Real-time Time-dependent Density Functional Theory Research Articles

Long-Lived Hot Electron in a Metallic Particle for Plasmonics and Catalysis: Ab Initio Nonadiabatic Molecular Dynamics with Machine Learning.

Multiple experiments provide evidence for photovoltaic, catalytic, optoelectronic, and plasmonic processes involving hot, i.e., high energy, electrons in nanoscale materials. However, the mechanisms of such processes remain elusive, because electrons rapidly lose energy by relaxation through dense manifolds of states. We demonstrate a long-lived hot electron state in a Pt nanocluster adsorbed on the MoS2 substrate. For this purpose, we develop a simulation technique, combining classical molecular dynamics based on machine learning potentials with ab initio nonadiabatic molecular dynamics and real-time time-dependent density functional theory. Choosing Pt20/MoS2 as a prototypical system, we find frequent shifting of a top atom in the Pt particle occurring on a 50 ps time scale. The distortion breaks particle symmetry and creates unsaturated chemical bonds. The lifetime of the localized state associated with the broken bonds is enhanced by a factor of 3. Hot electrons aggregate near the shifted atom and form a catalytic reaction center. Our findings prove that distortion of even a single atom can have important implications for nanoscale catalysis and plasmonics and provide insights for utilizing machine learning potentials to accelerate ab initio investigations of excited state dynamics in condensed matter systems.

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 [PavanelloM.; J. Chem. Phys.2015, 142, 15411625903875]. 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.

Multiscale simulations of electron and ion dynamics in self-irradiated silicon

The interaction of energetic ions with the electronic and ionic system of target materials is an interesting but challenging multi-scale problem and understanding of the early stages after impact of heavy, initially charged ions is particularly poor. At the same time, energy deposition during these early stages determines later formation of damage cascades. We address the multi-scale character by combining real-time time-dependent density functional theory for electron dynamics with molecular dynamics simulations of damage cascades. Our first-principles simulations prove that core electrons affect electronic stopping and have an unexpected influence on the charge state of the projectile. We show that this effect is absent for light projectiles, but dominates the stopping physics for heavy projectiles. By parameterizing an inelastic energy loss friction term in the molecular dynamics simulations using our first-principles results, we also show a qualitative influence of electronic stopping physics on radiation-damage cascades.

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, Se(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 Se(v) along nm-sized trajectories. However, it is still a challenge to obtain a meaningful statistically averaged Se(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 Se(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, ϕR(rp→O), for a trajectory of a length similar to those sampled experimentally. Then, short trajectories are sequentially selected so that the accumulated PDF reproduces ϕR(rp→O) to increasingly high accuracy. Using these pre-sampled trajectories, we demonstrate that the averaged Se(vp) 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 Se(vp) curve to experimental data and assess widely used empirical tables based on Bragg’s rule.

Driving Orbital Magnetism in Metallic Nanoparticles through Circularly Polarized Light: A Real-Time TDDFT Study

Transfer of angular momentum from helicity-controlled laser fields to a nonmagnetic electronic system can lead to the creation of magnetization. The underlying mechanism in metallic nanoparticles h...

Effect of chemical disorder on the electronic stopping of solid solution alloys

The electronic stopping power of nickel-based equiatomic solid solutions alloys NiCr, NiFe and NiCo for protons and alpha projectiles is investigated in detail using real-time time-dependent density functional theory over a wide range of velocities. Recently developed numerical electronic structure methods are used to probe fundamental aspects of electron-ion coupling non-perturbatively and in a fully atomistic context, capturing the effect of the atomic scale disorder. The effects of particular electronic band structures and density of states reflect in the low velocity limit behavior. We compare our results for the alloys with those of a pure nickel target to understand how alloying affects the electronic stopping. We discover that NiCo and NiFe have similar stopping behavior as Ni while NiCr has an asymptotic stopping power that is more than a factor of two larger than its counterparts for velocities below 0.1 a.u.. We show that the low-velocity limit of electronic stopping power can be manipulated by controlling the broadening of the d-band through the chemical disorder. In this regime, the Bragg’s additive rule for the stopping of composite materials also fails for NiCr.

Study of Charge Transfer in Radical Reactions of Hydrogen Atom Detachment Involving Triplet Nitro Compounds

The hypothesis of the formation of a radical anion during the dark stage of the reaction of hydrogen atom transfer from the hydrogen sulfide molecule to a triplet molecule of a nitro compound has been verified by quantum chemistry methods. Analysis of changes in spin density during the reaction, as well as analysis of changes in electron density using real-time time-dependent density functional theory (RT TD-DFT), has not revealed charge transfer between the reactants. At the same time, the detected weak dependence of the energy parameters of the reaction on the dielectric permittivity of the solvent supports the hypothesis of charge transfer.

Excitation effect of d electrons on the electronic energy loss of energetic protons colliding with a Zn atom

By using a nonequilibrium approach based on real-time time-dependent density-functional theory combined with molecular dynamics simulations, the effects of $d$-electron excitation on the electronic energy loss of energetic protons colliding with atomic zinc target are studied. The results show that the semicore electrons play a crucial role in the electronic energy loss in an extended energy range. In the low-energy regime, the electronic energy loss displays the threshold effect before it is proportional to velocity, which is explained by the quantization of the energy levels of zinc atom, and the charge transfer contributes greatly to the electronic energy loss, especially at 0.1 a.u. In addition, due to the electron resonance excitation, the number of excited electrons and charge transfer is significantly increased at the velocity thresholds for electron excitation. In the high-energy regime, the electronic energy loss is greatly enhanced as the the impact parameter decreases, which is ascribed to the excitation of $3d$ electrons. We also calculated the stopping cross section for energetic protons colliding with atomic zinc, which is in a good agreement with the experimental values in both low- and high-velocity regimes.

First-Principles Simulations of X-ray Transient Absorption for Probing Attosecond Electron Dynamics.

X-ray transient absorption spectroscopy (XTAS) is a promising technique for measuring electron dynamics in molecules and solids with attosecond time resolutions. In XTAS, the elemental specificity and spatial locality of core-to-valence X-ray absorption is exploited to relate modulations in the time-resolved absorption spectra to local electron density variations around particular atoms. However, interpreting these absorption modulations and frequency shifts as a function of the time delay in terms of dynamics can be challenging. In this paper, we present a first-principles study of attosecond XTAS in a selection of simple molecules based on real-time time-dependent density functional theory (RT-TDDFT) with constrained DFT to emulate the state of the system following the interaction with a ultraviolet pump laser. In general, there is a decrease in the optical density and a blue shift in the frequency with increasing electron density around the absorbing atom. In carbon monoxide (CO), modulations in the O K-edge occur at the frequency of the valence electron dynamics, while for dioxygen (O2) they occur at twice the frequency, due to the indistinguishability of the oxygen atoms. In 4-aminophenol (H2NC6H4OH), likewise, there is a decrease in the optical density and a blue shift in the frequency for the oxygen and nitrogen K-edges with increasing charge density on the O and N, respectively. Similar effects are observed in the nitrogen K-edge for a long-range charge-transfer excitation in a benzene (C6H6)–tetracyanoethylene (C6N4; TCNE) dimer but with weaker modulations due to the delocalization of the charge across the entire TCNE molecule. Additionally, in all cases, there are pre-edge features corresponding to core transitions to depopulated orbitals. These potentially offer a background-free signal that only appears in pumped molecules.

Ultrafast processes in photochromic material YHxOy studied by excited-state density functional theory simulation

Oxygen-containing rare-earth metal hydride, YHxOy, is a newly found photochromic material showing fast photoresponse. While its preparation method, optical properties and structural features have been studied extensively, the photochromic mechanism in YHxOy remains unknown. Here, using excited-state molecular dynamics simulation based on the recently developed real-time time-dependent density functional theory (RT-TDDFT) method, we study the photochemical reactions in YHxOy. We find that under photoexcitation, dihydrogen defects are formed within 100 fs. The dihydrogen defect behaves as a shallow donor and renders the material strongly n-type doped, which could be responsible for the photochromic effect observed in YHxOy. We also find that oxygen concentration affects the metastability of the dihydrogen species, meaning that the energy barrier for the dihydrogen to dissociate is related to the oxygen concentration. The highest barrier of 0.28 eV is found in our model with O/Y=1:8. If the oxygen concentration is too low, the dihydrogen will quickly dissociate when the excitation is turned off. If the oxygen concentration is too high, the dihydrogen dissociates even when the excitation is still on.

Dual Resonant Sum Frequency Generations from Two-Dimensional Materials.

We propose dual resonant optical sum frequency generation (SFG), where the two most singular resonances could be selected, and report for the monolayer (1L-) WSe2 when one (ω1) of two excitation pulses is resonant to A exciton and their sum frequency (ω1 + ω2) to D exciton. The dual resonant SFG confirms that, under an irradiation of ω1 and ω2 pulses with the same fluence of ∼1.4 × 1010 W/m2, its signal intensity could be enhanced about 20 times higher than the resonant SHG (i.e., 2ω1 to the D excitonic absorption). Further, the dual resonant SFG intensity of 1L-WSe2 is found to be 1 order of magnitude higher than the single resonant SFG intensity of 1L-WS2 under the same condition of two-pulse irradiation. Finally, observations of the dual resonant SFG are thoroughly examined using real-time time-dependent density functional theory (rt-TDDFT), and the relevant nonlinear optical characteristics are scrutinized using the Greenwood-Kubo formalism.

Hole Transfer in Cumulenic and Polyynic Carbynes

We study hole transfer in open cumulenic and polyynic nanowires made of N carbon atoms, using real-time time-dependent density functional theory (RT-TDDFT) and tight-binding (TB) wire models. For R...

ReSpect: Relativistic spectroscopy DFT program package.

With the increasing interest in compounds containing heavier elements, the experimental and theoretical community requires computationally efficient approaches capable of simultaneous non-perturbative treatment of relativistic, spin-polarization, and electron correlation effects. The ReSpect program has been designed with this goal in mind and developed to perform relativistic density functional theory (DFT) calculations on molecules and solids at the quasirelativistic two-component (X2C Hamiltonian) and fully relativistic four-component (Dirac-Coulomb Hamiltonian) level of theory, including the effects of spin polarization in open-shell systems at the Kramers-unrestricted self-consistent field level. Through efficient algorithms exploiting time-reversal symmetry, biquaternion algebra, and the locality of atom-centered Gaussian-type orbitals, a significant reduction of the methodological complexity and computational cost has been achieved. This article summarizes the essential theoretical and technical advances made in the program, supplemented by example calculations. ReSpect allows molecules with >100 atoms to be efficiently handled at the four-component level of theory on standard central processing unit-based commodity clusters, at computational costs that rarely exceed a factor of 10 when compared to the non-relativistic realm. In addition to the prediction of band structures in solids, ReSpect offers a growing list of molecular spectroscopic parameters that range from electron paramagnetic resonance parameters (g-tensor, A-tensor, and zero-field splitting), via (p)NMR chemical shifts and nuclear spin-spin couplings, to various linear response properties using either conventional or damped-response time-dependent DFT (TDDFT): excitation energies, frequency-dependent polarizabilities, and natural chiroptical properties (electronic circular dichroism and optical rotatory dispersion). In addition, relativistic real-time TDDFT electron dynamics is another unique feature of the program. Documentation, including user manuals and tutorials, is available at the program's website http://www.respectprogram.org.

Combining Lindblad Master Equation and Surface Hopping to Evolve Distributions of Quantum Particles

Motivated by the need to study nonequilibrium evolutions of many-electron systems at the atomistic ab initio level, as they occur in modern devices and applications, we developed a quantum dynamics approach bridging master equations and surface hopping (SH). The Lindblad master equation (LME) allows us to propagate efficiently ensembles of particles, while SH provides nonperturbative evaluation of transition rates that evolve in time and depend explicitly on nuclear geometry. We implemented the LME-SH technique within real-time time-dependent density functional theory using global flux SH, and we demonstrated its efficiency and utility by modeling metallic films, in which charge-phonon dynamics was studied experimentally and showed an unexpectedly strong dependence on adhesion layers. The LME-SH approach provides a general framework for modeling efficiently quantum dynamics in a broad range of complex many-electron condensed-matter and nanoscale systems.

Real-time time-dependent density functional theory in Quantum Espresso and related codes

Real-time time-dependent density functional theory in Quantum Espresso and related codes

PyBERTHART: A Relativistic Real-Time Four-Component TDDFT Implementation Using Prototyping Techniques Based on Python.

We present a real-time time-dependent four-component Dirac-Kohn-Sham (RT-TDDKS) implementation based on the BERTHA code. This new implementation takes advantage of modern software engineering, including the prototyping techniques. The software design follows a three step approach: (i) the prototype implementation of a time-propagation algorithm in nonrelativistic real-time TDDFT within the Psi4NumPy framework, which provides a suitable environment for the creation of a clear, readable, and easy to test reference code in Python, (ii) the design of an original Python application programming interface for the relativistic four-component code BERTHA (PyBERTHA), which has an efficient computational kernel for relativistic integrals written in FORTRAN, and (iii) the porting of the time-propagation scheme enveloped within the Psi4NumPy framework to PyBERTHA. The propagation scheme consequently resides in a single readable Python computer code that is easy to maintain and in which the key quantities, such as the Dirac-Kohn-Sham and dipole matrices, can be accessed directly from the PyBERTHA module. For linear algebra operations (matrix-matrix multiplications and diagonalization) we use the highly optimized procedures implemented in the popular NumPy library. The overhead introduced by the Python interface to BERTHA is almost negligible (less than 1% evaluated on the SCF procedure), and the interoperability between different programming languages (FORTRAN, C, and Python) does not affect the numerical stability of the time-propagation scheme. Our new RT-TDDKS implementation has been employed to investigate the stability of the time-propagation procedure in combination with a density-fitting algorithm (both for the Coulomb and for the exchange-correlation matrix construction), which are employed in BERTHA to speed up the Dirac-Kohn-Sham matrix evaluation. On the basis of systematic calculations, employing several density-fitting basis sets of increasing accuracy, we showed that quantitative agreement can be achieved in combination with extended-fitting basis sets, with an error in the Coulomb energy below 1 μ-hartree. Convergence of the transition energies increasing of quality of the fitting basis sets has been also observed. Our data suggest that the error in the Coulomb energy may also represent a good estimate of the fitting basis set quality for real-time electron dynamics simulations. Further, we study the applicability of the RT-TDDKS method in combination with both weak- and extreme strong-field regime. Numerical results of excited-state transitions for the Group 12 atoms are reported and compared with a previous real-time Dirac-Kohn-Sham implementation (Repisky et al. J. Chem. Theory Comput. 2015, 11, 980-991). Finally, calculations of high harmonic generation in the hydrogen molecule and Au dimer have been also carried out. We were able to generate high harmonics with relatively well-defined peaks up to the 21st and 13th order in the case of H2 and Au2, respectively. Our findings show that the four-component structure of the Dirac-Kohn-Sham Hamiltonian provides a suitable theoretical framework, with no intrinsic unfavorable features, to study molecules in the strong-field regime.

Element Specificity of Transient Extreme Ultraviolet Magnetic Dichroism.

In this work we combine theory and experiment to study transient magnetic circular dichroism (TRMCD) in the extreme ultraviolet spectral range in bulk Co and CoPt. We use the abinitio method of real-time time-dependent density functional theory to simulate the magnetization dynamics in the presence of short laser pulses. From this we demonstrate how TRMCD may be calculated using an approximation to the excited-state linear response. We apply this approximation to Co and CoPt and show computationally that element-specific dynamics of the local spin moments can be extracted from the TRMCD in the extreme ultraviolet energy range, as is commonly assumed. We then compare our theoretical prediction for the TRMCD for CoPt with experimental measurement and find excellent agreement at many different frequencies including the M_{23} edge of Co and N_{67} and O_{23} edges of Pt.

Identification and Resolution of Unphysical Multielectron Excitations in the Real-Time Time-Dependent Kohn-Sham Formulation.

We resolve a fundamental issue associated with the conventional Kohn-Sham formulation of real-time time-dependent density functional theory. We show that unphysical multielectron excitations, generated during time propagation of the Kohn-Sham equations due to fixation of the total number of Kohn-Sham orbitals and their occupations, result in incorrect electron density and, therefore, wrong predictions of physical properties. A new formulation is proposed in that the number of Kohn-Sham orbitals and their occupations are updated on the fly, the unphysical multielectron excitations are removed, and the correct electron density is determined. The correctness of the new formulation is demonstrated by simulations of Rabi oscillation, as analytical results are available for comparison in the case of noninteracting electrons.

Understanding Beam-Induced Electronic Excitations in Materials.

Optical electronic absorption spectroscopy and corresponding selection rules have played a prominent role in the development of the theory of electronic structure of materials. In this work, we expand the modern toolbox of chemistry and materials science to include electron and ion microscopies and spectroscopies, allowing spatially resolved interrogation of materials' atomic and electronic structures by beams of charged particles. Specifically, we formulate and discuss the selection rules for electronic excitation due to the interaction between materials and beams of charged particles. We show that transition probabilities for point charge-induced electronic excitations depend strongly on the position of the externally charged particles and can significantly deviate from those derived from the electric dipole (long-wavelength) approximation. We present and implement expressions within the linear response time-dependent density functional theory (TD-DFT) framework for rates of transition between the ground and excited states induced by an external point charge. The point charge-induced transition rates for particular electronic excitations from linear response TD-DFT were validated through comparison to excited state populations from real time TD-DFT simulations following an impulsive point charge perturbation, then evaluated on a three-dimensional grid to map their spatial dependence for a small polybenzoid. This method, when combined with information about excited state energy gradients, represents a first step toward an ab initio framework for probing the structural response of materials under irradiation by charged particles resulting from inelastic scattering. Engineering electron beam interaction with matter to manipulate single atoms and localized electronic states offers a revolutionary new regime beyond laser excitation.

Ultrafast charge ordering by self-amplified exciton\u2013phonon dynamics in TiSe2

The origin of charge density waves (CDWs) in TiSe{}_{2} has long been debated, mainly due to the difficulties in identifying the timescales of the excitonic pairing and electron–phonon coupling (EPC). Without a time-resolved and microscopic mechanism, one has to assume simultaneous appearance of CDW and periodic lattice distortions (PLD). Here, we accomplish a complete separation of ultrafast exciton and PLD dynamics and unravel their interplay in our real-time time-dependent density functional theory simulations. We find that laser pulses knock off the exciton order and induce a homogeneous bonding–antibonding transition in the initial 20 fs, then the weakened electronic order triggers ionic movements antiparallel to the original PLD. The EPC comes into play after the initial 20 fs, and the two processes mutually amplify each other leading to a complete inversion of CDW ordering. The self-amplified dynamics reproduces the evolution of band structures in agreement with photoemission experiments. Hence we resolve the key processes in the initial dynamics of CDWs that help elucidate the underlying mechanism.