# Effective Normal Modes from Finite Temperature Molecular Dynamics Simulations

Saturday, July 28, 2007 - 9:40am - 10:00am

EE/CS 3-180

Rodolphe Vuilleumier (Université de Paris VI (Pierre et Marie Curie))

Ab initio Molecular Dynamics has been recognized lately as a powerful tool to compute infrared spectra of a variety of systems. The main advantage of this approach with respect to the usual normal mode analysis approach at the optimized geometry is the explicit treatment of temperature and environmental effects, without need for an harmonic approxiamation. However, the interpretation of the simulated spectra in temrs of atomic motions, phonons or vibrational modes is still a challenge.

Here, a general method for obtaining effective normal modes from Molecular Dynamics simulations is presented. The method is based on a localization criterion for the fourier transformed velocity time-correlation functions (FTVCF) of the effective modes. For a given choice of the localization function used, the method becomes equivalent to the principal mode analysis (PMA) based on covariance matrix diagonalization. On the other hand, proper choice of the localization function leads to a novel method with strong analogy with the usual normal mode analysis of equilibrium structures, where the system's Hessian at the minimum energy structure is replaced by the thermal averaged Hessian, although the Hessian itself is never actually calculated. This method does not introduce any extra numerical cost during the simulation and bears the same simplicity as PMA itself. It can thus be readily applied to ab initio Molecular Dynamics simulations. Some examples will be given here.

Here, a general method for obtaining effective normal modes from Molecular Dynamics simulations is presented. The method is based on a localization criterion for the fourier transformed velocity time-correlation functions (FTVCF) of the effective modes. For a given choice of the localization function used, the method becomes equivalent to the principal mode analysis (PMA) based on covariance matrix diagonalization. On the other hand, proper choice of the localization function leads to a novel method with strong analogy with the usual normal mode analysis of equilibrium structures, where the system's Hessian at the minimum energy structure is replaced by the thermal averaged Hessian, although the Hessian itself is never actually calculated. This method does not introduce any extra numerical cost during the simulation and bears the same simplicity as PMA itself. It can thus be readily applied to ab initio Molecular Dynamics simulations. Some examples will be given here.