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The performance of thermoelectric materials is determined by their electrical and thermal transport properties that are very sensitive to small modifications of composition and microstructure. Discovery and design of next-generation materials are starting to be accelerated by computational guidance. We review progress and challenges in the development of accurate and efficient first-principles methods for computing transport coefficients and illustrate approaches for both rapid materials screening and focused optimization. Particularly important and challenging are computations of electron and phonon scattering rates that enter the Boltzmann transport equations, and this is where there are many opportunities for improving computational methods. We highlight the first successful examples of computation-driven discoveries of high-performance materials and discuss avenues for tightening the interaction between theoretical and experimental materials discovery and optimization.
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