Research Overview

Our research centers on foundational and methodological developments in electronic structure theory, with a focus on the relationship between density functional theory (DFT) and wavefunction-based (ab initio) approaches. Much of our work seeks mathematical insights that reinterpret established concepts in new ways, revealing connections to other ideas and suggesting unexpected approaches to computation.

Recent highlights

• Extension of density functionals to particles of arbitrary spin: We showed that the classic Fermi–Amaldi functional remains exact for any number of fermions and bosons of arbitrary spin, provided that all particles occupy the same spatial orbital. This insight offered a clearer interpretation of spin-scaling relations and established a formal foundation for multicomponent density-functional methods.
• Exchange-correlation potentials at atomic nuclei: We demonstrated that exchange–correlation potentials can exhibit jump discontinuities at atomic nuclei when computed in finite basis sets, and proved that these discontinuities vanish in the complete basis-set limit through. This fact in its turn revealed prevoiusly unknown properties of kinetic energy densities.
• Analytic reconstruction of density matrices from electron densities: We discovered an exact method to construct one-electron reduced density matrices from electron densities represented by basis-set expansions. Our key insight is that such calculations require basis sets with exact linear dependencies among basis-function products, a new concept that merits further exploration.
• Orbital subspaces: We introduced the concept of linear subspaces of orbitals associated with v-representable densities in the Kohn–Sham formalism. This concept allows one to determine which densities can be exactly inverted to potentials within finite basis sets.

A prominent theme of our current work is the study of how electron densities and total energies are related within incomplete (finite) basis sets, and how various DFT quantities are represented—or distorted—in finite-basis-set calculations.

In parallel with our theoretical work, we apply DFT to chemical systems such as catalysts, fluorescent emitters, radicals, and materials under pressure. These studies often involve collaborations that bridge electronic structure theory with real-world molecular and materials applications and test theoretical predictions against experimental data.

For a full list of our publications, visit the Publications page.