A local algebraic approach to describe vibrational excitations of molecules presenting both local and normal mode behaviors is presented. This approach allows the connection with configuration space to be established. The model consists in expanding the kinetic energy as well as the potential in terms of coordinates and momenta. An algebraic representation is obtained by introducing creation and destruction bosonic operators associated with the harmonic oscillators. From the resulting Hamiltonian a local algebraic representation is obtained through a canonical transformation to local bosonic operators. Finally an anharmonization is carried out by changing the local bosonic operators to ladder operators associated with the Morse or Poschl-Teller functions. Since the model is connected with configuration space, non linear curvilinear coordinates are contemplated. Our model is applied to the vibrational spectroscopic description of the ~(12)C~(16)O_2 molecule. The eigenstates are tested by calculating the derivatives for the polarizability for this molecule.
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