Theoretical prediction of properties of atomistic systems : Density functional theory and machine learning

Abstract

The prediction of ground state properties of atomistic systems is of vital importance in technological advances as well as in the physical sciences. Fundamentally, these predictions are based on a quantum-mechanical description of many-electron systems. One of the hitherto most prominent theories for the treatment of such systems is density functional theory (DFT). The main reason for its success is due to its balance of acceptable accuracy with computational efficiency. By now, DFT is applied routinely to compute the properties of atomic, molecular, and solid state systems.The general approach to solve the DFT equations is to use a densityfunctional approximation (DFA). In Kohn-Sham (KS) DFT, DFAs are applied to the unknown exchange-correlation (xc) energy. In orbitalfree DFT on the other hand, where the total energy is minimized directly with respect to the electron density, a DFA applied to the noninteracting kinetic energy is also required. Unfortunately, central DFAs in DFT fail to qualitatively capture many important aspects of electronic systems. Two prime examples are the description of localized electrons, and the description of systems where electronic edges are present.In this thesis, I use a model system approach to construct a DFA for the electron localization function (ELF). The very same approach is also taken to study the non-interacting kinetic energy density (KED) in the slowly varying limit of inhomogeneous electron densities, where the effect of electronic edges are effectively included. Apart from the work on model systems, extensions of an exchange energy functional with an improved KS orbital description are presented: a scheme for improving its description of energetics of solids, and a comparison of its description of an essential exact exchange feature known as the derivative discontinuity with numerical data for exact exchange.An emerging alternative route towards the prediction of the properties of atomistic systems is machine learning (ML). I present a number of ML methods for the prediction of solid formation energies, with an accuracy that is on par with KS DFT calculations, and with orders-ofmagnitude lower computational cost. V Svensk sammanfattningAtt kunna förutsäga egenskaper hos atomistiska system utgör en viktig del av vår teknologiska utveckling, samt spelar en betydande roll i de fysikaliska vetenskaperna. Sådana förutsägelser bygger på en kvantmekanisk beskrivning av mångelektronsystem. En av de mest framstående teorierna för att behandla den här typen av system är täthets-funktionalteorin (DFT). Den främsta orsaken till dess framgång är att den lyckas kombinera skaplig noggrannhet med en bra beräkningsef-fektivitet. DFT används numera rutinmässigt för att beräkna storheter hos atomer, molekyler, och fasta kroppar.Generellt sett löses ekvationerna inom DFT genom att man inför en täthetsfunktionalapproximation (DFA). I Kohn-Sham (KS) DFT, används DFAer för att approximera utbytes-korrelationsenergin. Inom orbitalfri DFT, där målet är att direkt minimera den totala ...

Machine learning with force-field-inspired descriptors for materials: Fast screening and mapping energy landscape

“…The total number of descriptors found by combining the structural and chemical descriptors is 1557. It is to be noted that the CFID is independent of using primitive, conventional or supercell structures of a material, hence, it provides great advantage over many conventional methods such as Coulomb matrix where primitive structure must be used for representing a material [27].…”

Anomalous Phonon Lifetime Shortening in Paramagnetic CrN Caused by Spin-Lattice Coupling: A Combined Spin and Ab Initio Molecular Dynamics Study

“…The lattice vibrations enter the spin dynamics through their effect on the exchange interactions J ij (R ij ). The CrN exchange interactions have been determined in [32] and depend mostly on the Cr-Cr atomic pair distances. The range of interactions in paramagnetic CrN was found to be very short and could be well described with only first and second Cr-Cr neighbor terms [32,33].…”

“…The CrN exchange interactions have been determined in [32] and depend mostly on the Cr-Cr atomic pair distances. The range of interactions in paramagnetic CrN was found to be very short and could be well described with only first and second Cr-Cr neighbor terms [32,33]. The parametrization of these interactions are determined by magnetic direct cluster averaging using the same electronic structure framework and approximations as used for our AIMD runs [32] (see supplement [34]).…”

“…The range of interactions in paramagnetic CrN was found to be very short and could be well described with only first and second Cr-Cr neighbor terms [32,33]. The parametrization of these interactions are determined by magnetic direct cluster averaging using the same electronic structure framework and approximations as used for our AIMD runs [32] (see supplement [34]). Within our notation, the magnitudes of the effective magnetic moments m i and m j are absorbed into the exchange interactions J ij (R ij ).…”