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# Do Electron Current Densities Determine All There Is to Know?

# Do Electron Current Densities Determine All There Is to Know?

## Young CAS Workshop

## Principal investigators

## Abstract

In both chemistry and physics, the Schrödinger equation *H**Ψ** = E**Ψ** *is the central equation since it describes the interactions among the building blocks of atoms and molecules. To fully determine the properties of such systems, one therefore seeks effective methods to solve this equation. However, due to the fact that the electrons are interacting, the Schrödinger equation cannot be solved exactly for all but the simplest systems. Furthermore, the complexity of solving this equation increases as the system size increases, since the wave function depends on the position of each particle. Consequently, wave function-based methods in quantum chemistry are very computationally expensive.

On the other hand, density-functional theory uses instead the particle density. The particle density is a reduced probability distribution obtained from the wave function. By definition, it depends only on the space coordinates and does not scale with the system size. It is the most widely used method of quantum chemistry and constitutes a very successful approach describing electronic structure, especially for large systems.

The aim of the workshop is to construct a mathematically rigorous foundation for magnetic field effects in density-functional theory. Furthermore, there will also be a focus on whether such a formulation can pave the way for new kinds of practical approximations.