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)

Value*(1+A1*m+APR2*m^2+(J'=J")*AQ2*J"*(J"+1))

The expression is used to correct the value of the transition moment matrix element in the basis used, not the transition moment matrix elements after diagonalization.

The function should be written to correct the transition moment matrix element in terms of Value, the value before correction. As this is a matrix element, the intensity will normally vary as the square of the value.

Most standard mathematical forms and functions are available in the expression.

The comparison operators =, <>, >, <, >= and <= evaluate to 1 for true, 0 for false. Note the use in the perpendicular band formula above.

A built in polynomial function, poly, is also available, which may be more convenient if many terms are used; for a quadratic function use poly(x,a0,a1,a2) = a0+a1.x+a2.x^2. Add more coefficients for a higher order polynomial.

In the current initial implementation, the function is given in the Comment field; this will probably change in future versions.

Any unknown variables in the function are automatically created as parameters on simulating, or on right clicking on the node and selecting "Check Variables"

Unwanted variables that are no longer in the expression can be removed by right clicking on the parameter and selecting remove.

' and " are used to indicate quantum numbers for the bra and ket as displayed, respectively. The available quantum numbers are listed below. Note that these are for the basis state, not the final state after diagonalisation.

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

Omega

The Omega quantum number

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.

Custom Transition Moment Functions

Built In Variables

Settings

References

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