Unbiased materials design: the inverse problem in electronic structure calculations

• Applicant: Professor Dr. Miguel Marques
• Subject Area: Theoretical Condensed Matter Physics
• Term: from 2015 to 2020
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 274774632

• Final Report Year: 2021

Final Report Abstract

Due to continued advances in theory, scientific software, and high-performance computers, the calculation of the electronic band structure of materials is, by now, a routine problem. Unfortunately, the inverse problem, i.e., to devise a crystal structure with a certain electronic structure, is much more complicated. We developed a first principles approach that may allow us to tackle the inverse problem. Its only input is the periodic table of the elements and the basic laws of quantum mechanics, and it is based on a combination of genetic algorithms (that optimize the chemical composition) and global structural prediction methods (that obtain the crystal structure). Underneath, there is a density-functional theory code that provides forces, energies, and the electronic density of states. We performed genetic algorithm simulations where we tried to invert the electronic density of states of three emblematic materials, particularly graphene, MgB2 and FeSe. In all cases, our framework managed to optimize the problem, and to find materials that had density of states similar to the target material. Unfortunately, only for MgB2 our simulations arrived at the target. In fact, our results were particularly impressive in this case, where we also found a number of (novel) materials that mimic the electronic behavior of MgB2 close to the Fermi level, and that turned out to be superconducting with very reasonable transition temperatures. The largest problem with our approach is computational efficiency. In fact, due to the use of density-functional theory, our calculations are extremely time-consuming. To circumvent this problem, we are currently developing surrogate models based on machine learning methods. To train these models, we performed a large number of calculations (using high-throughput techniques) to provide training data.

Publications

• “High-throughput search of ternary chalcogenides for p-type transparent electrodes.” In: Scientific Reports 7.1 (2017)
  J. Shi, T. F. T. Cerqueira, W. Cui, F. Nogueira, S. Botti, and M. A. L. Marques
  
• “Predicting the Thermodynamic Stability of Solids Combining Density Functional Theory and Machine Learning.” In: Chemistry of Materials 29.12 (2017), pp. 5090–5103
  J. Schmidt, J. Shi, P. Borlido, L. Chen, S. Botti, and M. A. L. Marques
  
• “Structural prediction of two-dimensional materials under strain.” In: 2D Materials 4.4 (2017), p. 045009
  P. Borlido, C. Steigemann, N. N. Lathiotakis, M. A. L. Marques, and S. Botti
  
• “Nitrogen-hydrogen-oxygen ternary phase diagram: New phases at high pressure from structural prediction.” In: Physical Review Materials 2.2 (2018)
  J. Shi, W. Cui, S. Botti, and M. A. L. Marques
  
• “Predicting the stability of ternary intermetallics with density functional theory and machine learning.” In: The Journal of Chemical Physics 148.24 (2018), p. 241728
  J. Schmidt, L. Chen, S. Botti, and M. A. L. Marques
  
• “Stable hybrid organic–inorganic halide perovskites for photovoltaics from ab initio high-throughput calculations.” In: Journal of Materials Chemistry A 6.15 (2018), pp. 6463–6475
  S. Krbel, M. A. L. Marques, and S. Botti
  
• “The CECAM electronic structure library and the modular software development paradigm.” In: The Journal of Chemical Physics 153.2 (2020), p. 024117
  M. J. T. Oliveira et al