The goal of this project is to go beyond the state of the art in the calculation of non-perturbative anharmonic spectra and of the electron-phonon couplings by combining the stochastic self-consistent harmonic approximation (SSCHA) with advanced approximations for the exchange correlation potential including various degrees of Hartree-Fock exchange. In several previous works, we have demonstrated that the SSCHA developed by some of us allows for accurate description of anharmonic phonon spectra in the non-perturbative limit in superconductors, ferroelectrics and charge density wave systems. We found, however, that SSCHA calculations based on total energies and force constants obtained via density functional theory with LDA/GGA functionals, substantially underestimate the critical temperatures for ferroelectric and charge density wave phase transitions. This is due to the error introduced by the approximate exchange correlation functional on total energies, forces and volumes. Moreover, in the case of Graphene, TiSe2, ZrNCl and HfNCl, the electron-phonon interaction is substantially underestimated by using state-of-the art linear response calculations based on LDA/GGA exchange kernel. This is a general feature of low dimensional system at low carrier concentration. In this proposal, we plan to go far beyond state of the art in the calculation of phonon spectra by (i) developing a systematic finite difference approach to evaluate the electron- phonon coupling in solids with the inclusion of exact exchange and (ii) obtain non-perturbative temperature-dependent anharmonic phonon spectra by applying the SSCHA with inclusion of hybrid functionals as total energy and force engines. We will apply the method to technologically relevant materials. In more details we will study: (i) the structural distortion and electron-phonon coupling in carbyne (linear carbon chain), the prototypical system for the Peierls instability, and other recently synthesized 1D chains such as NbSe3, (ii) the ferroelectric instability in bulk SnTe and single layer SnTe thermoelectrics, (iii) the determination of charge density wave critical temperatures and temperature dependent vibrational spectra in single layers TiTe2 and bulk TiSe2, and CuxTiSe2. Our proposal will lead to a new paradigm and benchmark in the calculation of vibrational phonon spectra of solids and in the description of the electron-phonon interaction due to the better inclusion of exchange effects. Finally, our results will be of paramount importance in the field of energy-saving applications (thermoelectrics) and in the field of 2D materials beyond graphene. The implications of our work will also have conceptually important consequences, as at the moment there is no theory able to predict the ferroelectric or charge density wave (CDW) transition from first principles, particularly in systems where competing orders like CDW and superconductivity do occur. Simulating realistic quantum transport of energy and charge in nanostructured organic materials with non- perturbative, nonlinear phonon-phonon coupling also presents a major theoretical challenge.