Time-dependent Approach Research Articles

Time-dependent abinitio molecular-orbital decomposition for high-harmonic generation spectroscopy.

We propose a real-time time-dependent abinitio approach within a configuration-interaction-singles ansatz to decompose the high-harmonic generation (HHG) signal of molecules in terms of individual molecular-orbital (MO) contributions. Calculations have been performed by propagating the time-dependent Schrödinger equation with complex energies, in order to account for ionization of the system, and by using tailored Gaussian basis sets for high-energy and continuum states. We have studied the strong-field electron dynamics and the HHG spectra in aligned CO2 and H2O molecules. Contribution from MOs in the strong-field dynamics depends on the interplay between the MO ionization energy and the coupling between the MO and the laser-pulse symmetries. Such contributions characterize different portions of the HHG spectrum, indicating that the orbital decomposition encodes nontrivial information on the modulation of the strong-field dynamics. Our results correctly reproduce the MO contributions to HHG for CO2 as described in the literature experimental and theoretical data and lead to an original analysis of the role of the highest occupied molecular orbitals HOMO, HOMO-1, and HOMO-2 of H2O according to the polarization direction of the laser pulse.

The importance of boundary evolution for solar-wind modelling

The solar wind is a continual outflow of plasma and magnetic field from the Sun’s upper atmosphere—the corona—that expands to fills the solar system. Variability in the near-Earth solar-wind conditions can produce adverse space weather that impacts ground- and space-based technologies. Consequently, numerical fluid models of the solar wind are used to forecast conditions a few days ahead. The solar-wind inner-boundary conditions are supplied by models of the corona that are, in turn, constrained by observations of the photospheric magnetic field. While solar eruptions—coronal mass ejections (CMEs)—are treated as time-dependent structures, a single coronal “snapshot” is typically used to determine the ambient solar-wind for a complete model run. Thus, all available time-history information from previous coronal-model solutions is discarded and the solar wind is treated as a steady-state flow, unchanging in the rotating frame of the Sun. In this study, we use 1 year of daily-updated coronal-model solutions to comprehensively compare steady-state solar-wind modelling with a time-dependent method. We demonstrate, for the first time, how the SS approach can fundamentally misrepresent the accuracy of coronal models. We also attribute three key problems with current space-weather forecasting directly to the steady-state approach: (1) the seemingly paradoxical result that forecasts based on observations from 3-days previous are more accurate than forecasts based on the most recent observations; (2) high inconsistency, with forecasts for a given day jumping significantly as new observations become available, changing CME propagation times by up to 17 h; and (3) insufficient variability in the heliospheric magnetic field, which controls solar energetic particle propagation to Earth. The time-dependent approach is shown to alleviate all three issues. It provides a consistent, physical solution which more accurately represents the information present in the coronal models. By incorporating the time history in the solar wind along the Sun-Earth line, the time-dependent approach will provide improvements to forecasting CME propagation to Earth.

Differential Cross-Sections for the Vibrationally Excited H + HOD(vOH = 1-4) → H2 + OD Reactions.

Using the time-dependent wave-packet approach, we calculate the first fully converged state-to-state differential cross-sections for the H + HOD(vOH = 1-4) → H2 + OD reactions on a highly accurate neural network PES. It is found that, unlike the loss of memory effect observed in the product distributions for low vibrational excitation reactions, high initial OH vibrational excitation significantly influences not only the product vibrational distribution but also the angular distribution. Furthermore, for the H + HOD(vOH = 3,4) reactions, the total integral cross-sections maintain the pronounced oscillatory structures in the J = 0 probabilities at low collision energies, which originate from the prereactive van der Waals resonances. Notably, the product angular distributions exhibit forward-backward peaked behavior at these energies, akin to those observed in the complex-forming system with deep potential wells. This is attributed to the much longer lifetimes of these resonances compared to those of conventional transition state resonances.

Modulational instability for a cubic-quintic model of coupled Gross–Pitaevskii equations with residual nonlinearities

Abstract We demonstrate the existence of modulational instability (MI) in both trapped miscible and immiscible two component Bose-Einstein condensates. The study is addressed theoretically and numerically in the framework of one-dimensional coupled Gross-Pitaevskii equations incorporating intra- and interspecies cubic-quintic nonlinearities with higher order ones. Using the time-dependent variational approach, we derive the new Euler-Langrange equations for the time evolution of the phase and amplitude of the modulational perturbation as well as the effective potential and the instability criteria of the system. We examine the effects of higher-order nonlinearities on the instability dynamics of the condensates. We show that the modulational properties of the chosen wave numbers are significantly modified. Direct numerical simulations run by the split step Fourier method confirm the analytical predictions.

Modelling Sea-Surface Wave Motion and Ship Response Using Smoothed Particle Hydrodynamics and Finite Element Analysis

The response of a ship or other vessel to surface sea waves, including extreme waves, may compromise crew and vessel safety and long-term operational capability. Herein, a novel high-fidelity numerical time-dependent simulation approach is presented using Smoothed Particle Hydrodynamics (SPH) for modelling sea waves coupled with Finite Element Analysis for modelling vessel structural response under wave loading conditions. The results are compared with physical scale model wave tank test results. Good agreement was obtained for heave and pitch motions and vertical bending moments for various forward (head) speeds in regular head waves, heave and pitch motions, and vertical bending moments. High computational demands can be met by the increasing availability of computation power. Ongoing research is outlined. The implications for the design of vessels such as ships and for through-life assessment are discussed.

Role of Near-IR Sensitive Asymmetric A-DA′D–π–A-type Non-Fullerene Acceptors for Efficient Organic Solar Cells: A Theoretical Insight

Non-fullerene acceptor (NFA) molecules attracted huge attention from the photovoltaic community for their potential use in organic solar cells (OSCs). Herein, we designed a series of NFA materials (AR1–AR9) for OSCs by altering end-capped moieties. We employed various advanced density functional theory (DFT) and time-dependent (TD-DFT) approaches to characterize this designed AR1–AR9 series. Compared to the synthetic reference molecule ([Formula: see text], designed molecules AR1–AR9 revealed a smaller bandgap (1.85 eV), and improved absorption spectra ([Formula: see text] 741 nm) in comparison to [Formula: see text] ([Formula: see text] 668 nm), indicating the better potential for the tailored molecules. Furthermore, the designed series (AR1–AR9) shows lower reorganization energy values (for holes and electrons) and lower binding energies (0.323 eV), whereas, improved charge mobilities, showing them better candidates for OSCs. Moreover, frontier molecular orbitals (FMO), open-circuit voltages ([Formula: see text] and improved charge-transfer characteristics have also been investigated. These findings revealed that all developed NFAs exhibited a wide range of exciton dissociation constants and enhanced absorption efficiency with a relatively lower LUMO energy level. Therefore, we believe that these materials will be beneficial in boosting the power conversion efficiency (PCE) of OSC devices by improving their optoelectronic and photophysical properties.

A multi-layer multi-configurational time-dependent Hartree approach to lattice models beyond one dimension.

The multi-layer multi-configurational time-dependent Hartree (MCTDH) approach is an efficient method to study quantum dynamics in real and imaginary time. The present work explores its potential to describe quantum fluids. The multi-layer MCTDH approach in second quantization representation is used to study lattice models beyond one dimension at finite temperatures. A scheme to map the lattice sites onto the MCTDH tree representation for multi-dimensional lattice models is proposed. A statistical sampling scheme previously used in MCTDH calculations is adapted to facilitate an efficient description of the thermal ensemble. As example, a two-dimensional hard-core Bose-Hubbard model is studied considering up to 64 × 64 lattice sites. The single particle function basis set size required to obtain converged results is found to not increase with the lattice size. The numerical results properly simulate the finite temperature Berezinskii-Kosterlitz-Thouless phase transition.

Crystal Growth, Structural Elucidation, Chemical Reactivity, Topology Exploration (ELF, LOL, AIM, RDG) and NLO Activity of 4-Cumyl Phenol Crystal Using Quantum Chemical Calculation

The main objective of the study is to analyze the structural behavior and NLO activity of 4-cumyl phenol by experimental and theoretical spectroscopic techniques. Its computational result is compared with the cumene compound. The optimized structural parameters of the title compound were computationally obtained at the B3LYP/6-31G (d, p) basis set. The fundamental modes of vibration were examined by experimental FT-IR, and FT-Raman techniques. The distribution of the vibrational bands was carried out with the help of normal coordinate analysis (NCA). The resulting harmonic wavenumbers were scaled by using NCA method. Topological analysis, such as Electron localization function (ELF), natural bond orbital analysis (NBO), reduced density gradient (RDG) and atoms in molecule (AIM) analysis, molecular electrostatic potential (MEP) have been used to evaluate the intermolecular interaction, especially the hydrogen bonds. UV-visible spectrum of the compound was recorded in the region 200–900 nm and the electronic properties and HOMO-LUMO energies were calculated by time dependent density functional theory approach.

Simulating temperature and tautomeric effects for vibrationally resolved XPS of biomolecules: Combining time-dependent and time-independent approaches to fingerprint carbonyl groups.

Carbonyl groups (C=O) play crucial roles in the photophysics and photochemistry of biological systems. O1s x-ray photoelectron spectroscopy allows for targeted investigation of the C=O group, and the coupling between C=O vibration and O1s ionization is reflected in the fine structures. To elucidate its characteristic vibronic features, systematic Franck-Condon simulations were conducted for six common biomolecules, including three purines (xanthine, caffeine, and hypoxanthine) and three pyrimidines (thymine, 5F-uracil, and uracil). The complexity of simulation for these biomolecules lies in accounting for temperature effects and potential tautomeric variations. We combined the time-dependent and time-independent methods to efficiently account for the temperature effects and to provide explicit assignments, respectively. For hypoxanthine, the tautomeric effect was considered by incorporating the Boltzmann population ratios of two tautomers. The simulations demonstrated good agreement with experimental spectra, enabling differentiation of two types of carbonyl oxygens with subtle local structural differences, positioned between two nitrogens (O1) or between one carbon and one nitrogen (O2). The analysis provided insights into the coupling between C=O vibration and O1s ionization, consistently showing an elongation of the C=O bond length (by 0.08-0.09Å) upon O1s ionization.

The effects of processing parameters on the shape of particle size distribution and grinding rate in a stirred mill

The study of particle size distribution (PSD) of materials is a crucial aspect of mineral processing. It not only determines the appropriate beneficiation process and equipment but also has a significant impact on the grade and recovery of concentrate. This study utilizes a pin-stirred mill for the wet fine grinding of limonite to examine four different widths of PSD functions and compares their quantitative descriptions of the PSD. Skewness is a parameter introduced to quantitatively describe the asymmetry of the PSD. This study aims to investigate the effect of the stirrer speed, the density and the size of the grinding media on the shape of the PSD and on the grinding rate. The results show that a lower stirrer speed and a lower density of the grinding media result in a narrower and a more symmetrical PSD of the grinding products. Moreover, the time-dependent approach succeeds in simulating and proving the evolution behavior of the median particle size. It was found that the optimum mixing ratio of the grinding media can effectively adjust the shape of the PSD and improve the grinding efficiency.

Dynamic characteristics and performance analysis of a double-stage energy storage heat transformer with a large temperature lift

Intermittence and low grade are significant barriers for the widespread application of renewable/waste energy. An absorption energy storage heat transformer with adequate energy storage and temperature lift characteristics effectively addresses this challenge. An advancement in this technology is the double-stage energy storage heat transformer (DESHT), which further enhances the range of temperature upgrade through twice temperature lifts. This paper proposes a time-dependent approach for a comprehensive study of the DESHT cycle with a working pair of LiBr/H2O. Firstly, the dynamic characteristics of the DESHT cycle are shown. Subsequently, the effects of discharging temperatures, charging temperatures, and solution mass ratio on cycle performance are analyzed. Results show that the DESHT cycle can achieve a temperature lift from 35 °C to 55 °C. 90 % of the total storage capacity can be reached in 60–70 % of the total charging time. The maximum discharging time per unit of charging time is achieved at a temperature lift of 45 °C. Besides, compared to the conventional double-stage absorption energy storage cycle, the DESHT cycle shows a higher exergy efficiency. Optimizing the solution mass ratio can enhance the cycle performance. These findings can serve as a valuable reference in exploring the DESHT cycle.

Theoretical Study on Vibrationally Resolved Electronic Spectra of Chiral Nanographenes.

Nanographenes are of increasing importance owing to their potential applications in the photoelectronic field. Meanwhile, recent studies have primarily focused on the pure electronic spectra of nanographenes, which have been found to be inadequate for describing the experimental spectra that contain vibronic progressions. In this study, we focused on the vibronic effect on the electronic transition of a range of chiral nanographenes, especially in the low-energy regions with distinct vibronic progressions, using theoretical calculations. All the calculations were performed at the PBE0-D3(BJ)/def2-TZVP level of theory, adopting both time-dependent and time-independent approaches with Franck-Condon approximation. The resulting calculated curves exhibited good alignment with the experimental data. Notably, for the nanographenes incorporating helicene units, owing to the increasing π-extension, the major vibronic modes in the vibrationally resolved spectra differed significantly from those of the primitive helicenes. This investigation suggests that calculations that account for the vibronic effect could have better reproducibility compared with calculations based solely on pure electronic transitions. We anticipate that this study could pave the way for further investigations into optical and chiroptical properties, with a deeper understanding of the vibronic effect, thereby providing theoretical explanations with higher precision on more sophisticated nanographenes.

Tensor-Train Format Hierarchical Equations of Motion Formalism: Charge Transfer in Organic Semiconductors via Dissipative Holstein Models.

Hierarchical Equations of Motion (HEOM) in the Tensor-Train (TT) representation is applied to study the charge-transfer dynamics in organic semiconductors (OSCs). The theoretical formulation as well as the basic computational aspects of HEOM-TT are discussed in detail. Charge transfer in OSCs is modeled using dissipative polaronic models that incorporate the effects of both high- and low-frequency molecular vibrations, and it is simulated in a fully quantum and nonperturbative manner, which has not been studied intensively. The capability of treating complex electron-vibrational systems is examined by analyzing and comparing the numerical behavior of the time-dependent variational approach and the time-Alternating Minimal Energy methods and by calculating the current autocorrelation function and diffusivity across various models. Our results indicate that the HEOM-TT framework offers a robust tool for the detailed analysis of complex polaronic systems, suggesting its potential for broader applications.

Dynamic topic modelling for exploring the scientific literature on coronavirus: an unsupervised labelling technique

AbstractThe work presented in this article focusses on improving the interpretability of probabilistic topic models created from a large collection of scientific documents that evolve over time. Several time-dependent approaches based on topic models were compared to analyse the annual evolution of latent concepts in the CORD-19 corpus: Dynamic Topic Model, Dynamic Embedded Topic Model, and BERTopic. Then COVID-19 period (December 2019–present) has been analysed in greater depth, month by month, to explore the evolution of what is written about the disease. The evaluations suggest that the Dynamic Topic Model is the best choice to analyse the CORD-19 corpus. A novel topic labelling strategy is proposed for dynamic topic models to analyse the evolution of latent concepts. It incorporates content changes in both the annual evolution of the corpus and the monthly evolution of the COVID-19 disease. The generated labels are manually validated using two approaches: through the most relevant documents on the topic and through the documents that share the most semantically similar label topics. The labelling enables the interpretation of topics. The novel method for dynamic topic labelling fits the content of each topic and supports the semantics of the topics.

Improved switching condition for reachable set estimation of discrete-time switched delayed neural networks

This research delves into the reachable set estimation (RSE) problem for general switched delayed neural networks (SDNNs) in the discrete-time context. Note that existing relevant research on SDNNs predominantly relies on either time-dependent or state-dependent switching approaches. The time-dependent versions necessitate the stability of each subnetwork beforehand, whereas the state-dependent switching strategies solely depend on the current state, thus disregarding the historical information of the neuron states. For fully harnessing the historical information pertaining to neuron states, a delicate combined switching strategy (CSS) is formulated with the explicit goal of furnishing a relaxed and less conservative design framework tailored for discrete-time SDNNs, where all subnetworks can also be unstable. By resorting to the established time-dependent multiple Lyapunov–Krasovskii functional (TDMLF) technique, the improved criteria are subsequently presented, ensuring that the reachable set encompassing all potential states of SDNNs is confined to an anticipated bounded set. Ultimately, the practicality and superiority of the presented RSE approach are thoroughly validated by two illustrative simulation examples.

Good Rates From Bad Coordinates: The Exponential Average Time-dependent Rate Approach.

Our ability to calculate rate constants of biochemical processes using molecular dynamics simulations is severely limited by the fact that the time scales for reactions, or changes in conformational state, scale exponentially with the relevant free-energy barrier heights. In this work, we improve upon a recently proposed rate estimator that allows us to predict transition times with molecular dynamics simulations biased to rapidly explore one or several collective variables (CVs). This approach relies on the idea that not all bias goes into promoting transitions, and along with the rate, it estimates a concomitant scale factor for the bias termed the "CV biasing efficiency" γ. First, we demonstrate mathematically that our new formulation allows us to derive the commonly used Infrequent Metadynamics (iMetaD) estimator when using a perfect CV, where γ = 1. After testing it on a model potential, we then study the unfolding behavior of a previously well characterized coarse-grained protein, which is sufficiently complex that we can choose many different CVs to bias, but which is sufficiently simple that we are able to compute the unbiased rate directly. For this system, we demonstrate that predictions from our new Exponential Average Time-Dependent Rate (EATR) estimator converge to the true rate constant more rapidly as a function of bias deposition time than does the previous iMetaD approach, even for bias deposition times that are short. We also show that the γ parameter can serve as a good metric for assessing the quality of the biasing coordinate. We demonstrate that these results hold when applying the methods to an atomistic protein folding example. Finally, we demonstrate that our approach works when combining multiple less-than-optimal bias coordinates, and adapt our method to the related "OPES flooding" approach. Overall, our time-dependent rate approach offers a powerful framework for predicting rate constants from biased simulations.

Rise and Fall of Anderson Localization by Lattice Vibrations: A Time-Dependent Machine Learning Approach.

The intricate relationship between electrons and the crystal lattice is a linchpin in condensed matter, traditionally described by the Fröhlich model encompassing the lowest-order lattice-electron coupling. Recently developed quantum acoustics, emphasizing the wave nature of lattice vibrations, has enabled the exploration of previously uncharted territories of electron-lattice interaction not accessible with conventional tools such as perturbation theory. In this context, our agenda here is two-fold. First, we showcase the application of machine learning methods to categorize various interaction regimes within the subtle interplay of electrons and the dynamical lattice landscape. Second, we shed light on a nebulous region of electron dynamics identified by the machine learning approach and then attribute it to transient localization, where strong lattice vibrations result in a momentary Anderson prison for electronic wavepackets, which are later released by the evolution of the lattice. Overall, our research illuminates the spectrum of dynamics within the Fröhlich model, such as transient localization, which has been suggested as a pivotal factor contributing to the mysteries surrounding strange metals. Furthermore, this paves the way for utilizing time-dependent perspectives in machine learning techniques for designing materials with tailored electron-lattice properties.

New conjugated copolymer MEH-PPV-P3HT with donor-acceptor system for organic optoelectronics applications: Experimental and theoretical study

Donor-acceptor architecture was designed of new diblocks copolymer MEH-PPV-P3HT synthesis. The new copolymer was elaborated through oxidative pathway. The correlation structure-properties and their potential photophysical characteristics of the obtained material were reported utilizing several characterization analyses (InfraRed, Raman, TGA, UV visible spectroscopy, as well as PL and TRPL). To define the model's geometric structure, vibrational, and optoelectronic properties of the studied copolymer, Density Functional Theory DFT and Time-dependent Density Functional Theory TD-DFT approach were carried out. The obtained copolymer exhibits great thermal stability and substantial absorption in the visible range. An energy gap lower than the original materials by the amount of 1.74 eV which proves the presence of the charge transfer process. In addition, due to Forster energy transfer from the MEH-PPV to the P3HT an enhancement of the exciton average lifetime was detected. The obtained results from the copolymer characterization suggest a potential for application in organic optoelectronic devices. A good accordance between experimental and theoretical results based DFT calculations is obtained.

Systematic Modeling of N-Type D–A–D Conjugated Small Molecule-Based Nonfullerene Acceptors for Organic Photovoltaics

This study investigates the impact of six novel (SPZ1–SPZ6) small molecular conjugated nonfullerene acceptors (NFAs), for organic solar cells (OSCs). The designed NFAs are characterized by various advanced quantum chemical simulations of density functional theory (DFT) and time-dependent (TD-DFT) approaches. We revealed in-depth information regarding molecules’ structural-property relationship charge transfer and optical absorption characteristics of designed molecules and compared them with synthetic reference molecules (R). The designed SPZ1–SPZ6 molecules exhibit red-shifted absorption, reduced bandgaps and increased extinction coefficients, indicating improved molecular phase separation during thin-film deposition during device fabrication. Moreover, the modeled SPZ1–SPZ6 molecules significantly enhance photophysical, optoelectronic and photovoltaic parameters compared to R. Among these, the designed small molecule SPZ2 exhibits superior UV–Vis absorption of 730.44 nm, surpassing R and others. SPZ2 features the smallest bandgap (2.00 eV) and has a substantial improvement over R’s 2.37 eV, and this is due to our efficient molecular modeling strategy. Further investigation revealed efficient charge transfer between the SPZ2 acceptor molecule and PTB7-Th donor molecule complex, making this design capable of producing efficient OSCs in the future.

A non-hierarchical multi-layer multi-configurational time-dependent Hartree approach for quantum dynamics on general potential energy surfaces.

The correlation discrete variable representation (CDVR) enables multi-layer multi-configurational time-dependent Hartree (MCTDH) quantum dynamics simulations on general potential energy surfaces. In a recent study [R. Ellerbrock and U. Manthe, J. Chem. Phys. 156, 134107 (2022)], an improved CDVR that can account for the symmetry properties of a tree-shaped wavefunction representation has been introduced. This non-hierarchical CDVR drastically reduces the number of grid points required in the time-dependent quadrature used to evaluate all potential energy matrix elements. While the first studies on the non-hierarchical CDVR approach have been restricted to single-layer calculations, here the complete theory required for the implementation of the non-hierarchical CDVR approach in the multi-layer MCTDH context will be presented. Detailed equations facilitating the efficient recursive computation of all matrix elements are derived, and a new notation adapted to the symmetry properties of the tree-shaped representation is introduced. Calculations studying the non-adiabatic quantum dynamics of photoexcited pyrazine in 24 dimensions illustrate the properties of the non-hierarchical multi-layer CDVR.