A cartographer receives a sheet with distances between hundreds of unnamed islands. No island is labeled, but the distances repeat, forming triangles and quadrilaterals. From these repetitions, the cartographer reconstructs the map of the archipelago, not knowing which island is which. This is roughly how the new work in molecular spectroscopy works.
Previously, to understand a molecular spectrum, lines had to be 'assigned', meaning each pair of energy levels had to be identified. For this, a model describing the molecule's energy was built and manually fitted to the data. For molecules with dense spectra, such as methane or water, thousands of lines remained unassigned. The new work removes this barrier: levels are recovered directly from raw frequencies, without a model and without names.
The algorithm looks for repeating frequency differences. If two lines are separated by the same energy gap, it is like two paths between the same islands. Closures of four such paths, 'four-cycles', reveal the positions of the levels themselves. From 686 unlabeled water lines in the range 1537–1605 nm, the algorithm assembled 158 levels, grouped into two networks.
The map is assembled without a single name. The islands are placed in their positions, and the distances between them are known to within a meter, but the algorithm does not know which island is which. Names can be added later by comparing with known maps. The main point is that the map already exists, and it is more accurate than previous ones.
This is the first demonstration of model-independent reconstruction of a molecule's energy network with kilohertz accuracy. The method opens the way to automatic construction of spectroscopic databases for molecules where traditional analysis drowns in line density. The cartographer no longer needs to wait for someone to label the islands.
The effective absorption path length in the SCALS cavity is about 28 km, which is like light passing through a sample the length of a marathon course, even though the cell itself is only 42 cm.
The idea of recovering hidden structure from indirect measurements recalls plots where a map of unknown territory is reconstructed from fragments of data. In Carl Sagan's novel Contact, the alien signal contains instructions for building a machine, and here too, a coherent network of levels is assembled from disparate frequencies.