Yuri Grin: Chemistry of strongly correlated systems

Continuing the discussion on materials design, Yuri Grin gave a chemists perspective on the problem. Yuri argued that design requires an understanding of the chemistry, and that one of the major problems chemists face, is a lack of understanding of the principles that govern the combinations of elements in intermetallics. Normally, one uses the concept of valence to determine the best combinations of elements. But this idea in its simplest form doesn't work in intermetallics. For example, consider combinations of Eu and Ga - you can make

EuGa,         EuGa4,   Eu5Ga9


Another issue that chemists face,  is to understand the bonding of electrons fare from the Fermi surface. One needs to know what combinations work - and he said that these considerations have led him, and his collaborators to develop a new method for calculating oxidation numbers.  These methods have been very successful for developing and discovering a new range of clathrate compounds.


The heart of the problem seems to be that one needs better tools to separate out the ionic and covalent parts of electron bonding. To this end, they have developed a new technique called the "electron localization indicator".

Here's the blogger's understanding of what this means. The point is, that density alone is poor indicator of individual electron localization- a better way is to use a weighted measure of the electron density, given by

                
where the integral is over small regions of space (omega) around the point r, and the denominator is the equal spin pair correlation function.   This is my rendition of the electron localizability indicator.
(See Becke and Edgcombe, J. Chem. Phys. 92, 5397 (1990); doi:10.1063/1.458517 ;Miroslav Kohout, Int J. Mod. Quantum Chemistry, 97, 651 (2004)). In regions of space where electrons are better localized, the pair correlation function will be smaller (lower momentum, higher wavelength, bigger correlation hole), which enhances the above index.  In regions of space where electrons are less well localized, the correlation hole will be much smaller, and zeta will be bigger.  The denominator can be calculated within a Hartree scheme to give a simple formula for zeta(r)>

Yuri showed us how this index gives a very nice indication of electron shells, and can be used to delineate covalent bonds, and well-defined clusters of atoms, behaving effectively as a single ion.
For instance,  in the clathrate compound Na24Si_136, 136 Si atoms form a cluster with charge 24+.

With this scheme, one can show how various clusters of atoms behave as single units , and one can account for the anomalous oxidation numbers of such clusters.    The increase in understanding, he argued is helping his group navigate and synthesize new kinds of clathrates that are of interest for their thermo-electric properties.










The talk aroused a lot of interest, particularly amongst physicists actively involved in materials synthesis.