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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:

## State Dependent Widths

## 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):

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

There are two ways of calculating quantum number dependent
widths:

- Custom Width Functions provide a simple empirical way of specifying the width as a formula involving the quantum numbers for the state
- 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 c
_{i}^{2}w_{i}for each state where c_{i}is the coefficient of the wavefunction for each basis state i and w_{i}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
*K _{a}* is available in both, but will have integer
values in method 1, but can have fractional values in method 2.

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. |