Generalized Normal Coordinates for the Vibrational Analysis of Molecular Dynamics Simulations

The computation of vibrational spectra via molecular dynamics (MD) simulations has made lively progress in recent years. In particular, infrared spectra are accessible employing ab initio MD, for which only the total dipole moment has to be computed “on the fly” from the electronic structure along the trajectory. The analysis of such spectra in terms of the normal modes of intramolecular motion, however, still poses a challenge to theory. Here, we present an algorithm to extract such normal modes from MD trajectories by combining several ideas available in the literature. The algorithm allows one to compute both the normal modes and their vibrational bands without having to rely on an equipartition assumption, which hampered previous methods. Our analysis is based on a tensorial definition of the vibrational density of states, which spans both the frequency resolved cross- and auto-correlations of the molecular degrees of freedom. Generalized normal coordinates are introduced as orthonormal transforms of mass-weighted coordinates, which minimize their mutual cross-correlations. The generalized normal coordinates and their associated normal modes are iteratively constructed by a minimization scheme based on the Jacobi diagonalization. Furthermore, the analysis furnishes mode local temperatures, which provide not only a measure for the convergence of the computed intensities but also permits one to correct these intensities a posteriori toward the ensemble limit. As a first non-trivial test application we analyze the infrared spectrum of isoprene based on ab initio MD, which is an important building block of various dye molecules in molecular biology.