Reflections On Complex Adaptive
Materials: Widespread Relevance Of Strong Correlations On Variable Valence Ions
Professor Dan Cox
University of California at Davis
407 Physics Geology, 1 Shields Avenue
Davis, CA 95616
(530) 752-1789
There is a common thread among some the following very diverse problems: 1) strongly correlated electronic materials (such as cuprate superconductors, metallic plutonium, and heavy electron metals), 2) environmental chemistry (e.g., redox reactions of Cr and Pu in the environment), and 3) function and structure of many biomolecules (e.g., proteins, and the recent chlorophyll-analogue Ru dye photovoltaics). Namely, these compounds, systems, and molecules contain variable valence ions that have strong local electronic interactions, residing in d or f electron orbitals. For example, in the heavy electron metals and cuprate superconductors, the prevalence of antiferromagnetism is tied to these local interactions, and many believe they drive the superconductivity. In the case of environmental redox reactions, the correlation effects surely play a role in stabilizing different valences in different contexts. In the case of such biomolecules (or analogues) as hemoglobin or the above mentioned Ru dyes, the transition metal ions play the key role in the chemistry and photochemistry.
Many theoretical physicists are beginning to appreciate that two primary modern thrusts of condensed matter physics, electronic structure theory in the form of density functional methods and many body theory, can, when married, make an important contribution to this broad area of science.
Density functional methods do treat correlation effects among electrons in what may be described, for existing approximations, as a sophisticated molecular field theory, it is far from clear whether they can ever capture the delicate energy differences between states needed to describe such phenomena as superconductivity, subtle structural transitions in such systems as elemental Ce and Pu, or the physics of the heavy electron state. These methods do provide a powerful method for obtaining total energies and total energy differences relevant for calculating gross structural properties and interpreting many spectroscopy experiments. They also have the advantage of being quite efficient, particularly in the Order N forms now available for insulating materials.
Many body theory has had considerable success in characterizing such physics as the Mott transition, antiferromagnetism, and the origin of the heavy fermion state through the Kondo effect. This success depends upon reliable calculation of the delicate low energy dynamics in terms of theoretical models with few parameters and only low energy degrees of freedom, often at the expense of proper treatments of structure and symmetry.
We note that existing widely distributed quantum chemistry codes based upon configuration interaction, which does treat the correlations in principle, are applied most frequently to relatively small molecules containing low Z nuclei, and are problematic for large molecules due to the poor scaling properties with system size.
We are now beginning to see treatments of strongly correlated solids which combine electronic structure inputs with many body algorithms for computing the dynamical (self energy corrections) to the density functional theory results, via an approximation which treats the correlation effects locally (dynamical mean field theory). Given the somewhat whimsical name of ìLDA++î by Lichtenstein, the strategy is to use the density functional theory to give model parameters and effective one electron inputs, and uses the localized many body algorithms, which are quite sophisticated now, to solve the remainder of the problem (apart from a self-consistent connection of the local physics to the rest of the system for lattices).
For example, Lichtenstein and collaborators have examined transition metal oxide MO materials, and even Fe itself and found that they can produce an exceedingly good description; Han and collaborators have produced calculations of Fermi energy trends in the class of heavy fermion compounds CeM (M=Pb,In,Sn,Pd); Wolenski and collaborators have done realistic calculations for the grand-daddy Mott insulator, V2O3.
I believe that this prescription of combining local strong correlations with electronic structure calculations in the framework of density functional theory to study the much wider class of problems discussed above. The long-term goal is to develop relatively standard numerical codes that augment the widespread quantum chemistry and density functional programs when applied to this broad class of systems which require a proper treatment of correlation effects. I would like to present some motivating viewgraphs with such a broad perspective at the CAM meeting in December.