We develop a first-principles approach for the treatment of vibronic interactions in solids that overcomes the main limitations of state-of-the-art electron-phonon coupling formalisms. In particular, anharmonic effects in the nuclear dynamics are accounted to all orders via ab initio molecular dynamics simulations. This non-perturbative, self-consistent approach evaluates the response of the wave functions along the computed anharmonic trajectory; thus it fully considers the coupling between nuclear and electronic degrees of freedom. We validate and demonstrate the merits of the concept by calculating temperature-dependent, momentum-resolved spectral functions for silicon and the cubic perovskite SrTiO3, a strongly anharmonic material featuring soft modes. In the latter case, our approach reveals that anharmonicity and higher-order vibronic couplings contribute substantially to the electronic-structure at finite-temperatures, noticeably affecting band gaps and effective masses, and hence macroscopic properties such as transport coefficients.
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