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Explore advanced computational methods in quantum mechanics and materials science through this comprehensive lecture series from the 2023 Advanced Quantum ESPRESSO school held at the University of Pavia. Delve into density-functional theory fundamentals, exchange-correlation functionals, and maximally localized Wannier functions before progressing to sophisticated topics including density-functional perturbation theory for phonon calculations and electron-phonon coupling from first principles. Master DFT+U and DFT+U+V methodologies with practical applications in ferroic materials, learn first-principles calculation of Hubbard parameters using linear-response theory, and discover the dynamical extension of DFT+U through U(ω) approaches. Examine Koopmans functionals from basic concepts through practical implementation, including spectral functionals in periodic boundary conditions and their role in functional theory of spectral density. Study ab initio many-body perturbation theory, computational workflows for accelerated materials design, and specialized tools like AiiDA-Vibroscopy for infrared and Raman spectra calculations. Gain insights into phase diagrams, phase transitions beyond harmonic phonons, and the successes and limitations of various computational approaches in modern materials research.
