Time-dependent Method Research Articles

MPSDynamics.jl: Tensor network simulations for finite-temperature (non-Markovian) open quantum system dynamics.

The MPSDynamics.jl package provides an easy-to-use interface for performing open quantum systems simulations at zero and finite temperatures. The package has been developed with the aim of studying non-Markovian open system dynamics using the state-of-the-art numerically exact Thermalized-Time Evolving Density operator with Orthonormal Polynomials Algorithm based on environment chain mapping. The simulations rely on a tensor network representation of the quantum states as matrix product states (MPS) and tree tensor network states. Written in the Julia programming language, MPSDynamics.jl is a versatile open-source package providing a choice of several variants of the Time-Dependent Variational Principle method for time evolution (including novel bond-adaptive one-site algorithms). The package also provides strong support for the measurement of single and multi-site observables, as well as the storing and logging of data, which makes it a useful tool for the study of many-body physics. It currently handles long-range interactions, time-dependent Hamiltonians, multiple environments, bosonic and fermionic environments, and joint system-environment observables.

Sorting of dynamical crystallization from dynamical fermionization: A quantum many-body approach

Dynamical fermionization refers to the phenomenon when the momentum distribution of impenetrable bosons asymptotically reaches that of non interacting fermions on sudden release from the trap. Whereas on sudden change in trap frequency results to Bose-Fermi oscillation which has been experimentally confirmed in the case of the Lieb-Liniger model in the Tonks-Girardeau (TG) regime. Crystallization happens for sufficiently strongly interacting repulsive bosons with dipolar interactions in one spatial dimension. Crystallization resembles fermionization but distinctly different due to long-range interaction. The present work aims to distinguish dynamical crystallization from dynamical fermionization in the expansion and breathing dynamics of N=4 strongly interacting bosons in TG limit. Our results suggest that the N-fold complete splitting in one-body density for dipolar bosons makes a clear signature of crystallization in the Bose-Fermi oscillation. We investigate the many-body dynamics by employing multiconfigurational time-dependent Hartree method for bosons which solve the N-body time-dependent Schrödinger equation numerically exactly.

Non-adiabatic dynamics studies of the C+(2P1/2, 3/2) + H2 reaction: Based on global diabatic potential energy surfaces of CH2.

Global diabatic potential energy surfaces (PESs) of CH2+ are constructed using the neural network method with a specific function based on 18 213 abinitio points. The multi-reference configuration interaction method with the aug-cc-pVQZ basis set is adopted to perform the abinitio calculations. The topographical properties of the diabatic PESs are examined in detail. In general, the diabatic PESs provide an accurate quasi-diabatic representation. To validate the diabatic PESs, the dynamics studies of the C+(2P1/2, 3/2) + H2 (v0 = 0, j0 = 0) → H + CH+(X1Σ+) reaction are performed using the time-dependent wave packet method. The reaction probabilities, integral cross sections, differential cross sections, and rate constants are calculated and compared with the experimental and theoretical results. Non-adiabatic dynamics results are in good agreement with experimental data. In addition, the non-adiabatic effect in the C+(2P1/2, 3/2) + H2 reaction is significant due to the non-adiabatic results being obviously larger than adiabatic values. The reasonable non-adiabatic dynamics results indicate that present diabatic PESs can be recommended for any type of dynamics study.

Novel investigation on adsorption analysis of safranal interacting with boron nitride and aluminum nitride fullerene-like cages: Drug delivery system

This study illustrates the effective control of COVID-19 infection through the adsorption of safranal (SAF) on B16N16 and Al16N16 fullerene-like cages. The SAF adsorption onto the B16N16 and Al16N16 surfaces in gas, water (H2O), and chloroform (CHCl3) environments were assessed using density functional theory (DFT) and time-dependent (TD) density functional theory methods, analyzing the substrates and their complexes. The Al16N16/SAF complex exhibited the most negative binding energy and structural stability in the water phase compared to the B16N16/SAF complex at the PBE0-D3 level. The thermodynamic parameters indicated that the adsorption of SAF onto the fullerene-like cages is exothermic, particularly for the Al16N16/SAF complex. Additionally, the interaction of SAF with the fullerene-like cages in the water phase is more pronounced than in gas and chloroform environments. The complexes' energy gap (Eg) decreases in all three environments compared to the perfect systems, with a significant reduction of over 21 % in all phases. This substantial decrease in the energy gap suggests that the complexes have increased reactivity and sensitivity to SAF, likely due to a significant change in electronic conductivity. The results of molecular docking indicate that the Al16N16/SAF complex in the water phase exhibited a strong binding affinity compared to the other compounds studied. These findings suggest that the Al16N16/SAF complex holds promise as a potential inhibitor for COVID-19 and as a valuable material for biomedical applications and drug delivery systems.

Nonadiabatic Exciton Dynamics and Energy Gradients in the Framework of FMO-LC-TDDFTB.

We introduce a novel methodology for simulating the excited-state dynamics of extensive molecular aggregates in the framework of the long-range corrected time-dependent density-functional tight-binding fragment molecular orbital method (FMO-LC-TDDFTB) combined with the mean-field Ehrenfest method. The electronic structure of the system is described in a quasi-diabatic basis composed of locally excited and charge-transfer states of all fragments. In order to carry out nonadiabatic molecular dynamics simulations, we derive and implement the excited-state gradients of the locally excited and charge-transfer states. Subsequently, the accuracy of the analytical excited-state gradients is evaluated. The applicability to the simulation of exciton transport in organic semiconductors is illustrated on a large cluster of anthracene molecules. Additionally, nonadiabatic molecular dynamics simulations of a model system of benzothieno-benzothiophene molecules highlight the method's utility in studying charge-transfer dynamics in organic materials. Our new methodology will facilitate the investigation of excitonic transfer in extensive biological systems, nanomaterials, and other complex molecular systems consisting of thousands of atoms.

Investigations of fluorescence emission Mechanism: Formation of ring-like structures by interactions influenced by hydroxyl group and deprotonation

As one of the gaseous signaling molecules in biological systems, hydrogen sulfide(H2S) is involved in numerous physiological processes and diseases. Therefore, rapid, effective, and real-time detection of H2S is of great importance. Based on its excellent optical properties, dicyanoisophorone has attracted much attention in recent years, and a large number of corresponding probes have been developed to detect H2S in biological systems. In this paper, the fluorescence mechanisms of three dicyanoisophorone-based fluorescent probes are investigated and the near-infrared (NIR) fluorescence attribution of the products is discussed by density-functional theory and time-dependent density-functional theory methods. Frontier molecular orbital analysis shows that the non-fluorescence of the probes is attributed to the photo-induced electron transfer process. Structural change and reduced density gradient analyses indicate that the position of the hydroxyl group and the deprotonation have a non-negligible influence on the interactions within the products. The five- or six-membered ring-like structures formed by interactions make the molecule stain as a planar and the fluorescence emission, while the twist exists the fluorescence quenching. In addition, spectral information shows that the emission of NIR fluorescence originates from the deprotonated form of the product.

Electron Nuclear Dynamics of H+ + C2H2 at ELab = 30, 200, and 450 eV.

We present a complete simplest-level electron nuclear dynamics (SLEND) investigation of H+ + C2H2 at collision energies ELab = 30, 200, and 450 eV. This reaction is relevant in astrophysics and provides a computationally feasible prototype for proton cancer therapy reactions. SLEND is a time-dependent, variational, direct, and nonadiabatic method that adopts a classical-mechanics description for the nuclei and a Thouless single-determinantal wave function for the electrons. We perform this study with our code PACE, which incorporates the One Electron Direct/Electron Repulsion Direct (OED/ERD) atomic integrals package developed by the Bartlett group. Current SLEND simulations with the 6-31G** basis set involves 2,646 trajectory calculations from 9 nonredundant, symmetry-inequivalent projectile-target orientations. For H+ + C2H2 at ELab = 30 eV, SLEND/6-31G** simulations predict one simple scattering process, and three reactive ones: C2H2 hydrogen substitution, C2H2 fragmentation into two CH moieties, and C2H2 fragmentation into CHC and H moieties, respectively. We reveal and analyze the mechanisms of these processes through computer animations; this valuable chemical information is inaccessible by experiments. The SLEND/6-31G** scattering angle functions exhibit primary and secondary rainbow scattering features that vary with the projectile-target orientations and collision energies. SLEND/6-31G** predicts 1-electron-transfer (1-ET) integral cross sections at ELab = 30, 200, and 450 eV in good agreement with their experimental counterparts. SLEND/6-31-G** predicts 1-ET differential cross sections (DCSs) at ELab = 30 eV that agree well with their experimental counterparts over all the measured scattering angles. In addition, SLEND/6-31G** predicts 0-ET DCSs at ELab = 30 eV that agree well with their experimental counterparts at low scattering angles, but less satisfactorily at higher ones. Remarkably, both the 0- and 1-ET DCSs from SLEND/6-31G** exhibit distinct primary rainbow scattering signatures in excellent agreement with their experimentally inferred counterparts. Furthermore, both SLEND/6-31G** and the experiment indicate that the primary rainbow scattering angles from the 0- and 1-ET DCSs are identical (an unusual fact in proton-molecule collisions). Through these rainbow scattering predictions, SLEND has also validated a procedure to extract primary rainbow angles from structureless DCSs. We analyze the obtained theoretical results in comparison with available experimental data and discuss forthcoming developments in the SLEND method.

Optimal tree tensor network operators for tensor network simulations: Applications to open quantum systems.

Tree tensor network states (TTNS) decompose the system wavefunction to the product of low-rank tensors based on the tree topology, serving as the foundation of the multi-layer multi-configuration time-dependent Hartree method. In this work, we present an algorithm that automatically constructs the optimal and exact tree tensor network operators (TTNO) for any sum-of-product symbolic quantum operator. The construction is based on the minimum vertex cover of a bipartite graph. With the optimal TTNO, we simulate open quantum systems, such as spin relaxation dynamics in the spin-boson model and charge transport in molecular junctions. In these simulations, the environment is treated as discrete modes and its wavefunction is evolved on equal footing with the system. We employ the Cole-Davidson spectral density to model the glassy phonon environment and incorporate temperature effects via thermo-field dynamics. Our results show that the computational cost scales linearly with the number of discretized modes, demonstrating the efficiency of our approach.

Inverse scattering for repulsive potential and strong singular interactions

In a previous work of 2014 on a quantum system governed by the repulsive Hamiltonian, the author proved uniqueness for short-range interactions described by a scattering operator consisting of regular and singular parts. In this paper, the singular part is assumed to have much stronger singularities and the same uniqueness theorem is proved. By applying the time-dependent method invented by Enss and Weder [J. Math. Phys. 36(8), 3902–3921 (1995)], the high-velocity limit for a wider class of the scattering operator with stronger singularities also uniquely determines the interactions of a multi-dimensional system.

Effective Reproduction Number of Smear-Positive Pulmonary Tuberculosis in Iran: A Registry-Based Study (2011-2021).

Tuberculosis (TB) remains a major public health issue in Iran, especially smear-positive pulmonary tuberculosis (SPPTB), due to its high transmission rate. Examining the effective reproduction number(Rt ) of SPPTB and patient characteristics is crucial for crafting targeted TB control measures. This study aimed to assess the Rt of SPPTB in Iran from 2011 to 2021 and profile SPPTB patient demographics, initial smear bacilli density, diagnosis delays, and spatial distribution. Study Design: This is a historical cohort study. A time-dependent method was used to estimate Rt , and monthly data from the national TB registry were scrutinized from 2011 to 2021. A decline was observed in SPPTB incidence rates of 50909 SPPTB cases in Iran from 2011 to 2021. Approximately 29.1% of the cases were diagnosed within a month, while 44.5% experienced a one to three-month delay in diagnosis. The analysis revealed substantial heterogeneity in TB transmission dynamics across various provinces of Iran. Provinces such as Sistan and Baluchestan, Golestan, Guilan, Khuzestan, Tehran, and Khorasan Razavi exhibited the highest effective reproduction numbers. Additionally, there was a decreasing trend in the effective reproduction numbers across all provinces from 2011 to 2020. Effective reproduction numbers declined in most provinces from 2011 to 2020 but increased moderately after the COVID-19 pandemic, highlighting the need for targeted public health interventions. Although SPPTB incidence rates are declining nationally, elevated incidence rates and effective reproduction numbers in regions such as Sistan and Baluchestan, Golestan, Guilan, Khuzestan, Tehran, and Khorasan Razavi signify the need for persistent TB management efforts in Iran.

Laser pulse induced second- and third-harmonic generation of gold nanorods with real-time time-dependent density functional tight binding (RT-TDDFTB) method.

In this study, we investigate second- and third-harmonic generation processes in Au nanorod systems using the real-time time-dependent density functional tight binding method. Our study focuses on the computation of nonlinear signals based on the time dependent dipole response induced by linearly polarized laser pulses interacting with nanoparticles. We systematically explore the influence of various laser parameters, including pump intensity, duration, frequency, and polarization directions, on harmonic generation. We demonstrate all the results using Au nanorod dimer systems arranged in end-to-end configurations, and disrupting the spatial symmetry of regular single nanorod systems is crucial for second-harmonic generation processes. Furthermore, we study the impact of nanorod lengths, which lead to variable plasmon energies, on harmonic generation, and estimates of polarizabilities and hyper-polarizabilities are provided.

Effect of number of intramolecular double bonds on photophysical properties and ESIPT processes for Cha-NH2 and its derivatives: A theoretical study

In recent years, the research on excited-state intramolecular proton transfer (ESIPT) reactions has aroused increasingly attention theoretically and experimentally. For a deep exploration, we designed three derivatives of Cha-NH2 with different numbers of carbon–carbon double bonds: Cha-NH2-1, Cha-NH2-2, and Cha-NH2-3. Using density functional theory and time-dependent density functional theory methods, we systematically studied the photophysical properties and ESIPT processes of Cha-NH2 and its derivatives. Detailed analysis revealed that the number of carbon–carbon double bonds within the molecule has a significant impact on the ESIPT behavior and spectral properties of Cha-NH2 and its derivatives. Specifically, as the number of carbon–carbon double bonds increases, the strength of intramolecular hydrogen bond is gradually weakened, leading to a red shift in the spectrum and a increase in the forward energy barrier for ESIPT, which is unfavorable for the occurrence of the ESIPT reaction. Therefore, this finding opens up broad application prospects for the adjustment and optimization of future ESIPT process.

Core Hole Effect to Valence Excitations: Tracking and Visualizing the Same Excitation in XPS Shake-Up Satellites and UV Absorption Spectra.

Introducing a core hole significantly alters the electronic structure of a molecule, and various X-ray spectroscopy techniques are available for probing the valence electronic structure in the presence of a core hole. In this study, we visually demonstrate the influence of a core hole on valence excitations by computing the ultraviolet absorption spectra and the shake-up satellites in X-ray photoelectron spectra for pyrrole, furan, and thiophene, as complemented by the natural transition orbital (NTO) analysis over transitions with and without a core hole. Employing equivalent core hole time-dependent density functional theory (ECH-TDDFT) and TDDFT methods, we achieved balanced accuracy in both spectra for reliable comparative analysis. We tracked the same involved valence transition in both spectra, offering a vivid illustration of the core hole effect via the change in corresponding particle NTOs introduced by a 1s core hole on a Cα, Cβ, or O atom. Our analysis deepens the understanding of the core hole effect on valence transitions, a phenomenon ubiquitously observed in general X-ray spectroscopic analyses.

A Globally Accurate Neural Network Potential Energy Surface and Quantum Dynamics Studies on Be+(2S) + H2/D2 → BeH+/BeD+ + H/D Reactions.

Chemical reactions between Be+ ions and H2 molecules have significance in the fields of ultracold chemistry and astrophysics, but the corresponding dynamics studies on the ground-state reaction have not been reported because of the lack of a global potential energy surface (PES). Herein, a globally accurate ground-state BeH2+ PES is constructed using the neural network model based on 18,657 ab initio points calculated by the multi-reference configuration interaction method with the aug-cc-PVQZ basis set. On the newly constructed PES, the state-to-state quantum dynamics calculations of the Be+(2S) + H2(v0 = 0; j0 = 0) and Be+(2S) + D2(v0 = 0; j0 = 0) reactions are performed using the time-dependent wave packet method. The calculated results suggest that the two reactions are dominated by the complex-forming mechanism and the direct abstraction process at relatively low and high collision energies, respectively, and the isotope substitution has little effect on the reaction dynamics characteristics. The new PES can be used to further study the reaction dynamics of the BeH2+ system, such as the effects of rovibrational excitations and alignment of reactant molecules, and the present dynamics data could provide an important reference for further experimental studies at a finer level.

Numerical Computation of 2D Domain Integrals in Boundary Element Method by (α, β) Distance Transformation for Transient Heat Conduction Problems

When the time-dependent boundary element method, also termed the pseudo-initial condition method, is employed for solving transient heat conduction problems, the numerical evaluation of domain integrals is necessitated. Consequently, the accurate calculation of the domain integrals is of crucial importance for analyzing transient heat conduction. However, as the time step decreases progressively and approaches zero, the integrand of the domain integrals is close to singular, resulting in large errors when employing standard Gaussian quadrature directly. To solve the problem and further improve the calculation accuracy of the domain integrals, an (α, β) distance transformation is presented. Distance transformation is a simple and efficient method for eliminating near-singularity, typically applied to nearly singular integrals. Firstly, the (α, β) coordinate transformation is introduced. Then, a new distance transformation for the domain integrals is constructed by replacing the shortest distance with the time step. With the new method, the integrand of the domain integrals is substantially smoothed, and the singularity arising from small time steps in the domain integrals is effectively eliminated. Thus, more accurate results can be obtained by the (α, β) distance transformation. Different sizes of time steps, positions of source point, and shapes of integration elements are considered in numerical examples. Comparative studies of the numerical results for the domain integrals using various methods demonstrate that higher accuracy and efficiency are achieved by the proposed method.

Time-Dependent Multireference Coupled-Cluster Method (TDMRCCM) for the Bath-Dynamics in System-Bath Approach to Nonadiabatic Dynamics.

The time-dependent multireference coupled-cluster method (TDMRCCM) fits well in the scheme of the system-bath separation used to study the nonadiabatic dynamics. In TDMRCCM, a projection operator is defined as one that projects the full Hilbert space onto the space spanned by the collection of system degrees of freedom, called the model space. The inverse of this projection operator is a wave operator that acts on the model space and takes its projection back to the full wave function. This wave operator is defined as an exponential of the excitation terms and, hence, can be expanded into a Taylor series, which we have truncated in this work at the second-order of excitations. The attraction of using TDMRCCM for describing the bath dynamics is due to the exponential nature of the ansatz used in the method, which makes it possible for the higher-order excitations to be absorbed by the lower-order terms, even upon truncating the series. This improves the accuracy of the numerical calculations using TDMRCCM as an approximation for the bath-mode dynamics in the system-bath framework for nonadiabatic dynamics. We present the theoretical details of TDMRCCM and the numerical results for implementing this method to study the dynamics in the butatriene cation.

Sensitivity and perturbation analysis of alpha-eigenvalue with time-dependent Monte Carlo perturbation techniques

Sensitivity analysis and perturbation calculation methods for prompt neutron decay constants α using the Monte Carlo method, such as iterative fission probability (IFP), differential operator sampling (DOS), and correlated sampling (CS), have been proposed thus far. However, these methods require a significant amount of memory storage. The method developed in this study applies DOS and CS techniques during a time-dependent Monte Carlo simulation for the pulsed neutron method in subcritical systems. The time variation of the neutron flux is fitted to an exponential function during the time range when the flux decays with the fundamental mode α. By applying the least squares method to the results of time-dependent DOS and CS, the sensitivity coefficients with respect to nuclear data and the change in α due to perturbation can be calculated. In contrast to the existing methods that require storing the total fission or time sources per generation over several (∼10) generations, the proposed method only needs to store the weighting coefficient of a single source particle until it dies. The additional memory storage per parameter is comparable to that of conventional time-dependent Monte Carlo simulations and much less than that of existing methods. Numerical tests for the proposed method have demonstrated the accuracy and usefulness of the time-dependent DOS and CS methods.

Quantum rates in dissipative systems with spatially varying friction.

We investigate whether making the friction spatially dependent on the reaction coordinate introduces quantum effects into the thermal reaction rates for dissipative reactions. Quantum rates are calculated using the numerically exact multi-configuration time-dependent Hartree method, as well as the approximate ring-polymer molecular dynamics (RPMD), ring-polymer instanton methods, and classical molecular dynamics. By conducting simulations across a wide range of temperatures and friction strengths, we can identify the various regimes that govern the reactive dynamics. At high temperatures, in addition to the spatial-diffusion and energy-diffusion regimes predicted by Kramer's rate theory, a (coherent) tunneling-dominated regime is identified at low friction. At low temperatures, incoherent tunneling dominates most of Kramer's curve, except at very low friction, when coherent tunneling becomes dominant. Unlike in classical mechanics, the bath's influence changes the equilibrium time-independent properties of the system, leading to a complex interplay between spatially dependent friction and nuclear quantum effects even at high temperatures. More specifically, a realistic friction profile can lead to an increase (or decrease) of the quantum (classical) rates with friction within the spatial-diffusion regime, showing that classical and quantum rates display qualitatively different behaviors. Except at very low frictions, we find that RPMD captures most of the quantum effects in the thermal reaction rates.

Standard Response Calculation of Electric Dipole Polarizability and Specific Optical Rotation Power Densities.

A time-dependent method has been developed to solve the standard response equation for the calculation of dynamic molecular property densities, endowed with the characteristic of being origin-invariant, entirely in the atomic orbital basis at both HF and DFT level of theory. The method has been tuned in particular for the calculation of origin-independent electric dipole polarizability density and specific rotation power density. Some demonstrations are given for the hexabenzocoronene molecule and the Tröger's base.

Efficient Time-Dependent Method for Strong-Field Ionization of Atoms with Smoothly Varying Radial Steps

We present an efficient numerical method to solve the time-dependent Schrödinger equation in the single-active electron picture for atoms interacting with intense optical laser fields. Our approach is based on a non-uniform radial grid with smoothly increasing steps for the electron distance from the residual ion. We study the accuracy and efficiency of the method, as well as its applicability to investigate strong-field ionization phenomena, the process of high-order harmonic generation, and the dynamics of highly excited Rydberg states.