An Effective Procedure for Analyzing Molecular Vibrations in Terms of Local Fragment Modes

Normal mode analysis is nowadays routinely performed in most quantum chemistry codes as a valuable tool for studying molecular motions. In systems formed by several molecular units, such as noncovalently bound donor-acceptor systems, normal modes are frequently delocalized over the whole structure, leading to a complicated interpretation of vibrations. Here, we propose a simple procedure to localize normal modes, based on the definition of fragment Hessian submatrices that lead to legitimate local fragment modes. These fragment modes can be defined for any arbitrary number of atoms and fragments and form in general a complete basis that can be used to expand the total normal modes. We use this fragment basis to explore the molecular origin of the normal modes of benzene, and several peaks in the infrared spectrum of tetraalanine. Additionally, we propose a criteria to define breathing modes in noncovalently bound systems, based on the fact that motions of the center of mass of fragments are not translational and rotational invariant with respect to the total center of mass of the system. By using the Sayvetz-Eckart conditions of fragments, we can quantify the contribution of rotation and translation of the fragments center of mass on the normal modes of the total system.