Loomis-Wood windows (assignment functions)

The Loomis-Wood windows have similar and even more powerful tools for assigning quantum numbers to transitions from the peaklist. An assignment is performed by right-clicking on the symbol of a peak (triangle) in the display area of the LW window. This opens the same pop-up menu as is opened by a right-click in the Assignments window. Selecting the Assign to branch # command performs the assignment action. This is followed by a corresponding change in the Assignments window where the assignment is shown in blue in the WnObs column. In the Spectrum window the corresponding peak is centered horizontally. With the assignment done, the triangle in the LW window and the peak marker in SpWin are filled with the color of the branch.

Now we come to the most powerful feature of several LW windows being opened simultaneously. By definition, we will call the LW window, in which we can actively navigate the cursor, an active LW window. The remaining open LW windows will be called related LW windows. For every peak under cursor in the active LW window, the information is displayed in the title bar, as described in the section Loomis-Wood windows (display functions). As the cursor is navigated around the display area, this information is updated not only in the active LW window, but in all related LW windows in such a way, that in the related LW windows always a peak with the Error closest to the Error in the active window is found and put under cursor. Similar values of Errors in all LW windows are an indication, that transitions of different branches with a common upper level are in fact checked by Lower State Combination Differences (LSCD). During the navigation, the J_upper quantum number is the same for all LW windows, while the quantum number J_lower is individual windows correspond to the selection rule DJ of each individual branch.

Such a case of similar errors may be a coincidence for one J value (one ‘line’ in the LW diagram}. But when a series of such ‘coincidences’ is found several subsequent J values, the probability of correctness of assignment is increased towards certitude.

Another important point about the LW diagrams is that continuous series of transitions form visually recognizable patterns. Similar patterns in several LW diagrams are a good hint for checking these series for LSCD consistence. With the current possibility of checking errors of transitions sharing a common upper level in all LW windows simultaneously one can efficiently perform LSCD checking along such visually recognized series.

The described procedures are based on the assumption that the energies of the lower vibrational level pertaining to the studied rovibrational band are known accuracy higher than the estimated accuracy of peak wavenumbers. This also means that if we have transitions in more than one LW window with very similar errors, we can simply bring them on the central vertical line of the LW diagram (equivalent to zero error) by adding a certain correction to the upper state energy. Because the uppers state is common to transitions in all three windows, the alignment to the center occurs in all LW diagrams. In addition to this, because the branches form continuous patterns, the correction to upper state energies can be applied by adding a simple J-dependent correction function to upper state energies. Coefficients of a polynomial function can be fitted by a least-squares method. This can be done in a Fit window

The fit is done on assigned transitions of the active branch. But because the correction function is added to the upper state energies, it has a similar aligning effect on all branches with the same SeriesID, provided that they are correctly assigned. The use of correction function makes the use of multiple assigning feature in the Assignments window very effective.

A typical strategy of assignment consists in assigning several transitions (usually with the lowest J values) in the most clearly visible series in one of the LW diagrams. This has to be done on individual peaks of the active LW window, with controlling the consistency of errors in related LW windows.  The number of assigned peaks has to be obviously higher than the number of fitted parameters of the correction function. After aligning the series along the central line of the LW diagrams by fitting the correction function, assignments can be continued in the Assignment window, which allows making multiple assignments.