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Custom Transition Moment Functions

To allow for a variation in the vibronic transition dipole moment with rotational state, commonly described in terms of Herman-Wallis factors, an arbitrary function can be associated with any Transition Moment object. To do this, create a Custom Transition Function under the transition moment of interest (right click on the transition moment, select "Add New" and then "Custom Transition Function") and enter the required expression in the "Comment" field of the object. To enter a typical form for a parallel band in a linear molecule (see Watson 1987) use:
Value*(1+A1*m+A2*m^2)
Here m is N+1 for an R branch and -N for a P branch. To use the form suggested by Watson for a perpendicular band a more complicated form is required:
Value*(1+A1*m+APR2*m^2+(J'=J")*AQ2*J"*(J"+1))
Notes:

Built In Variables

Value
The value PGOPHER would use if Active were set to false
m
N+1 for an R branch and -N for a P branch. 0 for a Q branch.
J', J"
J values for the states involved
N', N" N values for the states involved
F', F" F values for the states involved

Additional quantum numbers are also available, depending on the molecule type. As for the variables listed above, use ' and " to indicate bra and ket quantum numbers respectively.

For asymmetric tops the standard quantum numbers Ka and Kc are available.

For linear molecules:
Omega
The Omega quantum number
Fn The spin component, 1 for F1, 2 for F2, etc.

For symmetric tops:
K
The absolute value of K
Kl The sign of Kl

Settings

Active Set true to use the function provided to calculate the population

References