The temperature dependent effective potential (TDEP) method is generalized beyond pair interactions. The second and third order force constants are determined consistently from ab initio molecular dynamics simulations at finite temperature. The relia
bility of the approach is demonstrated by calculations of the Mode Gruneisen parameters for Si. We show that the extension of TDEP to higher order allows for an efficient calculation of the phonon life time, in Si as well as in $epsilon$-FeSi, a system that exhibits anomalous softening with temperature.
An accurate and easily extendable method to deal with lattice dynamics of solids is offered. It is based on first-principles molecular dynamics simulations and provides a consistent way to extract the best possible harmonic - or higher order - potent
ial energy surface at finite temperatures. It is designed to work even for strongly anharmonic systems where the traditional quasiharmonic approximation fails. The accuracy and convergence of the method are controlled in a straightforward way. Excellent agreement of the calculated phonon dispersion relations at finite temperature with experimental results for bcc Li and bcc Zr is demonstrated.
