Abstract
The model of Regularized Quantum Mechanical Force Field (RQMFF) was applied to the joint treatment of ab initio and experimental vibrational data of the four primary nucleobases using a new algorithm based on the scaling procedure in Cartesian coordinates. The matrix of scaling factors in Cartesian coordinates for the considered molecules includes diagonal elements for all atoms of the molecule and off-diagonal elements for bonded atoms and for some non-bonded atoms (1–3 and some 1–4 interactions). The choice of the model is based on the results of the second-order perturbation analysis of the Fock matrix for uncoupled interactions using the Natural Bond Orbital (NBO) analysis. The scaling factors obtained within this model as a result of solving the inverse problem (regularized Cartesian scale factors) of adenine, cytosine, guanine, and thymine molecules were used to correct the Hessians of the canonical base pairs: adenine–thymine and cytosine–guanine. The proposed procedure is based on the block structure of the scaling matrix for molecular entities with non-covalent interactions, as in the case of DNA base pairs. It allows avoiding introducing internal coordinates (or coordinates of symmetry, local symmetry, etc.) when scaling the force field of a compound of a complex structure with non-covalent H-bonds.
Highlights
Inverse Problems of Vibrational SpectroscopyVibrational spectroscopy is a very important source about the structure of molecules, in particular, in different states of aggregation, including the presence of intra- and intermolecular interactions
If we consider the intramolecular part of the force field for macroscopic systems expressed in terms of force constants corresponding to molecular internal coordinates, we encounter a significant problem related to the invariance of individual internal force constants with respect to the chosen set of coordinates: the force constants of the intramolecular force field are not invariant with respect to the choice of internal coordinates
We present the results of applying these algorithms for fitting the molecular force fields in Cartesian coordinates for primary nucleobases and subsequent use of these scale factors to correct the force constant matrices of canonical pairs in Cartesian coordinates
Summary
Vibrational spectroscopy is a very important source about the structure of molecules, in particular, in different states of aggregation, including the presence of intra- and intermolecular interactions. Using regularizing algorithms to refine ab initio force fields, it is possible to obtain solutions to the inverse vibrational problem that retain significant features of the ab initio force constant matrix It allows to keep the potential energy distribution (PED) or composition of normal-mode eigenvectors, thereby providing accurate use of information obtained by powerful ab initio methods, transfer, and comparison of force constants in a series of related molecules. Weinhold [7,8,9,10] carried out for a series of substituted alkanes with the goal of determining the regularities in molecular parameters upon fluoro– Later, this approach to solving the inverse vibrational problem was extended for the very popular Pulay model of scaled force constant matrix (expressed in internal or symmetry/local symmetry coordinates) [11,12,13]. The corresponding regularizing algorithms provide the matrix Fα with the following properties: the solution is closest by norm to the QM matrix F0 , or the scale matrix B is closest to the unit matrix [1,14]
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