Time-resolved spectroscopy of attosecond quantum dynamics

The advent of attosecond pulsed radiation leads to a large unexplored scientific area in chemical physics: the direct time-resolved measurement of electronic quantum dynamics. Major scientific goals include spectroscopy of single- and multi-electron motion and dynamical electron correlations, relating to orbital interactions in valence and core electronic levels of atoms and molecules. The results of such studies address a wide array of scientific and technological applications. Here, the current state-of-the-art of attosecond-dynamics measurements is reviewed and several novel spectroscopic methods are discussed that are particularly important for applications in chemical physics: attosecond transient absorption/dispersion spectroscopy, laser-induced-dipole spectroscopy, and absolute-phase spectroscopy.     

A measure of electron localizability

A functional of the same‐spin electron pair density is proposed as a measure of electron localizability. This functional yields the average number of same‐spin electron pairs in a region Ω enclosing a fixed charge. The functional equals zero if the fixed charge in Ω originates from one electron only, with all other same‐spin electrons outside the region Ω. Then, the correlation of the electronic motion in Ω and thus the localizability of an electron is high. If the motion of the same‐spin electrons becomes less correlated, more electrons participate in the fixed charge contained in Ω, the average number of same‐spin electron pairs (the functional) increases. In the Hartree–Fock approximation the Taylor expansion of the proposed localizability functional can be related to the electron localization function of Becke and Edgecombe without using an arbitrary reference to the uniform electron gas. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2004     

Fragment momentum distributions obtained from coupled electron-nuclear dynamics

We theoretically investigate fragmentation processes induced by femtosecond laser pulses within a model which incorporates electronic and nuclear motion. Single-pulse excitation leads to diffraction patterns in the electron momentum distribution which depend on the nature of the electronic state and also on the nuclear charge distribution. Additional structures appear in the nuclear momentum distribution if two time-delayed pulses produce fragments in the same dissociation channel. It is shown that these functions are modified by the electronic degree-of-freedom. A simultaneous excitation of two different electronic states results in further interferences which are related to electronic wave-packet dynamics on the attosecond time-scale.     

Charge transfer driven by electron correlation: a non-Dyson propagator approach

A hole charge created in a molecular system, for instance, by ionization, can migrate through the system solely driven by electron correlation. This charge transfer due to electron correlation is referred to as charge migration. We introduce in this work a new ab initio method analyzing charge migration due to electron correlation in molecules. This method, a third-order "non-Dyson" propagator approach, aims in the long run, in particular, at the calculation of charge migration in relatively large molecules such as oligopeptides. First results of the new non-Dyson method are compared with a previously used propagator approach.     

Ultrafast electron transfer from oligo(p-phenylene-ethynylene)thiol to gold

The electron transfer dynamics of oligo(p-phenylene-ethynylene) (OPE) SAM on Au(111) was studied by resonant photoemission spectroscopy. The ultrafast electron transfer from OPE molecules to Au substrate was clearly observed. The time scale for this charge transfer is much less than 6 fs, the core-hole lifetime for C 1s. This strongly suggests that there is an intense interfacial electronic coupling between OPE molecules and the Au substrate.     

Visualizing Progressive Atomic Change in the Metal Surface Structure Made by Ultrafast Electronic Interactions in an Ambient Environment

Understanding the atomic and molecular phenomena occurring in working catalysts and nanodevices requires the elucidation of atomic migration originating from electronic excitations. The progressive atomic dynamics on metal surface under controlled electronic stimulus in real time, space, and gas environments are visualized for the first time. By in situ environmental transmission electron microscopy, the gas molecules introduced into the biased metal nanogap could be activated by electron tunneling and caused the unpredicted atomic dynamics. The typically inactive gold was oxidized locally on the positive tip and field‐evaporated to the negative tip, resulting in the atomic reconstruction on the negative tip surface. This finding of a tunneling‐electron‐attached‐gas process will bring new insights into the design of nanostructures such as nanoparticle catalysts and quantum nanodots and will stimulate syntheses of novel nanomaterials not seen in the ambient environment.     

Visualization and interpretation of attosecond electron dynamics in laser-driven hydrogen molecular ion using Bohmian trajectories

We analyze the attosecond electron dynamics in hydrogen molecular ion driven by an external intense laser field using the Bohmian trajectories. To this end, we employ a one-dimensional model of the molecular ion in which the motion of the protons is frozen. The Bohmian trajectories clearly visualize the electron transfer between the two protons in the field and, in particular, confirm the recently predicted attosecond transient localization of the electron at one of the protons and the related multiple bunches of the ionization current within a half cycle of the laser field. Further analysis based on the quantum trajectories shows that the electron dynamics in the molecular ion can be understood via the phase difference accumulated between the Coulomb wells at the two protons.     

Charge and energy dynamics in photo-excited poly(para-phenylenevinylene) systems

We report results from simulations of charge and energy dynamics in poly(para-phenylenevinylene) (PPV) and PPV interacting with C60. The simulations were performed by solving the time-dependent Schrodinger equation and the lattice equation of motion simultaneously and nonadiabatically. The electronic system and the coupling of the electrons to the lattice were described by an extended three-dimensional version of the Su-Schrieffer-Heeger model, which also included an external electric field. Electron and lattice dynamics following electronic excitations at different energies have been simulated. The effect of additional lattice energy was also included in the simulations. Our results show that both exciton diffusion and transitions from high to lower lying excitations are stimulated by increasing the lattice energy. Also field induced charge separation occurs faster if the lattice energy is increased. This separation process is highly nonadiabatic and involves a significant rearrangement of the electron distribution. In the case of PPV coupled to C60, we observe a spontaneous charge separation. The separation time is in this case limited by the local concentration of C60 molecules close to the PPV chain.     

Evaluation of elastic‐scattering cross sections for electrons and positrons over a wide energy range

Quantification of surface‐ and bulk‐analytical methods, e.g. Auger‐electron spectroscopy (AES), X‐ray photoelectron spectroscopy (XPS), electron‐probe microanalysis (EPMA), and analytical electron microscopy (AEM), requires knowledge of reliable elastic‐scattering cross sections for describing electron transport in solids. Cross sections for elastic scattering of electrons and positrons by atoms, ions, and molecules can be calculated with the recently developed code ELSEPA (Elastic Scattering of Electrons and Positrons by Atoms) for kinetic energies of the projectile from 10 eV to 50 eV. These calculations can be made after appropriate selection of the basic input parameters: electron‐density distribution, a model for the nuclear‐charge distribution, and a model for the electron‐exchange potential (the latter option applies only to scattering of electrons). Additionally, the correlation‐polarization potential and an imaginary absorption potential can be considered in the calculations. We report comparisons of calculated differential elastic‐scattering cross sections (DCSs) for silicon and gold at selected energies (500 eV, 5 keV, 30 keV) relevant to AES, XPS, EPMA, and AEM, and at 100 MeV as a limiting case. The DCSs for electrons and positrons differ considerably, particularly for medium‐ and high‐atomic‐number elements and for kinetic energies below about 5 keV. The DCSs for positrons are always monotonically decreasing functions of the scattering angle, while the DCSs for electrons have a diffraction‐like structure with several minima and maxima. A significant influence of the electron‐exchange correction is observed at 500 eV. The correlation‐polarization correction is significant for small scattering angles at 500 eV, while the absorption correction is important at energies below about 10 keV. Copyright © 2005 John Wiley & Sons, Ltd.     

Superconducting first‐order pairing: Finite‐temperature simulations

A recently developed first‐order mechanism for superconducting pairing has been extended from T = 0 K to finite temperatures. On the basis of quantum statistical considerations, we have suggested a direct pairing interaction that does not necessarily involve second‐order elements, such as the electron–phonon coupling or specific magnetic interactions submitted by spin fluctuations. The driving force for the (energy‐driven) first‐order pairing is an attenuation of the destabilizing influence of the Pauli antisymmetry principle (PAP). Only the moves of unpaired fermions are controlled by the PAP, while the moves of superconducting Cooper pairs are not. The quantum statistics of Cooper pairs is of a mixed type, as it combines fermionic on‐site and bosonic intersite properties. The strong correlation between the strength of PAP constraints and system topology in combination with the electron number has been discussed for some larger clusters. Detailed finite‐temperature simulations on first‐order pairing have been performed for four‐center–four‐electron clusters with different topologies. A canonical ensemble statistics has been employed to derive the electronic energy, the electronic configuration entropy, and the free energy of paired and unpaired states in thermal equilibrium. The simulations show that pairing can be caused by either the electronic energy or the electronic configuration entropy. The coexistence of two different sets of quantum particles in paired states (i.e., the Cooper pairs and the unpaired electrons) can lead to an enhanced configuration entropy. In this context, we discuss the possibility of an entropy‐driven high‐temperature superconductor emerging from a low‐temperature unpaired state. The charge and spin degrees of freedom of the four‐center–four‐electron systems have been studied with the help of the charge and spin fluctuations. The spin fluctuations are helpful in judging the validity of pairing theories based on magnetic interactions. The charge fluctuations are a measure for the carrier delocalization in unpaired and paired states. The well‐known proximity between Jahn–Teller activity and superconductivity is analyzed in the zero‐temperature limit. It is demonstrated that both processes compete in their ability to reduce PAP constraints. All theoretical results have been derived within the framework of the simple Hubbard Hamiltonian. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

A surface science approach to ultrafast electron transfer and solvation dynamics at interfaces

Excess electrons in polar media, such as water or ice, are screened by reorientation of the surrounding molecular dipoles. This process of electron solvation is of vital importance for various fields of physical chemistry and biology as, for instance, in electrochemistry or photosynthesis. Generation of such excess electrons in bulk water involves either photoionization of solvent molecules or doping with e.g. alkali atoms, involving possibly perturbing interactions of the system with the parent-cation. Such effects are avoided when using a surface science approach to electron solvation: in the case of polar adsorbate layers on metal surfaces, the substrate acts as an electron source from where photoexcited carriers are injected into the adlayer. Besides the investigation of electron solvation at such interfaces, this approach allows for the investigation of heterogeneous electron transfer, as the excited solvated electron population continuously decays back to the metal substrate. In this manner, electron transfer and solvation processes are intimately connected at any polar adsorbate-metal interface. In this tutorial review, we discuss recent experiments on the ultrafast dynamics of photoinduced electron transfer and solvation processes at amorphous ice-metal interfaces. Femtosecond time-resolved two-photon photoelectron spectroscopy is employed as a direct probe of the electron dynamics, which enables the analysis of all elementary processes: the charge injection across the interface, the subsequent electron localization and solvation, and the dynamics of electron transfer back to the substrate. Using surface science techniques to grow and characterize various well-defined ice structures, we gain detailed insight into the correlation between adsorbate structure and electron solvation dynamics, the location (bulk versus surface) of the solvation site, and the role of the electronic structure of the underlying metal substrate on the electron transfer rate.     

Dynamic imaging of molecules using high order harmonic generation

We review recent progress towards imaging the electronic wavefunctions and nuclear dynamics of small molecules using the high order harmonics emitted when a molecule experiences an intense laser field. We illustrate that the essence of high harmonic emission is contained in the recombination amplitude between the continuum portion of the electronic wavefunction, that is formed through field ionization and which is accelerated and driven back to recollide in the laser field, and the bound electronic state. We review for the non-specialist some recent experimental and theoretical work dealing with high harmonic generation (HHG) in molecules. Particular attention is paid to two types of experiment recently performed in our group. The first of these types of experiment is the measurement of signatures of molecular electronic structure using HHG from molecules with a fixed orientation in space. The second is the use of HHG to track extremely fast proton rearrangement following ionization in light molecules, using the intrinsic temporal variation of the recolliding electron energy to extract these dynamics from measurements of the high harmonics.     

The Local Kinetic Energy Profile of an Inverted CarbonCarbon Bond Reveals and Refines its Charge‐Shift Character

Analysis of the kinetic energy density within a molecule identifies patterns in its electronic structure that are linked to the concept of charge‐shift bonding. This is illustrated in a detailed study of twelve molecules, possessing carbon‐carbon covalent as well as carbon‐carbon charge‐shift bonds in various degrees of orders, including propellanes and heteropropellanes. Regions of slow electrons are fundamental for such a correlation, and a RoSE (region of slow electrons) indicator ν_±, based on the positive definite kinetic energy density τ, is employed to characterize classes of charge‐shift bonds in terms of its full topology of all critical points of rank three.     

An open‐source framework for analyzing N‐electron dynamics. II. Hybrid density functional theory/configuration interaction methodology

In this contribution, we extend our framework for analyzing and visualizing correlated many‐electron dynamics to non‐variational, highly scalable electronic structure method. Specifically, an explicitly time‐dependent electronic wave packet is written as a linear combination of N‐electron wave functions at the configuration interaction singles (CIS) level, which are obtained from a reference time‐dependent density functional theory (TDDFT) calculation. The procedure is implemented in the open‐source Python program det CI@ORBKIT, which extends the capabilities of our recently published post‐processing toolbox (Hermann et al., J. Comput. Chem. 2016, 37, 1511). From the output of standard quantum chemistry packages using atom‐centered Gaussian‐type basis functions, the framework exploits the multideterminental structure of the hybrid TDDFT/CIS wave packet to compute fundamental one‐electron quantities such as difference electronic densities, transient electronic flux densities, and transition dipole moments. The hybrid scheme is benchmarked against wave function data for the laser‐driven state selective excitation in LiH. It is shown that all features of the electron dynamics are in good quantitative agreement with the higher‐level method provided a judicious choice of functional is made. Broadband excitation of a medium‐sized organic chromophore further demonstrates the scalability of the method. In addition, the time‐dependent flux densities unravel the mechanistic details of the simulated charge migration process at a glance. © 2017 Wiley Periodicals, Inc.     

Photoinduced charge carrier dynamics of Zn-porphyrin-TiO2 electrodes: the key role of charge recombination for solar cell performance

Time resolved absorption spectroscopy has been used to study photoinduced electron injection and charge recombination in Zn-porphyrin sensitized nanostructured TiO(2) electrodes. The electron transfer dynamics is correlated to the performance of dye sensitized solar cells based on the same electrodes. We find that the dye/semiconductor binding can be described with a heterogeneous geometry where the Zn-porphyrin molecules are attached to the TiO(2) surface with a distribution of tilt angles. The binding angle determines the porphyrin-semiconductor electron transfer distance and charge transfer occurs through space, rather than through the bridge connecting the porphyrin to the surface. For short sensitization times (1 h), there is a direct correlation between solar cell efficiency and amplitude of the kinetic component due to long-lived conduction band electrons, once variations in light harvesting (surface coverage) have been taken into account. Long sensitization time (12 h) results in decreased solar cell efficiency because of decreased efficiency of electron injection.     

Excited-state dynamics of donor-acceptor bridged systems containing a boron-dipyrromethene chromophore: interplay between charge separation and reorientational motion

The excited-state dynamics of a series of electron donor-acceptor bridged systems (DABS) consisting of a boron-dipyrromethene chromophore covalently linked to a dinitro-substituted triptycene has been investigated using femtosecond time-resolved spectroscopy. The chromophores differ by the number of bromine atom substituents. The fluorescence lifetime of the DABS without any bromine atom is strongly reduced when going from toluene to polar solvents, this shortening being already present in chloroform. This effect is about 10 times weaker with a single bromine atom and negligible with two bromine atoms on the chromophore. The excited-state lifetime shortening is ascribed to a charge transfer from the excited chromophore to a nitrobenzene moiety, the driving force of this process depending on the number of bromine substituents. The occurrence of this process is further confirmed by the investigation of the excited-state dynamics of the chromophore alone in pure nitrobenzene. Surprisingly, no correlation between the charge separation time constant and the dielectric properties of the solvents could be observed. However, a good correlation between the charge separation time constant and the diffusional reorientation time of the chromophore alone, measured by fluorescence anisotropy, was found. Quantum chemistry calculations suggest that quasi-free rotation about the single bond linking the chromophore to the triptycene moiety permits a sufficient coupling of the donor and the acceptor to ensure efficient charge separation. The charge separation dynamics in these molecules is thus controlled by the reorientational motion of the donor relative to the acceptor.     

Theoretically Rational Designs of Transport Organic Semiconductors Based on Heteroacenes

A Marcus electron transfer theory coupled with an incoherent polaron hopping and charge diffusion model in combining with first‐principle quantum chemistry calculation was applied to investigating the effects of heteroatom on the intermolecular charge transfer rate for a series of heteroacene molecules. The influences of intermolecular packing and charge reorganization energy were discussed. It was found that the sulphur and nitrogen substituted heteroacenes were intrinsically hole‐transporting materials due to the reduced hole reorganization energy and the enhanced overlap between HOMOs. For the oxygen‐substituted heteroacene, it was found that both the electronic couplings and the reorganization energies for holes and electrons were comparative, indicating the application potential of ambipolar devices. Most interestingly, for the boron‐substituted heteroacenes, theoretical calculations predicted a promising electron‐transport material, which is rare for organic materials. These findings provide insights into rationally designing organic semiconductors with specific properties.     

Watching electrons move in real time: ultrafast infrared spectroscopy of a polymer blend photovoltaic material

The dynamics of photoinduced charge separation and the motion of the resulting electrons are examined in an organic photovoltaic material with a combination of ultrafast two-dimensional infrared (2D IR) and visible pump-infrared probe (Vis-IR) spectroscopy. The carbonyl (C=O) stretch of the butyric acid methyl ester group of a functionalized fullerene, PCBM, is probed as a local vibrational reporter of the dynamics in a blend of the fullerene with a conjugated polymer, CN-MEH-PPV. Charge transfer occurs preferentially at the interfaces between the roughly spherical domains of fullerene molecules and the polymer. Comparison of the Vis-IR and 2D IR spectra reveals that the fullerene molecules at the interfaces of the domains possess higher frequency carbonyl vibrational modes, while molecules in the centers of the domains have lower frequency modes relative to the center of the transition. The correlation between the frequency of a carbonyl mode and the spatial position of its host fullerene molecule provides a means to observe the motion of electrons within individual domains through the spectral evolution of the carbonyl bleach. From the spectral evolution, we find that the average radial velocity of electrons is 1-2 m/s, which suggests an intrinsic mobility that is at least one order of magnitude greater than the mobility in the polymer blend. The results indicate that organic solar cells with higher mobility and thus efficiency may be realized by controlling the morphology of the polymer and fullerene materials.