Molecule Types Vibrational Structure Vibrational Energy Levels and Franck-Condon Factors

Vibrational Perturbation

Add one one these items for every extra term required in the Hamiltonian. To see the actual matrix elements used in any particular case, right click on the perturbation and select "Matrix Elements". The resulting expressions will be displayed in the log window, and should be understood as being multiplied by the Value parameter.

Settings

`Nucleus`	Not used
`SymSelect`	Symmetry select
`ScalePrev`	Scale factor with respect to preceding perturbation
`Op`	Type of perturbation: x, q, qSigned, Gaussian. See below for details
`EffectiveQno`	Set to group together states connected by this perturbation when assigning quantum numbers.
`FromForceField`	If true value is set from the "Other Potential Terms" specified in the internal coordinates or symmetry coordinates objects. If not set up in these objects, the value is forced to zero.
`v1`	One entry per mode; power of each mode (n_i) in the overall perturbation operator
`v2`
`...`

Parameters

`Value`	Size of perturbation; the expressions and operators given here should be understood to be multiplied by this.
`Exponent`	Exponent for Gaussian type perturbation

Perturbation Types

In the formulae below, d_i is the degeneracy of mode i and n_i is the vi setting, as above.

x	Simple diagonal matrix elements with value: (v₁+d₁/2)^n₁(v₂+d₂/2)^n₂... For example to add a conventional x₁₂ term set Op = x, v1 = 1, v2 = 1.
q	Product of normal mode operators: q₁^n₁q₂^n₂... n₁, n₂ should all be >= 0
qSigned	Product of normal mode operators: q₁^n₁q₂^n₂... with the additional selection rule that: Δv₁ = n₁, Δv₂ = n₂, ... or Δv₁ = -n₁, Δv₂ = -n₂, ... In this case the signs of n₁, n₂... are important.
Gaussian	Matrix element of exp(-bq_i²) where b is the Exponent parameter above for the mode with non zero n_i. More than one n_i can be set non-zero, though this is probably not useful.
`qp`	Product of normal mode momentum operators: p₁^n₁p₂^n₂... Values of n < 0 are taken as the corresponding position operators. (Not currently implemented for degenerate modes.)