# 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 (ni) 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, di is the degeneracy of mode i and ni 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: q1n1q2n2... n1, n2 should all be >= 0 qSigned Product of normal mode operators: q1n1q2n2... 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(-bqi2) where b is the Exponent parameter above for the mode with non zero ni. More than one ni can be set non-zero, though this is probably not useful. qp Product of normal mode momentum operators: p1n1p2n2... Values of n < 0 are taken as the corresponding position operators. (Not currently implemented for degenerate modes.)