Molecule Types Linear Molecules Transition Moments | <Prev Next> |

This transition moment must be
used for multiphoton or Raman
transitions. It is also appropriate for single photon transitions
classified as parallel or perpendicular, as noted below. For
linear molecules the "Strength" number is the value of the
vibronic only matrix element:

T(k,q) = <stateA, Λ+q| μ | stateB,
Λ>

where k is the "Rank" and
q the "Component" setting,
normally chosen to be >= 0. The corresponding matrix element:T(k,-q) = <stateA, -Λ-q| μ | stateB,
-Λ>

is then computed by symmetry. The
order of the states (which can be significant in cases involving
multiple transition moments) is as displayed in the constants
window. Strictly all the above matrix elements should have
selection rules Δ*S* = 0 (and ΔΣ = 0 for
linear molecules), but as an extension PGOPHER relaxes this requirement for Δ*S*
≠ 0 transitions and only enforces the |ΔΩ| = q rule. See the section on Forbidden Transitions in Linear Molecules
for a more detailed discussion of this. See also Forbidden Transition Moment.
## Relationship to other quantities.

##

For an electronic transition, this is the product of the square
of the electronic transition moment and the Franck-Condon
factor. While expressed in spherical tensor form above, the
transformation to Cartesian components is straightforward for
the normal electric dipole transitions, which have the rank 1.
The *q* = 0 component is simply the *z* matrix
element between the states. The *q* = 1 component is
strictly the matrix element of the complex operator 2^{-1/2}(μ_{x}+*i*μ_{y})
between wavefunctions with values of Λ differing by one,
but it can be shown to be the same as the matrix elements of the
μ_{x} or μ_{y} operator
between electronic states that transform as *x* or *y*.
The latter will typically be produced by electronic structure
calculations, so no conversion is necessary though the matrix
elements calculated are not formally identical.

Rank | Rank of transition: 1 for a normal electric dipole transition; see here for multiphoton or Raman transitions |

Component | Projection quantum number of transition moment. The
default is auto,
which for simple cases implies taking the only value of the
component which
gives an allowed transitions. In the standard one photon
case it will be 0 for a parallel transition and 1 for a
perpendicular transition. For more complicated cases auto will not work
and the component must be specified. |

Strength | Transition (dipole) moment. For one photon transitions this has units of Debye. Note that the relative intensity is proportional to the square of this value. |