Geodesic
The efficiency of regularizing algorithm for scaling quantum chemical force fields in Cartesian coordinates: applications to biologically important molecules
Numerical methods and programming, Tome 25 (2024) no. 1, pp. 101-114.

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In our study, we conducted calculations to determine scale factors in Cartesian coordinates for the inverse problem, revealing the consistency of regularized coefficients for atoms and fragments within the molecules we analyzed. Furthermore, we observed the transfer of the scale factors among similar fragments in related compounds for two molecules — piperidine and 4-piperidinemethanol. This work confirms the effectiveness of previously developed algorithms for calculating regularized scale factors for correcting the matrix of force constants (Hessian) in Cartesian coordinates.
Keywords: inverse spectroscopic problem, ill-posed problems, regularized scaling factors, numerical methods, piperidine, 4-piperidinemethanol. 
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A. V. Stepanova; I. B. Davydova; G. M. Kuramshina. The efficiency of regularizing algorithm for scaling quantum chemical force fields in Cartesian coordinates: applications to biologically important molecules. Numerical methods and programming, Tome 25 (2024) no. 1, pp. 101-114. http://geodesic.mathdoc.fr/item/VMP_2024_25_1_a8/