Molecule Types Vibrational Structure Vibrational Energy Levels and
Franck-Condon Factors |
Molecule Types Vibrational Structure Vibrational Energy Levels and
Franck-Condon Factors |
<Prev Next> |
This contains the normal mode displacement and mixing for one mode for a pair of electronic states connected by a Multidimensional Franck Condon factor object. In general the normal modes for the two states (Q, Q') are related by the matrix equation:
Q' = JQ + K
where K represents change in equilibrium geometry and J accounts for mixing between modes (The Dushinsky effect). J and K are calculated from the l matrices for the electronic states involved if Calculate is true in the enclosing Multidimensional Franck Condon factor object, in which case the settings below are ignored.
If Calculate is false, then the elements of J and K for are derived from the settings below. Note that the J matrix is expressed as a product of rotations so that, for example, if there are 3 modes then:J = R12(θ12)R13(θ13)R23(θ23)
where R12(θ) is the 2×2 rotation:
| ( |
cos θ | -sin θ | 0 |
) |
|
| R12(θ12)= | ( |
sin θ | cos θ | 0 |
) |
| ( |
0 |
0 |
1 |
) |
The angles θ12, θ13, ... are
the last parameters below.
| Symmetry | Symmetry of this vibrational mode. Note that this setting
is shared with every state in the molecule. |
| Displacement | Displacement along normal mode between the two electronic states; contains one element of the K vector. Only used if Calculate is false in the enclosing Multidimensional Franck Condon factor object. |
| v1 v2 ... |
For mode n, θ1n, θ2n..., the Dushinsky mixing of this mode with the lower numbered normal modes expressed as an angle in degrees. Mode n will have n-1 entries. Only used if Calculate is false in the enclosing Multidimensional Franck Condon factor object. |