Periodic Reporting for period 1 - newDFT (Transforming applicability of density functional theory simulations)
Période du rapport: 2021-10-15 au 2023-10-14
Quantum modelling has become an integral part of research in disciplines that stretch from chemistry to material science. Owing to its high accuracy-to-cost ratio, density functional theory (DFT) is presently the most employed method in quantum modelling simulation. The key barrier precluding DFT from having high accuracy and predictive power accuracy across chemistry and material science is the inability of practical DFT methods to capture the 'strong correlation' regime. Strong correlation limits the applicability of DFT for many technologically-relevant problems, as many critical chemical systems and processes are strongly correlated, such as catalysis involving transition metals with half-filled orbitals.
In the present project, researcher Stefan Vuckovic worked in the group of Fabio Della Sala and aimed at addressing the strong corellation problem in DFT. Specifically, Vuckovic sought to improve a specific strong correlation DFT method, called “Multiple-radii functional” (MRF), in order to address the strong correlation problem in DFT. The MRF methodology has been designed to overcome shortcomings of DFT for challenging systems characterized by “strong correlation”, such as those with stretched chemical bonds and with elements with half-filled orbitals.
In the present project, researcher Stefan Vuckovic worked in the group of Fabio Della Sala and aimed at addressing the strong corellation problem in DFT. Specifically, Vuckovic sought to improve a specific strong correlation DFT method, called “Multiple-radii functional” (MRF), in order to address the strong correlation problem in DFT. The MRF methodology has been designed to overcome shortcomings of DFT for challenging systems characterized by “strong correlation”, such as those with stretched chemical bonds and with elements with half-filled orbitals.
The project lasted 13 months and by the planned work packages for this period, the following steps towards the improvement of MRF so it can be used routinely in DFT calculations were made:
(1) researcher implemented the required ingredients for MRF (“spherically averaged electronic density and its spherically averaged integrals”) and the MRF method itself in a standard quantum-chemical “Gaussian” code. The development of the integral package was also done to enable the MRF implementation. The code has been validated against a slower, but highly precise previous code. In addition to the implementation of MRF, researcher has also implemented the so-called MRF reverse machinery, that he had proposed earlier in 2019. This implemented MRF reverse machinery enables one to ‘translate’ the exact quantities to the MRF ones and use the latter ones as a feedback loop for refining the MRF method.
(2) The issues that MRF has for describing “weakly correlated” main-group molecules at equilibrium were identified and solutions for fixing this problem by incorporating additional constraints to the MRF functional have been proposed.
(3) Researchers described the mathematical features of MRF when applied to the “uniform electron gas”, and developed the exact physical constraints for the MRF functional when applied to “uniform and scaled densities” and the physical constraint ensuring the “non-positivity of its correlation energy density”. The resulting insights have been then used to construct improved MRF forms and strategies for using the MRF features for machine learning of new DFT methods have been discussed.
During the 13-month period of the project, researcher has published five peer review articles and an additional article will be submitted shortly.
The following articles have been published:
[1] Vuckovic, S., Gerolin, A., Daas, T. J., Bahmann, H., Friesecke, G., & Gori‐Giorgi, P. (2022). Density functionals based on the mathematical structure of the strong‐interaction limit of DFT. Wiley Interdisciplinary Reviews: Computational Molecular Science, e1634.
[2]. Sim, E., Song, S., Vuckovic, S., & Burke, K. (2022). Improving results by improving densities: Density-corrected density functional theory. Journal of the American Chemical Society, 144(15), 6625-6639.
[3] Vuckovic, S. (2022). Quantification of geometric errors made simple: application to main-group molecular structures. The Journal of Physical Chemistry A, 126(7), 1300-1311.
[4] Song, S., Vuckovic, S., Sim, E., & Burke, K. (2022). Density-corrected DFT explained: Questions and answers. Journal of chemical theory and computation, 18(2), 817-827.
[5] Song, S., Vuckovic, S., Kim, Y., Sim, E., & Burke, K. (2022). Extending density functional theory with near chemical accuracy beyond pure water. arXiv preprint arXiv:2207.04169. [accepted in Nature communications]
Ref. [1] reviews the key elements of the methods that are developed in this project (e.g. MRF). Refs. [2, 4] expand on the theory of 'Density Corrected DFT', to which researcher has contributed significantly over the last several years. In Ref. [5], accepted in Nature communications, researcher and his team have developed a method that gives an unprecedented level of accuracy (for the low-cost DFT method) when applied to water and molecules in solutions. This article has been accepted by Nature communications. In Ref. [3], researcher develops a new method for 'quantifying geometric errors in molecular structures from electronic structure methods'. This article has been published as a single author, and this greatly reinforced researcher's independence.s
(1) researcher implemented the required ingredients for MRF (“spherically averaged electronic density and its spherically averaged integrals”) and the MRF method itself in a standard quantum-chemical “Gaussian” code. The development of the integral package was also done to enable the MRF implementation. The code has been validated against a slower, but highly precise previous code. In addition to the implementation of MRF, researcher has also implemented the so-called MRF reverse machinery, that he had proposed earlier in 2019. This implemented MRF reverse machinery enables one to ‘translate’ the exact quantities to the MRF ones and use the latter ones as a feedback loop for refining the MRF method.
(2) The issues that MRF has for describing “weakly correlated” main-group molecules at equilibrium were identified and solutions for fixing this problem by incorporating additional constraints to the MRF functional have been proposed.
(3) Researchers described the mathematical features of MRF when applied to the “uniform electron gas”, and developed the exact physical constraints for the MRF functional when applied to “uniform and scaled densities” and the physical constraint ensuring the “non-positivity of its correlation energy density”. The resulting insights have been then used to construct improved MRF forms and strategies for using the MRF features for machine learning of new DFT methods have been discussed.
During the 13-month period of the project, researcher has published five peer review articles and an additional article will be submitted shortly.
The following articles have been published:
[1] Vuckovic, S., Gerolin, A., Daas, T. J., Bahmann, H., Friesecke, G., & Gori‐Giorgi, P. (2022). Density functionals based on the mathematical structure of the strong‐interaction limit of DFT. Wiley Interdisciplinary Reviews: Computational Molecular Science, e1634.
[2]. Sim, E., Song, S., Vuckovic, S., & Burke, K. (2022). Improving results by improving densities: Density-corrected density functional theory. Journal of the American Chemical Society, 144(15), 6625-6639.
[3] Vuckovic, S. (2022). Quantification of geometric errors made simple: application to main-group molecular structures. The Journal of Physical Chemistry A, 126(7), 1300-1311.
[4] Song, S., Vuckovic, S., Sim, E., & Burke, K. (2022). Density-corrected DFT explained: Questions and answers. Journal of chemical theory and computation, 18(2), 817-827.
[5] Song, S., Vuckovic, S., Kim, Y., Sim, E., & Burke, K. (2022). Extending density functional theory with near chemical accuracy beyond pure water. arXiv preprint arXiv:2207.04169. [accepted in Nature communications]
Ref. [1] reviews the key elements of the methods that are developed in this project (e.g. MRF). Refs. [2, 4] expand on the theory of 'Density Corrected DFT', to which researcher has contributed significantly over the last several years. In Ref. [5], accepted in Nature communications, researcher and his team have developed a method that gives an unprecedented level of accuracy (for the low-cost DFT method) when applied to water and molecules in solutions. This article has been accepted by Nature communications. In Ref. [3], researcher develops a new method for 'quantifying geometric errors in molecular structures from electronic structure methods'. This article has been published as a single author, and this greatly reinforced researcher's independence.s
The developed methodology of the present project aimed at fixing deficiencies of state-of-the-art DFT when applied to strongly correlated systems. The developed MRF method is designed for strong correlation and has a mathematical structure that is inspired by the exact mathematics of strong correlation in DFT. As such, its mathematical form of MRF is drastically different and far more involved than that of the state-of-the-art DFT methods. For this reason, in the present project, one could not follow standard routes used for improving semilocal functionals to refine MRF. For example, making a semilocal approximation exact for the uniform electron gas (a standard DFT paradigm) is trivial for semilocal approximations, but to make the MRF exact for the uniform electron gas new strategies have been devices in the project. At the same time, the new mathematical structure of MRF required the researcher to develop new techniques for its implementation in the standard quanatum chemical codes. The underlying new ingredients that have been implemented can be used by the DFT community for the construction of other methods inspired by the MRF form.
Potential impact - I expect the results (the implementation of new ingredients and the developed theory) to have the most direct impact on the development of machine-learned DFT methods. For example, the development of machine-learned DFT methods has become a hot topic in the DFT/quantum chemistry community, with perhaps the most notable example being DM21 developed by Deep Mind [Science, 374(6573), pp.1385-1389. ]. Even though DM21 has made a breakthrough in using machine learning to build DFT methods, DM21 still suffers from deficiencies inherent to the limitations of the state-of-the-art features (i.e. ingredient / mathematical forms) it uses. This project provides the new (MRF) features that expand the space where machines can learn new DFT methods and which are designed to solve the (arguably) most difficult problem in DFT - strong correlation.
Potential impact - I expect the results (the implementation of new ingredients and the developed theory) to have the most direct impact on the development of machine-learned DFT methods. For example, the development of machine-learned DFT methods has become a hot topic in the DFT/quantum chemistry community, with perhaps the most notable example being DM21 developed by Deep Mind [Science, 374(6573), pp.1385-1389. ]. Even though DM21 has made a breakthrough in using machine learning to build DFT methods, DM21 still suffers from deficiencies inherent to the limitations of the state-of-the-art features (i.e. ingredient / mathematical forms) it uses. This project provides the new (MRF) features that expand the space where machines can learn new DFT methods and which are designed to solve the (arguably) most difficult problem in DFT - strong correlation.