5.8e-15 2.468(13)e-11 v5 v5 HK
11 -8.506523576180e-12 -8.506258452295e-12 1.404e-13 0.0019 2.7e-15 -8.51(14)e-12 v5 v5 HKJ
12 6.0851978998364e-13 6.0845390262616e-13 3.874e-14 -0.0017 5.5e-16 6.08(39)e-13 v5 v5 HJK
13 3.2546543105758e-14 3.2544072150759e-14 7.059e-16 -0.0035 1.7e-17 3.254(71)e-14 v5 v5 HJ
14 9.3287154157998e-12 9.3265923563956e-12 1.093e-12 -0.0019 2.4e-14 9.3(11)e-12 v5 v5 phiK
15 9.1433719046933e-15 8.9794294026524e-15 3.885e-14 -0.0042 1.7e-15 9(39)e-15 v5 v5 phiJK
16 1.6315297574380e-14 1.6314230317462e-14 3.931e-16 -0.0027 1.4e-17 1.631(39)e-14 v5 v5 phiJ

Correlation Matrix
Largest off-diagonal element = 0.980 at 14,12 = v5 v5 phiK, v5 v5 HJK
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
1 1.000
2 -0.651 1.000
3 -0.737 0.241 1.000
4 -0.102 -0.101 0.329 1.000
5 -0.338 0.803 -0.062 -0.149 1.000
6 -0.478 0.626 0.370 -0.060 0.136 1.000
7 -0.423 0.030 0.754 0.495 -0.043 -0.116 1.000
8 -0.027 -0.028 0.096 0.355 0.060 -0.357 0.653 1.000
9 -0.113 -0.108 0.364 0.944 -0.101 -0.182 0.629 0.459 1.000
10 -0.155 0.392 -0.037 -0.029 0.650 -0.178 0.139 0.258 0.055 1.000
11 -0.093 0.221 0.000 -0.112 0.109 0.363 -0.248 -0.353 -0.182 -0.664 1.000
12 -0.096 0.059 0.143 0.112 0.015 0.003 0.258 0.310 0.146 0.679 -0.918 1.000
13 -0.248 -0.037 0.525 0.498 0.001 -0.302 0.935 0.778 0.666 0.267 -0.393 0.353 1.000
14 -0.019 -0.015 0.052 0.105 0.036 -0.165 0.247 0.368 0.157 0.713 -0.952 0.980 0.387 1.000
15 -0.033 -0.035 0.115 0.388 0.053 -0.358 0.661 0.970 0.512 0.314 -0.430 0.384 0.827 0.442 1.000
16 -0.110 -0.105 0.353 0.819 -0.048 -0.281 0.698 0.557 0.946 0.237 -0.387 0.337 0.800 0.369 0.640 1.000

C. C2H235Cl37Cl

The next most abundant species can now be assigned. An initial simulation is provided in 3537initial.pgo. This is set up in much the same way as above, with the exception of the band origin, which is set 2 cm-1 below the origin determined above. For this molecule the PseudoC2v flag is set, as this speeds up the calculation and also avoids problems with state assignments at high J. The analysis then proceeds as above, with some minor differences. Using exactly the same autofit selection as above does produce a successful trial, but at the bottom of the list. (It is trial number 10 if MinCheck is set to 0.) There are a couple of approaches that can be taken to improving fits. Simply changing the two transitions chosen as trial fit transitions makes a big difference:
There is no simple way to predict what is going to work, but it is straightforward to try a few different fit choices. Alternatively, a range can be specified for one or more of the parameters. Not only is this more selective, but this can also speed up the search, as trials are discarded more quickly. In the current case, comparing the difference between ground and excited state constants in the fit above suggests a range of 0.003 cm-1 would be sensible for BBar. To search with this constraint:
  1. If you have not done so already, press the Reset button to discard any current autofit assignments
  2. To limit the range of a particular parameter, set the maximum permitted change (+ or -) as the "Std Dev" for the parameter in the constants window. In this case set "Std Dev" for the excited state BBar to 0.003. Tip: to avoid unexpected constraints, make sure that the standard deviations of all floated parameters are blank before autofitting. (Click on the down arrow in the autofit window and select "Clear Parameter Ranges" to do this.)
A file set up in this way is saved as 3537A.pgo and immediately after running the autofit as 3537Aafter.pgo. For this set up, 28% of the trials are rejected and the correct trial rises to number 7 with nOk = 20.

Given this start, the fit can then proceed as above. The file after assigning Ka' = 1 is available as 3537E.pgo, and the final file as 3537F.pgo. Again the regions around some band heads show a reasonable match, though not as good as above as this is a less abundant species.

D. C2H235Cl2 hot band

The next most prominent band is likely to be the hot band of the 35Cl2 species, i.e. v5=2 ← v5=1, given the low frequency of the ν5 mode (169 cm-1) and the low abundance of the 37Cl2 species. To test this, add a hot band to the 35Cl2 simulation as follows:
  1. Duplicate the v5 manifold (Right click on the upper v5 in the constants window, select "Copy With Linked Items" then right click again and select "Paste". In the rename dialog that is offered, change "v5" to "Copy of v5" and "Ground" to "v5" to give the desired transition moment. To avoid confusion, rename both items in the new manifold to v5=2.)
  2. For the rotational constants, we use a simple linear extrapolation involving v5=0 and v5=1. For the v5=2 origin we use twice the v5=1 value.
  3. To include transitions with v5 = 1 as the lower state, Initial for the v5=1 manifold must be set to true.
  4. This is enough for an initial simulation. To allow the bands to be distinguished set colours on the states, perhaps navy on v5=0 and brown for v5=1. Any colour set elsewhere should be cleared; note that, as described in Determining Colours and J ranges, the lower state colour takes preference. The simulation now confirms the hot bad should indeed have significant intensity:
To prepare the file to fit the hot band:
  1. Clear all the lines in the linelist
  2. Fix all parameters, and clear all the standard deviations.
The file at this stage starting from 3535F.pgo is saved as 3535HotInitial.pgo.

We can now proceed as above, starting with the Ka'=0 lines in the hot band. The only difference is in the transitions window, in that you will have to use one of the State/Manifold drop downs to select the hot band. Interestingly, scanning the offset in the nearset lines window indicates two promising assignments without further adjustment:
You can use the "Y Range" and "Offset" settings to zoom in on these individually; note that the mouse wheel can be used to adjust these. The file at this stage is saved as 3535HotA.pgo.

More detailed investigation of the lower one indicates that it is actually the cold band, and if you assign from this you will generate the same assignments derived above for the cold band, albeit with J shifted by one. (An additional diagnostic is that trying to fit from this does not give transitions below J' = 20.) The upper one is more promising, and just floating the v5=2 origin and BBar gives a good fit for J' = 10-85. (Tip: the offset on the nearest lines window will need resetting to zero after the first fit.) The file at this stage is saved as 3535HotB.pgo.

The process given above then works straightforwardly to generate a final fit with similar quality to the cold bands in 3535HotF.pgo, with promising simulations in regions where both bands are prominent:

For this plot the lines have been made thicker to bring out the colours with "Plot", "Plot Options", "Line Width..." and selecting 2.

E. Other bands

The hot band for C2H235Cl37Cl can be assigned following the procedures above; the initial file is available as 3537HotInitial.pgo and the final file as 3537HotF.pgo.

At this stage some other bands can be considered. The C2H237Cl2 species is probably too weak to see, and an attempt with estimated constants did not suggest any possible assignments, at least using the nearest lines plot. This is not surprising, given that the abundance is 10% of the most abundant isotopologue. Interestingly, setting up estimated constants for the v5=3 ← v5=2 (very) hot band for the C2H235Cl2 species gives a shows a possible assignment in the nearest lines plot for both Ka' = 0 and 1 without a search, and a reasonable fit for this can be obtained. The initial file is available as 3535_3-2initial.pgo, the file with Ka' = 0 and 1assigned as 3535_3-2A.pgo and the final fit as 3535_3-2F.pgo. The corresponding C2H235Cl37Cl band does not seem to be visible.

The appearance of the v5=3 ← v5=2 band, but not the cold C2H237Cl2 species is perhaps surprising, given that both should have similar intensity at this temperature, and some independent confirmation would be in order. A simulation containing all the assigned bands makes sense at this point; this can be achieved by loading one of the files and using "File", "Merge File...". The result after a little tidying up is in nu5.pgo. With a little hunting, a few lines can be found that are entirely from the v5=3 ← v5=2 band, though most of the assigned lines are blends. For example see the orange lines in the centre of the plot. (The black line is the overall simulation.)

For completeness, a file with estimated constants for the C2H237Cl2 cold band and the v5=3 ← v5=2 band for C2H235Cl37Cl is available as nu5tests.pgo.

References.