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The inverse problem of molecular force fields calculation is considered within the theory of regularization. In our strategy, we choose the stabilizing matrixF  0F^{0}    as a result of quantum mechanical calculations. The solution of the inverse problem is finding a matrix  which is the nearest by the chosen Euclidean norm to the given ab initioF  0F^{0}   . The optimized solution is referred to as  regularized quantum mechanical force field  (RQMFF). Regularizing algorithms of molecular force fields calculation based on the joint treatment of experimental and ab initio quantum mechanical data have been applied to the calculations of molecular force fields (matrices of force constants) for small water clusters (H 2 O)   (n  =   2  ,  3n=2,3   ).

Stable numerical methods for determination of the molecular clusters force fields