Real-Time Time-Dependent Density Functional Theory for Simulating Nonequilibrium Electron Dynamics.

The explicit real-time propagation approach for time-dependent density functional theory (RT-TDDFT) has increasingly become a popular first-principles computational method for modeling various time-dependent electronic properties of complex chemical systems. In this Perspective, we provide a nontechnical discussion of how this first-principles simulation approach has been used to gain novel physical insights into nonequilibrium electron dynamics phenomena in recent years. Following a concise overview of the RT-TDDFT methodology from a practical standpoint, we discuss our recent studies on the electronic stopping of DNA in water and the Floquet topological phase as examples. Our discussion focuses on how RT-TDDFT simulations played a unique role in deriving new scientific understandings. We then discuss existing challenges and some new advances at the frontier of RT-TDDFT method development for studying increasingly complex dynamic phenomena and systems.

Theory of moment propagation for quantum dynamics in single-particle description.

We present a novel theoretical formulation for performing quantum dynamics in terms of moments within the single-particle description. By expressing the quantum dynamics in terms of increasing orders of moments, instead of single-particle wave functions as generally done in time-dependent density functional theory, we describe an approach for reducing the high computational cost of simulating the quantum dynamics. The equation of motion is given for the moments by deriving analytical expressions for the first-order and second-order time derivatives of the moments, and a numerical scheme is developed for performing quantum dynamics by expanding the moments in the Taylor series as done in classical molecular dynamics simulations. We propose a few numerical approaches using this theoretical formalism on a simple one-dimensional model system, for which an analytically exact solution can be derived. The application of the approaches to an anharmonic system is also discussed to illustrate their generality. We also discuss the use of an artificial neural network model to circumvent the numerical evaluation of the second-order time derivatives of the moments, as analogously done in the context of classical molecular dynamics simulations.

Electronic Excitation Response of DNA to High-Energy Proton Radiation in Water.

The lack of molecular-level understanding for the electronic excitation response of DNA to charged particle radiation, such as high-energy protons, remains a fundamental scientific bottleneck in advancing proton and other ion beam cancer therapies. In particular, the dependence of different types of DNA damage on high-energy protons represents a significant knowledge void. Here we employ first-principles real-time time-dependent density functional theory simulation, using a massively parallel supercomputer, to unravel the quantum-mechanical details of the energy transfer from high-energy protons to DNA in water. The calculations reveal that protons deposit significantly more energy onto the DNA sugar-phosphate side chains than onto the nucleobases, and greater energy transfer is expected onto the DNA side chains than onto water. As a result of this electronic stopping process, highly energetic holes are generated on the DNA side chains as a source of oxidative damage.

First-Principles Approach for Coupled Quantum Dynamics of Electrons and Protons in Heterogeneous Systems.

The coupled quantum dynamics of electrons and protons is ubiquitous in many dynamical processes involving light-matter interaction, such as solar energy conversion in chemical systems and photosynthesis. A first-principles description of such nuclear-electronic quantum dynamics requires not only the time-dependent treatment of nonequilibrium electron dynamics but also that of quantum protons. Quantum mechanical correlation between electrons and protons adds further complexity to such coupled dynamics. Here we extend real-time nuclear-electronic orbital time-dependent density functional theory (RT-NEO-TDDFT) to periodic systems and perform first-principles simulations of coupled quantum dynamics of electrons and protons in complex heterogeneous systems. The process studied is an electronically excited-state intramolecular proton transfer of o-hydroxybenzaldehyde in water and at a silicon (111) semiconductor-molecule interface. These simulations illustrate how environments such as hydrogen-bonding water molecules and an extended material surface impact the dynamical process on the atomistic level. Depending on how the molecule is chemisorbed on the surface, excited-state electron transfer from the molecule to the semiconductor surface can inhibit ultrafast proton transfer within the molecule. This Letter elucidates how heterogeneous environments influence the balance between the quantum mechanical proton transfer and excited electron dynamics. The periodic RT-NEO-TDDFT approach is applicable to a wide range of other photoinduced heterogeneous processes.

First Principles Dynamics Study of Excited Hole Relaxation in DNA.

A recent theoretical work showed that ion irradiation generates excited holes deep within the valence band of DNA. In this work, we investigate the excited hole relaxation toward HOMO using a first-principles computational method following such ionization events. The excited hole relaxation is found to depend significantly on the energetic position of the excited hole generated. The relaxation process is found to be an order of magnitude slower for holes that are generated deeper than 20 eV than those generated within 10 eV, where the probability for the initial ionization events is the highest. However, the excited holes that are generated in different spatial moieties such as DNA nucleotide bases and phosphate backbones do not show noticeable differences in terms of the relaxation time. Our work also shows that decoherence due to nuclei dynamics slows down the relaxation by a factor of two or more. At the same time, the relaxation time is found to be less than a couple of picoseconds, much shorter than typical timescales associated with chemical bond dissociation.

Nonlinear electronic excitation in water under proton irradiation: a first principles study.

Nonlinear dynamics of electronic excitation bridge physical and physicochemical stages of water radiolysis under proton irradiation, a multi-scale physicochemical process that is fundamental to a wide range of technological and medical applications of high-energy protons. We study the spatial and temporal changes to the excited holes generated in this ionization event using first-principles theory simulation. A significant majority of holes are formed in the immediate vicinity of the irradiating proton paths, and these holes decay rapidly, while secondary excitations are simultaneously induced in regions farther away. While the hole population remains constant, the observed spatially spreading hole distribution cannot be described as concentration-dependent diffusion current. Compared to the primary excitation induced by the irradiating protons, the secondary excitation farther away is somewhat less energetic. The first-principles theory simulation here provides a detailed description of how the primary excitation by proton radiation precedes the formation of cationic holes, which undergo ultrafast chemical processes in water radiolysis.

Nuclear-electronic orbital approach to quantization of protons in periodic electronic structure calculations.

The nuclear-electronic orbital (NEO) method is a well-established approach for treating nuclei quantum mechanically in molecular systems beyond the usual Born-Oppenheimer approximation. In this work, we present a strategy to implement the NEO method for periodic electronic structure calculations, particularly focused on multicomponent density functional theory (DFT). The NEO-DFT method is implemented in an all-electron electronic structure code, FHI-aims, using a combination of analytical and numerical integration techniques as well as a resolution of the identity scheme to enhance computational efficiency. After validating this implementation, proof-of-concept applications are presented to illustrate the effects of quantized protons on the physical properties of extended systems, such as two-dimensional materials and liquid-semiconductor interfaces. Specifically, periodic NEO-DFT calculations are performed for a trans-polyacetylene chain, a hydrogen boride sheet, and a titanium oxide-water interface. The zero-point energy effects of the protons as well as electron-proton correlation are shown to noticeably impact the density of states and band structures for these systems. These developments provide a foundation for the application of multicomponent DFT to a wide range of other extended condensed matter systems.

Excitation energy-dependent photocurrent switching in a single-molecule photodiode.

The direction of electron flow in molecular optoelectronic devices is dictated by charge transfer between a molecular excited state and an underlying conductor or semiconductor. For those devices, controlling the direction and reversibility of electron flow is a major challenge. We describe here a single-molecule photodiode. It is based on an internally conjugated, bichromophoric dyad with chemically linked (porphyrinato)zinc(II) and bis(terpyridyl)ruthenium(II) groups. On nanocrystalline, degenerately doped indium tin oxide electrodes, the dyad exhibits distinct frequency-dependent, charge-transfer characters. Variations in the light source between red-light (∼1.9 eV) and blue-light (∼2.7 eV) excitation for the integrated photodiode result in switching of photocurrents between cathodic and anodic. The origin of the excitation frequency-dependent photocurrents lies in the electronic structure of the chromophore excited states, as shown by the results of theoretical calculations, laser flash photolysis, and steady-state spectrophotometric measurements.

Dynamical transition orbitals: A particle-hole description in real-time TDDFT dynamics.

We expand the concept of natural transition orbitals in the context of real-time time-dependent density functional theory (RT-TDDFT) and show its application in practical calculations. Kohn-Sham single-particle wavefunctions are propagated in RT-TDDFT simulation, and physical properties remain invariant under their unitary transformation. In this work, we exploit this gauge freedom and expand the concept of natural transition orbitals, which is widely used in linear-response TDDFT, for obtaining a particle-hole description in RT-TDDFT simulation. While linear-response TDDFT is widely used to study electronic excitation, RT-TDDFT can be employed more generally to simulate non-equilibrium electron dynamics. Studying electron dynamics in terms of dynamic transitions of particle-hole pairs is, however, not straightforward in the RT-TDDFT simulation. By constructing natural transition orbitals through projecting time-dependent Kohn-Sham wave functions onto occupied/unoccupied eigenstate subspaces, we show that linear combinations of a pair of the resulting hole/particle orbitals form a new gauge, which we refer to as dynamical transition orbitals. We demonstrate the utility of this framework to analyze RT-TDDFT simulations of optical excitation and electronic stopping dynamics in the particle-hole description.

All-electron real-time and imaginary-time time-dependent density functional theory within a numeric atom-centered basis function framework.

Real-time time-dependent density functional theory (RT-TDDFT) is an attractive tool to model quantum dynamics by real-time propagation without the linear response approximation. Sharing the same technical framework of RT-TDDFT, imaginary-time time-dependent density functional theory (it-TDDFT) is a recently developed robust-convergence ground state method. Presented here are high-precision all-electron RT-TDDFT and it-TDDFT implementations within a numerical atom-centered orbital (NAO) basis function framework in the FHI-aims code. We discuss the theoretical background and technical choices in our implementation. First, RT-TDDFT results are validated against linear-response TDDFT results. Specifically, we analyze the NAO basis sets' convergence for Thiel's test set of small molecules and confirm the importance of the augmentation basis functions for adequate convergence. Adopting a velocity-gauge formalism, we next demonstrate applications for systems with periodic boundary conditions. Taking advantage of the all-electron full-potential implementation, we present applications for core level spectra. For it-TDDFT, we confirm that within the all-electron NAO formalism, it-TDDFT can successfully converge systems that are difficult to converge in the standard self-consistent field method. We finally benchmark our implementation for systems up to ∼500 atoms. The implementation exhibits almost linear weak and strong scaling behavior.

Simulating electronic excitation and dynamics with real-time propagation approach to TDDFT within plane-wave pseudopotential formulation.

We give a perspective on simulating electronic excitation and dynamics using the real-time propagation approach to time-dependent density functional theory (RT-TDDFT) in the plane-wave pseudopotential formulation. RT-TDDFT is implemented in various numerical formalisms in recent years, and its practical application often dictates the most appropriate implementation of the theory. We discuss recent developments and challenges, emphasizing numerical aspects of studying real systems. Several applications of RT-TDDFT simulation are discussed to highlight how the approach is used to study interesting electronic excitation and dynamics phenomena in recent years.

Temperature dependence of nuclear quantum effects on liquid water via artificial neural network model based on SCAN meta-GGA functional.

We investigate the temperature dependence of nuclear quantum effects (NQEs) on structural and dynamic properties of liquid water by training a neural network force field using first-principles molecular dynamics (FPMD) based on the strongly constrained and appropriately normed meta-generalized gradient approximation exchange-correlation approximation. The FPMD simulation based on density functional theory has become a powerful computational approach for studying a wide range of condensed phase systems. However, its large computational cost makes it difficult to incorporate NQEs in the simulation and investigate temperature dependence of various properties. To circumvent this difficulty, we use an artificial neural network model and employ the thermostatted ring polymer MD approach for studying the temperature dependence of NQEs on various properties. The NQEs generally bring the radial distribution functions closer to the experimental measurements. Translational diffusivity and rotational dynamics of water molecules are both slowed down by the NQEs. The competing inter-molecular and intra-molecular quantum effects on hydrogen bonds, as discussed by Habershon, Markland, and Manolopoulos [J. Chem. Phys. 131(2), 024501 (2019)], can explain the observed temperature dependence of the NQEs on the dynamical properties in our simulation.

All-electron ab initio Bethe-Salpeter equation approach to neutral excitations in molecules with numeric atom-centered orbitals.

The Bethe-Salpeter equation (BSE) based on GW quasiparticle levels is a successful approach for calculating the optical gaps and spectra of solids and also for predicting the neutral excitations of small molecules. We here present an all-electron implementation of the GW+BSE formalism for molecules, using numeric atom-centered orbital (NAO) basis sets. We present benchmarks for low-lying excitation energies for a set of small organic molecules, denoted in the literature as "Thiel's set." Literature reference data based on Gaussian-type orbitals are reproduced to about one millielectron-volt precision for the molecular benchmark set, when using the same GW quasiparticle energies and basis sets as the input to the BSE calculations. For valence correlation consistent NAO basis sets, as well as for standard NAO basis sets for ground state density-functional theory with extended augmentation functions, we demonstrate excellent convergence of the predicted low-lying excitations to the complete basis set limit. A simple and affordable augmented NAO basis set denoted "tier2+aug2" is recommended as a particularly efficient formulation for production calculations. We finally demonstrate that the same convergence properties also apply to linear-response time-dependent density functional theory within the NAO formalism.

Electronic Excitation Dynamics in DNA under Proton and α-Particle Irradiation.

Electronic excitations are produced when matter is exposed to ion irradiation comprising highly energetic ions. These electronic stopping excitations are responsible for ion beam-induced DNA damage by energetic protons and α-particles, the chemistry and physics of which are central to burgeoning radiation cancer therapies. By simulating the non-perturbative electronic response of DNA to irradiating protons and α-particles, our first-principles dynamics simulations enable us to test the validity of the commonly used linear response theory description, and they also reveal unprecedented details of the quantum dynamics of electronic excitations. In this work, we discuss the extent to which the linear response theory is valid by comparing to the first-principles determination of electronic stopping power, the energy-transfer rate from ions to electronic excitation. The simulations show that electronic excitations induced by proton and α-particle irradiation cause ionization of DNA, resulting in the generation of holes. By studying the excited hole generation in terms of both the energetic and spatial details in DNA, our work reveals remarkable differences with the excitation behavior of DNA under more commonly used ionizing irradiation sources such as X/γ-ray photons. Furthermore, we find that the generation of excited holes does not directly correlate with the energy-transfer rate as a function of the irradiating ion velocity, in contrast to what is often assumed in the chemistry and physics of radiation oncology.

K-Shell Core-Electron Excitations in Electronic Stopping of Protons in Water from First Principles.

Understanding the role of core-electron excitation in liquid water under proton irradiation has become important due to the growing use of proton beams in radiation oncology. Using a first-principles, nonequilibrium simulation approach based on real-time, time-dependent density functional theory, we determine the electronic stopping power, the velocity-dependent energy transfer rate from irradiating ions to electrons. The electronic stopping power curve agrees quantitatively with experimental data over the velocity range available. At the same time, significant differences are observed between our first-principles result and commonly used perturbation theoretic models. Excitations of the water molecules' oxygen core electrons are a crucial factor in determining the electronic stopping power curve beyond its maximum. The core-electron contribution is responsible for as much as one third of the stopping power at the high proton velocity of 8.0 a.u. (1.6 MeV). K-shell core-electron excitations not only provide an additional channel for the energy transfer-they also significantly influence the valence electron excitations. In the excitation process, generated holes remain highly localized within a few angstroms around the irradiating proton path, whereas electrons are excited away from the path. In spite of their great contribution to the stopping power, K-shell electrons play a rather minor role in terms of the excitation density; only 1% of the hole population composes K-shell holes, even at the high proton velocity of 8.0 a.u. The excitation behavior revealed is distinctly different from that of photon-based ionizing radiation such as x or γ rays.

Propagation of maximally localized Wannier functions in real-time TDDFT.

Real-time, time-dependent density functional theory (RT-TDDFT) has gained popularity as a first-principles approach to study a variety of excited-state phenomena such as optical excitations and electronic stopping. Within RT-TDDFT simulations, the gauge freedom of the time-dependent electronic orbitals can be exploited for numerical and scientific convenience while the unitary transformation does not alter physical properties calculated from the quantum dynamics of electrons. Exploiting this gauge freedom, we demonstrate the propagation of maximally localized Wannier functions within RT-TDDFT. We illustrate its great utility through a number of examples including its application to optical excitation in extended systems using the so-called length gauge, interpreting electronic stopping excitation, and simulating electric field-driven quantized charge transport. We implemented the approach within our plane-wave pseudopotential RT-TDDFT module of the QB@LL code, and the performance of the implementation is also discussed.

Tunable Semiconductors: Control over Carrier States and Excitations in Layered Hybrid Organic-Inorganic Perovskites.

For a class of 2D hybrid organic-inorganic perovskite semiconductors based on π-conjugated organic cations, we predict quantitatively how varying the organic and inorganic component allows control over the nature, energy, and localization of carrier states in a quantum-well-like fashion. Our first-principles predictions, based on large-scale hybrid density-functional theory with spin-orbit coupling, show that the interface between the organic and inorganic parts within a single hybrid can be modulated systematically, enabling us to select between different type-I and type-II energy level alignments. Energy levels, recombination properties, and transport behavior of electrons and holes thus become tunable by choosing specific organic functionalizations and juxtaposing them with suitable inorganic components.

Dependence of hot electron transfer on surface coverage and adsorbate species at semiconductor-molecule interfaces.

Developing a molecular-level understanding of how a hot electron transfer process can be enhanced at semiconductor-molecule interfaces is central to advancing various future technologies. Using first-principles quantum dynamics simulations, we investigate how surface coverage and molecular adsorbate species influence the hot electron transfer at semiconductor-molecule interfaces. Counterintuitively, hot electron transfer from the semiconductor to molecules was found to be lessened with increased surface coverage because the inter-molecular interaction changes nonadiabatic couplings across the semiconductor and adsorbed molecules. The adsorbate molecular species itself was found to be an important factor in hot electron transfer not simply because of the energy level alignments at the interface, but also because the transfer is quite sensitive to nonadiabatic couplings. Our work shows that relatively minor variations of the couplings could lead to significant changes in hot electron transfer characteristics at semiconductor-molecule interfaces. Controlling nonadiabatic couplings must be part of developing a molecular-level "design principle" for enhancing hot electron transfer in addition to the well-recognized importance of energy level alignments.

Plane-wave pseudopotential implementation and performance of SCAN meta-GGA exchange-correlation functional for extended systems.

We present the implementation and performance of the strongly constrained and appropriately normed, SCAN, meta-GGA exchange-correlation (XC) approximation in the planewave-pseudopotential (PW-PP) formalism using the Troullier-Martins pseudopotential scheme. We studied its performance by applying the PW-PP implementation to several practical applications of interest in condensed matter sciences: (a) crystalline silicon and germanium, (b) martensitic phase transition energetics of phosphorene, and (c) a single water molecule physisorption on a graphene sheet. Given the much-improved accuracy over the GGA functionals and its relatively low computational cost compared to hybrid XC functionals, the SCAN functional is highly promising for various practical applications of density functional theory calculations for condensed matter systems. At same time, the SCAN meta-GGA functional appears to require more careful attention to numerical details. The meta-GGA functional shows more significant dependence on the fast Fourier transform grid, which is used for evaluating the XC potential in real space in the PW-PP formalism, than other more conventional GGA functionals do. Additionally, using pseudopotentials that are generated at a different/lower level of XC approximation could introduce noticeable errors in calculating some properties such as phase transition energetics.

Diffusion quantum Monte Carlo study of martensitic phase transition energetics: The case of phosphorene.

Recent technical advances in dealing with finite-size errors make quantum Monte Carlo methods quite appealing for treating extended systems in electronic structure calculations, especially when commonly used density functional theory (DFT) methods might not be satisfactory. We present a theoretical study of martensitic phase transition energetics of a two-dimensional phosphorene by employing diffusion Monte Carlo (DMC) approach. The DMC calculation supports DFT prediction of having a rather diffusive barrier that is characterized by having two transition states, in addition to confirming that the so-called black and blue phases of phosphorene are essentially degenerate. At the same time, the DFT calculations do not provide the quantitative accuracy in describing the energy changes for the martensitic phase transition even when hybrid exchange-correlation functional is employed. We also discuss how mechanical strain influences the stabilities of the two phases of phosphorene.