Advancing relativistic electronic structure methods for solids and in the time domain

Paper I and III are not available in Munin Paper I: Repisky, M., Konecny, L., Kadek, M., Komorovsky, S., Malkin, O.L., Malkin, V.G. & Ruud, K. (2015). Excitation Energies from Real-Time Propagation of the Four-Component Dirac–Kohn–Sham Equation. Available in Journal of Chemical Theory and Computation, 11(3), 980-991. Paper III: Konecny, L., Kadek, M., Komorovsky, S., Malkina, O.L., Ruud, K. & Repisky, M. (2016). Acceleration of Relativistic Electron Dynamics by Means of X2C Transformation: Application to the Calculation of Nonlinear Optical Properties. Available in Journal of Chemical Theory and Computation, 12(12), 5823-5833.Effects arising from the special theory of relativity significantly influence the electronic structure and properties of molecules and solid-state materials containing heavy elements. At the same time, the inclusion of the relativistic effects in theoretical and computational models increases their methodological complexity and the computational cost. In the solid state, additional challenges to the mathematical and algorithmic robustness of methods arise due to the infinite extent of the systems. In this thesis, I present two extensions of quantum-chemical relativistic methods based on Gaussian-type basis functions in the study of the electronic ground-state of molecules: band-structure calculations of materials in the solid state, and simulations of the response of molecules that are subjected to an external time-dependent field by propagating their perturbed state in real time. The development of the relativistic methods for solids was preceded by an independent implementation of the theory at the nonrelativistic level. In comparison to methods based on plane waves, the use of Gaussian-type basis functions in the solid-state community is limited. The relativistic method presented here is the first ever implementation of the Dirac-type equations using Gaussian-type basis functions for solid-state systems, and can be used to study one-, two-, and three-dimensional periodic systems on an equal footing for the entire periodic table. The time propagation method is a technically simpler alternative to perturbation approaches, and is applied here to probe relativistic effects on absorption and X-ray spectra, and nonlinear optical and chiroptical properties of molecules. Our work in the both areas provides a technology with the potential to predict properties of novel materials, and to support the interpretation of experiments

Relativistic Real-Time Methods

Recent advances in laser technology enable to follow electronic motion at its natural time-scale with ultrafast pulses, leading the way towards atto- and femtosecond spectroscopic experiments of unprecedented resolution. Understanding of these laser-driven processes, which almost inevitably involve non-linear light-matter interactions and non-equilibrium electron dynamics, is challenging and requires a common effort of theory and experiment. Real-time electronic structure methods provide the most straightforward way to simulate experiments and to gain insights into non-equilibrium electronic processes. In this Chapter, we summarize the fundamental theory underlying the relativistic particle-field interaction Hamiltonian as well as equation-of-motion for exact-state wave function in terms of the one- and two-electron reduced density matrix. Further, we discuss the relativistic real-time electron dynamics mean-field methods with an emphasis on Density-Functional Theory and Gaussian basis, starting from the four-component (Dirac) picture and continue to the two-component (Pauli) picture, where we introduce various flavours of modern exact two-component (X2C) Hamiltonians for real-time electron dynamics. We also overview several numerical techniques for real-time propagation and signal processing in quantum electron dynamics. We close this Chapter by listing selected applications of real-time electron dynamics to frequency-resolved and time-resolved spectroscopies

X-ray absorption resonances near L2,3-edges from real-time propagation of the Dirac–Kohn–Sham density matrix

Published version. Source at http://doi.org/10.1039/c5cp03712c.The solution of the Liouville–von Neumann equation in the relativistic Dirac–Kohn–Sham density matrix formalism is presented and used to calculate X-ray absorption cross sections. Both dynamical relaxation effects and spin–orbit corrections are included, as demonstrated by calculations of the X-ray absorption of SF6 near the sulfur L2,3-edges. We also propose an analysis facilitating the interpretation of spectral transitions from real-time simulations, and a selective perturbation that eliminates nonphysical excitations that are artifacts of the finite basis representation

Cost-Efficient High-Resolution Linear Absorption Spectra Through Extrapolating the Dipole Moment from Real-Time Time-Dependent Electronic-Structure Theory

Accepted manuscript, submitted to Journal of Chemical Theory and Computation: https://pubs.acs.org/action/doSearch?AllField=Journal+of+Chemical+Theory+and+Computation.We present a novel function fitting method for approximating the propagation of the time-dependent electric dipole moment from real-time electronic structure calculations. Real-time calculations of the electronic absorption spectrum require discrete Fourier transforms of the electric dipole moment. The spectral resolution is determined by the total propagation time, i.e. the trajectory length of the dipole moment, causing a high computational cost. Our developed method uses function fitting on shorter trajectories of the dipole moment, achieving arbitrary spectral resolution through extrapolation. Numerical testing shows that the fitting method can reproduce high-resolution spectra using short dipole trajectories. The method converges with as little as 100 a.u. dipole trajectories for some systems, though the difficulty converging increases with the spectral density. We also introduce an error estimate of the fit, reliably assessing its convergence and hence the quality of the approximated spectrum

Band structures and Z2\mathbb{Z}_2 invariants of 2D transition metal dichalcogenide monolayers from fully-relativistic Dirac-Kohn-Sham theory using Gaussian-type orbitals

Two-dimensional (2D) materials exhibit a wide range of remarkable phenomena, many of which owe their existence to the relativistic spin-orbit coupling (SOC) effects. To understand and predict properties of materials containing heavy elements, such as the transition-metal dichalcogenides (TMDs), relativistic effects must be taken into account in first-principles calculations. We present an all-electron method based on the four-component Dirac Hamiltonian and Gaussian-type orbitals (GTOs) that overcomes complications associated with linear dependencies and ill-conditioned matrices that arise when diffuse functions are included in the basis. Until now, there has been no systematic study of the convergence of GTO basis sets for periodic solids either at the nonrelativistic or the relativistic level. Here we provide such a study of relativistic band structures of the 2D TMDs in the hexagonal (2H), tetragonal (1T), and distorted tetragonal (1T') structures, along with a discussion of their SOC-driven properties (Rashba splitting and $\mathbb{Z}_2$ topological invariants). We demonstrate the viability of our approach even when large basis sets with multiple basis functions involving various valence orbitals (denoted triple- and quadruple-$\zeta$) are used in the relativistic regime. Our method does not require the use of pseudopotentials and provides access to all electronic states within the same framework. Our study paves the way for direct studies of material properties, such as the parameters in spin Hamiltonians, that depend heavily on the electron density near atomic nuclei where relativistic and SOC effects are the strongest.Comment: 15 pages, 3 figures, 2 table

Advancing relativistic electronic structure methods for solids and in the time domain

Effects arising from the special theory of relativity significantly influence the electronic structure and properties of molecules and solid-state materials containing heavy elements. At the same time, the inclusion of the relativistic effects in theoretical and computational models increases their methodological complexity and the computational cost. In the solid state, additional challenges to the mathematical and algorithmic robustness of methods arise due to the infinite extent of the systems. In this thesis, I present two extensions of quantum-chemical relativistic methods based on Gaussian-type basis functions in the study of the electronic ground-state of molecules: band-structure calculations of materials in the solid state, and simulations of the response of molecules that are subjected to an external time-dependent field by propagating their perturbed state in real time. The development of the relativistic methods for solids was preceded by an independent implementation of the theory at the nonrelativistic level. In comparison to methods based on plane waves, the use of Gaussian-type basis functions in the solid-state community is limited. The relativistic method presented here is the first ever implementation of the Dirac-type equations using Gaussian-type basis functions for solid-state systems, and can be used to study one-, two-, and three-dimensional periodic systems on an equal footing for the entire periodic table. The time propagation method is a technically simpler alternative to perturbation approaches, and is applied here to probe relativistic effects on absorption and X-ray spectra, and nonlinear optical and chiroptical properties of molecules. Our work in the both areas provides a technology with the potential to predict properties of novel materials, and to support the interpretation of experiments

Relativistic Real-Time Methods

Recent advances in laser technology enable to follow electronic motion at its natural time-scale with ultrafast pulses, leading the way towards atto- and femtosecond spectroscopic experiments of unprecedented resolution. Understanding of these laser-driven processes, which almost inevitably involve non-linear light-matter interactions and non-equilibrium electron dynamics, is challenging and requires a common effort of theory and experiment. Real-time electronic structure methods provide the most straightforward way to simulate experiments and to gain insights into non-equilibrium electronic processes. In this Chapter, we summarize the fundamental theory underlying the relativistic particle–field interaction Hamiltonian as well as equation-of-motion for exact-state wave function in terms of the one- and two-electron reduced density matrix. Further, we discuss the relativistic real-time electron dynamics mean-field methods with an emphasis on Density-Functional Theory and Gaussian basis, starting from the four-component (Dirac) picture and continue to the two-component (Pauli) picture, where we introduce various flavours of modern exact two-component (X2C) Hamiltonians for real-time electron dynamics. We also overview several numerical techniques for real-time propagation and signal processing in quantum electron dynamics. We close this Chapter by listing selected applications of real-time electron dynamics to frequency-resolved and time-resolved spectroscopies

All-electron fully relativistic Kohn-Sham theory for solids based on the Dirac-Coulomb Hamiltonian and Gaussian-type functions

We present the first full-potential method that solves the fully relativistic four-component Dirac-Kohn-Sham equation for materials in the solid state within the framework of atom-centered Gaussian-type orbitals (GTOs). Our GTO-based method treats one-, two-, and three-dimensional periodic systems on an equal footing, and allows for a seamless transition to the methodology commonly used in studies of molecules with heavy elements. The scalar relativistic effects as well as the spin-orbit interaction are handled variationally. The full description of the electron-nuclear potential in the core region of heavy nuclei is straightforward due to the local nature of the GTOs and does not pose any computational difficulties. We show how the time-reversal symmetry and a quaternion algebra-based formalism can be exploited to significantly reduce the increased methodological complexity and computational cost associated with multiple wave-function components coupled by the spin-orbit interaction. We provide a detailed description of how to employ the matrix form of the multipole expansion and an iterative renormalization procedure to evaluate the conditionally convergent infinite lattice sums arising in studies of periodic systems. Next, we investigate the problem of inverse variational collapse that arises if the Dirac operator containing a repulsive periodic potential is expressed in a basis that includes diffuse functions, and suggest a possible solution. Finally, we demonstrate the validity of the method on three-dimensional silver halide (AgX) crystals with large relativistic effects and two-dimensional honeycomb structures (silicene and germanene) exhibiting the spin-orbit-driven quantum spin Hall effect. Our results are well-converged with respect to the basis set limit using standard bases developed for molecular calculations and indicate that the common rule of removing basis functions with small exponents should not be applied when transferring the molecular basis to solids

Electrochemical Potential of the Metal Organic Framework MIL-101(Fe) as Cathode Material in Li-Ion Batteries

We discuss the characteristic factors that determine the electrochemical potentials in a metal-organic framework used as cathode for Li-ion batteries via density functional theory-based simulations. Our focus is on MIL-101(Fe) cathode material. Our study gives insight into the role of local atomic environment and structural deformations in generating electrochemical potential

Anodic Activity of Hydrated and Anhydrous Iron (II) Oxalate in Li-Ion Batteries

We discuss the applicability of the naturally occurring compound Ferrous Oxalate Dihydrate (FOD) (FeC2O4·2H2O) as an anode material in Li-ion batteries. Using first-principles modeling, we evaluate the electrochemical activity of FOD and demonstrate how its structural water content affects the intercalation reaction and contributes to its performance. We show that both Li0 and Li+ intercalation in FOD yields similar results. Our analysis indicates that fully dehydrated ferrous oxalate is a more promising anodic material with higher electrochemical stability: it carries 20% higher theoretical Li storage capacity and a lower voltage (0.68 V at the PBE/cc-pVDZ level), compared to its hydrated (2.29 V) or partially hydrated (1.43 V) counterparts