Development and Application of Nonempirical Density-Functional Methods

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Prof. Staroverov's group develops electronic structure theory-a branch of quantum science used to understand chemical bonding and predict outcomes of chemical reactions. He specializes in the approach called density-functional theory (DFT) and holds a globally recognized leadership position in the exploration of Kohn-Sham effective potentials, the fundamental ingredients of DFT. The power of DFT is not yet fully realized because this method has to rely on imperfect approximations to the unknown exchange-correlation functional. The overriding goal of this proposal is to advance the capabilities of DFT by exploring highly original new ways of computing exact Kohn-Sham potentials and approximating the exchange-correlation functional. The short-term objectives fall within three interrelated themes. Computational methods. All practical DFT calculations use basis sets, but Kohn-Sham effective potentials are computed by formulas derived as if basis sets never existed, which leads to confusing inconsistencies. To address this issue, we will develop an unprecedented method for constructing exchange-correlation potentials that works properly in all situations. We will also devise a numerically superior procedure for computing exchange-correlation potentials from finite-basis-set densities, which will become part of density-embedding schemes used in computational materials research. Finally, we will explore a novel idea to make density-functional approximations work correctly for molecules with stretched bonds, which will drastically expand the power of existing density functionals in computational catalysis. Theoretical framework. We will initiate a systematic exploration of a new way to compute effective potentials in finite basis sets in order to eliminate the ambiguities of existing methods used for that purpose. We will also advance the theory of effective potentials by deriving mathematical tests which will enable DFT researchers to tell whether their models are physically sensible for calculating molecular properties in finite basis sets. Chemical applications. We will tackle two puzzles in the chemistry of functional materials: What are the essential differences between the ground and electronically excited states of boron-formazanate dyes that can explain the unusual optical properties of these molecules? Why do conventional density functionals fail for describing crystalline boron hydrides? Answers to these questions will guide experimental chemists making efficient energy conversion materials and will open up new ways of improving DFT. The outcomes of this research will be important to thousands of scientists who use DFT in the form of software packages to solve problems in theoretical, organic, inorganic, and materials chemistry. Prof. Staroverov's trainees will gain an exceptional set of technical and professional skills, and a formative experience preparing them for highly impactful careers in science and technology.