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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 expression 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 "Expression" field of the object. To enter a typical form for a parallel band in a linear molecule (see Watson 1987) use:
Here m is N+1 for an R branch and -N for a P branch. Important Note: the upper state is taken to be the one on the left (Bra) side of the object. To use the form suggested by Watson for a perpendicular band a more complicated form is required:
For linear molecules with S > 0 be aware that the selection rules on Σ are not enforced, so a starting point for a parallel band might be:
This illustrates the use of a conditional expression Sigma'=Sigma", which evaluates to 1 if true and 0 otherwise, thus enforcing the normal ΔΣ = 0 selection rule. Note that Signed must be set to True to use Sigma.


Built In Variables

The value PGOPHER would use if Active were set to false, though see the note about a special case for linear molecules below.
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
Phase', Phase"
Where basis functions are expressed as, for example |J,K> ± |J,-K> for symmetrization, phase gives the relative sign of two parts of wavefunction. It takes values of +1, -1 or 0 where 0 indicates only one part.

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

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

For linear molecules:
The Ω quantum number; note this is evaluated here taking Λ ≥ 0.
Fn The spin component, 1 for F1, 2 for F2, etc.
Note that for versions before 8.0.171 the values were divided by 2.
If Signed is true, then additional variables are available:
Lambda', Lambda"
Λ for the bra (') and ket (") states.
Sigma', Sigma"
Σ for the bra (') and ket (") states.
As a special case for linear molecules, the selection rule normally applied on Σ is not enforced, so for S > 0 it will be necessary set Signed to True and use Value*(Sigma'=Sigma") instead of simply Value to reproduce the calculation PGOPHER would otherwise perform.

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

For vibrating molecules:
v1', v2', ...
Bra vibrational quantum numbers
v1", v2", ...
Ket vibrational quantum numbers
l1', l2', ...
Bra vibrational angular momentum quantum number, for degenerate modes only.
l1", l2", ... Ket vibrational angular momentum quantum number, for degenerate modes only.
Bra electronic orbital angular momentum, Λ'.
Lambda" Ket electronic orbital angular momentum, Λ".
Bra Electronic angular momentum, Ω'.
Omega" Ket Electronic angular momentum, Ω".


Active Set true to use the function provided to calculate the transition moment.
nDebug If non zero, write the values of all the variables and the value of the function on each evaluation to the log window. See debugging for options on the output. To see any output the expression must not be blank - simply set to "Value" to see the defaults in action.
Signed True to apply to unsymmetrized basis functions, as in |J,K> and |J,-K> separately above rather then |J,K> ± |J,-K>.