  One of the most promising techniques used for studying the electronic
properties of materials is based on Density Functional Theory (DFT) approach
and its extensions.
  DFT has been widely applied in traditional solid state physics problems where
periodicity and symmetry play a crucial role in reducing the computational
workload. With growing compute power capability and the development of improved
DFT methods, the range of potential applications is now including other
scientific areas such as Chemistry and Biology. However, cross disciplinary
combinations of traditional Solid-State Physics, Chemistry and Biology
drastically improve the system complexity while reducing the degree of
periodicity and symmetry. Large simulation cells containing of hundreds or even
thousands of atoms are needed to model these kind of physical systems. The
treatment of those systems still remains a computational challenge even with
modern supercomputers. In this paper we describe our work to improve the
scalability of Quantum ESPRESSO \cite{Quantum-Espresso} for treating very large
cells and huge numbers of electrons. To this end we have introduced an extra
level of parallelism, over \emph{\emph{electronic bands}}, in three kernels for
solving 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-Parrinello
routines (Car-Parrinello dynamics, package CP). Final benchmarks show our
success in computing the Nuclear Magnetic Response (NMR) chemical shift of a
large biological assembly, the electronic structure of defected amorphous
silica with hybrid exchange-correlation functionals and the equilibrium atomic
structure of height Porphyrins anchored to a Carbon Nanotube, on many thousands
of CPU cores.
