The Chemistry Division and Division of Materials Research contribute funds to this award. It supports theoretical and computational research and education to advance first principles electronic structure theory. To calculate the ground-state nuclear framework, energy, and electron spin densities of an atom, molecule, biomolecule, solid, surface, or nanostructure within Kohn-Sham density functional theory, it is only necessary to solve self-consistent quantum mechanical one-electron equations. The results would be exact if the employed exchange-correlation energy as a functional of the electron density were exact.
The exact functional is not computable in practice, but practical approximations to it are improvable by adding additional semilocal or nonlocal ingredients to the exchange-correlation energy density to satisfy more exact constraints. Meta-generalized gradient approximations can enable accurate calculation of the properties of many material systems at or near equilibrium. However, they can surprisingly fail to predict accurate structural energy differences and transition pressures for solids as simple as silicon and silicon dioxide. The PI will develop a new meta-generalized gradient approximation which satisfies all possible exact constraints while recovering more of the intermediate-range van der Waals interaction, and test it for these and other problems.
For the description of stretched bonds over which electrons are shared, and thus of the 'strongly correlated' transition-metal oxides and lanthanides, hybrid functionals that employ a nonlocal exact-exchange ingredient have been surprisingly successful. However, these functionals typically rely on one or more empirical parameters, and can fail to satisfy basic exact constraints that even semilocal functionals satisfy. The PI will use a conjectured long-range limit to develop a nonempirical hybrid model for the correlation hole, for use with exact exchange. A byproduct will be a needed nonlocal correction to the random phase approximation.
An early self-interaction correction to the local spin density approximation has had some success for strongly-correlated systems, although its description of the equilibrium properties of more normal molecules and solids is disappointing and does not much improve with improvement of the underlying semilocal functional. The PI aims to fix these problems by eliminating the nodes of the self-interaction correction orbital densities through the use of complex orbitals, and by applying the self-interaction correction to the PI's improved new meta-generalized gradient approximation, which will have an improved description of compact one-electron densities.
A major recent development is the incorporation of long-range van der Waals interaction which is important for soft and biological matter, into density functional theory. The PI plans two different ways to add these effects to the best semi-local and nonlocal functionals that omit them. One involves the accurate calculation of van der Waals coefficients of all orders, with a summation of the infinite series and a short-range cutoff, and the other involves the extraction of the long-range part of a nonlocal van der Waals correlation energy functional.
Kohn-Sham density functional theory is widely used in chemistry and materials, and is increasingly used in engineering and geophysics. The improved functionals that result from this research will facilitate the computer design of new molecules and materials with desired properties. This award also supports educating postdoctoral fellows and students at all levels from high-school through graduate school.
NONTECHNICAL SUMMARY:
The Chemistry Division and Division of Materials Research contribute funds to this award. It supports theoretical and computational research and education to advance the ability to compute the properties of materials accurately. Ordinary matter (atoms, molecules, and solids) is made up of electrons and nuclei. To predict its properties on the computer, and to design new materials with desired properties, we need to find the energy and spatially varying density of the electrons, including the effects of quantum mechanics and electrostatic repulsion.
Kohn-Sham density functional theory is a widely used method to calculate these properties. The energy and density can be found by minimizing a functional or rule for the energy in terms of the density. Reasonable approximations to this functional are known, and usefully describe the formation of atoms and the binding of atoms to form molecules and solids. The aim of this project is to use the knowledge we have about the exact functional to construct approximations that are more accurate but still computationally efficient. Better approximations for "nature's glue" that binds atoms to form molecules and solids leads to more accurate predictions of materials properties from the identity of the constituent atoms and the potential to design materials with desired properties.
New functionals that result from this research could be applied with good results in chemistry, biochemistry, nanoscience, materials science, condensed matter physics, and other fields. This award also supports education for postdoctoral fellows and students at all levels from high-school through graduate school.
