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## Improving the accuracy of ab-initio predictions for materials

#### CECAM-FR-MOSER

#### Organisers

Ab-initio simulation methods are the major tool to perform research in condensed matter physics, materials science, quantum and molecular chemistry. They can be classified in terms of their accuracy and efficiency, but typically more accurate means less efficient and vice-versa. The accuracy depends mainly on how accurate one can solve the electronic problem. The most accurate algorithms are the wave-function based methods, such as Full CI, Coupled Cluster (CC), and Quantum Monte Carlo (QMC) followed by the Density Functional Theory-(DFT)-based methods and finally more approximate methods such as Tight-Binding. Another impor- tant consideration is how the accuracy of a given method scales with the size of the system under consideration. Among the wave-function based methods, the accuracy of traditional quantum chemistry methods can be sys- tematically improved but their scaling with system size limits their applicability to small molecules. On the other hand, QMC methods have a much more tractable scaling and have, in spite of the “fermion sign problem” and the commonly used fixed-node approximation, because the energies are variational upper bounds, a way of systematically improving the accuracy. Recently there has been much progress in the use of pseudopotentials and the systematic improvement of nodal surfaces using backflow, and multiple determinants. [1, 2, 3]

Conversely DFT based methods are based on a plethora of different self-consistent mean field approxima- tions, each one tuned to best represent a class of systems but with limited transferability. Despite progress in developing more general functionals [4, 5, 6], DFT is missing an "internal" accuracy scale; its accuracy is gen- erally established against more fundamental theories (like CC or QMC) or against experiments. DFT methods are very popular because their favorable scaling with system size, the same as for QMC, but with a smaller prefactor.

In a number of recent applications [7, 8] it was found that inclusion of nuclear quantum effects (NQE) worsen considerably the agreement between DFT predictions and experiments. This is ascribed to the inac- curacies of DFT. This illustrates the importance of not using experimental data alone to improve the DFT functional but instead calculations using more fundamental methods. There has been a recent effort to establish the accuracy of DFT approximations by benchmarking with QMC calculations not only for equilibrium geome- tries but also for thermal configurations. This benchmarking can be customized for the individual molecules at a given temperature and pressure and geometry [9, 10, 11, 12].

Another important aspect concerns finite size effects in modelling extended systems. Although corrections can be developed for homogenous systems, for more complex situations with several characteristic length scales one needs to consider systems sizes that cannot be tackled by ab-initio methods. In these applications one needs to use an effective interaction energy. A recent development is the use of Machine Learning (ML) techniques to obtain energy functions with ab-initio accuracy [13, 14, 15]. Their transferability and accuracy assessment is still unsolved to some extent but progress is rapid. A related development is to use ML methods to by-passing the Kohn-Sham paradigm of DFT and directly address potential-density map [16, 17, 18]

The following is a list of topics that will be discussed during the meeting:

• Benchmarking existing DFT functionals with QMC. DFT has the potential to be accurate, but the main problem with its predictive power is that its accuracy can be system dependent. QMC was instrumental in developing the first exchange-correlation approximations (e. g. LDA), and we envisage that it can play a substantial role to help the discovery and tuning of new functionals. In particular, the tuning of dispersion interactions appears to be a crucial elements still not fully controlled in modern DFT approximations while it plays a crucial role in many systems like hydrogen and hydrogen based materials such as water.

• ML approaches with QMC accuracy. Machine Learning (ML) has attracted significant interest recently, mainly because of its potential to study real life systems, and also to explore the phase space at a scale that is not available to ab-initio methods. However, crucial for the ML method is the quality of the training set. It is often possible to train a ML potential on small systems, where accurate energies and forces can be obtained by quantum chemistry methods. However, training sets including larger systems are needed. QMC has the potential to provide them especially going forward with exascale computing.

• opportunity for new exascale applications of QMC to impact simulation for larger systems and longer time scale. QMC is capable of exploiting parallelism very efficiently, and is probably one of the few methods already capable of running at the exascale level. ML methods on large data set are also inherently parallel and directly usable on exascale machines.

• We will address the problem of using and testing the force field derived for a small systems to those of a much larger size.

• We will discuss the use of ML methods to derive new classes of wave functions for QMC calculations of complex systems.

## References

**France**

Michele Casula (Institut de Minéralogie, de Physique des Matériaux et de Cosmochimie, Sorbonne Université) - Organiser

**Italy**

CARLO PIERLEONI (University of L'Aquila) - Organiser

**United Kingdom**

Dario Alfe (UCL) - Organiser

**United States**

David Ceperley (University of Illinois Urbana-Champaign) - Organiser