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

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.

Time-dependent density functional theory with the orthogonal projector augmented wave method

The projector augmented wave (PAW) method of Blöchl linearly maps smooth pseudo wavefunctions to the highly oscillatory all-electron DFT orbitals. Compared to norm-conserving pseudopotentials (NCPP), PAW has the advantage of lower kinetic energy cutoffs and larger grid spacing at the cost of having to solve for non-orthogonal wavefunctions. We earlier developed orthogonal PAW (OPAW) to allow the use of PAW when orthogonal wavefunctions are required. In OPAW, the pseudo wavefunctions are transformed through the efficient application of powers of the PAW overlap operator with essentially no extra cost compared to NCPP methods. Previously, we applied OPAW to DFT. Here, we take the first step to make OPAW viable for post-DFT methods by implementing it in real-time time-dependent (TD) DFT. Using fourth-order Runge-Kutta for the time-propagation, we compare calculations of absorption spectra for various organic and biological molecules and show that very large grid spacings are sufficient, 0.6-0.7 bohr in OPAW-TDDFT rather than the 0.4-0.5 bohr used in traditional NCPP-TDDFT calculations. This reduces the memory and propagation costs by around a factor of 3. Our method would be directly applicable to any post-DFT methods that require time-dependent propagations such as the GW approximation and the Bethe-Salpeter equation.

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.

Reconciling TD-DFT and CASPT2 electronic structure methods for describing the photophysics of DNA

Time-dependent density functional theory (TD-DFT) and multiconfigurational second-order perturbation theory (CASPT2) are two of the most widely used methods to investigate photoinduced dynamics in DNA-based systems. These methods sometimes give diverse dynamics in physiological environments usually modeled by quantum mechanics/molecular mechanics (QM/MM) protocol. In this work, we demonstrate for the uridine test case that the underlying topology of the potential energy surfaces of electronic states involved in photoinduced relaxation is similar in both electronic structure methods. This is verified by analyzing surface-hopping dynamics performed at the QM/MM level on aqueous solvated uridine at TD-DFT and CASPT2 levels. By constraining the dynamics to remain onπ π * state we observe similar fluctuations in energy and relaxation lifetimes in surface-hopping dynamics in both TD-DFT and experimentally validated CASPT2 methods. This finding calls for a systematic comparison of the ES potential energy surfaces of DNA and RNA nucleosides at the single- and multi-reference levels of theory. The anomalous long excited state lifetime at the TD-DFT level is explained byn π * trapping due to the tendency of TD-DFT in QM/MM schemes with electrostatic embedding to underestimate the energy of theπ π * state leading to a wrongπ π * / n π * energetic order. A study of the FC energetics suggests that improving the description of the surrounding environment through polarizable embedding or by the expansion of QM layer with hydrogen-bonded waters helps restore the correct state order at TD-DFT level. Thus by combining TDDFT with an accurate modeling of the environment, TD-DFT is positioned as the standout protocol to model photoinduced dynamics in DNA-based aggregates and multimers.

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.

Ion-Type Dependence of DNA Electronic Excitation in Water under Proton, α-Particle, and Carbon Ion Irradiation: A First-Principles Simulation Study

Understanding how the electronic excitation of DNA changes in response to different high-energy particles is central to advancing ion beam cancer therapy and other related approaches, such as boron neutron capture therapy. While protons have been the predominant ions of choice in ion beam cancer therapy, heavier ions, particularly carbon ions, have drawn significant attention over the past decade. Carbon ions are expected to transfer larger amounts of energy according to linear response theory. However, molecular-level details of the electronic excitation under heavier ion irradiation remain unknown. In this work, we use real-time time-dependent density functional theory simulations to examine the quantum-mechanical details of DNA electronic excitations in water under proton, α-particle, and carbon ion irradiation. Our results show that the energy transfer does indeed increase for the heavier ions, while the excitation remains highly conformal. However, the increase in the energy transfer rate, measured by electronic stopping power, does not match the prediction by the linear response model, even when accounting for the velocity dependence of the irradiating ion's charge. The simulations also reveal that while the number of holes generated on DNA increases for heavier ions, the increase is only partially responsible for the larger stopping power. Larger numbers of highly energetic holes formed from the heavier ions also contribute significantly to the increased electronic stopping power.

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.

Meta-generalized gradient approximations in time dependent generalized Kohn-Sham theory: Importance of the current density correction

We revisit the use of Meta-Generalized Gradient Approximations (mGGAs) in time-dependent density functional theory, reviewing conceptual questions and solving the generalized Kohn-Sham equations by real-time propagation. After discussing the technical aspects of using mGGAs in combination with pseudopotentials and comparing real-space and basis set results, we focus on investigating the importance of the current-density based gauge invariance correction. For the two modern mGGAs that we investigate in this work, TASK and r2SCAN, we observe that for some systems, the current density correction leads to negligible changes, but for others, it changes excitation energies by up to 40% and more than 0.8 eV. In the cases that we study, the agreement with the reference data is improved by the current density correction.

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.

Quantum simulation of exact electron dynamics can be more efficient than classical mean-field methods

Quantum algorithms for simulating electronic ground states are slower than popular classical mean-field algorithms such as Hartree-Fock and density functional theory but offer higher accuracy. Accordingly, quantum computers have been predominantly regarded as competitors to only the most accurate and costly classical methods for treating electron correlation. However, here we tighten bounds showing that certain first-quantized quantum algorithms enable exact time evolution of electronic systems with exponentially less space and polynomially fewer operations in basis set size than conventional real-time time-dependent Hartree-Fock and density functional theory. Although the need to sample observables in the quantum algorithm reduces the speedup, we show that one can estimate all elements of the k-particle reduced density matrix with a number of samples scaling only polylogarithmically in basis set size. We also introduce a more efficient quantum algorithm for first-quantized mean-field state preparation that is likely cheaper than the cost of time evolution. We conclude that quantum speedup is most pronounced for finite-temperature simulations and suggest several practically important electron dynamics problems with potential quantum advantage.

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.

Size-dependent errors in real-time electron density propagation

Real-time (RT) electron density propagation with time-dependent density functional theory (TDDFT) or Hartree-Fock (TDHF) is one of the most popular methods to model the charge transfer in molecules and materials. However, both RT-TDHF and RT-TDDFT within the adiabatic approximation are known to produce inaccurate evolution of the electron density away from the ground state in model systems, leading to large errors in charge transfer and erroneous shifting of peaks in absorption spectra. Given the poor performance of these methods with small model systems and the widespread use of the methods with larger molecular and material systems, here we bridge the gap in our understanding of these methods and examine the size-dependence of errors in RT density propagation. We analyze the performance of RT density propagation for systems of increasing size during the application of a continuous resonant field to induce Rabi-like oscillations, during charge-transfer dynamics, and for peak shifting in simulated absorption spectra. We find that the errors in the electron dynamics are indeed size dependent for these phenomena, with the largest system producing the results most aligned with those expected from linear response theory. The results suggest that although the RT-TDHF and RT-TDDFT methods may produce severe errors for model systems, the errors in charge transfer and resonantly driven electron dynamics may be much less significant for more realistic, large-scale molecules and materials.

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.

Analyzing Excitation-Energy Transfer Based on the Time-Dependent Density Functional Theory in Real Time

Excitation-energy transfer is a key step in processes such as photosynthesis that convert light into other forms of energy. Time-dependent density functional theory (DFT) in real time is ideal for the first-principles simulation of such processes due to its computational efficiency. We here demonstrate how real-time DFT can be used for analyzing excitation-energy transfer from first-principles. We discuss several measures of energy transfer that are based solely on the time-dependent density, are well founded in the DFT framework, allow for intuitive understanding and visualization, and reproduce important limiting cases of an analytical model. We demonstrate their usefulness in calculations for model systems, both with static nuclei and in the context of DFT-based Ehrenfest dynamics.

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.

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.