Functional sensitivity analysis approach to retrieve the potential energy function from the quantum second virial coefficient

Intermolecular forces play a central role in theoretical chemistry and many studies focus on the establishment of accurate potential energy curves. The potential energy function can be obtained by ab initio methods, representing a direct problem. On the other hand, it can be obtained as an inverse problem dealing directly with experimental data. This work explores the inverse problem to obtain the potential energy function, for the helium system, from second virial coefficient data at low temperatures. The methodology used was the functional sensitivity analysis approach. In this methodology a new proposal to obtain the sensitivity density of the phase shift with respect to the potential energy function is presented. From the sensitivity density of the second virial coefficient the most suitable temperature range for recovering the region of the potential well can be determined (3 to 20 K). The inverse problem was addressed in a single nonlinear step. Using functional sensitivity analysis and the Tikhonov regularization an estimate of the potential energy function was optimized with an average error of 3.7% against 7.6% in the initial approximation when compared to the reference potential energy function. The calculated second virial coefficient with this new potential gives an absolute deviation between 4.2×10−4 cm3mol−1 and 0.15 cm3mol−1 against 3.6 cm3mol−1 and 29.1 cm3mol−1 in the initial approximation.