Contour fitting allows fitting the overall
shape of an experimental spectrum to a simulation, and is useful
for low resolution spectra in which the rotational structure is
not fully resolved. It is also appropriate for determining
temperature or population distribution for a known band. Note that
the results from this sort of fit are typically less reliable than
for a line position fit
, and a line
position fit is to be preferred to determine rotational constants.
- To start a contour fit, Overlay the
experimental spectrum over the PGOPHER simulation. The
initial match must be quite good for a contour fit to work - a
contour fit will typically not move a peak more than the peak
width, for example. The simulation must account for all the
significant features in the spectrum; if, for example, there are
nearby bands that you have not included you should remove the
appropriate frequency range from the experimental data. The Crop
command described in the Experimental Overlay
section may help with this.
- It is easier to work if the intensity units of both the
overall overlay, and the specific overlay(s) to be floated are
set to "Normalised",
rather than arbitrary. Go to the overlays
window (View, Overlays), click on the topmost item and
ensure that "IntensityUnits"
are set to "Normalized".
Click on the specific overlay and check the same setting. After
doing this the "Baseline"
and "Scale" will
typically need to be adjusted manually for a reasonable match
with the simulated spectra as the vertical autoscaling is now
- Open the constants window
(View, Constants) and click on "Fix", "Fix All
Parameters" and select "Mixture" to ensure
that no molecular constants are floated to start with.
- The first parameters to be floated must be the scale and
baseline of the overlayed spectrum. Go to the overlays window (View, Overlays),
select the overlay required (probably the first one unless you
have more than one experimental spectrum overlaid) and float
these two parameters (click in the float column so it reads
- (Optional step) If the required "Scale" is several orders of magnitude
different from one, consider scaling the original data to avoid
problems with the fitting process later. "Operate", "Scale"
provides a command to do this for numerical data.
- Bring up the log window by
selecting (View, Log) and choose "Contour" as the fit type in the top left.
On pressing the "Fit"
button a separate plot showing the obs-calc (difference between
the experimental spectrum and the simulation) is shown in the
main window (see below for an example), along with the
simulation. The log window now shows new values for the floated
parameters and their errors, the average error, and a
correlation matrix. The error will typically be very large at
- Press the "Fit"
button repeatedly, until the average error is as low as
possible, and a simulation that roughly matches the experimental
spectrum is shown. If you have problems you may have to fix some
of the parameters and try manually changing them.
- To further improve the fit, start floating molecular
parameters. Floating many parameters simultaneously will often
cause the fit to make wild changes in some of the parameters
unless the fit is very good. For best results float additional
parameters one or two at a time, starting with the most
important. The Undo Fit button allows you go back to previous
fits, if you find you have gone too far from a reasonable fit.
For example, the excited state origin might be the first
molecular constant to float (“View”,
“Constants”, and click on the “no” next
to the constant to change it to yes.). Again, press
“Contour fit” repeatedly until the error reaches a
minimum, and converges.
- Other parameters to consider are A or B
rotational constants, the linewidth and rotational temperature.
Eventually, the simulation should closely resemble the
experimental spectrum, and the obs-calc will be much smaller.
The log window will show details of the fit,
including estimated standard deviations of the parameters. The
standard deviations are calculated using the standard methods
for least squares fitting, using derivatives estimated with
numerical differences, but experience with contour fitting
indicates that the error bars on the parameters are typically
too small, and the most reliable estimates of the error are
obtained by comparing the results of fits to different data