In his pioneering work in 1928, Condon recognized that molecular spectra and their temperature dependence can be, at least in principal, calculated from a knowledge of the potential energy surfaces involved in the corresponding quantum transition. Similarly, the potential energy surfaces can be calculated from the physical laws, which determine the shape and structure of a molecule.

The complexity of the calculation of potential energy surfaces and molecular transitions requires the use of numerical methods to achieve the required accuracy. In recent years the development of fast computer hardware and the accompanying development of powerful numerical algorithms has made the accurate computation of molecular spectra possible. In contrast, potential energy surfaces cannot be yet computed with the required accuracy for spectroscopic applications (< 0.1 cm^-1).

The current compromise is to determine potential energy surfaces by fitting them to experimental data. This approach provides both a critical assessment of the experimental data and a theoretically correct method for the interpolation between (and to some extent extrapolation to) temperatures and wavelengths that were not accessed experimentally. The ultimate goal of this approach is the ab initio computation of spectra from a knowledge of the physics. This will be possible when potential energy surfaces become computable at the required accuracy.