A significant truncation can be assumed here for the sake of computational brevity. If the symmetry point group goes unchanged, changes to the atomic configuration due to normal mode transitions are non-zero only for symmetric modes . Lin further confirms that only transition participating modes are relevant . In other words, since the Franck-Condon factors decrease as the occupation increase, selection rules can then be applied. This means that the (0,1) transition can be assumed as the only non-zero term in the transition integral. This simplification of course fails for many systems, and should be used carefully. These equations can also be cast in terms of a morse potential rather than a harmonic one, which allows for the treatment of anharmonic effects. In particular, it is derived to tackle -H-type anharmonicity, which has been shown to be very important for high/mid-high energy oscillators . That formalism can be found in Refs. 41, 42, 75, and 43.