Report

Teaser, summary, work performed and final results

Periodic Reporting for period 2 - corr-DFT (Improving the accuracy and reliability of electronic structure calculations: New exchange-correlation functionals from a rigorous expansion at infinite coupling strength)

Teaser

Being able, by means of solely computer simulations, to make a preselection of pharmaceutical drugs that deserve to be tested experimentally, to predict the mechanisms of DNA damaging by specific compounds, or to design materials with specific properties, is of unquestionable...

Summary

Being able, by means of solely computer simulations, to make a preselection of pharmaceutical drugs that deserve to be tested experimentally, to predict the mechanisms of DNA damaging by specific compounds, or to design materials with specific properties, is of unquestionable interest for the whole society, in terms of both technological progress and economic and energetic saving.
In some aspects, this is already a reality: computer simulations of very many physical, chemical, biochemical and biomedical processes are successful, and of great help in understanding and guiding the experiments. On the other hand, there are still basic unsolved problems that hamper a complete reliability of the results and conclusions of such calculations.
It is important to understand that the systems of interest from the biological, medical, or nanotechnology point of view have sizes spanning several orders of magnitude. The effects important in the behaviour of such compounds also have different nature: some of them can be treated on a classical footing, other need to be studied at the quantum mechanical level. Because of the nature of quantum particles and the many-body interaction between the electrons, the quantum mechanical calculations are most demanding in terms of computational effort. Therefore, the accuracy and efficiency of the methods that treat the quantum mechanical part of such complex calculations are major concerns.
In principle, the laws of quantum mechanics are sufficient to predict how electrons arrange to bind together new molecules and biomolecules and to determine the properties of novel materials or new drugs. But in practice, even with the most powerful computers, this remains impossible, and we have to rely on approximations. The problem is that electrons interact with each other, which influences their behaviour – particularly in complicated reactions and complex materials. The idea of this project is to assume that the interactions between the electrons become infinitely strong, which represents a mathematical problem that is actually solvable. This is a completely new approach, which opens new routes to build approximations that have been shown to work very well for prototypical cases in which standard approaches fail.
The project will bring this approach to full maturity, by going beyond the proof-of-principle results, extending and exploiting the new mathematical findings to build practical approximations that increase the predictive power of computational chemistry and materials science.

Work performed

The project attacks the problem in two complementary ways: 1) by deriving exact results, particularly collaborating with the mathematics community of optimal transport, and 2) by starting immediately to construct and test approximations inspired to the mathematical structure of the exact results. These two strategies interact and reinforce each other.
In the first period (August 2015 - January 2017) we have made significant progress on both strategies:

1) Exact results: we have characterized the structure of exact solutions and shown that conceptually simple approximations yield very accurate results. We have also investigated how to add spins in the limit of infinite interaction.

2) Approximations: we have built new approximations based on the mathematical structure of 1) and tested them on chemical systems, with very encouraging results (see list of publications)

Final results

The new approximations that we have proposed and tested already solve some long-standing problems of standard approaches (indeed, three of the publications have been selected as Editor\'s choice by the American Chemical Society and by the American Institute of Physics because of their innovative character). The new approximations are not perfect yet and need further improvement, but they have raised interest in the scientific community for their clear potential and for the new conceptual line of work. Other research groups have started to work on similar ideas, building on our results and implementing our approximations.