Joint treatment of ab initio and experimental data in molecular force field calculations with Tikhonov’s method of regularization

We describe a novel method for employing calculated ab initio potential data together with Tikhonov’s variational procedure to extract fundamental molecular force field parameters from experimental spectral data, the formal ‘‘inverse problem’’ of vibrational spectroscopy. In this approach, the ab initio quantities serve to ‘‘regularize’’ the initially ill-posed problem (in the sense of Tikhonov), leading to variationally stable and unique force field parameters that optimally mimic overall patterns of the (approximate) ab initio quantities, but exactly reproduce the available experimental data within specified experimental precision. In this manner, ab initio and experimental data can be jointly combined to produce more stable and reliable force fields (improvable to any degree through higher level ab initio treatment, additional experimental data, etc.) than could be attained by theoretical or experimental methods alone. The proposed procedure allows use of any system of generalized coordinates, including redundant systems of internal or symmetry coordinates, simplifying the transfer and comparison of force constants in series of related molecules. The procedure is illustrated with numerical application to CHF2Cl and its isotopomers at MP2/3-21G*, MP2/6-31G* levels of theory, demonstrating the stability and consistency of force fields obtained from different levels of theoretical input.