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Personne# Tommaso Chiarotti

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Empowered by ever-increasing computational power and algorithmic developments, electronic-structure simulations continue to drive research and innovation in materials science. In this context, ab-initio calculations offer an unbiased platform for the understanding, development, design, and discovery of materials. The treatment of the electron interactions is at the core of any ab-initio method, with the accuracy of its solution affecting the final result. Here, dynamical functionals can play a crucial role in allowing the accurate prediction of spectral and thermodynamic properties of materials.In this thesis we develop a framework to deal with dynamical quantities, and a novel dynamical functional to address the electronic structure of correlated materials.We design the so-called sum-over-poles representation for dynamical propagators to perform accurately the calculations in dynamical frameworks. Then, we draw a link between the funda- mental equation of Greenâs function formalism, the Dyson equation, and nonlinear eigenvalue problems, also highlighting that the Dyson equation is the (nonlinear) generalization of the SchrÃ¶dinger equation for embedded systems. Notably, the sum-over-poles representation of the dynamical potential allows for an exact solution of the nonlinear problem by mapping the interacting system to a non-interacting âfictitiousâ system with augmented degrees of freedom and having the same Greenâs function of the interacting system, with the spurious degrees of freedom traced away. The (linear) diagonalization of the effective Hamiltonian for the âfictitiousâ system yields the Dyson orbitals of the material, as a solution of the nonlinear problem, and its excitation energies as poles of the Greenâs function. Also, the sum-over-poles representation of the Greenâs function is known and allows for the computation of accurate spectroscopic and thermodynamic quantities.Furthermore, we introduce a novel approximation to the exchange-correlation part of the Luttinger-Ward functional, that generalizes the energy functional of DFT+U to host a dy- namically screened potential U(Ï). Exploiting a localized-GW approach, we combine the precision of DFT+U for ground-state properties with the accuracy of GW for spectroscopic quantities and design the so-called dynamical Hubbard (Luttinger-Ward) functional. This yields a localized-GW self-energy as derivative, and simplifies to DFT+U in the case of a static screening.To test the approach, we use the algorithmic-inversion method on sum over poles to calculate the spectroscopic and thermodynamic quantities of the homogeneous electron gas at the GW level, finding very good agreement with previous results.Finally, we combine the algorithmic-inversion method on sum over poles with the dynamical Hubbard functional, to study the electronic structure of correlated materials. We apply the framework to compute the spectral, thermodynamic, and vibrational properties of SrVO3, finding results in excellent agreement with experiments and state-of-the-art computational methods, at a negligible computational cost.

Tommaso Chiarotti, Nicola Marzari

Dynamical potentials appear in many advanced electronic-structure methods, including self-energies from many-body perturbation theory, dynamical mean-field theory, electronic-transport formulations, and many embedding approaches. Here, we propose a novel treatment for the frequency dependence, introducing an algorithmic inversion method that can be applied to dynamical potentials expanded as sum over poles. This approach allows for an exact solution of Dyson-like equations at all frequencies via a mapping to a matrix diagonalization, and provides simultaneously frequency-dependent (spectral) and frequency-integrated (thermodynamic) properties of the Dyson-inverted propagators. The transformation to a sum over poles is performed introducing nth order generalized Lorentzians as an improved basis set to represent the spectral function of a propagator. Numerical results for the homogeneous electron gas at the G(0)W(0) level are provided to argue for the accuracy and efficiency of such unified approach.

Tommaso Chiarotti, Nicola Marzari, Giuliana Materzanini

Superionics are fascinating materials displaying both solid- and liquid-like characteristics: as solids, they respond elastically to shear stress; as liquids, they display fast-ion diffusion at normal conditions. In addition to such scientific interest, superionics are technologically relevant for energy, electronics, and sensing applications. Characterizing and understanding their elastic properties is, e.g., urgently needed to address their feasibility as solid-state electrolytes in all-solid-state batteries. However, static approaches to elasticity assume well-defined reference positions around which atoms vibrate, in contrast with the quasi-liquid motion of the mobile ions in fast ionic conductors. Here, we derive the elastic tensors of superionics from ensemble fluctuations in the isobaric-isothermal ensemble, exploiting extensive Car-Parrinello simulations. We apply this approach to paradigmatic Li-ion conductors, and complement with a block analysis to compute statistical errors. Static approaches sampled over the trajectories often overestimate the response, highlighting the importance of a dynamical treatment in determining elastic tensors in superionics.