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This page covers both Raman transitions and multiphoton transitions, as similar settings are used for both. The key is the use of spherical tensor notation, as commonly used for multiphoton transitions. Normal Raman spectroscopy uses two photons, and this has the same selection rules as two photon transitions. For both of these you must specify a Rank and a Component, which PGOPHER labels overall as T(Rank, Component). For two photon and Raman transitions possible values for Rank are 0, 1 (often weak or absent) and 2; in general the highest rank is the number of photons involved. For each Rank, k, there will be 2k+1 components from -k to +k. It is common to need more than one of these to simulate a given transition, as in the one photon case where more than one Cartesian component of the transition moment may be required for asymmetric tops. Note also that for asymmetric tops the different signs of the components have a special meaning and correspond to different transition moments as defined here and you will need to choose the right one (or possibly both will be required).

For a linear molecule the following components might be expected to contribute to a two photon transition:

Σ-Σ | T(0,0) (normally dominant) and T(2,0) |

Σ-Π | T(2,1) |

Π-Π | T(0,0) (normally dominant),
T(2,0) and T(2,2) |

Σ-Δ | T(2,2) |

The general selection rule for the component, q, is |q| = |Λ'-Λ"| or |q| = Λ'+Λ".

For an example in symmetric tops using two transition moments simultaneously see The 2+1 multiphoton ionization spectrum of the C'-X transition in NHRaman and multiphoton spectra are
always plotted against difference in state energy, as for normal
transitions, so changing the type of transition does not change
the region in which the simulation appears. When overlaying
spectra on such simulations I suggest adjusting the scale on the
experimental spectrum to account for this, which can typically be
done via the FrequencyOffset
or FrequencyScale
settings of an overlay. For example a transition with a band
origin at 40000 cm^{-1} will appear at 20000 cm^{-1}
in a two photon transition. When overlaying a two photon spectrum
with a scale in cm^{-1} a FrequencyScale of 2 will shift the
experimental spectrum to the equivalent two photon energy. (Use
0.5 for a spectrum against vacuum wavelength; for a spectrum
against air wavelength use the "Convert Units" button in the
overlay window to switch to a unit that is linear in energy.)