Inverting experimental data provides a powerful technique for obtaining information about molecular Hamiltonians. However, rigorously quantifying how laboratory error propagates through the inversion algorithm has always presented a challenge. In this paper, we develop an inversion algorithm that realistically treats experimental error. It propagates the distribution of observed laboratory measurements into a family of Hamiltonians that are statistically consistent with the distribution of the data. This algorithm is built upon the formalism of map-facilitated inversion to alleviate computational expense and permit the use of powerful nonlinear optimization algorithms. Its capabilities are demonstrated by identifying inversion families for the $X{}^1{\Sigma }_g^{+}$ and $a{}^3{\Sigma }_u^{+}$ states of ${\mathrm{Na}}_2$ that are consistent with the laboratory data.

• Received 30 August 2002

DOI:https://doi.org/10.1103/PhysRevA.67.022711