Objects Mixture Species Molecule Manifold | <Prev Next> |

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:

Notes:

- 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;
see expressions for more
information.

- 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)`=*a*_{0}+*a*_{1}.*x*+*a*_{2}.*x*^{2}. Add more coefficients for a higher order polynomial. A Table object may also be useful.

- The function is held in the comment field for the object; in the constants window an enlarged text window replaces the normal comments window. (If you want to add comments to the function use # or // to start the comment, or enclose it in {...} or /* ... */.)
- 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.

Value |
The value PGOPHER
would use if Active
were set to false, though see the note about a special case
for linear molecules below. |

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 |

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

For linear molecules:

Omega |
The Ω quantum number; note this is evaluated here taking Λ ≥ 0. |

Fn | The spin component, 1 for F_{1},
2 for F_{2}, etc.Note that for versions before 8.0.171 the values were divided by 2. |

Lambda', Lambda" |
Λ for the bra (') and ket (") states. |

Sigma', Sigma" |
Σ for the bra (') and ket (") states. |

For symmetric tops:

K |
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. |

Lambda' |
Bra electronic orbital angular momentum, Λ'. |

Lambda" |
Ket electronic orbital angular momentum, Λ". |

Omega' |
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>. |

- "Quadratic Herman-Wallis factors in the fundamental bands of
linear molecules", J K G Watson, J Mol Spec,
**125**428 (1987).