The concept of working with branches
Assignment procedures of the LWW program are based on working with branches which are sets of transitions with just one rotational quantum number changing and the remaining ones kept fixed. In our case, a spectral branch is to be understood as a series of transitions with the total angular momentum quantum number J being increased by 1 between two subsequent members of this series. All other quantum numbers (vibrational and rotational) of both lower and upper states remain the unchanged in one spectral branch. These remaining fixed QN, common to the whole branch, are the lower/upper state {K, l} in case of symmetric top molecules or {Ka, Kc} in case of asymmetric top molecules. The difference between these {QN} in the lower and the upper state is also given by the dipole moment selection rules.
The idea of making the spectral branches logical units of assignment procedures is used because in a spectrum without resonances the transition wavenumbers in each such branch series are smooth, continuous functions of the J quantum number. In a graphical representation of the spectrum (e.g. the Loomis-Wood diagram), these series form visually recognizable patterns among other spectral peaks that do not belong the particular branch. Once several transitions in the branch are assigned and aligned, further assignments can be propagated following the continuous branch pattern.
This first assumption of continuous branch patterns enables a significant acceleration of routine assignment procedures in spectra, where an experienced inspection can be followed by more or less straightforward assignments. But the main advantage of the current LWW program will show itself in analyses of congested and/or perturbed spectra. In that case the application of Lower State Combination Difference (LSCD or shortly CD) checking, logically combined with a special graphical representation of intervals between adjacent transitions in the branches (LW diagrams) increase dramatically the power of assignment procedures.
The idea of LSCD linking of several spectral branches together can
be explained with the help of a scheme of rovibrational energies and
corresponding series transitions, where certain groups of transitions share
common upper levels. Because of dipole moment selection rules, transitions with
–1 or 0
or +1 are generally allowed in IR spectra (
and 
denote the upper and lower state J
values, respectively), which correspond to the so called P/Q/R
branches, respectively. This means that if all other QN of the upper and lower
states are fixed by dipole moment selection rules, for each upper rovibrational
level there will exist three transitions (triad of P/Q/R transitions) from
three different lower rovibrational levels. If the energy differences of the
lower levels are known with sufficient accuracy (like in the frequent case when
the lower state is the vibrational ground state studied previously by
rotational spectroscopy), then the differences between the three P/Q/R transitions
to the common upper level will be exactly the same as the energy differences
between the three particular lower states (these are the so-called LSCD).
This is used with advantage in assignments: when a transition in one of the three branches linked with LSCD is tentatively assigned, then the wavenumbers in the two other branches can be calculated. If lines are found in the predicted positions, the correctness of assignments of the whole triad is confirmed with a high degree of certainty. Such coincidence can be of course accidental, but it can hardly occur for many triads of transitions belonging to branches linked with LSCD. Therefore continuous series of transitions satisfying LSCD checks provide reliable assignments of quantum numbers to transition frequencies.
