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One of the most promising techniques used for studying the electronicproperties of materials is based on Density Functional Theory (DFT) approachand its extensions.  DFT has been widely applied in traditional solid state physics problems whereperiodicity and symmetry play a crucial role in reducing the computationalworkload. With growing compute power capability and the development of improvedDFT methods, the range of potential applications is now including otherscientific areas such as Chemistry and Biology. However, cross disciplinarycombinations of traditional Solid-State Physics, Chemistry and Biologydrastically improve the system complexity while reducing the degree ofperiodicity and symmetry. Large simulation cells containing of hundreds or eventhousands of atoms are needed to model these kind of physical systems. Thetreatment of those systems still remains a computational challenge even withmodern supercomputers. In this paper we describe our work to improve thescalability of Quantum ESPRESSO \cite{Quantum-Espresso} for treating very largecells and huge numbers of electrons. To this end we have introduced an extralevel of parallelism, over \emph{\emph{electronic bands}}, in three kernels forsolving computationally expensive problems: the Sternheimer equation solver(Nuclear Magnetic Resonance, package QE-GIPAW), the Fock operator builder(electronic ground-state, package PWscf) and most of the Car-Parrinelloroutines (Car-Parrinello dynamics, package CP). Final benchmarks show oursuccess in computing the Nuclear Magnetic Response (NMR) chemical shift of alarge biological assembly, the electronic structure of defected amorphoussilica with hybrid exchange-correlation functionals and the equilibrium atomicstructure of height Porphyrins anchored to a Carbon Nanotube, on many thousandsof CPU cores.

Enhancement of DFT-calculations at Petascale: Nuclear Magnetic Resonance, Hybrid Density Functional Theory and Car-Parrinello calculations