First-principles calculations of physical properties of crystals

Prediction of physical properties of materials based only on their chemical composition has long been an intriguing task. In 1929 Paul Dirac wrote: "The fundamental laws necessary for the mathematical treatment of a large part of physics and the whole of chemistry are thus completely known, and the difficulty lies only in the fact that application of these laws leads to equations that are too complex to be solved".

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.

Selected publications:

Physics of Semiconductors division