Plane-wave pseudopotential implementation of explicit integrators for time-dependent Kohn-Sham equations in large-scale simulations

Hot carrier transfer from plasmon decay in Ag20at H-Si(111) surface: real-time TDDFT simulation in Wannier gauge

Plasmon decay is believed to play an essential role in inducing hot carrier transfer at the interfaces between plasmonic nanoparticles and semiconductor surfaces. In this work, we employ real-time time-dependent density functional theory (RT-TDDFT) simulation in the Wannier gauge to gain quantum-mechanical insights into the nonlinear dynamics of the plasmon decay in the Ag20nanoparticle at a semiconductor surface. The first-principles simulations show that the plasmon decay is more than two times faster when the Ag20nanoparticle is adsorbed on a hydrogen-terminated Si(111) surface, taking place within 100 femtoseconds of the plasmon excitation. Hot carrier transfer across the interface is observed as the plasmon decay takes place, and nearly 30% of holes are generated deep in the valence band of the semiconductor surface. The use of Wannier gauge in RT-TDDFT simulation is particularly convenient for gaining quantum-mechanical insights into non-equilibrium electron dynamics in complex heterogeneous systems.

Efficient exact exchange using Wannier functions and other related developments in planewave-pseudopotential implementation of RT-TDDFT

The plane-wave pseudopotential (PW-PP) formalism is widely used for the first-principles electronic structure calculation of extended periodic systems. The PW-PP approach has also been adapted for real-time time-dependent density functional theory (RT-TDDFT) to investigate time-dependent electronic dynamical phenomena. In this work, we detail recent advances in the PW-PP formalism for RT-TDDFT, particularly how maximally localized Wannier functions (MLWFs) are used to accelerate simulations using the exact exchange. We also discuss several related developments, including an anti-Hermitian correction for the time-dependent MLWFs (TD-MLWFs) when a time-dependent electric field is applied, the refinement procedure for TD-MLWFs, comparison of the velocity and length gauge approaches for applying an electric field, and elimination of long-range electrostatic interaction, as well as usage of a complex absorbing potential for modeling isolated systems when using the PW-PP formalism.

Chiral Spectroscopy of Bulk Systems with Propagated Localized Orbitals

We present approaches for the simulation of electronic circular dichroism, Raman, and Raman optical activity (ROA) spectra for isolated and periodic systems as well as subsystem analysis thereof. The method is based on the use of time-dependent maximally localized Wannier functions in the CP2K package and accounts for origin dependencies inherent to the Gaussian and plane wave with pseudopotentials approach as well as the origin dependence of the magnetic dipole and electric quadrupole operators. Tests on the H-bonded enantiomers of alanine by harmonic normal-mode analysis and on an aqueous solution of l-alanine by ab initio molecular dynamics obeying periodic boundary conditions (PBCs) are presented as total and subsystem-resolved spectra. To our knowledge, this is the first instance of an ROA spectrum derived from real-time propagation obeying PBCs and the first ROA simulation considering off-, pre-, and on-resonance effects within PBCs.

Modeling of High-Harmonic Generation in the C60 Fullerene Using Ab Initio, DFT-Based, and Semiempirical Methods

We report calculations of the high-harmonic generation spectra of the C60 fullerene molecule carried out by employing a diverse set of real-time time-dependent quantum chemical methods. All methodologies involve expanding the propagated electronic wave function in bases consisting of the ground and singly excited time-independent eigenstates obtained through the solution of the corresponding linear-response equations. We identify the correlation and exchange effect in the spectra by comparing the results from methods relying on the Hartree-Fock reference determinant with those obtained using approaches based on the density functional theory with different exchange-correlation functionals. The effect of the full random-phase approximation treatment of the excited electronic states is also analyzed and compared with the configuration interaction singles and the Tamm-Dancoff approximation. We also showcase the fact that the real-time extension of the semiempirical method INDO/S can be effectively applied for an approximate description of laser-driven dynamics in large systems.

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.

Molecular Control of Floquet Topological Phase in Non-adiabatic Thouless Pumping

Non-adiabatic Thouless pumping of electrons is studied in the framework of topological Floquet engineering, particularly with a focus on how atomistic changes to chemical moieties control the emergence of the Floquet topological phase. We employ real-time time-dependent density functional theory to investigate the extent to which the topological invariant, the winding number, is impacted by molecular-level changes to trans-polyacetylene. In particular, several substitutions to trans-polyacetylene are studied to examine different effects on the electronic structure, including the mesomeric effect, inductive effect, and electron conjugation effect. Maximally localized Wannier functions are employed to relate the winding number to the valence bond description by expressing the topological pumping as the transport dynamics of the localized Wannier functions. By further exploiting the gauge invariance of the quantum dynamics in terms of the minimal particle-hole excitations, the topological pumping of electrons can be also represented as a cyclic transition among the bonding and antibonding orbitals. Having connected the topological invariant to the chemical concepts, we demonstrate molecular-level control of the emergence of the Floquet topological phase, presenting an exciting opportunity for the intuitive engineering of molecular systems with such an exotic topological phase.

Ab initio real-time quantum dynamics of charge carriers in momentum space

Application of the non-adiabatic molecular dynamics (NAMD) approach is limited to studying carrier dynamics in the momentum space, as a supercell is required to sample the phonon excitation and electron-phonon (e-ph) interaction at different momenta in a molecular dynamics simulation. Here we develop an ab initio approach for the real-time charge carrier quantum dynamics in the momentum space (NAMD_k) by directly introducing e-ph coupling into the Hamiltonian based on the harmonic approximation. The NAMD_k approach maintains the zero-point energy and includes memory effects of carrier dynamics. The application of NAMD_k to the hot carrier dynamics in graphene reveals the phonon-specific relaxation mechanism. An energy threshold of 0.2 eV-defined by two optical phonon modes-separates the hot electron relaxation into fast and slow regions with lifetimes of pico- and nanoseconds, respectively. The NAMD_k approach provides an effective tool to understand real-time carrier dynamics in the momentum space for different materials.

Efficient All-Electron Time-Dependent Density Functional Theory Calculations Using an Enriched Finite Element Basis

We present an efficient and systematically convergent approach to all-electron real-time time-dependent density functional theory (TDDFT) calculations using a mixed basis, termed as enriched finite element (EFE) basis. The EFE basis augments the classical finite element basis (CFE) with a compactly supported numerical atom-centered basis, obtained from atomic ground-state DFT calculations. Particularly, we orthogonalize the enrichment functions with respect to the classical finite element basis to ensure good conditioning of the resultant basis. We employ the second-order Magnus propagator in conjunction with an adaptive Krylov subspace method for efficient time evolution of the Kohn-Sham orbitals. We rely on a priori error estimates to guide our choice of an adaptive finite element mesh as well as the time step to be used in the TDDFT calculations. We observe close to optimal rates of convergence of the dipole moment with respect to spatial and temporal discretizations. Notably, we attain a 50-100 times speedup for the EFE basis over the CFE basis. We also demonstrate the efficacy of the EFE basis for both linear and nonlinear responses by studying the absorption spectra in sodium clusters, the linear to nonlinear response transition in the green fluorescence protein chromophore, and the higher harmonic generation in the magnesium dimer. Lastly, we attain good parallel scalability of our numerical implementation of the EFE basis for up to ∼1000 processors, using a benchmark system of a 50-atom sodium nanocluster.

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.

Ab Initio Prediction of a Negative Barkas Coefficient for Slow Protons and Antiprotons in LiF

We report the ab initio prediction of a negative Barkas coefficient in lithium fluoride (LiF) insulator at low velocity (v<0.25  a.u., E_{kin}∼2  keV). The electronic stopping power of protons in LiF has been extensively studied both experimentally and theoretically because of a controversial threshold effect. While our time-dependent density-functional theory simulations confirm the presence of a velocity threshold below which the proton stopping power vanishes, our calculations demonstrate that the antiprotons do not experience such a threshold. The combination of those two contrasting behaviors gives rise to an unprecedented negative Barkas effect: the stopping power of antiprotons is larger than that of protons. We identify that the slow antiproton at close encounter destabilizes a p orbital of the F^{-} anion pointing toward the antiproton. This particular orbital becomes highly polarizable and hence contributes much to the stopping power.

Inq, a Modern GPU-Accelerated Computational Framework for (Time-Dependent) Density Functional Theory

We present inq, a new implementation of density functional theory (DFT) and time-dependent DFT (TDDFT) written from scratch to work on graphic processing units (GPUs). Besides GPU support, inq makes use of modern code design features and takes advantage of newly available hardware. By designing the code around algorithms, rather than against specific implementations and numerical libraries, we aim to provide a concise and modular code. The result is a fairly complete DFT/TDDFT implementation in roughly 12 000 lines of open-source C++ code representing a modular platform for community-driven application development on emerging high-performance computing architectures.

Local approaches for electric dipole moments in periodic systems and their application to real-time time-dependent density functional theory

Within periodic boundary conditions, the traditional quantum mechanical position operator is ill-defined, necessitating the use of alternative methods, most commonly the Berry phase formulation in the modern theory of polarization. Since any information about local properties is lost in this change of framework, the Berry phase formulation can only determine the total electric polarization of a system. Previous approaches toward recovering local electric dipole moments have been based on applying the conventional dipole moment operator to the centers of maximally localized Wannier functions (MLWFs). Recently, another approach to local electric dipole moments has been demonstrated in the field of subsystem density functional theory (DFT) embedding. We demonstrate in this work that this approach, aside from its use in ground state DFT-based molecular dynamics, can also be applied to obtain electric dipole moments during real-time propagated time-dependent DFT (RT-TDDFT). Moreover, we present an analogous approach to obtain local electric dipole moments from MLWFs, which enables subsystem analysis in cases where DFT embedding is not applicable. The techniques were implemented in the quantum chemistry software CP2K for the mixed Gaussian and plane wave method and applied to cis-diimide and water in the gas phase, cis-diimide in aqueous solution, and a liquid mixture of dimethyl carbonate and ethylene carbonate to obtain absorption and infrared spectra decomposed into localized subsystem contributions.

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.

Real-Time Exciton Dynamics with Time-Dependent Density-Functional Theory

Linear-response time-dependent density-functional theory (TDDFT) can describe excitonic features in the optical spectra of insulators and semiconductors, using exchange-correlation (xc) kernels behaving as -1/k^{2} to leading order. We show how excitons can be modeled in real-time TDDFT, using an xc vector potential constructed from approximate, long-range corrected xc kernels. We demonstrate, for various materials, that this real-time approach is consistent with frequency-dependent linear response, gives access to femtosecond exciton dynamics following short-pulse excitations, and can be extended with some caution into the nonlinear regime.

Anomalous Stopping and Charge Transfer in Proton-Irradiated Graphene

We use first-principles calculations to uncover and explain a new type of anomalous low-velocity stopping effect in proton-irradiated graphene. We attribute a shoulder feature that occurs exclusively for channeling protons to enhanced electron capture from σ- and π-orbitals. Our analysis of electron emission indicates that backward emission is more sensitive to proton trajectory than forward emission and could thus produce higher contrast images in ion microscopy. For slow protons, we observe a steep drop in emission, consistent with predictions from analytical models.

First-Principles Demonstration of Nonadiabatic Thouless Pumping of Electrons in a Molecular System

We demonstrate nonadiabatic Thouless pumping of electrons in trans-polyacetylene in the framework of Floquet engineering using first-principles theory. We identify the regimes in which the quantized pump is operative with respect to the driving electric field for a time-dependent Hamiltonian. By employing the time-dependent maximally localized Wannier functions in real-time time-dependent density functional theory simulation, we connect the winding number, a topological invariant, to a molecular-level understanding of the quantized pumping. While the pumping dynamics constitutes the opposing movement of the Wannier functions that represent both double and single bonds, the resulting current is unidirectional due to the greater number of double-bond electrons. Using a gauge-invariant formulation called dynamical transition orbitals, an alternative viewpoint on the nonequilibrium dynamics is obtained in terms of the particle-hole excitation. A single time-dependent transition orbital is found to be largely responsible for the observed quantized pumping. In this representation, the pumping dynamics manifests itself in the dynamics of this single orbital as it undergoes changes from its π bonding orbital character at equilibrium to acquiring resonance and antibonding character in the driving cycle. The work demonstrates the Floquet engineering of the nonadiabatic topological state in an extended molecular system, paving the way for experimental realization of the new quantum material phase.

PyRad: A software shell for simulating radiolysis with Qball package

The assessment of the radiolytic stability of media is an important task in the fields of nuclear power engineering and radiochemistry. Such studies must be carried out in special laboratory conditions with the use of sources of ionizing radiation, which may increase personal doses of the staff. In addition, difficulties arise in studying the products of irradiated media. While it is impossible to abandon experiments to obtain reliable results in this area, computational methods of quantum chemistry can reduce the number of experiments and help understand the mechanisms of the reactions that occur during radiolysis. Here we would like to present a software shell of the Qb@ll program performing time-dependent density functional theory simulations of the radiolysis process.

Simulation of photo-electron spectrum and electron scattering by dual time propagation

A dual time propagation approach is introduced to describe electron scattering and ionization. The space is divided into two regions, a central region with a full time-dependent Hamiltonian and an outer region where the kinetic operator and the laser field dominate. The two regions are connected by a source term. Time-dependent density functional theory calculations of wave packet scattering on molecules and photoelectron spectrum due to circularly polarized laser are presented to illustrate the efficiency and applicability of the approach.

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.

Real-time time-dependent density functional theory using density fitting and the continuous fast multipole method

An implementation of real-time time-dependent density functional theory (RT-TDDFT) within the TURBOMOLE program package is reported using Gaussian-type orbitals as basis functions, second and fourth order Magnus propagator, and the self-consistent field as well as the predictor-corrector time integration schemes. The Coulomb contribution to the Kohn-Sham matrix is calculated combining density fitting approximation and the continuous fast multipole method. Performance of the implementation is benchmarked for molecular systems with different sizes and dimensionalities. For linear alkane chains, the wall time for density matrix time propagation step is comparable to the Kohn-Sham (KS) matrix construction. However, for larger two- and three-dimensional molecules, with up to about 5,000 basis functions, the computational effort of RT-TDDFT calculations is dominated by the KS matrix evaluation. In addition, the maximum time step is evaluated using a set of small molecules of different polarities. The photoabsorption spectra of several molecular systems calculated using RT-TDDFT are compared to those obtained using linear response time-dependent density functional theory and coupled cluster methods.

Environmental Effects with Frozen-Density Embedding in Real-Time Time-Dependent Density Functional Theory Using Localized Basis Functions

Frozen-density embedding (FDE) represents a versatile embedding scheme to describe the environmental effect on electron dynamics in molecular systems. The extension of the general theory of FDE to the real-time time-dependent Kohn-Sham method has previously been presented and implemented in plane waves and periodic boundary conditions [Pavanello, M.; J. Chem. Phys. 2015, 142, 154116]. In the current paper, we extend our recent formulation of the real-time time-dependent Kohn-Sham method based on localized basis set functions and developed within the Psi4NumPy framework to the FDE scheme. The latter has been implemented in its "uncoupled" flavor (in which the time evolution is only carried out for the active subsystem, while the environment subsystems remain at their ground state), using and adapting the FDE implementation already available in the PyEmbed module of the scripting framework PyADF. The implementation was facilitated by the fact that both Psi4NumPy and PyADF, being native Python API, provided an ideal framework of development using the Python advantages in terms of code readability and reusability. We employed this new implementation to investigate the stability of the time-propagation procedure, which is based on an efficient predictor/corrector second-order midpoint Magnus propagator employing an exact diagonalization, in combination with the FDE scheme. We demonstrate that the inclusion of the FDE potential does not introduce any numerical instability in time propagation of the density matrix of the active subsystem, and in the limit of the weak external field, the numerical results for low-lying transition energies are consistent with those obtained using the reference FDE calculations based on the linear-response TDDFT. The method is found to give stable numerical results also in the presence of a strong external field inducing nonlinear effects. Preliminary results are reported for high harmonic generation (HHG) of a water molecule embedded in a small water cluster. The effect of the embedding potential is evident in the HHG spectrum reducing the number of the well-resolved high harmonics at high energy with respect to the free water. This is consistent with a shift toward lower ionization energy passing from an isolated water molecule to a small water cluster. The computational burden for the propagation step increases approximately linearly with the size of the surrounding frozen environment. Furthermore, we have also shown that the updating frequency of the embedding potential may be significantly reduced, much less than one per time step, without jeopardizing the accuracy of the transition energies.

Efficient ab initio calculation of electronic stopping in disordered systems via geometry pre-sampling: Application to liquid water

Knowledge of the electronic stopping curve for swift ions, S_e(v), particularly around the Bragg peak, is important for understanding radiation damage. Experimentally, however, the determination of such a feature for light ions is very challenging, especially in disordered systems such as liquid water and biological tissue. Recent developments in real-time time-dependent density functional theory (rt-TDDFT) have enabled the calculation of S_e(v) along nm-sized trajectories. However, it is still a challenge to obtain a meaningful statistically averaged S_e(v) that can be compared to observations. In this work, taking advantage of the correlation between the local electronic structure probed by the projectile and the distance from the projectile to the atoms in the target, we devise a trajectory pre-sampling scheme to select, geometrically, a small set of short trajectories to accelerate the convergence of the averaged S_e(v) computed via rt-TDDFT. For protons in liquid water, we first calculate the reference probability distribution function (PDF) for the distance from the proton to the closest oxygen atom, ϕ_R(r_p→O), for a trajectory of a length similar to those sampled experimentally. Then, short trajectories are sequentially selected so that the accumulated PDF reproduces ϕ_R(r_p→O) to increasingly high accuracy. Using these pre-sampled trajectories, we demonstrate that the averaged S_e(v_p) converges in the whole velocity range with less than eight trajectories, while other averaging methods using randomly and uniformly distributed trajectories require approximately ten times the computational effort. This allows us to compare the S_e(v_p) curve to experimental data and assess widely used empirical tables based on Bragg's rule.

Propagators for Quantum-Classical Models: Commutator-Free Magnus Methods

We consider the numerical propagation of models that combine both quantum and classical degrees of freedom, usually, electrons and nuclei, respectively. We focus, in our computational examples, on the case in which the quantum electrons are modeled with time-dependent density-functional theory, although the methods discussed below can be used with any other level of theory. Often, for these so-called quantum-classical molecular dynamics models, one uses some propagation technique to deal with the quantum part and a different one for the classical equations. While the resulting procedure may, in principle, be consistent, it can however spoil some of the properties of the methods, such as the accuracy order with respect to the time step or the preservation of the geometrical structure of the equations. Few methods have been developed specifically for hybrid quantum-classical models. We propose using the same method for both the quantum and classical particles, in particular, one family of techniques that proves to be very efficient for the propagation of Schrödinger-like equations: the (quasi)-commutator free Magnus expansions. These have been developed, however, for linear systems, yet our problem is nonlinear: formally, the full quantum-classical system can be rewritten as a nonlinear Schrödinger equation, i.e., one in which the Hamiltonian depends on the system itself. The Magnus expansion algorithms for linear systems require the application of the Hamiltonian at intermediate points in a given propagating interval. For nonlinear systems, this poses a problem as this Hamiltonian is unknown due to its dependence on the state. We approximate it by employing a higher order extrapolation using previous steps as input. The resulting technique can then be regarded as a multistep technique or, alternatively, as a predictor corrector formula.

First-Principles Modeling of Electronic Stopping in Complex Matter under Ion Irradiation

Electronic stopping refers to the dynamical energy-transfer process to electrons in matter from highly energetic charged particles such as high-velocity protons. We discuss recent progress in theoretical studies of electronic stopping in condensed matter under ion irradiation, focusing on modern electronic structure theory's role in enabling the study of electronic excitation dynamics that result from the energy transfer. In the last few decades, first-principles simulation approaches based on real-time time-dependent density functional theory have greatly advanced the field. While linear response theory is widely used to study electronic stopping processes, especially for simple solids, novel first-principles dynamics approaches now allow us to study chemically complex systems and also yield detailed descriptions of electronic excitations at the molecular scale. Outstanding challenges for further advancement of electronic stopping modeling are also discussed from the viewpoint of electronic structure theory.

Real-time ab initio simulation of inelastic electron scattering using the exact, density functional, and alternative approaches

Inelastic electron scattering phenomena in chemical/physical/materials interests: electron radiation damage in materials; DNA damaged by electron scattering; electron therapy; electron microscope; electron-beam-induced deposition for nanofabrication.

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.

Hot-Electron-Mediated Ion Diffusion in Semiconductors for Ion-Beam Nanostructuring

Ion-beam-based techniques are widely utilized to synthesize, modify, and characterize materials at the nanoscale, with applications from the semiconductor industry to medicine. Interactions of the beam with the target are fundamentally interesting, as they trigger multilength and time-scale processes that need to be quantitatively understood to achieve nanoscale precision. Here we demonstrate for magnesium oxide, as a testbed semiconductor material, that in a kinetic-energy regime in which electronic effects are usually neglected, a proton beam efficiently excites oxygen-vacancy-related electrons. We quantitatively describe the excited-electron distribution and the emerging ion dynamics using first-principles techniques. Contrary to the common picture of charging the defect, we discover that most of the excited electrons remain locally near the oxygen vacancy. Using these results, we bridge time scales from ultrafast electron dynamics directly after impact to ion diffusion over migration barriers in semiconductors and discover a diffusion mechanism that is mediated by hot electrons. Our quantitative simulations predict that this mechanism strongly depends on the projectile-ion velocity, suggesting the possibility of using it for precise sample manipulation via nanoscale diffusion enhancement in semiconductors with a deep, neutral, intrinsic defect.

ODE integration schemes for plane-wave real-time time-dependent density functional theory

Integration schemes are implemented with a plane-wave basis in the context of real-time time-dependent density functional theory. Crank-Nicolson methods and three classes of explicit integration schemes are explored and assessed in terms of their accuracy and stability properties. Within the framework of plane-wave density functional theory, a graphene monolayer system is used to investigate the error, stability, and serial computational cost of these methods. The results indicate that Adams-Bashforth and Adams-Bashforth-Moulton methods of orders 4 and 5 outperform commonly used methods, including Crank-Nicolson and Runge-Kutta methods, in simulations where a relatively low error is desired. Parallel runtime scaling of the most competitive serial methods is presented, further demonstrating that the Adams-Bashforth and Adams-Bashforth-Moulton methods are efficient methods for propagating the time-dependent Kohn-Sham equations. Our integration schemes are implemented as an extension to the Quantum ESPRESSO code.

Momentum-resolved TDDFT algorithm in atomic basis for real time tracking of electronic excitation

Ultrafast electronic dynamics in solids lies at the core of modern condensed matter and materials physics. To build up a practical ab initio method for studying solids under photoexcitation, we develop a momentum-resolved real-time time dependent density functional theory (rt-TDDFT) algorithm using numerical atomic basis, together with the implementation of both the length and vector gauge of the electromagnetic field. When applied to simulate elementary excitations in two-dimensional materials such as graphene, different excitation modes, only distinguishable in momentum space, are observed. The momentum-resolved rt-TDDFT is important and computationally efficient for the study of ultrafast dynamics in extended systems.

Core Electrons in the Electronic Stopping of Heavy Ions

Electronic stopping power in the keV/Å range is accurately calculated from first principles for high atomic-number projectiles and the effect of core states is carefully assessed. The energy loss to electrons in self-irradiated nickel is studied using real-time time-dependent density functional theory. Different core states are explicitly included in the simulations to understand their involvement in the dissipation mechanism. The core electrons of the projectile are found to open additional dissipation channels as the projectile velocity increases. Almost all of the energy loss is accounted for, even for high projectile velocities, when core electrons as deep as 2s^{2}2p^{6} are explicitly treated. In addition to their expected excitation at high velocities, a flapping dynamical response of the projectile core electrons is observed at intermediate velocities. The empirical reference data are well reproduced in the projectile velocity range of 1.0-12.0 a.u. (1.5-210 MeV).

Propagators for the Time-Dependent Kohn-Sham Equations: Multistep, Runge-Kutta, Exponential Runge-Kutta, and Commutator Free Magnus Methods

We examine various integration schemes for the time-dependent Kohn-Sham equations. Contrary to the time-dependent Schrödinger's equation, this set of equations is nonlinear, due to the dependence of the Hamiltonian on the electronic density. We discuss some of their exact properties, and in particular their symplectic structure. Four different families of propagators are considered, specifically the linear multistep, Runge-Kutta, exponential Runge-Kutta, and the commutator-free Magnus schemes. These have been chosen because they have been largely ignored in the past for time-dependent electronic structure calculations. The performance is analyzed in terms of cost-versus-accuracy. The clear winner, in terms of robustness, simplicity, and efficiency is a simplified version of a fourth-order commutator-free Magnus integrator. However, in some specific cases, other propagators, such as some implicit versions of the multistep methods, may be useful.

Langevin Dynamics with Spatial Correlations as a Model for Electron-Phonon Coupling

Stochastic Langevin dynamics has been traditionally used as a tool to describe nonequilibrium processes. When utilized in systems with collective modes, traditional Langevin dynamics relaxes all modes indiscriminately, regardless of their wavelength. We propose a generalization of Langevin dynamics that can capture a differential coupling between collective modes and the bath, by introducing spatial correlations in the random forces. This allows modeling the electronic subsystem in a metal as a generalized Langevin bath endowed with a concept of locality, greatly improving the capabilities of the two-temperature model. The specific form proposed here for the spatial correlations produces a physical wave-vector and polarization dependency of the relaxation produced by the electron-phonon coupling in a solid. We show that the resulting model can be used for describing the path to equilibration of ions and electrons and also as a thermostat to sample the equilibrium canonical ensemble. By extension, the family of models presented here can be applied in general to any dense system, solids, alloys, and dense plasmas. As an example, we apply the model to study the nonequilibrium dynamics of an electron-ion two-temperature Ni crystal.

Charge Transport in Molecular Materials: An Assessment of Computational Methods

The booming field of molecular electronics has fostered a surge of computational research on electronic properties of organic molecular solids. In particular, with respect to a microscopic understanding of transport and loss mechanisms, theoretical studies assume an ever-increasing role. Owing to the tremendous diversity of organic molecular materials, a great number of computational methods have been put forward to suit every possible charge transport regime, material, and need for accuracy. With this review article we aim at providing a compendium of the available methods, their theoretical foundations, and their ranges of validity. We illustrate these through applications found in the literature. The focus is on methods available for organic molecular crystals, but mention is made wherever techniques are suitable for use in other related materials such as disordered or polymeric systems.

Stopping power beyond the adiabatic approximation

Energetic ions traveling in solids deposit energy in a variety of ways, being nuclear and electronic stopping the two avenues in which dissipation is usually treated. This separation between electrons and ions relies on the adiabatic approximation in which ions interact via forces derived from the instantaneous electronic ground state. In a more detailed view, in which non-adiabatic effects are explicitly considered, electronic excitations alter the atomic bonding, which translates into changes in the interatomic forces. In this work, we use time dependent density functional theory and forces derived from the equations of Ehrenfest dynamics that depend instantaneously on the time-dependent electronic density. With them we analyze how the inter-ionic forces are affected by electronic excitations in a model of a Ni projectile interacting with a Ni target, a metallic system with strong electronic stopping and shallow core level states. We find that the electronic excitations induce substantial modifications to the inter-ionic forces, which translate into nuclear stopping power well above the adiabatic prediction. In particular, we observe that most of the alteration of the adiabatic potential in early times comes from the ionization of the core levels of the target ions, not readily screened by the valence electrons.

Electronic Excitation Dynamics in Liquid Water under Proton Irradiation

Molecular behaviour of liquid water under proton irradiation is of great importance to a number of technological and medical applications. The highly energetic proton generates a time-varying field that is highly localized and heterogeneous at the molecular scale, and massive electronic excitations are produced as a result of the field-matter interaction. Using first-principles quantum dynamics simulations, we reveal details of how electrons are dynamically excited through non-equilibrium energy transfer from highly energetic protons in liquid water on the atto/femto-second time scale. Water molecules along the path of the energetic proton undergo ionization at individual molecular level, and the excitation primarily derives from lone pair electrons on the oxygen atom of water molecules. A reduced charge state on the energetic proton in the condensed phase of water results in the strongly suppressed electronic response when compared to water molecules in the gas phase. These molecular-level findings provide important insights into understanding the water radiolysis process under proton irradiation.

Electron Elevator: Excitations across the Band Gap via a Dynamical Gap State

We use time-dependent density functional theory to study self-irradiated Si. We calculate the electronic stopping power of Si in Si by evaluating the energy transferred to the electrons per unit path length by an ion of kinetic energy from 1 eV to 100 keV moving through the host. Electronic stopping is found to be significant below the threshold velocity normally identified with transitions across the band gap. A structured crossover at low velocity exists in place of a hard threshold. An analysis of the time dependence of the transition rates using coupled linear rate equations enables one of the excitation mechanisms to be clearly identified: a defect state induced in the gap by the moving ion acts like an elevator and carries electrons across the band gap.

Kinetic theory molecular dynamics and hot dense matter: theoretical foundations

Electrons are weakly coupled in hot, dense matter that is created in high-energy-density experiments. They are also mildly quantum mechanical and the ions associated with them are classical and may be strongly coupled. In addition, the dynamical evolution of plasmas under these hot, dense matter conditions involve a variety of transport and energy exchange processes. Quantum kinetic theory is an ideal tool for treating the electrons but it is not adequate for treating the ions. Molecular dynamics is perfectly suited to describe the classical, strongly coupled ions but not the electrons. We develop a method that combines a Wigner kinetic treatment of the electrons with classical molecular dynamics for the ions. We refer to this hybrid method as "kinetic theory molecular dynamics," or KTMD. The purpose of this paper is to derive KTMD from first principles and place it on a firm theoretical foundation. The framework that KTMD provides for simulating plasmas in the hot, dense regime is particularly useful since current computational methods are generally limited by their inability to treat the dynamical quantum evolution of the electronic component. Using the N-body von Neumann equation for the electron-proton plasma, three variations of KTMD are obtained. Each variant is determined by the physical state of the plasma (e.g., collisional versus collisionless). The first variant of KTMD yields a closed set of equations consisting of a mean-field quantum kinetic equation for the electron one-particle distribution function coupled to a classical Liouville equation for the protons. The latter equation includes both proton-proton Coulombic interactions and an effective electron-proton interaction that involves the convolution of the electron density with the electron-proton Coulomb potential. The mean-field approach is then extended to incorporate equilibrium electron-proton correlations through the Singwi-Tosi-Land-Sjolander (STLS) ansatz. This is the second variant of KTMD. The STLS contribution produces an effective electron-proton interaction that involves the electron-proton structure factor, thereby extending the usual mean-field theory to correlated but near equilibrium systems. Finally, a third variant of KTMD is derived. It includes dynamical electrons and their correlations coupled to a MD description for the ions. A set of coupled equations for the one-particle electron Wigner function and the electron-electron and electron-proton correlation functions are coupled to a classical Liouville equation for the protons. This latter variation has both time and momentum dependent correlations.