# Molecular Noninteracting Kinetic Energy by Machine Learning

In this project the candidate will learn cutting-edge techniques from the fields of convex analysis and machine learning to develop new approaches to the kinetic energy of electronic systems — the key to unlocking the full potential of Density-functional theory.

Density-functional theory (DFT) is the standard approach to quantum-mechanical simulations of molecules, striking a good balance between accuracy and efficiency by calculating the energy from the density r rather than the many-body wave function. Today, this goal is only partially achieved, however, since a noninteracting wave function is introduced to calculate the noninteracting kinetic energy *T*[r] accurately. To unlock the full potential of DFT, also the noninteracting wave function must be avoided by calculating the kinetic energy for a given density in a different manner.

Taking advantage of the convexity of the *T*[r] in r, we propose to obtain it by convex conjugation of the noninteracting energy *E*[*v*] as a function of the external potential. Since the noninteracting energy is much simpler than its interacting counterpart, it can be readily calculated accurately for any potential *v*, providing the large datasets needed for machine learning. The DFT kinetic energy *T*[r] may then be obtained accurately and quickly by convex conjugation of machine-learned energies.

## Requirements

- The candidate should have a MSc in Physics, Chemistry, Materials Sciences, or close subjects; preferably in the fields of condensed matter, statistical or computational physics, as well as in the fields of theoretical, computational, or physical chemistry.
- Candidates with documented experience in scientific programming and/or multiscale modelling will be prioritised.

## Supervisors

## Call 2: Project start autumn 2022

This project is in call 2, starting autumn 2022.