Time-dependent Dipole Moment Research Articles

Electronic structure, absorption spectra and oxidation dynamics in polyynes and dicyanopolyynes.

The advent of femtosecond to attosecond experimental tools has made now possible to study such ultrafast carrier dynamics, e.g., the spatial and temporal charge density evolution, after an initial oxidation or reduction in molecules, candidates for atomic wires like polyynes and dicyanopolyynes. Here, we study the electronic structure and hole transfer in symmetric molecules containing carbon, nitrogen and hydrogen, the first members in the series of polyynic carbynes and dicyanopolyynes, using methods based on density functional theory (DFT): constrained DFT (CDFT), time-dependent DFT (TDDFT) and real-time TDDFT (RT-TDDFT), with Löwdin population analysis, comparing many levels of theory and obtaining convergence of the results. For the same purposes, we develop a tight binding (TB) variant using all valence orbitals of all atoms. This TB variant is applied here in linear molecules, but it is also adequate for electronic structure, charge transfer and charge transport of non-linear molecules and clusters of molecules. We calculate the electronic structure, the time-dependent dipole moment and the probabilities of finding the hole at each site, their mean over time values, the mean transfer rates from the oxidation site to other sites and the frequency content (using charge as well as dipole moment oscillations). We take into account zero-point motion. The initial conditions for RT-TDDFT are obtained by CDFT. For TB, we explore different initial conditions: we place the hole at a particular orbital or distribute it among a number of orbitals; it is also possible to include phase differences between orbitals. Finally, we compare with available experimental data.

Cost-Efficient High-Resolution Linear Absorption Spectra through Extrapolating the Dipole Moment from Real-Time Time-Dependent Electronic-Structure Theory.

We present a novel function fitting method for approximating the propagation of the time-dependent electric dipole moment from real-time electronic structure calculations. Real-time calculations of the electronic absorption spectrum require discrete Fourier transforms of the electric dipole moment. The spectral resolution is determined by the total propagation time, i.e., the trajectory length of the dipole moment, causing a high computational cost. Our developed method uses function fitting on shorter trajectories of the dipole moment, achieving arbitrary spectral resolution through extrapolation. Numerical testing shows that the fitting method can reproduce high-resolution spectra by using short dipole trajectories. The method converges with as little as 100 a.u. dipole trajectories for some systems, though the difficulty converging increases with the spectral density. We also introduce an error estimate of the fit, reliably assessing its convergence and hence the quality of the approximated spectrum.

Attosecond Real-Time Observation of Recolliding Electron Trajectories in Helium at Low Laser Intensities.

Laser-driven recollision physics is typically accessible only at field intensities high enough for tunnel ionization. Using an extreme ultraviolet pulse for ionization and a near-infrared (NIR) pulse for driving of the electron wave packet lifts this limitation. This allows us to study recollisions for a broad range of NIR intensities with transient absorption spectroscopy, making use of the reconstruction of the time-dependent dipole moment. Comparing recollision dynamics with linear vs circular NIR polarization, we find a parameter space, where the latter favors recollisions, providing evidence for the so far only theoretically predicted recolliding periodic orbits.

Waveform Modulation of High-Order Harmonics Generated from an Atom Irradiated by a Laser Pulse and a Weak Orthogonal Electrostatic Field

The detailed characteristics of the harmonics emission of atoms driven via a linearly polarized laser field combined with an orthogonal, weaker electrostatic field were investigated by numerically solving the time-dependent Schrödinger equation. It was found that the direction of the laser polarization and the polarization of the attosecond light, which is synthesized from the harmonic, can be controlled by the amplitude of the electrostatic field. With the analysis of the spatial distribution of the time-dependent dipole moment and the time-dependent evolution of the electronic wave packet, the control mechanism for the harmonic characters was investigated. The generation of harmonics in the vertical direction of the laser electric field is caused by the breaking of the symmetry of the time wave packet distribution. With this mechanism, we obtained circularly polarized attosecond light.

Surface termination dependent optical characteristics of MXene nanoflakes

Two-dimensional (2D) transition metal carbides, nitrides, and carbonitrides, known as MXenes, are an expanding class of 2D materials. With the compositional diversity and range of surface terminations, they have the potential to facilitate the development of novel devices. Herein, based on quantum-mechanical simulations via time-dependent density functional theory, we investigate how the M element (Ti or V) and surface terminations (Tx such as F and O) affect the optical and plasmonic characteristics of M2CTx MXene nanoflakes. We reveal the formation of localized surface plasmon resonances (LSPRs) in MXene nanoflakes. Interestingly, the Janus MXene nanoflake Ti2CFO (top surface terminated with F and bottom surface terminated with O) produces the strongest and narrowest infrared LSPR, which is attributable to its largest out-of-plane time-dependent dipole moment. The findings of this study may be helpful to those exploring on MXene plasmonics.

Quantum-Compute Algorithm for Exact Laser-Driven Electron Dynamics in Molecules.

In this work, we investigate the capability of known quantum computing algorithms for fault-tolerant quantum computing to simulate the laser-driven electron dynamics of excitation and ionization processes in small molecules such as lithium hydride, which can be benchmarked against the most accurate time-dependent full configuration interaction (TD-FCI) calculations. The conventional TD-FCI wave packet propagation is reproduced using the Jordan-Wigner transformation for wave function and operators and the Trotter product formula for expressing the propagator. In addition, the time-dependent dipole moment, as an example of a time-dependent expectation value, is calculated using the Hadamard test. To include non-Hermitian operators in the ionization dynamics, a similar approach to the quantum imaginary time evolution (QITE) algorithm is employed to translate the propagator, including a complex absorption potential, into quantum gates. The computations are executed on a quantum computer simulator. By construction, all quantum computer algorithms, except for the QITE algorithm used only for ionization but not for excitation dynamics, would scale polynomially on a quantum computer with fully entangled qubits. In contrast, TD-FCI scales exponentially. Hence, quantum computation holds promises for substantial progress in the understanding of electron dynamics of excitation processes in increasingly large molecular systems, as has already been witnessed in electronic structure theory.

Accelerating Real-Time Coupled Cluster Methods with Single-Precision Arithmetic and Adaptive Numerical Integration.

We explore the framework of a real-time coupled cluster method with a focus on improving its computational efficiency. Propagation of the wave function via the time-dependent Schrödinger equation places high demands on computing resources, particularly for high level theories such as coupled cluster with polynomial scaling. Similar to earlier investigations of coupled cluster properties, we demonstrate that the use of single-precision arithmetic reduces both the storage and multiplicative costs of the real-time simulation by approximately a factor of 2 with no significant impact on the resulting UV/vis absorption spectrum computed via the Fourier transform of the time-dependent dipole moment. Additional speedups─of up to a factor of 14 in test simulations of water clusters─are obtained via a straightforward GPU-based implementation as compared to conventional CPU calculations. We also find that further performance optimization is accessible through sagacious selection of numerical integration algorithms, and the adaptive methods, such as the Cash-Karp integrator, provide an effective balance between computing costs and numerical stability. Finally, we demonstrate that a simple mixed-step integrator based on the conventional fourth-order Runge-Kutta approach is capable of stable propagations even for strong external fields, provided the time step is appropriately adapted to the duration of the laser pulse with only minimal computational overhead.

Theory of dipole moment reconstruction by attosecond transient absorption spectroscopy

We propose a general procedure for the reconstruction of time-dependent dipole moment via transient absorption spectrum, within the framework of linear response theory. The reconstruction method is demonstrated with two examples: the self-reconstruction of extreme-ultraviolet-light-atom interaction (analytically) and the infrared-dressed helium system (numerically). A correlation coefficient is introduced to quantify the fidelity of the reconstruction, which reaches almost 100$%$ over a wide range of laser parameters and thus indicates the robustness of our reconstruction method. Our theory provides a solid basis for understanding the recent experiment [Phys. Rev. Lett. 121, 173005 (2018)], explaining when and why the dipole moment can be well reconstructed solely from the absorption spectrum even without exact knowledge of the attosecond probe pulse.

Effects of Structural Dynamics on Charge Carrier Transfer in B-DNA: A Combined MD and RT-TDDFT Study.

Hole transfer along the axis of duplex DNA has been the focus of physical chemistry research for decades, with implications in diverse fields, from nanotechnology to cell oxidative damage. Computational approaches are particularly amenable for this problem, to complement experimental data for interpretation of transfer mechanisms. To be predictive, computational results need to account for the inherent mobility of biological molecules during the time frame of experimental measurements. Here, we address the structural variability of B-DNA and its effects on hole transfer in a combined molecular dynamics (MD) and real-time time-dependent density functional theory (RT-TDDFT) study. Our results show that quantities that characterize the charge transfer process, such as the time-dependent dipole moment and hole population at a specific site, are sensitive to structural changes that occur on the nanosecond time scale. We extend the range of physical properties for which such a correlation has been observed, further establishing the fact that quantitative computational data on charge transfer properties should include statistical averages. Furthermore, we use the RT-TDDFT results to assess an efficient tight-binding method suitable for high-throughput predictions. We demonstrate that charge transfer, although affected by structural variability, on average, remains strong in AA and GG dimers.

Nuclear-electronic orbital Ehrenfest dynamics.

The recently developed real-time nuclear-electronic orbital (RT-NEO) approach provides an elegant framework for treating electrons and selected nuclei, typically protons, quantum mechanically in nonequilibrium dynamical processes. However, the RT-NEO approach neglects the motion of the other nuclei, preventing a complete description of the coupled nuclear-electronic dynamics and spectroscopy. In this work, the dynamical interactions between the other nuclei and the electron-proton subsystem are described with the mixed quantum-classical Ehrenfest dynamics method. The NEO-Ehrenfest approach propagates the electrons and quantum protons in a time-dependent variational framework, while the remaining nuclei move classically on the corresponding average electron-proton vibronic surface. This approach includes the non-Born-Oppenheimer effects between the electrons and the quantum protons with RT-NEO and between the classical nuclei and the electron-proton subsystem with Ehrenfest dynamics. Spectral features for vibrational modes involving both quantum and classical nuclei are resolved from the time-dependent dipole moments. This work shows that the NEO-Ehrenfest method is a powerful tool to study dynamical processes with coupled electronic and nuclear degrees of freedom.

Real-Time Time-Dependent Nuclear-Electronic Orbital Approach: Dynamics beyond the Born-Oppenheimer Approximation.

The quantum mechanical treatment of both electrons and nuclei is crucial in nonadiabatic dynamical processes such as proton-coupled electron transfer. The nuclear-electronic orbital (NEO) method provides an elegant framework for including nuclear quantum effects beyond the Born-Oppenheimer approximation. To enable the study of nonequilibrium properties, we derive and implement a real-time NEO (RT-NEO) approach based on time-dependent Hatree-Fock or density functional theory, in which the electronic and nuclear degrees of freedom are propagated in a time-dependent variational framework. Nuclear and electronic spectral features can be resolved from the time-dependent dipole moment computed using the RT-NEO method. The test cases show the dynamical interplay between the quantum nuclei and the electrons through vibronic coupling. Moreover, vibrational excitation in the RT-NEO approach is demonstrated by applying a resonant driving field, and electronic excitation is demonstrated by simulating excited state intramolecular proton transfer. This work shows that the RT-NEO approach is a promising tool to study nonadiabatic quantum dynamical processes within a time-dependent variational description for the coupled electronic and nuclear degrees of freedom.

Ultrafast electron transfer through a silicon–vacuum interface induced by the action of an intense femtosecond laser pulse

A theoretical study of the influence of a quasistationary electric field formed during emission separation of charges on ultrafast electron transfer near a silicon–vacuum interface irradiated by femtosecond laser pulses was carried out. The values of the strength of the arising quasistationary field during irradiation by femtosecond pulses with fluences near and above the silicon damage thresholds were estimated. The possibility of the formation of a dynamic optically layered structure in the near-surface layers of silicon irradiated by a femtosecond pulse, resulting from a modification of its optical properties due to the depletion of electrons in the surface layer, was studied. It is suggested that the time-dependent dipole moment induced by the emission separation of charges should lead to the generation of electromagnetic radiation from the terahertz frequency range. The basic properties of this radiation were theoretically investigated.

Relativistic Real-Time Time-Dependent Equation-of-Motion Coupled-Cluster

We present a relativistic time-dependent equation-of-motion coupled-cluster with single and double excitations (TD-EOM-CCSD) formalism. Unlike other explicitly time-dependent quantum chemical methods, the present approach considers the time correlation function of the dipole operator, as opposed to the expectation value of the time-dependent dipole moment. We include both scalar relativistic effects and spin-orbit coupling variationally in this scheme via the use of the exact two-component (X2C) wave function as the reference that enters the coupled-cluster formalism. In order to evaluate the accuracy of X2C-TD-EOM-CCSD, we compare zero-field splitting in atomic absorption spectra of open-shell systems (Na, K, Mg+, and Ca+) with values obtained from experiment. In closed-shell species (Na+, K+, Mg2+, and Ca2+), we observe singlet-triplet mixing in the X2C-TD-EOM-CC calculations, which results from the use of the X2C reference. The effects of the X2C reference are evaluated by comparing spectra derived from X2C-TD-EOM-CC calculations to those from TD-EOM-CC calculations using a complex generalized Hartree-Fock ([Formula: see text]-GHF) reference.

Langevin equation for the dipole vector of an accidental symmetric top molecule

The Langevin equation governing the time dependent dipole moment μ(t) of an accidental symmetric top (i.e., the direction of μ(t) does not coincide with the axis of symmetry) in an external electric field is directly derived from the Euler-Langevin equation. Results which have been previously obtained in J. Mol. Liquids. 1991, 49, 79 are regained as special cases. The scalar Langevin equation governing the longitudinal component of μ(t) along a space fixed axis is also derived.

Subatomic scale study of atom-generated higher-order harmonic

<sec>The higher-order harmonics generated from an atom irradiated by ultarashort laser pulses is one of the important ways to obtain ultrashort attosecond pulses and coherent XUV sources. In order to produce a high-inntensity XUV source, one needs to study the mechanism of harmonic generation. The mechanism of the atomic high harmonic generation can be well understood by the semi-classical three-step model. First, the electron tunnels the barrier formed by the atomic potential and laser electric field, and then it propagates freely in the laser field and can be driven back to the mother ion where it recombines with the ground state of ion. Although the cutoff energy of the high harmonic can be predicted by this model, it cannot provide more information about the harmonic efficiency and the spectral structure. Recently, the generation mechanism of high harmonic has been studied by using the Bohmian trajectory scheme based on the time dependent wave packet. It is found that the harmonic structure can be reconstructed qualitatively by using a single Bohmian trajectory. The more accurate structure of harmonic spectrum needs more Bohmian trajectories. The calculation of these trajectories requires a lot of computation resources because the trajectory calculation is from the numerical solution for the time-dependent Schrödinger equation. In this work, we numerically solve the time-dependent Schrödinger equation of a model atom irradiated by ultrashort laser pulses. The time-dependent dipole moments at different spatial locations are calculated from the time-dependent wave function. The harmonic spectra are calculated from the Fourier transform of the time dipole moments. The harmonic spectra of different spatial locations show that the main emission positions of harmonic emission are near the nuclear region. One can observe the odd- and even-order harmonics at the different spatial positions. There has a larger radiation intensity for the integer-order harmonic. For the odd-order harmonics, their harmonic phases are the same on both sides of <i>x</i> = 0. For the even-order harmonics, their harmonic phases each have a pi difference on both side of <i>x</i> = 0. By using the filtering scheme, we analyze the phases of an harmonic at different spatial locations. It is found that the phase difference leads the odd-order harmonics to increase and the even-order harmonics to disappear. These findings contribute to the understanding of the physical mechanism of higher harmonic generated from an atom irradiated by strong laser pulses.</sec>

A general approach for the calculation and characterization of x-ray absorption spectra.

We present a general approach for the calculation and assignment of X-ray absorption spectra based on electronic wavepacket propagations performed using explicitly time-dependent electronic structure calculations. Such calculations have the appeal of yielding the entire absorption spectrum for the cost of a single set of electronic wavepacket propagations, obviating the need to explicitly calculate large numbers of core-excited states. The spectrum can either be calculated from the Fourier transform of the time-dependent dipole moment or from the Fourier transform of the wavepacket autocorrelation function. We propose that calculating the absorption spectrum using the latter approach will generally be the preferred option. This method has two important advantages. First, the autocorrelation functions can be obtained for twice the propagation time, resulting in a halving of the computational effort required to calculate the spectrum relative to the time-dependent dipole moment approach. Second, using the tools of filter diagonalisation, the autocorrelation functions may be used to determine the time-independent final core-excited states underlying the peaks of interest in the spectrum. The proposed scheme is validated by calculating and characterizing the X-ray absorption spectra of benzene and trifluoroacetonitrile at the time-dependent second-order algebraic diagrammatic construction level of theory.

Exact-exchange optimized effective potential and memory effect in time-dependent density functional theory

The memory effect in time-dependent density functional theory (TDDFT) is important in simulating many time-dependent physical processes, and its implementation in real time has been a longstanding challenge, thus limiting most of TDDFT applications to either adiabatic or linear-response regime. In this paper, we conduct the non-adiabatic calculations for a one-dimensional two-electron Helium model in a triplet state using the recently formulated Sturm-Liouville-type time-local equation for the time-dependent optimized effective potential (TDOEP) with the exact exchange functional, and the results agree with the exact time-dependent Schrodinger equation solutions. It is also found that the time-dependent dipole moment and probability density calculated from the TDOEP approach are more accurate than those from the adiabatic time-dependent Krieger-Li-Iafrate (TDKLI) approximation and the adiabatic local spin density approximation. Specifically, the non-adiabatic and memory-dependent terms in the time-local TDOEP equation correctly describe the time-dependent structure of exchange-correlation potential and yield the probability density evolution. These findings should provide important insights toward future studies on memory effects in TDDFT.

Ab initio calculations of the linear and nonlinear susceptibilities of N2 , O2 , and air in midinfrared laser pulses

We present first-principles calculations of the linear and nonlinear susceptibilities of N$_2$, O$_2$, and air in the mid-infrared wavelength regime, from $1-4$ $\mu$m. We extract the frequency-dependent susceptibilities from the full time-dependent dipole moment that is calculated using time-dependent density functional theory. We find good agreement with curves derived from experimental results for the linear susceptibility, and with measurements for the nonlinear susceptibility up to 2.4 $\mu$m. We also find that the susceptibilities are insensitive to the laser intensity even in the strong field regime up to $5\times 10^{13}$ W/cm$^2$. Our results will allow accurate calculations of the long-distance propagation of intense MIR laser pulses in air.

Nodeless vibrational amplitudes and quantum nonadiabatic dynamics in the nested funnel for a pseudo Jahn-Teller molecule or homodimer.

The nonadiabatic states and dynamics are investigated for a linear vibronic coupling Hamiltonian with a static electronic splitting and weak off-diagonal Jahn-Teller coupling through a single vibration with a vibrational-electronic resonance. With a transformation of the electronic basis, this Hamiltonian is also applicable to the anti-correlated vibration in a symmetric homodimer with marginally strong constant off-diagonal coupling, where the non-adiabatic states and dynamics model electronic excitation energy transfer or self-exchange electron transfer. For parameters modeling a free-base naphthalocyanine, the nonadiabatic couplings are deeply quantum mechanical and depend on wavepacket width; scalar couplings are as important as the derivative couplings that are usually interpreted to depend on vibrational velocity in semiclassical curve crossing or surface hopping theories. A colored visualization scheme that fully characterizes the non-adiabatic states using the exact factorization is developed. The nonadiabatic states in this nested funnel have nodeless vibrational factors with strongly avoided zeroes in their vibrational probability densities. Vibronic dynamics are visualized through the vibrational coordinate dependent density of the time-dependent dipole moment in free induction decay. Vibrational motion is amplified by the nonadiabatic couplings, with asymmetric and anisotropic motions that depend upon the excitation polarization in the molecular frame and can be reversed by a change in polarization. This generates a vibrational quantum beat anisotropy in excess of 2/5. The amplitude of vibrational motion can be larger than that on the uncoupled potentials, and the electronic population transfer is maximized within one vibrational period. Most of these dynamics are missed by the adiabatic approximation, and some electronic and vibrational motions are completely suppressed by the Condon approximation of a coordinate-independent transition dipole between adiabatic states. For all initial conditions investigated, the initial nonadiabatic electronic motion is driven towards the lower adiabatic state, and criteria for this directed motion are discussed.

Axion star collisions with neutron stars and fast radio bursts

Axions may make a significant contribution to the dark matter of the universe. It has been suggested that these dark matter axions may condense into localized clumps, called "axion stars." In this paper we argue that collisions of dilute axion stars with neutron stars, of the type known as "magnetars," may be the origin of most of the observed fast radio bursts. This idea is a variation of an idea originally proposed by Iwazaki. However, instead of the surface effect of Iwazaki, we propose a perhaps stronger volume effect caused by the induced time dependent electric dipole moment of neutrons.