Tracking Charge Migration with Frequency-Matched Strobo-Spectroscopy.

We present frequency-matched strobo-spectroscopy (FMSS) of charge migration (CM) in bromobutadiyne, simulated with time-dependent density functional theory. CM + FMSS is a pump-probe scheme that uses a frequency-matched high harmonic generation (HHG)-driving laser as an independent probe step, following the creation of a localized hole on the bromine atom that induces CM dynamics. We show that the delay-dependent harmonic yield tracks the phase of the CM dynamics through its sensitivity to the amount of electron density on the bromine end of the molecule. FMSS takes advantage of the intrinsic attosecond time resolution of the HHG process in which different harmonics are emitted at different times and thus probe different locations of the electron hole. Finally, we show that the CM-induced modulation of the HHG signal is dominated by the recombination step of the HHG process, with a negligible contribution from the ionization step.

The Ring-Closing Reaction of Cyclopentadiene Probed with Ultrafast X-ray Scattering.

The dynamics of cyclopentadiene (CP) following optical excitation at 243 nm was investigated by time-resolved pump-probe X-ray scattering using 16.2 keV X-rays at the Linac Coherent Light Source (LCLS). We present the first ultrafast structural evidence that the reaction leads directly to the formation of bicyclo[2.1.0]pentene (BP), a strained molecule with three- and four-membered rings. The bicyclic compound decays via a thermal backreaction to the vibrationally hot CP with a time constant of 21 ± 3 ps. A minor channel leads to ring-opened structures on a subpicosecond time scale.

Attochemistry Regulation of Charge Migration.

Charge migration (CM) is a coherent attosecond process that involves the movement of localized holes across a molecule. To determine the relationship between a molecule's structure and the CM dynamics it exhibits, we perform systematic studies of para-functionalized bromobenzene molecules (X-C6H4-R) using real-time time-dependent density functional theory. We initiate valence-electron dynamics by emulating rapid strong-field ionization leading to a localized hole on the bromine atom. The resulting CM, which takes on the order of 1 fs, occurs via an X localized → C6H4 delocalized → R localized mechanism. Interestingly, the hole contrast on the acceptor functional group increases with increasing electron-donating strength. This trend is well-described by the Hammett σ value of the group, which is a commonly used metric for quantifying the effect of functionalization on the chemical reactivity of benzene derivatives. These results suggest that simple attochemistry principles and a density-based picture can be used to predict and understand CM.

Real-Time Time-Dependent Electronic Structure Theory.

Real-time electronic structure methods provide an unprecedented view of electron dynamics and ultrafast spectroscopy on the atto- and femtosecond time scale with vast potential to yield new insights into the electronic behavior of molecules and materials. In this Review, we discuss the fundamental theory underlying various real-time electronic structure methods as well as advantages and disadvantages of each. We give an overview of the numerical techniques that are widely used for real-time propagation of the quantum electron dynamics with an emphasis on Gaussian basis set methods. We also showcase many of the chemical applications and scientific advances made by using real-time electronic structure calculations and provide an outlook of possible new directions.

Investigation of Interferences in Carbon Dioxide through Multidimensional Molecular-Frame High-Harmonic Spectroscopy.

We present molecular-frame high-harmonic spectroscopic measurements of the spectral intensity and group delay of carbon dioxide. Using four different driving wavelengths and a range of intensities at each wavelength for high-harmonic generation, we observe a well-characterized minimum in the harmonic emission that exhibits both a wavelength and intensity dependence. Using the intensity dependence at each driving wavelength, we classify the minimum as due to either a structural two-center interference or dynamic multichannel interference, consistent with previous literature. By additionally measuring the group delay at each driving wavelength and intensity, we find that the sign of the group delay excursion across the interference is an acute probe of the interference mechanism. The experimental results are confirmed by ab initio time-dependent density functional theory calculations of both the spectral intensity and the phase of the harmonic emission.

Molecular Modes of Attosecond Charge Migration.

First-principles calculations are employed to elucidate the modes of attosecond charge migration (CM) in halogenated hydrocarbon chains. We use constrained density functional theory (DFT) to emulate the creation of a localized hole on the halogen and follow the subsequent dynamics via time-dependent DFT. We find low-frequency CM modes (∼1 eV) that propagate across the molecule and study their dependence on length, bond order, and halogenation. We observe that the CM speed (∼4 Å/fs) is largely independent of molecule length, but is lower for triple-bonded versus double-bonded molecules. Additionally, as the halogen mass increases, the hole travels in a more particlelike manner as it moves across the molecule. These heuristics will be useful in identifying molecules and optimal CM detection methods for future experiments, especially for halogenated hydrocarbons which are promising targets for ionization-triggered CM.

Mapping static core-holes and ring-currents with X-ray scattering.

Measuring the attosecond movement of electrons in molecules is challenging due to the high temporal and spatial resolutions required. X-ray scattering-based methods are promising, but many questions remain concerning the sensitivity of the scattering signals to changes in density, as well as the means of reconstructing the dynamics from these signals. In this paper, we present simulations of stationary core-holes and electron dynamics following inner-shell ionization of the oxazole molecule. Using a combination of time-dependent density functional theory simulations along with X-ray scattering theory, we demonstrate that the sudden core-hole ionization produces a significant change in the X-ray scattering response and how the electron currents across the molecule should manifest as measurable modulations to the time dependent X-ray scattering signal. This suggests that X-ray scattering is a viable probe for measuring electronic processes at time scales faster than nuclear motion.

Strong-field induced fragmentation and isomerization of toluene probed by ultrafast femtosecond electron diffraction and mass spectrometry.

We investigate the fragmentation and isomerization of toluene molecules induced by strong-field ionization with a femtosecond near-infrared laser pulse. Momentum-resolved coincidence time-of-flight ion mass spectrometry is used to determine the relative yield of different ionic products and fragmentation channels as a function of laser intensity. Ultrafast electron diffraction is used to capture the structure of the ions formed on a picosecond time scale by comparing the diffraction signal with theoretical predictions. Through the combination of the two measurements and theory, we are able to determine the main fragmentation channels and to distinguish between ions with identical mass but different structures. In addition, our diffraction measurements show that the independent atom model, which is widely used to analyze electron diffraction patterns, is not a good approximation for diffraction from ions. We show that the diffraction data is in very good agreement with ab initio scattering calculations.

Simulated field-modulated x-ray absorption in titania.

In this paper, we present a method to compute the x-ray absorption near-edge structure (XANES) spectra of solid-state transition metal oxides using real-time time-dependent density functional theory, including spin-orbit coupling effects. This was performed on bulk-mimicking anatase titania (TiO2) clusters, which allows for the use of hybrid functionals and atom-centered all electron basis sets. Furthermore, this method was employed to calculate the shifts in the XANES spectra of the Ti L-edge in the presence of applied electric fields to understand how external fields can modify the electronic structure, and how this can be probed using x-ray absorption spectroscopy. Specifically, the onset of t2g peaks in the Ti L-edge was observed to red shift and the eg peaks were observed to blue shift with increasing fields, attributed to changes in the hybridization of the conduction band (3d) orbitals.

Monitoring the growth dynamics of colloidal gold-silver core-shell nanoparticles using in situ second harmonic generation and extinction spectroscopy.

The growth dynamics of gold-silver core-shell (Au@Ag) nanoparticles are studied using in situ time-dependent second harmonic generation (SHG) and extinction spectroscopy to investigate the nanoparticle shell formation. The silver shell is grown by reduction of silver cations onto a 14 nm gold core using ascorbic acid in colloidal aqueous solution under varying reaction concentrations producing Au@Ag nanoparticles of final sizes ranging from 51 to 78 nm in diameter. The in situ extinction spectra show a rapid increase in intensity on the timescale of 5-6 s with blue shifting and narrowing of the plasmonic peak during the silver shell formation. The in situ SHG signals show an abrupt rise at early times of the reaction, followed by a time-dependent biexponential decrease, where the faster SHG lifetime corresponds to the timescale of the shell growth, and where the slower SHG lifetime is attributed to changes in the nanoparticle surface charge density. A large enhancement in the SHG signal at early stages of the reaction is caused by plasmonic hot spots due to the nanoparticle surface morphology, which becomes smoother as the reaction proceeds. The final extinction spectra are compared to finite-difference time-domain (FDTD) calculations, showing general agreement with experiment, where the plasmon peak red shifts and increases in spectral width as the silver shell thickness increases. These in situ SHG and extinction spectroscopy results, combined with FDTD calculations, help characterize the complicated processes involved in colloidal nanoparticle shell formation in real time for developing potential plasmon-enhanced nanomaterial applications.

Angle-dependent strong-field ionization of halomethanes.

We study, experimentally and theoretically, the ionization probability of singly halogenated methane molecules, CH3Cl and CH3Br, in intense linearly polarized 800 nm laser pulses as a function of the angle between the molecular axis and the laser polarization. Experimentally, the molecules are exposed to two laser pulses with a relative time delay. The first, weaker pulse induces a nuclear rotational wave packet within the molecules, which are then ionized by the second, stronger pulse. The angle-dependent ionization yields are extracted from fits of the measured delay-dependent ionization signal to a superposition of moments of the rotational wave packet's angular distribution. Angle-dependent strong-field ionization (SFI) yields are also calculated using time-dependent density functional theory. Good agreement between measurements and theory is obtained. Interestingly, we find a marked difference between the angle-dependence of the ionization yields for these two halomethane species despite the similar structure of their highest occupied molecular orbitals. Calculations reveal that these differences are a result of multichannel (CH3Cl) vs single-channel (CH3Br) ionization and of increased hole localization on Br vs Cl. By adding calculations for CH3F, we can discern clear trends in the ionization dynamics with increasing halogen mass. These results are illustrative, as chemical functionalization and molecular alignment are likely to be important parameters for initiating and controlling charge migration dynamics via SFI.

Angle-dependent strong-field molecular ionization rates with tuned range-separated time-dependent density functional theory.

Strong-field ionization and the resulting electronic dynamics are important for a range of processes such as high harmonic generation, photodamage, charge resonance enhanced ionization, and ionization-triggered charge migration. Modeling ionization dynamics in molecular systems from first-principles can be challenging due to the large spatial extent of the wavefunction which stresses the accuracy of basis sets, and the intense fields which require non-perturbative time-dependent electronic structure methods. In this paper, we develop a time-dependent density functional theory approach which uses a Gaussian-type orbital (GTO) basis set to capture strong-field ionization rates and dynamics in atoms and small molecules. This involves propagating the electronic density matrix in time with a time-dependent laser potential and a spatial non-Hermitian complex absorbing potential which is projected onto an atom-centered basis set to remove ionized charge from the simulation. For the density functional theory (DFT) functional we use a tuned range-separated functional LC-PBE*, which has the correct asymptotic 1/r form of the potential and a reduced delocalization error compared to traditional DFT functionals. Ionization rates are computed for hydrogen, molecular nitrogen, and iodoacetylene under various field frequencies, intensities, and polarizations (angle-dependent ionization), and the results are shown to quantitatively agree with time-dependent Schrödinger equation and strong-field approximation calculations. This tuned DFT with GTO method opens the door to predictive all-electron time-dependent density functional theory simulations of ionization and ionization-triggered dynamics in molecular systems using tuned range-separated hybrid functionals.

Electron transfer beyond the static picture: a TDDFT∕TD-ZINDO study of a pentacene dimer.

We use time-dependent density functional theory and time-dependent ZINDO (a semi-empirical method) to study transfer of an extra electron between a pair of pentacene molecules. A measure of the electronic transfer integral is computed in a dynamic picture via the vertical excitation energy from a delocalized anionic ground state. With increasing dimer separation, this dynamical measurement of charge transfer is shown to be significantly larger than the commonly used static approximation (i.e., LUMO+1-LUMO of the neutral dimer, or HOMO-LUMO of the charged dimer), up to an order of magnitude higher at 6 Å. These results offer a word of caution for calculations involving large separations, as in organic photovoltaics, where care must be taken when using a static picture to model charge transfer.

A combined gas-phase photoelectron spectroscopic and theoretical study of Zeise's anion and its bromine and iodine analogues.

Shining light on Zeise: In a study of Zeise's anion, [PtCl(3)(C(2)H(4))](-), and its bromine and iodine analogues, electronic structure information for each species, derived from spectral features, is assigned through calculations at the coupled cluster level of theory. The calculations indicate that the electron binding energies decrease with halogen size and that there is a synergistic η(2) interaction between C(2)H(4) and the PtX(3)(-) anions.

Intruder Peak-Free Transient Inner-Shell Spectra Using Real-Time Simulations.

Real-time methods are convenient for simulating core-level absorption spectra but suffer from nonphysical intruder peaks when using atom-centered basis sets. In transient absorption spectra, these peaks exhibit highly nonphysical time-dependent modulations in their energies and oscillator strengths. In this paper, we address the origins of these intruder peaks and propose a straightforward and effective solution based on a filtered dipole operator. In combination with real-time time-dependent density functional theory (RT-TDDFT), we demonstrate how to compute intruder-free attosecond transient X-ray absorption spectra for the aminophenol (C6H7NO) oxygen and nitrogen K-edges and the α-quartz (SiO2) silicon L-edge. Without filtering, the computed spectra are qualitatively wrong. This procedure is suitable for both static and transient inner-shell spectroscopy studies and can easily be implemented in a range of real-time methodologies.

Modeling molecular effects on plasmon transport: silver nanoparticles with tartrazine.

Modulation of plasmon transport between silver nanoparticles by a yellow fluorophore, tartrazine, is studied theoretically. The system is studied by combining a finite-difference time-domain Maxwell treatment of the electric field and the plasmons with a time-dependent parameterized method number 3 simulation of the tartrazine, resulting in an effective Maxwell∕Schrödinger (i.e., classical∕quantum) method. The modeled system has three linearly arranged small silver nanoparticles with a radius of 2 nm and a center-to-center separation of 4 nm; the molecule is centered between the second and third nanoparticles. We initiate an x-polarized current on the first nanoparticle and monitor the transmission through the system. The molecule rotates much of the x-polarized current into the y-direction and greatly reduces the overall transmission of x-polarized current.

Near-field: a finite-difference time-dependent method for simulation of electrodynamics on small scales.

We develop near-field (NF), a very efficient finite-difference time-dependent (FDTD) approach for simulating electromagnetic systems in the near-field regime. NF is essentially a time-dependent version of the quasistatic frequency-dependent Poisson algorithm. We assume that the electric field is longitudinal, and hence propagates only a set of time-dependent polarizations and currents. For near-field scales, the time step (dt) is much larger than in the usual Maxwell FDTD approach, as it is not related to the velocity of light; rather, it is determined by the rate of damping and plasma oscillations in the material, so dt = 2.5 a.u. was well converged in our simulations. The propagation in time is done via a leapfrog algorithm much like Yee's method, and only a single spatial convolution is needed per time step. In conjunction, we also develop a new and very accurate 8 and 9 Drude-oscillators fit to the permittivity of gold and silver, desired here because we use a large time step. We show that NF agrees with Mie-theory in the limit of small spheres and that it also accurately describes the evolution of the spectral shape as a function of the separation between two gold or silver spheres. The NF algorithm is especially efficient for systems with small scale dynamics and makes it very simple to introduce additional effects such as embedding.

Growth Dynamics of Colloidal Silver-Gold Core-Shell Nanoparticles Studied by In Situ Second Harmonic Generation and Extinction Spectroscopy.

The in situ growth dynamics of colloidal silver-gold core-shell (Ag@Au CS) nanoparticles (NPs) in water are monitored in a stepwise synthesis approach using time-dependent second harmonic generation (SHG) and extinction spectroscopy. Three sequential additions of chloroauric acid, sodium citrate, and hydroquinone are added to the silver nanoparticle solution to grow a gold shell around a silver core. The first addition produces a stable urchin-like surface morphology, while the second and third additions continue to grow the gold shell thickness as the surface becomes more smooth and uniform, as determined using transmission electron microscopy. The extinction spectra after each addition are compared to finite-difference time-domain (FDTD) calculations, showing large deviations for the first and second additions due to the bumpy surface morphology and plasmonic hotspots while showing general agreement after the third addition reaches equilibrium. The in situ SHG signal is dominated by the NP surface, providing complementary information on the growth time scales due to changes to the surface morphology. This combined approach of synthesis and characterization of Ag@Au CS nanoparticles with in situ SHG spectroscopy, extinction spectroscopy, and FDTD calculations provides a detailed foundation for investigating complex colloidal nanoparticle growth mechanisms and dynamics in developing enhanced plasmonic nanomaterial technologies.

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.