Density-functional theory (DFT) is probably the most widespread method for simulating the quantum-chemical behaviour of electrons in matter and applications cover a wide range of fields such as materials research, chemistry or pharmacy. For aspects like designing the batteries, catalysts or drugs of tomorrow DFT is nowadays a key building block of the ongoing research. The aim to tackle even larger and more involved systems with DFT, however, keeps posing novel challenges with respect to physical models, reliability and performance. For tackling these aspects in the multidisciplinary context of DFT we recently started the density functional toolkit (DFTK), a DFT package written in pure Julia.
Aside from computing the DFT energy itself, most applications of DFT require also derivatives of the energy with respect to various computational parameters. Examples are the forces (derivative energy with respect to atomic positions) and stresses (derivative energy with respect to lattice parameters). While the expressions of these derivatives are well-known for the standard DFT approaches implementing these is still a laborious (and sometimes boring) task. Additionally deriving these forces and stresses expressions for novel models currently boils down to manually doing so on pen and paper, which for the more involved models can be non-trivial.
As an alternative we want to take a look at combining the automatic-differentiation (AD) capabilities of the Julia ecosystem with DFTK in order to compute stresses without implementing the derivatives by hand. Instead we want to make DFTK suitable for AD, such that stresses for our current (and future) DFT models can be computed automatically. Being able to combine DFTK and AD would not only give us stresses, but it would also pave the road for computing even more involved properties using AD. In this final stage of the project it would be required to AD through the whole of DFTK (including several layers of solvers).
Recommended skills: Interest to work on an multidisciplinary project bordering physics, mathematics and computer science with a good working knowledge of differential calculus and Julia. Detailed knowledge in the physical background (electrostatics, material science) or about automatic differentiation is not required, but be prepared to take a closer look at these domains during the project.
Expected results: Use automatic differentiation to implement stresses (derivatives of the total energy with respect to lattice parameters) into DFTK.
Mentors: Keno Fischer, Michael F. Herbst, Antoine Levitt
References: For a nice intro to DFT and DFTK.jl see Michael's talk at JuliaCon 2020 and the literature given in the DFTK documentation. A concise introduction into AD are Antoine's notes on the adjoint trick.