Unprecedental success in the development of computer hardware and software
enables now to perform the first-principles (*ab initio*) calculations
with an accuracy comparable with that obtained in experiment. These approaches
enable also to predict the behavior of materials in extreme conditions (for
example, at very high pressures inaccessible in laboratory conditions), to
study dangerous (radioactive, explosive) materials. They are very useful in
predicting new materials with interesting properties, which have never been
synthesized. Moreover, the first-principles calculations enable to improve
our understanding of physical phenomena occurring in known materials. The
Nobel Prizes awarded to Robert S. Mulliken (1966), Walter Kohn and John Pople
(1998) can be regarded as acknowledgment of their seminal contribution to
the development of first-principles methods in physics, chemistry, and
materials science.

The main interests of **Prof. Lebedev**'s
group are physical properties of crystals exhibiting structural instability,
in which different phase transitions (including the ferroelectric one) can
appear. Crystals of the perovskite family are the examples. One of the goal
of these studies is the search for new **off-center
impurities**, which can induce phase transitions in incipient
ferroelectrics. Another very interesting objects for investigations, which
are studied now, are the ferroelectric superlattices.

The calculations performed in our laboratory are based on the density functional theory (DFT) and use the plain-wave basis and atomic structure described with pseudopotentials. The calculations include finding of the equilibrium structure (the unit cell parameters, atomic positions), calculations of the lattice dynamics, the band structure and density of states, comparison of energies of different phases, computation of spontaneous polarization, the dielectric, piezoelectric, and elastic tensors, the second-order nonlinear optical susceptibilities, the mixing enthalpies of solid solutions. The pressure effect on the phase transitions is also studied.

As any first-principles calculations are extremely time-consuming, to
perform these calculations it is advantageous to use parallel computing,
in which calculations of the electronic structure at different *k*
points of the Brillouin zone are executed independently and on different
cores of a computer cluster. This speeds up the calculations considerably.
The times when first-principles calculations were carried out on personal
computers probably have gone away.

The computer cluster, which works under 64-bit Linux operating system and
has 10 nodes with dual-core Intel E8200, E8400, and quad-core Intel i5-760
processors (48 Gbytes of
distributed RAM, 2 TByte of disk memory, peak performance of 270 Gflops),
is used in our laboratory to perform first-principles calculations. OpenMPI
protocol and Gigabit Ethernet are used to organize the communications in
the cluster. The most time-consuming calculations are performed on two
largest supercomputers in Russia,
**SKIF-MGU supercomputer
("Chebyshev")** and
**Lomonosov
supercomputer**.

- A.I. Lebedev. Ab initio calculations of phonon spectra in ATiO
_{3}perovskite crystals (A = Ca, Sr, Ba, Ra, Cd, Zn, Mg, Ge, Sn, Pb). --**Physics of the Solid State**;**51**, 362 (2009)**e-print arXiv:1305.0240 (2013)**;**[local copy]**. - A.I. Lebedev. Ferroelectric phase transition in orthorhombic
CdTiO
_{3}: first-principles studies. --**Physics of the Solid State**;**51**, 802 (2009)**e-print arXiv:1507.06658 (2015)**;**[local copy]**. - A.I. Lebedev. Ferroelectric phenomena in CdSnO
_{3}: A first-principles study. --**Physics of the Solid State**;**51**, 1875 (2009)**e-print arXiv:1601.01472 (2016)**;**[local copy]**. - A.I. Lebedev. Ab initio study of dielectric, piezoelectric, and elastic
properties of BaTiO
_{3}/SrTiO_{3}ferroelectric superlattices. --**Physics of the Solid State**;**51**, 2324 (2009)**[local copy]**. - A.I. Lebedev. Ground state and properties of ferroelectric superlattices
based on crystals of the perovskite family. --
**Physics of the Solid State**;**52**, 1448 (2010)**[local copy]**. - A.I. Lebedev. Ground-state structure of KNbO
_{3}/KTaO_{3}superlattices: Array of nearly independent ferroelectrically ordered planes. --**Physica Status Solidi B 249, 789 (2012)**;**e-print arXiv:1102.1001 (2011)**;**[local copy]**. - A.I. Lebedev. Dielectric, piezoelectric, and elastic properties of
BaTiO
_{3}/SrTiO_{3}ferroelectric superlattices from first principles. --**J. Adv. Dielectrics 2, 1250003 (2012)**;**e-print arXiv:1105.5828 (2011)**;**[local copy]**. - A.I. Lebedev. Quasi-two-dimensional ferroelectricity in
KNbO
_{3}/KTaO_{3}superlattices. --**Physics of the Solid State**;**53**, 2463 (2011)**[local copy]**. - A.I. Lebedev. Ferroelectricity and pressure-induced phase transitions in
HgTiO
_{3}. --**Physics of the Solid State 54, 1663 (2012)**;**[local copy]**. - A.I. Lebedev. First-principles study of ferroelectricity and pressure-induced
phase transitions in HgTiO
_{3}. --**Phase Transitions 86, 442 (2013)**;**e-print arXiv:1203.2370 (2012)**. - A.I. Lebedev. Crystal structure and properties of barium thorate BaThO
_{3}from first principles. --**J. Alloys and Compounds 580, 487 (2013)**;**e-print arXiv:1302.5614 (2013)**. - A.I. Lebedev. Properties of BaTiO
_{3}/BaZrO_{3}ferroelectric superlattices with competing instabilities. --**Physics of the Solid State**;**55**, 1198 (2013)**e-print arXiv:1304.7596 (2013)**;**[local copy]**. - A.I. Lebedev, I.A. Sluchinskaya. Combined first-principles and EXAFS study of
structural instability in BaZrO
_{3}. --**Physics of the Solid State 55, 1941 (2013)**;**e-print arXiv:1304.6359 (2013)**;**[local copy]**. - A.I. Lebedev. Band offsets in heterojunctions between cubic perovskite oxides. --
**Physics of the Solid State 56, 1039 (2014)**;**e-print arXiv:1401.1157 (2014)**;**[local copy]**. - A.I. Lebedev. Ferroelectric properties of RbNbO
_{3}and RbTaO_{3}. --**Physics of the Solid State 57, 331 (2015)**;**e-print arXiv:1501.00670 (2015)**;**[local copy]**. - M.A. Terekhin, V.N. Makhov, A.I. Lebedev, I.A. Sluchinskaya. Effect of local
environment on crossluminescence kinetics in SrF2:Ba and CaF2:Ba solid solutions. --
**Journal of Luminescence 166, 137 (2015)**;**e-print arXiv:1506.02325 (2015)**. - A.I. Lebedev. Phase transitions and metastable states in stressed SrTiO
_{3}films. --**Physics of the Solid State 58, 300 (2016)**. - A.I. Lebedev. Metastability effects in strained and stressed SrTiO
_{3}films. --**J. Adv. Dielectrics 6, 1650016 (2016)**;**e-print arXiv:1509.00902 (2015)**. - A.I. Lebedev. Nonlinear optical properties of undoped and doped with Zr and Nb
KTiOPO4 crystals. --
**Bulletin of the Russian Academy of Science: Physics 80, 1038 (2016)**;**e-print arXiv:1610.02654 (2016)**.