 Procedures Details

# Widths and Lifetime Effects

Note that while PGOPHER can model complex state dependent widths and related effects, if all that is required is a constant width for all lines, (whether instrumental or molecular) then the Gaussian (Doppler and instrumental effects) and Lorentzian (for lifetime effects) in the main window should be used. (If both of these are set a Voigt profile is used.) These are added to any additional widths set as described below. Note also:
• A state dependent width can make the calculation slower.
• The number of points the spectrum is calculated (nDF) at can have a significant effect on the appearance; increase this parameter until the spectrum does not change. This is because the lineshape is only calculated on the grid points implied by nDF, and misleading results can be obtained if the grid spacing is comparable to the linewidth. In particular, if the width of a peak is less than 3*(Fmax-Fmin)/nDF, then the peak is plotted as a stick, rather than a full lineshape. This can give significant artifacts in the appearance of the spectrum.

## State Dependent Widths

There are two ways of calculating quantum number dependent widths:

1. Custom Width Functions provide a simple empirical way of specifying the width as a formula involving the quantum numbers for the state
2. Each state has a Width parameter which specifies the natural linewidth for that state. Currently symmetric and asymmetric tops have additional parameters (wK, wKa, wKb ...) which can be used to give a rotational state dependence to the widths; alternatively a rotational state dependent width can be modelled for other systems by mixing the state of interest with a state with a non zero Width; PGOPHER will evaluate Σ ci2wi for each state where ci is the coefficient of the wavefunction for each basis state i and wi is the width associated with that (basis) state.

The two methods can be combined; the Result variable in the Custom Width Function is the width calculated by the second method. The significant difference in the two methods is in the handling of approximate quantum numbers. For example, the asymmetric top quantum number Ka is available in both, but will have integer values in method 1, but can have fractional values in method 2.

## The LifeModel setting

The overall width associated with a transition is calculated by adding the width of the upper and lower states in the transition calculated as above. The use made of this calculated width depends on the LifeModel setting at the Simulation level; for some of these an additional parameter is used, RefWidth (also at the Simulation level):

 lmNone Simply ignore the calculated width from the simulation. lmWidth Include width in simulation, but do not scale the peak area. (The normalized lineshape used means that the peak height will scale as 1/Width) lmProductWidth Include width in simulation, and scale peak area as width/(width + RefWidth). This models the case where the result of a predissociation or other process is being detected, with a rate proportional to the given width, so that no width implies zero rate so no signal. In this case RefWidth is a measure of the strength of any competing process. As a special case, A RefWidth of 0 gives a peak area proportional to width. lmProduct Discard width from simulation but scale peak area as width/(width + RefWidth) or just width if RefWidth=0. This will give results the same as lmProductWidth if the molecular widths are rather smaller than the instrumental resolution, but can be rather faster to calculate. lmParentWidth Include width in simulation, and scale peak area as 1/(width + RefWidth). This models the case where predissociation or other process results in loss of the species being detected, so the larger the width (=rate) the smaller the signal. In this case RefWidth is the linewidth in the absence of the loss process. lmParent Discard width from simulation but scale peak area as 1/(width + RefWidth). This will give results the same as lmParentWidth if the molecular widths are rather smaller than the instrumental resolution, but can be rather faster to calculate. lmGateWidth Include width in simulation, and scale peak area as exp(-width * RefWidth). This models detecting fluorescence excited by a short pulse, where the integration (=gate) time is less than the duration of the fluorescence. Only a fraction of the florescence is then detected from states with a long lifetime (and thus small width), so transitions involving these states appear relatively weakly. In this case RefWidth is proportional to the gate width. lmGate Discard width from simulation but scale peak area as exp(-width * RefWidth). This will give results the same as lmGateWidth if the molecular widths are rather smaller than the instrumental resolution, but can be rather faster to calculate.

For all the above convolution with the global width settings ( Gaussian and Lorentzian) is applied after the calculating a lineshape for each transition.