We employ a var iational approach by optimizing the free energy of an anharmonic Hamiltoni an with respect to strain tensor\, interatomic coordinates and force const ants in an interacting electron-phonon system. The goal is to predict poss ible phase transitions in crystal structures at finite temperatures. The v ariational method is based on Bogoliubov inequality to get an approximatio n to the Helmholtz free energy in a lattice with anharmonic potential ener gy terms. A harmonic trial Hamiltonian is used for the minimization. The o ptimization will give the set of equations corresponding to atomic displac ements\, lattice strain\, IFCs and other order parameters\, leading to pho non frequencies at each k-point for every temperature. The reliability of the approach is then checked in 1D/3D cases\, comparing to available compu tational/experimental results and by applying DFT method to compute free e nergies of various phases at different temperatures.< /p>\n DTSTART:20190429T190000Z LOCATION:Mechanical & Aerospace Engineering Building\, Room 346 SUMMARY:A variational approach for phase transition in interacting electron -phonon system END:VEVENT END:VCALENDAR