Coordination of copper within a crystalline carbon nitride and its catalytic reduction of CO2.

Inherently disordered structures of carbon nitrides have hindered an atomic level tunability and understanding of their catalytic reactivity. Starting from a crystalline carbon nitride, poly(triazine imide) or PTI/LiCl, the coordination of copper cations to its intralayer N-triazine groups was investigated using molten salt reactions. The reaction of PTI/LiCl within CuCl or eutectic KCl/CuCl2 molten salt mixtures at 280 to 450 °C could be used to yield three partially disordered and ordered structures, wherein the Cu cations are found to coordinate within the intralayer cavities. Local structural differences and the copper content, i.e., whether full or partial occupancy of the intralayer cavity occurs, were found to be dependent on the reaction temperature and Cu-containing salt. Crystallites of Cu-coordinated PTI were also found to electrophoretically deposit from aqueous particle suspensions onto either graphite or FTO electrodes. As a result, electrocatalytic current densities for the reduction of CO2 and H2O reached as high as ∼10 to 50 mA cm-2, and remained stable for >2 days. Selectivity for the reduction of CO2 to CO vs. H2 increases for thinner crystals as well as for when two Cu cations coordinate within the intralayer cavities of PTI. Mechanistic calculations have also revealed the electrocatalytic activity for CO2 reduction requires a smaller thermodynamic driving force with two neighboring Cu atoms per cavity as compared to a single Cu atom. These results thus establish a useful synthetic pathway to metal-coordination in a crystalline carbon nitride and show great potential for mediating stable CO2 reduction at sizable current densities.

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

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

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

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

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.

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.

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.

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.

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

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

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.

All-Electron BSE@GW Method for K-Edge Core Electron Excitation Energies.

We present an accurate computational approach to calculate absolute K-edge core electron excitation energies as measured by X-ray absorption spectroscopy. Our approach employs an all-electron Bethe-Salpeter equation (BSE) formalism based on GW quasiparticle energies (BSE@GW) using numeric atom-centered orbitals (NAOs). The BSE@GW method has become an increasingly popular method for the computation of neutral valence excitation energies of molecules. However, it was so far not applied to molecular K-edge excitation energies. We discuss the influence of different numerical approximations on the BSE@GW calculation and employ in our final setup (i) exact numeric algorithms for the frequency integration of the GW self-energy, (ii) G0W0 and BSE starting points with ∼50% of exact exchange, (iii) the Tamm-Dancoff approximation and (iv) relativistic corrections. We study the basis set dependence and convergence with common Gaussian-type orbital and NAO basis sets. We identify the importance of additional spatially confined basis functions as well as of diffuse augmenting basis functions. The accuracy of our BSE@GW method is assessed for a benchmark set of small organic molecules, previously used for benchmarking the equation-of-motion coupled cluster method [Peng et al., J. Chem. Theory Comput., 2015, 11, 4146], as well as the medium-sized dibenzothiophene (DBT) molecule. Our BSE@GW results for absolute excitation energies are in excellent agreement with the experiment, with a mean average error of only 0.63 eV for the benchmark set and with errors <1 eV for the DBT molecule.

First Principles Dynamics Study of Excited Hole Relaxation in DNA.

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

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

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

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

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

Nuclear Quantum Effect and Its Temperature Dependence in Liquid Water from Random Phase Approximation via Artificial Neural Network.

We report structural and dynamical properties of liquid water described by the random phase approximation (RPA) correlation together with the exact exchange energy (EXX) within density functional theory. By utilizing thermostated ring polymer molecular dynamics, we examine the nuclear quantum effects and their temperature dependence. We circumvent the computational limitation of performing direct first-principles molecular dynamics simulation at this high level of electronic structure theory by adapting an artificial neural network model. We show that the EXX+RPA level of theory accurately describes liquid water in terms of both dynamical and structural properties.

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.

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.

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

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

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

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

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.