Describing static correlation in bond dissociation by Kohn-Sham density functional theory

We show that density functional theory within the RPA (random phase approximation for the exchange-correlation energy) provides a correct description of bond dissociation in H$_2$ in a spin-restricted Kohn-Sham formalism, i.e. without artificial symmetry breaking. We present accurate adiabatic connection curves both at equilibrium and beyond the Coulson-Fisher point. The strong curvature at large bond length implies important static (left-right) correlation, justifying modern hybrid functional constructions but also demonstrating their limitations. Although exact at infinite and accurate around the equilibrium bond length, the RPA dissociation curve displays unphysical repulsion at larger but finite bond lengths. Going beyond the RPA by including the exact exchange kernel (RPA+X), we find a similar repulsion. We argue that this deficiency is due to the absence of double excitations in adiabatic linear response theory. Further analyzing the H$_2$ dissociation limit we show that the RPA+X is not size-consistent, in contrast to the RPA.Comment: 15 pages, 5 figure

PhysNet: A Neural Network for Predicting Energies, Forces, Dipole Moments and Partial Charges

In recent years, machine learning (ML) methods have become increasingly popular in computational chemistry. After being trained on appropriate ab initio reference data, these methods allow to accurately predict the properties of chemical systems, circumventing the need for explicitly solving the electronic Schr\"odinger equation. Because of their computational efficiency and scalability to large datasets, deep neural networks (DNNs) are a particularly promising ML algorithm for chemical applications. This work introduces PhysNet, a DNN architecture designed for predicting energies, forces and dipole moments of chemical systems. PhysNet achieves state-of-the-art performance on the QM9, MD17 and ISO17 benchmarks. Further, two new datasets are generated in order to probe the performance of ML models for describing chemical reactions, long-range interactions, and condensed phase systems. It is shown that explicitly including electrostatics in energy predictions is crucial for a qualitatively correct description of the asymptotic regions of a potential energy surface (PES). PhysNet models trained on a systematically constructed set of small peptide fragments (at most eight heavy atoms) are able to generalize to considerably larger proteins like deca-alanine (Ala$_{10}$): The optimized geometry of helical Ala$_{10}$ predicted by PhysNet is virtually identical to ab initio results (RMSD = 0.21 \r{A}). By running unbiased molecular dynamics (MD) simulations of Ala$_{10}$ on the PhysNet-PES in gas phase, it is found that instead of a helical structure, Ala$_{10}$ folds into a wreath-shaped configuration, which is more stable than the helical form by 0.46 kcal mol$^{-1}$ according to the reference ab initio calculations.Comment: 23 pages, 9 figures, 7 table

Lernen von Repräsentationen für atomistische Systeme mit tiefen neuronalen Netzen

Learning Representations of Atomistic Systems with Deep Neural Networks Deep Learning has been shown to learn efficient representations for structured data such as image, text or audio. However, with the rise of applying machine learning to quantum chemistry, research has been largely focused on the development of hand-crafted descriptors of atomistic systems. In this thesis, we propose novel neural network architectures that are able to learn efficient representations of molecules and materials. We demonstrate the capabilities of our models by accurately predicting chemical properties across compositional and configurational space on a variety of datasets. Beyond that, we perform a study of the quantum-mechanical properties of C20-fullerene that would not have been computationally feasible with conventional ab initio molecular dynamics. Finally, we analyze the trained models to find evidence that they have learned local representations of chemical environments and atom embeddings that agree with basic chemical knowledge.Tiefes Lernen hat gezeigt, dass es effiziente Repräsentationen für strukturierte Daten wie Bilder, Texte oder Audio lernen kann. Mit der zunehmenden Anwendung von Maschinellem Lernen in der Quantenchemie hat sich die Forschung dort vor allem auf die manuelle Entwicklung von Deskriptoren für atomistische Systeme konzentriert. In dieser Arbeit schlagen wir zwei neuartige Architekturen für Neuronale Netze vor, die in der Lage sind, effiziente Repräsentationen für Moleküle und Materialien zu erlernen. Wir demonstrieren die Fähigkeiten unserer Modelle durch die genaue Vorhersage von chemischen Eigenschaften für Systeme mit verschiedenen Zusammensetzungen sowie verschiedenen Atomanordnungen. Darüber hinaus führen wir eine Studie der quantenmechanischen Eigenschaften von dem Fulleren C20 durch, welche mit konventionellen ab initio Moleküldynamik- Simulationen nicht möglich gewesen wäre. Schließlich zeigt eine umfassende Analyse der trainierten Modelle deutliche Hinweise darauf, dass sie lokale Repräsentationen von chemischen Umgebungen sowie Atomeinbettungen gelernt haben, die mit chemischem Grundlagenwissen übereinstimmen

From Fundamentals to Spectroscopic Applications of Density Functional Theory

Density functional theory (DFT) and its time-dependent counterpart (TDDFT) are crucial tools in material discovery, drug design, biochemistry, catalysis, and nanoscience. However, despite its exact theoretical basis, approximations are necessary throughout, from the description of electron exchange and correlation (xc) interactions to the representation of wavefunctions for ever larger systems and the use of calculated quantities to explain and predict real-world phenomena. To address long-standing problems related to the speed and accuracy of approximations to the xc functional, we develop neural networks to emulate two such approximations, the local density (LDA) and generalized gradient (PBE) approximations, within the DFT code gpaw. We present a strategy for retraining the network and assess which training data is necessary to optimize performance for total energies over a wide class of molecules and crystals. While certain classes of materials proved difficult to describe, neural network implementations were able to reproduce the LDA and PBE xc functionals with high accuracy and a reasonable computation time. In an effort to develop a more efficient, robust, and accurate method for predicting the optical properties of low-dimensional systems, we introduce the LCAO-TDDFT-k-ω code within gpaw, where a linear combination of atomic orbitals (LCAO) representation of the Kohn-Sham wavefunctions and TDDFT implementation in wavenumber k and frequency ω space provides substantial memory and time savings, and a first order derivative discontinuity correction to the electronic gap brings the optical spectra in line with experimental measurements. Convergence of the basis set, the use of low-dimensional response functions, and different ways to incorporate the energy correction are explored for a series of materials across all dimensions: 0D fullerene and chlorophyll monomers, 1D single-walled carbon nanotubes, 2D graphene and phosphorene monolayers, and 3D anatase and rutile titanium dioxide. We develop a set of visualization tools for resolving the energetic, spatial, and reciprocal space distributions of excitations, and find LCAO-TDDFT-k-ω yields qualitative and semi-quantitative agreement with other TDDFT methods and implementations at a fraction of the time and memory cost. Finally, we introduce a phenomenological hydrodynamic model for the optical conductivity of graphene, with contributions due to universal conductivity, Pauli blocking, and intraband transitions included in a systematic way, is fit empirically with results from TDDFT, and manages to reproduce experimental spectra across a wide range of energies within energy loss equations derived for 2D materials. We find experimental parameters such as the amount of doping in graphene, the size of the collection aperture, and the energy of incoming electrons influence the shape of the spectra in important ways, especially in the energy region accessible to higher resolution probing techniques

Computational design of new superconducting materials and their targeted experimental synthesis

In the last six years (2015-2021), many superconducting hydrides with critical temperatures $\textit{T}$$_C$ of up to 253 K, a record for today, have been discovered. Now, a special field of hydride superconductivity at ultrahigh pressures has developed. For the most part, the properties of superhydrides are well described by the Migdal-Eliashberg theory of strong electron-phonon interaction, especially when anharmonicity of phonons is taken into account. The isotope effect, the effect of the magnetic field (up to 60-70 T) on the critical temperature and critical current in the hydride samples, the dependence of $\textit{T}$$_C$ on the pressure and degree of doping - all data indicate that polyhydrides are conventional superconductors, the theory of which was created by Bardeen, Cooper, and Schrieffer in 1957. This work presents a retrospective analysis of data for 2015-2021 and describes the main directions for future research in the field of hydride superconductivity. The thesis consists of six chapters devoted to the study of the structure and superconductivity of binary and ternary superhydrides of thorium (ThH$_9$ and ThH$_{10}$), yttrium (YH$_6$ and YH$_9$), europium and other lanthanides (Ce, Pr, Nd), and lanthanum-yttrium (La-Y). This work describes the physical properties of cubic decahydrides, hexahydrides, and hexagonal metal nonahydrides, demonstrates high efficiency of evolutionary algorithms and density functional methods in predicting the formation of polyhydrides under high-pressure and high-temperature conditions. We proposed a theoretical-experimental algorithm for analyzing the superconducting properties of hydrides, which makes it possible to systematize the accumulated experimental data. In general, this research is a vivid example of the effectiveness and synergy of modern methods for studying the condensed state of matter under high pressures

The aperiodic nature of mullite

181 p.Different methods were applied to investigate the vacancy and Al/Si order in mullite. At first the symmetry was analysed thoroughly to derive constraints on the vacancy distribution based on crystal chemical premises. On this basis a superspace model was developed that defines the polyhedra network consisting of octahedra, tetrahedral tricluster units and tetrahedral dicluster units as a function of the modulation wave vector and the vacancy concentration. Refinements of superspace models based on synchrotron single crystal X-ray diffraction measurements indicate that in the real structure the identified pattern is present, but with a decreased degree of order. Different samples exhibit different degrees of order suggesting that mainly disordered and fully ordered mullite crystals exist. The Al/Si ordering could not be derived from symmetry constraints and the occupancy of Si could not be refined. Nevertheless, an Al/Si ordering pattern could be identified from the analysis of the displacive modulation.The dependence of the satellite reflections on the chemical composition was studied with precession electron diffraction tomography and density functional theory. This allowed to characterise the structural modulation on a new level and reveal the fundamental ordering patterns that define the crystal structure of mullite in terms of vacancy, tricluster and Al/Si order. The understanding of the crystal structure forms a new basis for future research on the properties of mullite and related applications

Machine Learning static RPA response properties for accelerating GW calculations

In this thesis, I explore the possibility of constructing machine-learning models of the interacting density-density response function (DDRF) and quantities derived from it. Accurate models of the DDRF are a crucial ingredient to enabling GW quasiparticle calculations of more complex systems. Model DDRFs bypass the expensive calculation and inversion of the dielectric matrix, which is the origin of the poor scaling of the GW method with the number of atoms. The thesis is organized as follows: • Chapter 2 systematically reviews common descriptors used for machine-learning physical quantities. The key ideas behind the construction of such descriptors are discussed. First, I introduce several descriptors that systematically incorporate symmetry transformations that leave the target quantity invariant. These descriptors can be used for learning quantities such as the ground-state energy, atomization energies and scalar polarizabilities. Next, I discuss several descriptors and models that are equivariant under transformations of the molecular structure. These descriptors are ideal for learning quantities which transform in a defined way under the action of a transformation, such as vectors, tensors and functions, including the DDRF. • In Chapter 3, I introduce the key electronic structure methods employed throughout the thesis. I start by introducing density functional theory, followed by a detailed introduction to the GW method and the DDRF. • In Chapter 4, I develop a machine-learning model of an invariant quantity derived from the random phase approximation (RPA) DDRF: the scalar polarizability. In this chapter, I calculate the DDRF of 110 hydrogenated silicon clusters. The results of these calculations are then used to train a model of the scalar polarizability based on the SOAP descriptor [16]. The resulting model is then used to predict the scalar polarizability of clusters with up to 3000 silicon atoms while converging to the correct silicon scalar polarizability bulk limit. The findings of this chapter indicate that the scalar polarizability - even though derived from the non-local DDRF - can be accurately predicted from structural descriptors that only encode the local environment of each atom. These results indicate that the response of a non-metallic system to an external potential described by the DDRF may also be approximated as a sum of localized atomic contributions, which forms the motivation for the following two chapters. • In Chapter 5, I develop an approximation to the DDRF of the silicon clusters based on a projection onto atom-centred auxiliary density-fitting basis sets. The results of this chapter indicate that the plane-wave DDRF can be efficiently represented by a small localized basis, thus significantly reducing the size of the DDRF. At the end of this section, I develop a simple neural-network model of the DDRF in this localized basis, highlighting the necessity for using an equivariant descriptor and motivating the next chapter’s developments. • In Chapter 6, I develop a new approximation to the DDRF, which allows a decomposition into atomic contributions. I further introduce the neighbourhood density matrix (NDM), a non-local extension of the SOAP descriptor, which transforms under rotations in the same way as the atomic contributions to the DDRF. The developed method is then applied to the silicon clusters from the previous chapters. Using the NDM, I develop a neural-network model capable of accurately predicting the atomic contributions to the DDRF. These atomic contributions are transformed into a plane-wave basis and summed to obtain the DDRF of a silicon cluster. The predicted DDRFs are then used in GW calculations, which show that the model DDRFs accurately reproduce the quasiparticle energy corrections from GW calculations, as obtained within the atomic decomposition of the DDRF. This methodology can be used to construct arbitrarily complex model DDRFs based on purely structural properties of clusters and nanoparticles, paving the way towards GW calculations of complex systems, such as disordered materials, liquids, interfaces and nanoparticles.Open Acces