Machine learning application for DFT exchange functionals

Abstract

Currently density functional theory is one of the most commonly used electronic structure calculation method, thanks to its good accuracy - computational cost ratio. Since its invention the performance of DFT drastically increased, due to improvements both in the numerical approaches and in the exchange-correlation(XC) functional approximations. XC functional approximations are often categorized based on their complexity and these categories are referred to steps on Jacob’s ladder of DFT. The lowest step consists of the local density approximations(LDAs), which use only the density to approximate the XC energy at a given point. The higher rungs contain the generalized gradient approximations(GGAs), which also use the gradient of the density, and the meta-generalized gradient approximations (mGGAs), which include the Laplacian of the density or the kinetic energy density as well. Since density functional approximations (DFAs) play a crucial role in the success of DFT, they are a focus of research.In the present thesis, we examine why the SCAN functional results in poor equilibrium lattice parameter predictions for alkali - and alkaline earth metals, while it performs well for the rest of the tested solids. It was found that the exchange part of the XC energy plays the dominant role in the lattice parameter predictions. We identified the semi-core region to be responsible for a push in the direction of larger lattice parameters in all solids, but in materials with more interstitial electrons this effect was suppressed by the much stronger effect of the interstitial region.Using principal component analysis we also explored how much information does the Laplacian of the density carry when it is used alongside the gradient of the density and the kinetic energy density for DFAs. We showed that in most cases the Laplacian can be reproduced as a linear combination of the other descriptors, an exception to this was only found in the middle of covalent bonds. As a result we concluded that while the Laplacian might contain some useful information its inclusion in DFAs alongside the kinetic energy density is not expected to cause significant improvements in accuracy. Employing unsupervised machine learning methods we developed a way to identify groups of materials in databases, which occupy similar regions in the space of mGGA functional descriptors. This method was able to reproduce groups formed based on chemical intuition in a purely data driven way. Using our method databases with strong biases can be identified and rebalanced to produce better benchmarking or training datasets forDFA development.To find the limits of mGGA functionals and understand how specific changes in their functional form affect their performance we trained 25 mGGAs with different weights on equilibrium lattice parameter, cohesive energy and band gap errors. The training was carried out on a set of 44 solids for lattice parameter and cohesive energy and on 440 materials for band gap. It was found that mGGAs express a similar trade off between the accuracy of lattice parameters and cohesive energies as it was seen for GGA functionals,but in the meantime they manage to predict the band gaps significantly better. Compared to other existing functionals the trained ones showed better performance on this three specific errors, hinting that this might be the limit of mGGAs. The functional trained mostly on cohesive energies showed similarities to the mBEEF functional, which also produce slow cohesive energy errors. And the functional trained mostly on band gaps resembled the TASK functional, which was created to produce good band gaps. The similarities with existing functionals indicate that our findings could be general rules for functionals which excel at these specific properties.Finally, we also developed a neural network based model to predict the infrared(IR)spectra of polycyclic aromatic hydrocarbons(PAHs). These molecules are a focus of interest for astronomers since they are abundant in the universe and are suspected to be responsible for the so called "unidentified infrared emission" features in the IR spectra of various interstellar sources. The vast number of possible PAH configurations makes the brute-force prediction of their IR spectra with DFT impossible. Our solution based on Morgan fingerprints is many magnitudes faster and the accuracy of predictions is on par with DFT results. We also proposed a way to asses the accuracy of the predictions based on an ensemble of neural networks and in cases of poor accuracy the calculation can fall back to the traditional DFT approach.