# Error bar assessment for ab initio prediction of vacancy formation energies

# Error bar assessment for ab initio prediction of vacancy formation energies

Promotor(en):**15_MAT04**/ Solid-state physics**S. Cottenier**/Computational materials scientists who work at the atomic scale using quantum physics, can predict observable properties of solids ‘from scratch’ (= ab initio, from first principles). No empirical or tunable parameters are used. This does not mean, however, that these predictions are exact. The reason is that one does not solve the original (Schrödinger) equation for the material, but a mildly simplified version of it. This inevitably introduces an error bar on the predicted properties.

When materials engineers want to use such predictions from computational materials scientists, they need to know which size of error bars can be expected. The increasing interaction between experimental materials engineers and the community of ab initio condensed matter physics has therefore triggered a renewed interest in determining with some confidence the error bars on a variety of predicted properties.

The Center for Molecular Modeling has gained an international reputation in error bar quantification for structural

^{[1]}and thermal properties^{[2]}. In this thesis, you can build upon our expertise to tackle a different class of properties, related to defects: the vacancy formation energy. With which accuracy can quantum physics predict this property for real materials?**Goal**This work will lead you through all areas of the periodic table to calculate vacancy formation energies in all of the elemental materials. This systematic data set will then be compared with text book collections of experimental values. You will not only be able to determine the typical error bars, you will also be able to identify classes of materials for which these methods fail, and/or you might find elemental solids where the experimental values are perhaps not as reliable as the text book tabulations suggest. In addition, vacancy formation energies have never been investigated as systematically before. By screening host materials over the entire periodic table, you may discover thus far hidden trends and correlations. Finally, you can also choose to go deeper into simulation techniques for vacancies within periodic structures^{[3-5]}, which have thus far not been extensively tested for different host materials.In short, you will get a lot of experience in applying ab initio methods for many different solids, and your result will contribute to the thoughtful use of ab initio predictions for experimental materials science.

- Study programmeMaster of Science in Engineering Physics [EMPHYS], Master of Science in Physics and Astronomy [CMFYST]ClustersFor Engineering Physics students, this thesis is closely related to the cluster(s) modelling, materials, nanoReferences
[1] K. Lejaeghere et al., 'Error Estimates for Solid-State Density-Functional Theory Predictions: An Overview by Means of the Ground-State Elemental Crystals', Crit. Rev. Solid State 39, 1-24 (2014). http://dx.doi.org/10.1080/10408436.2013.772503

[2] K. Lejaeghere et al., 'Ab initio based thermal property predictions at a low cost: An error analysis', Phys. Rev. B 89, 014304 (2014). http://dx.doi.org/10.1103/PhysRevB.89.014304

[3] M. I. J. Probert and M. C. Payne, 'Improving the convergence of defect calculations in supercells: An ab initio study of the neutral silicon vacancy', Phys. Rev. B 67, (2003). http://dx.doi.org/10.1103/10.1103/PhysRevB.67.075204

[4] C. W. M. Castleton et al., 'Density functional theory calculations of defect energies using supercells', Mod. Sim. Mater. Sci. Eng. 17, 084003 (2009).

http://dx.doi.org/10.1088/0965-0393/17/8/084003

[5] R. Nazarov et al., 'Vacancy formation energies in fcc metals: Influence of exchange-correlation functionals and correction schemes', Phys. Rev. B 85, 144118 (2012). http://dx.doi.org/10.1103/PhysRevB.85.144118