Inversion of two-dimensional potentials from frequency-resolved spectroscopic data.

We report the first successful reconstruction of two-dimensional potential energy surfaces (PES) using the magnitudes and positions of a set of frequency-resolved fluorescence (or absorption) lines. The inversion proceeds by first extracting the phases of the transition-dipole matrix elements, yielding, together with the (ground) PES to (from) which emission (absorption) occurs, a point by point reconstruction of the two-dimensional excited state PES. The inversion procedure is highly accurate even for PES with multiple minima and many missing lines, with typical RMS errors <0.002 cm(-1) in the classically allowed region and <0.018 cm(-1) in the classically forbidden region.