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.
We present a systematic application of Tikhonov’s regularization method to joint treatment of ab initio and experimental vibrational data for a series of mono-, di-, and tri-substituted haloethanes, based on uniform MP2/6-31G* level of theory. This leads to MP2/6-31G*-“regularized” force field parameters that exactly reproduce experimental frequencies and isotopomer shifts (within prescribed error levels) and are “closest” (in Euclidean norm) to the ab initio force field. We correct a number of previous experimental spectral assignments and investigate the limits of transferability (e.g., of methyl-group force field parameters from one species to another) and other common simplifying approximations (e.g., MVFF modified valence force field treatment). Our results demonstrate how one can systematically combine experimental and ab initio information to create a data base of freon-type force field parameters having greater accuracy and reliability than could be obtained from theory or experiment alone.
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