# Machine learning the derivative discontinuity of density-functional theory

@article{Gedeon2021MachineLT, title={Machine learning the derivative discontinuity of density-functional theory}, author={Johannes Gedeon and Jonathan Schmidt and M. Hodgson and Jack Wetherell and Carlos L Benavides-Riveros and Miguel A. L. Marques}, journal={Machine Learning: Science and Technology}, year={2021}, volume={3} }

Machine learning is a powerful tool to design accurate, highly non-local, exchange-correlation functionals for density functional theory. So far, most of those machine learned functionals are trained for systems with an integer number of particles. As such, they are unable to reproduce some crucial and fundamental aspects, such as the explicit dependency of the functionals on the particle number or the infamous derivative discontinuity at integer particle numbers. Here we propose a solution to…

## References

SHOWING 1-10 OF 82 REFERENCES

Machine Learning the Physical Nonlocal Exchange-Correlation Functional of Density-Functional Theory.

- Physics, MedicineThe journal of physical chemistry letters
- 2019

By using automatic differentiation, a capability present in modern machine-learning frameworks, the exact mathematical relation between the exchange-correlation energy and the potential is imposed, leading to a fully consistent method.

Completing density functional theory by machine learning hidden messages from molecules

- Computer Science, Physicsnpj Computational Materials
- 2020

This study demonstrates that the functional can be systematically constructed using accurate density distributions and energies in reference molecules via machine learning, and will help enrich the DFT framework by utilizing the rapidly advancing machine-learning technique.

Pure non-local machine-learned density functional theory for electron correlation

- MedicineNature communications
- 2021

A type of machine-learning (ML) based DFA is presented that is pure, non-local and transferable, and can be efficiently trained with fully quantitative reference methods and is applicable to non-covalent, ionic and covalent interactions, as well as across different system sizes.

Derivative discontinuities in density functional theory

- Physics
- 2014

Fifty years after the original formulation of density functional theory (DFT), subtle consequences of the mathematical mappings underlying its formalism continue to merit new views. In this article,…

Bypassing the Kohn-Sham equations with machine learning

- Computer Science, PhysicsNature Communications
- 2017

The first molecular dynamics simulation with a machine-learned density functional on malonaldehyde is performed and the authors are able to capture the intramolecular proton transfer process.

Deep learning and density-functional theory

- PhysicsPhysical Review A
- 2019

We show that deep neural networks can be integrated into, or fully replace, the Kohn-Sham density functional theory (DFT) scheme for multielectron systems in simple harmonic oscillator and random…

Systematic construction of density functionals based on matrix product state computations

- Physics
- 2016

We propose a systematic procedure for the approximation of density functionals in density functional theory that consists of two parts. First, for the efficient approximation of a general density…

The derivative discontinuity of the exchange-correlation functional.

- Physics, MedicinePhysical chemistry chemical physics : PCCP
- 2014

Two sides of the problem are investigated: the failure of currently used approximate exchange-correlation functionals in DFT and the importance of the derivative discontinuity in the exact electronic structure of molecules, as revealed by full configuration interaction (FCI).

Derivative discontinuity in the strong-interaction limit of density-functional theory.

- Physics, MedicinePhysical review letters
- 2013

The exact strong-interaction limit of the exchange-correlation energy of Kohn-Sham density functional theory is generalized to open systems with fluctuating particle numbers, and at finite correlation regimes the authors observe a slightly smoothened discontinuity.

Learning to Approximate Density Functionals.

- MedicineAccounts of chemical research
- 2021

This work detail efforts in this direction, beginning with an elementary proof of principle from 2012, namely, finding the kinetic energy of several Fermions in a box using kernel ridge regression, and shows how deep neural networks with differentiable programming can be used to construct accurate density functionals from very few data points by using the Kohn-Sham equations themselves as a regularizer.