Time-dependent Formalism Research Articles

MISTER-T: An open-source software package for quantum optimal control of multi-electron systems on arbitrary geometries

We present an open-source software package, MISTER-T (Manipulating an Interacting System of Total Electrons in Real-Time), for the quantum optimal control of interacting electrons within a time-dependent Kohn-Sham formalism. In contrast to other implementations restricted to simple models on rectangular domains, our method enables quantum optimal control calculations for multi-electron systems (in the effective mass formulation) on nonuniform meshes with arbitrary two-dimensional cross-sectional geometries. Our approach is enabled by forward and backward propagator integration methods to evolve the Kohn-Sham equations with a pseudoskeleton decomposition algorithm for enhanced computational efficiency. We provide several examples of the versatility and efficiency of the MISTER-T code in handling complex geometries and quantum control mechanisms. The capabilities of the MISTER-T code provide insight into the implications of varying propagation times and local control mechanisms to understand a variety of strategies for manipulating electron dynamics in these complex systems. Program summaryProgram Title: MISTER-TCPC Library link to program files:https://doi.org/10.17632/psymy4ddnw.1Licensing provisions: GNU General Public License 3Programming language: MATLABSupplementary material: animated movies of total electron densities under the influence of optimal control fields for (1) an asymmetric double-well potential for long propagation times, (2) an asymmetric double-well potential for short propagation times, and (3) a triple-well potential with a position-dependent effective mass.Nature of problem: The MISTER-T code solves quantum optimal control problems for interacting electrons within a time-dependent Kohn-Sham formalism. It can handle two-dimensional systems with arbitrary cross-sectional geometries within the effective mass formulation. The user-friendly code uses forward and backward propagator integration methods to evolve the Kohn-Sham equations with a pseudoskeleton decomposition algorithm for enhanced computational efficiency.Solution method: iterative solution of the quantum optimal control equations using finite element methods, effective mass formulation, pseudoskeleton decomposition, sparse matrix linear algebra, and nonuniform fast Fourier transforms.

Time-Dependent Multilevel Density Functional Theory.

We present a novel three-layer approach based on multilevel density functional theory (MLDFT) and polarizable molecular mechanics to simulate the electronic excitations of chemical systems embedded in an external environment within the time-dependent DFT formalism. In our method, the electronic structure of a target system, the chromophore, is determined in the field of an embedded inactive layer, which is treated as frozen. Long-range interactions are described by employing the polarizable fluctuating charge (FQ) force field. The resulting MLDFT/FQ thus accurately describes both electrostatics (and polarization) and non-electrostatic target-environment interactions. The robustness and reliability of the approach are demonstrated by comparing our results with experimental data reported for various organic molecules in solution.

Fast calculation of internal conversion rate constant using the time-dependent formalism

A new method for calculating the internal conversion rate constant, which takes into account all possible vibrational transitions between two adiabatic electronic states, is proposed. The simple analytical form of the correlation function obtained in the harmonic and anharmonic approximations and taking into account the Franck-Condon term makes it possible to perform fast calculations. In addition, the method takes into account temperature effects within harmonic kind, which extends its area of application to explain experimental processes. The approach has been applied to the study of molecules important for organic electronics, such as tetraoxa[8]circulene, free-base porphyrin and poly[n]fluorenes. The method provides valuable information on IC processes and facilitates the design of efficient molecular systems.

Coupled 3D (J ≥ 0) Time-Dependent Wave Packet Calculation for the F + H2 Reaction on Accurate Ab Initio Multi-State Diabatic Potential Energy Surfaces.

We had calculated adiabatic potential energy surfaces (PESs), nonadiabatic, and spin-orbit (SO) coupling terms among the lowest three electronic states (12A', 22A', and 12A″) of the F + H2 system using the multireference configuration interaction (MRCI) level of theory, and the adiabatic-to-diabatic transformation equations were solved to formulate the diabatic Hamiltonian matrix [J. Chem. Phys. 2020, 153, 174301] for the entire region of the nuclear configuration space. The accuracy of such diabatic PESs is explored by performing scattering calculations to evaluate integral cross sections (ICSs) and rate constants. The nonadiabatic and SO effects are studied by utilizing coupled 3D time-dependent wave packet formalism with zero and nonzero total angular momentum on multiple adiabatic/diabatic surfaces calculation. We depict the convergence profiles of reaction probabilities for the reactive as well as nonreactive processes on various electronic states at different collision energies with respect to total angular momentum including all helicity quantum numbers. Finally, total ICSs are calculated as functions of collision energies for the initial rovibrational state (v = 0, j = 0) of the H2 molecule along with the temperature-dependent rate coefficient, where those quantities are compared with previous theoretical and experimental results.

Nonlinear generalized master equations: quantum case

A system of N≫1 interacting spinless quantum particles, described by a statistical operator F(t), is considered. A time-dependent projection operator formalism for a family of projectors, which select a statistical operator FS(t) for a group of S < N relevant particles by integration of the variables of the irrelevant N − S ‘environment’ particles, is presented. This formalism results in a nonlinear version of the inhomogeneous Nakajima–Zwanzig generalized master equation (GME) for the relevant part of the statistical operator F(t), which contains an undesirable initial condition term related to the irrelevant part of the statistical operator depending on N variables. By introducing an additional operator identity, the obtained nonlinear inhomogeneous Nakajima–Zwanzig equation is exactly converted into a homogeneous nonlinear equation, accounting for initial correlations in the kernel governing its evolution. Both of these equations are equivalent to the corresponding evolution equations for FS(t) and take into account the dynamics of the environment particles. The equations for FS(t) are specialized in the linear approximation for the particle density n and analyzed for a one-particle statistical operator F1(t) . It turns out that, in addition to the correlations caused by interparticle interaction, the irrelevant initial condition term in the inhomogeneous equation for F1(t) , defined by the two-particle correlations, also contains quantum correlations conditioned by the quantum particle statistics. The latter do not vanish with time and cannot be disregarded in the conventional way by applying e.g. Bogoliubov’s principle of weakening of initial correlations. In order to take initial quantum and other correlations (commonly discarded in an unconvincing way) into consideration, the obtained nonlinear homogeneous GME has been applied. Exact in the first approximation in n, we obtain a new homogeneous equation for F1(t) , which accounts for correlations and is valid for any time moment t. It is shown how this reversible-in-time equation changes at different timescales and converts into the irreversible quantum Boltzmann equation on the macroscopic timescale without the use of the conventional approximations.

Electric field effect on [Formula: see text] clusters for applications in MOSFETs and DSSCs: a DFT study.

The structural, electronic, non-linear optical (NLO) and spectral properties of [Formula: see text] clusters with [Formula: see text] have been studied under the influence of an external electric field using density functional theory (DFT). The effect of variation in the Hf:Ti ratio on different properties of clusters is investigated. The motivation to study [Formula: see text] clusters lies in the fact that HfTiO thin films have wide applications in various optoelectronic and photovoltaic devices. So, it will be interesting to study the effect of electric field on [Formula: see text] clusters with the variation in the number of Hf, Ti and O atoms. It is observed that out of all the clusters, [Formula: see text] and [Formula: see text] are the most stable clusters with high values of binding energy and HOMO-LUMO gap. The application of an external electric field on these most stable clusters distorts their geometry and their HOMO-LUMO gap decreases, dipole moment and polarizability increases as the electric field is increased from 0 a.u. to 340 x[Formula: see text] a.u. The applied electric field increases the polar character of clusters due to electron cloud deformation and hence, increases the reactivity of the clusters, thus making these clusters suitable for electrocatalytic reactions. The electric field controlled high values of dielectric constant makes these clusters suitable to be used in the oxide layer of metal oxide semiconductor field effect transistors (MOSFETs) with better capacitance. Under the effect of an electric field, the absorption peaks of UV-VIS spectra gets red-shifted. Due to the tuning of absorption spectra from ultraviolet to visible region, [Formula: see text] clusters can be thought of as a good replacement for [Formula: see text] in dye-sensitized solar cells (DSSCs). The computational study of [Formula: see text] clusters has been performed using DFT. For the ground state of [Formula: see text] clusters, the optimization and frequency calculations have been performed using hybrid B3LYP (Becke three-parameter exchange functional combined with Lee, Yang and Parr correlation functional) functional with LANL2DZ (Los Alamos National Laboratory effective core potentials with Double Zeta atomic set) basis set under hybrid-GGA (generalized gradient approximation). Optimization and frequency calculations have been performed in each case. The excited state calculations have been carried out within time-dependent DFT formalism for a total of 50 excited states. The computational chemistry software package Gaussian 16 along with its graphical interface Gaussview have been employed for the current study of [Formula: see text] clusters.

On the photoinduced degradation of tamsulosin: The simpler the better

In this work, we present a comprehensive investigation of the decomposition of tamsulosin. Experiments were performed in an aqueous solution through photolysis with a 254 nm light source. In general, tamsulosin degradation was observed (presenting a rate of 35.4%, in 180 min), demonstrating that direct photoinduced decomposition is efficient. The simpler uncatalyzed process worked while previous experiments using solid catalysts showed negligible degradation. The kinetic constant of the photolysis process (17.6 ×10−3 min−1) was determined, considering first order kinetics, by fitting plots of ln([Tam]t −[Tam]∞)/ln([Tam]0 −[Tam]∞) versus irradiation time, where [Tam]t is the concentration of tamsulosin at time t, and [Tam]∞ is the limiting concentration of the reacting system. In addition, physical insights regarding tamsulosin photoexcitation and photolysis were obtained through quantum chemistry computations. Density functional theory (DFT) was used to investigate the ground state while its time-dependent formalism (TD-DFT) was used for determining vertical excitation energies and generalized oscillator strengths (GOSs). All the computations were undertaken at the CAM-B3LYP/6-311++G(d,p) level of theory, in water. Regarding the excited states, all five lowest-lying states were determined to have non-zero GOSs, with S3 (found at 5.73 eV (∼216 nm) at the TD-DFT/CAM-B3LYP/6–311++G(d,p) level of theory) presenting the highest GOS (0.1157) among all. Hence, these accessible states may be assigned as those responsible for the photoinduced degradation observed experimentally. Moreover, the computational results suggest tamsulosin undergoes photodecomposition through excited state chemical reaction rather than via a direct photolysis path.

Probing ground and low-lying excited states for indole derived compounds of potential herbicide action

In this work, we present a study on a series of recently synthesized indole derived compounds that were previously suggested by experimental tests as having herbicidal action. Density functional theory (DFT) and its time-dependent formalism (TD-DFT) were used for investigating ground and excited state properties, respectively. The M06-2X and CAM-B3LYP exchange-correlation functionals were used with the aug-cc-pVTZ basis set. Computations were performed in the gas-phase, water, and dimethyl sulfoxide. Solvation was found to play minor effects on the ground state structure of any given compound. On the other hand, solvation was found to cause a decrease in the excitation energies of the lowest-lying excited singlet states of almost all the compounds. More importantly, all the indole derived compounds presented excitation energies that are considerably lower than those determined for their parent molecule. For instance, the lowest-lying excited singlet was probed at 3.45 eV in the case of 6-chloro-8-nitro-2,3,4,9-tetrahydro-1H-carbazole (compound 15a) versus 5.00 eV for the corresponding state of the indole molecule, both values determined at the TD-DFT/M06-2X/aug-cc-pVTZ level in water. In addition, compound 15a along with 5-chloro-2,3-dimethyl-7-nitro-1H-indole (15b) presented three excited states (each) that are likely to be accessed (having oscillator strength ≳0.1 at the TD-DFT/M06-2X/aug-cc-pVTZ level of theory in water) among the five respective lowest-lying excited singlets. The existence of various excited states accessible at lower energies may provide competing alternative paths to the chlorophyll-solar radiation interaction, in detrimental manner to the photosynthetic process; an observation in agreement to the previous experimental findings. Frontier orbital analysis suggested electron delocalization (advent from structural modifications) to be responsible for lowering the excitation energies.

Calculation of the one- and two-photon absorption spectra of water-soluble stilbene derivatives using a multiscale QM/MM approach.

We calculated the one- (OPA) and two-photon absorption (TPA) spectra of two large water-soluble stilbene derivatives presenting TPA cross sections of about 400 GM. However, the reported experimental TPA spectra present a spectral gap region, and a theoretical study of these promising molecules seems now timely and relevant. These molecules are composed of 200 or more atoms, becoming a challenge to obtain the TPA spectra even using density functional theory at the time-dependent quadratic response formalism. Thus, both OPA and TPA were also calculated using the INDO-S semi-empirical method. We used explicit solvent molecules using the sequential-quantum mechanics/molecular mechanics to include the solvent effects. Our results show that different transitions are participating in the OPA and TPA processes and that exchange-correlation functionals, including larger Hartree-Fock contributions, provide a better description of the OPA spectra; however, the opposite trend is observed on the TPA spectra. Alternatively, INDO-S/CISD, including contributions from single and double excitations, systematically describes both OPA and TPA bands with similar shifts and better reproduces the relative intensities of the two TPA bands compared to the experimental ones. The OPA spectra are characterized by a Highest Occupied Molecular Orbital-Lowest Unoccupied Molecular Orbital (HOMO-LUMO) excitation, while the low-energy TPA band is ascribed to a single transition encompassing the (HOMO-1)-LUMO and HOMO-(LUMO+1) excitations and the high-energy one is a combination of several transitions. Thus, although more studies are required to better assess the capability of the INDO-S/CISD method in describing the TPA spectra of large molecules, our results corroborate that it is a promising alternative.

Electronic stopping power of protons in platinum: Direct valence and inner-shell-electron excitations from first-principles calculations

The electronic energy loss of proton in platinum (Pt) is studied through nonadiabatic electron-ion coupling dynamic simulations within time-dependent density functional formalism. We have clarified the counterintuitive deviation from velocity proportionality due to the existence of kink velocity of the $d$ electron excitation for a slow proton moving in metal Pt, whose valence $d$ band indeed extends up above the Fermi energy. We have also quantitatively investigated the involvement of the host core electron excitation in the ion-target interaction, through monitoring the evolution of the bound electron number on a specific orbital of the host atom during the close encounter with the flying incident ion. It is found that the low-lying $5p$, $5s$, and $4f$ configuration excitations play significant roles in determining the profile of the stopping curve around and above the stopping maximum.

The hierarchy of Davydov's Ansätze: From guesswork to numerically "exact" many-body wave functions.

This Perspective presents an overview of the development of the hierarchy of Davydov's Ansätze and a few of their applications in many-body problems in computational chemical physics. Davydov's solitons originated in the investigation of vibrational energy transport in proteins in the 1970s. Momentum-space projection of these solitary waves turned up to be accurate variational ground-state wave functions for the extended Holstein molecular crystal model, lending unambiguous evidence to the absence of formal quantum phase transitions in Holstein systems. The multiple Davydov Ansätze have been proposed, with increasing Ansatz multiplicity, as incremental improvements of their single-Ansatz parents. For a given Hamiltonian, the time-dependent variational formalism is utilized to extract accurate dynamic and spectroscopic properties using Davydov's Ansätze as its trial states. A quantity proven to disappear for large multiplicities, the Ansatz relative deviation is introduced to quantify how closely the Schrödinger equation is obeyed. Three finite-temperature extensions to the time-dependent variation scheme are elaborated, i.e., the Monte Carlo importance sampling, the method of thermofield dynamics, and the method of displaced number states. To demonstrate the versatility of the methodology, this Perspective provides applications of Davydov's Ansätze to the generalized Holstein Hamiltonian, variants of the spin-boson model, and systems of cavity-assisted singlet fission, where accurate dynamic and spectroscopic properties of the many-body systems are given by the Davydov trial states.

Emergence of Wigner oscillations in a model of real time cooling process: a time-dependent density-functional theory approach

Friedel and Wigner oscillations are well known phenomena occurring in quantum systems. Specifically, in a system composed by N confined fermions, the former are characterized by the presence of peaks in the density distributions, whereas the last by N peaks. Here, we consider N = 2 fermions harmonically confined in one-dimensional quantum dots. It is known that the transition from the Friedel to the Wigner oscillations is induced by the increment of interaction between the fermions. The increment of temperature, on the other hand, acts on eliminating the oscillations. In this context, by employing a time-dependent density-functional theory formalism, we here obtain the emergence of Wigner oscillations in a model which simulates a real time cooling process.

Driven responses of periodically patterned superconducting films

We simulate the motion of a commensurate vortex lattice in a periodic lattice of artificial circular pinning sites having different diameters, pinning strengths, and spacings using the time-dependent Ginzburg-Landau formalism. Above some critical DC current density ${J}_{\mathrm{c}}$, the vortices depin, and the resulting steady-state motion then induces an oscillatory electric field $E(t)$ with a defect ``hopping'' frequency ${f}_{0}$, which depends on the applied current density and the pinning landscape characteristics. The frequency generated can be locked to an applied AC current density over some range of frequencies, which depends on the amplitude of the DC as well as the AC current densities. Both synchronous and asynchronous collective hopping behaviors are studied as a function of the supercell size of the simulated system and the (asymptotic) synchronization threshold current densities determined.

Кинетические коэффициенты в формализме временны́х функций Грина при конечной температуре

Обсуждается микроскопическое обоснование возникновения диссипации в модельной ферми- или бозе-системе со слабым локальным взаимодействием. Рассматривается динамика равновесных флуктуаций в формализме Келдыша-Швингера, обсуждается связь диссипации с пинчевыми сингулярностями диаграмм теории возмущений. С помощью уравнения Дайсона определен и вычислен в двухпетлевом приближении параметр диссипации. Показано, что он является прямым аналогом кинетического коэффициента Онзагера и связан с наличием затухания в квазичастичном спектре.

Unitary evolution for a two-level quantum system in fractional-time scenario.

The time-evolution operator obtained from the fractional-time Schrödinger equation(FTSE) is said to be nonunitary since it does not preserve the norm of the vector state in time. As done in the time-dependent non-Hermitian quantum formalism, for a traceless non-Hermitian two-level quantum system, we demonstrate that it is possible to map the nonunitary time-evolution operator in a unitary one. It is done by considering a dynamical Hilbert space with a time-dependent metric operator, constructed from a Hermitian time-dependent Dyson map, in respect to which the system evolves in a unitary way, and the standard quantum mechanics interpretation can be made properly. To elucidate our approach, we consider three examples of Hamiltonian operators and their corresponding unitary dynamics obtained from the solutions of FTSE, and the respective Dyson maps.

Computational Method for Evaluating the Thermoelectric Power Factor for Organic Materials Modeled by the Holstein Model: A Time-Dependent Density Matrix Renormalization Group Formalism.

Organic/polymeric materials are of emerging importance for thermoelectric conversion. The soft nature of these materials implies strong electron-phonon coupling, often leading to carrier localization. This poses great challenges for the conventional Boltzmann transport description based on relaxation time approximation and band structure calculations. In this work, combining the Kubo formula with the finite-temperature time-dependent density matrix renormalization group (FT-TD-DMRG) in the grand canonical ensemble, we developed a nearly exact algorithm to calculate the thermoelectric power factor PF = α2 σ, where α is the Seebeck coefficient and σ is the electrical conductivity, and apply the algorithm to Holstein Hamiltonian with electron-phonon coupling to model organic materials. Our algorithm can provide a unified description covering the weak coupling limit described by the bandlike Boltzmann transport to the strong coupling hopping limit.

Non-linear Hamiltonian models for DNA.

Nucleic acids' physical properties have been investigated by theoretical methods based both on fully atomistic representations and on coarse-grained models, e.g., the worm-like-chain, taken from polymer physics. In this review article, I discuss an intermediate (mesoscopic) approach and show how to build a three-dimensional Hamiltonian model which accounts for the main interactions responsible for the stability of the helical molecules. While the 3D mesoscopic model yields a sufficiently detailed description of the helix at the level of the base pair, it also allows one to predict the thermodynamical and structural properties of molecules in solution. Relying on the idea that the base pair fluctuations can be conceived as trajectories, I have built over the past years a computational method based on the time-dependent path integral formalism to derive the partition function. While the main features of the method are presented, I focus here in particular on a newly developed statistical method to set the maximum amplitude of the base pair fluctuations, a key parameter of the theory. Some applications to the calculation of DNA flexibility properties are discussed together with the available experimental data.

Prediction of Effective Photoelectron and Hole Separation in Type-I MoS2/PtSe2 van der Waals Junction.

Understanding the dynamics of charge transfer at vertical heterostructures of transition metal dichalcogenide monolayers is fundamentally important for future technological applications, given the unique feature of van der Waals interactions at the interface. Here, we employ time-dependent density functional theory formalism combined with molecular dynamics to investigate photoexcited electrons and holes in the type-I MoS2/PtSe2 van der Waals heterobilayer. While type-I junctions have been traditionally viewed as being ineffective in photocarrier separation, we show that here a different mechanism from type-II is at play, which effectively separates photoelectrons from photoholes. The key is the phonon bottleneck, arising from the characteristically different dynamic band alignments in the valence and conduction bands, respectively, which only affects the transfer of holes but not electrons. The disparity between electron and hole transfer rates offers a new direction for effective control of charge separation at interfaces.

Understanding probability and irreversibility in the Mori-Zwanzig projection operator formalism

Explaining the emergence of stochastic irreversible macroscopic dynamics from time-reversible deterministic microscopic dynamics is one of the key problems in philosophy of physics. The Mori-Zwanzig (MZ) projection operator formalism, which is one of the most important methods of modern nonequilibrium statistical mechanics, allows for a systematic derivation of irreversible transport equations from reversible microdynamics and thus provides a useful framework for understanding this issue. However, discussions of the MZ formalism in philosophy of physics tend to focus on simple variants rather than on the more sophisticated ones used in modern physical research. In this work, I will close this gap by studying the problems of probability and irreversibility using the example of Grabert’s time-dependent projection operator formalism. This allows to better understand how general proposals for understanding probability in statistical mechanics, namely (a) quantum approaches and (b) almost-objective probabilities, can be accomodated in the MZ formalism. Moreover, I will provide a detailed physical analysis, based on the MZ formalism, of various proposals from the philosophical literature, such as (a) Robertson’s theory of justifying coarse-graining via autonomous macrodynamics, (b) Myrvold’s problem of explaining autonomous macrodynamics, and (c) Wallace’s simple dynamical conjecture.

Accurate Calculation of Rate Constant and Isotope Effect for the F + H2 Reaction by the Coupled 3D Time-Dependent Wave Packet Method on the Newly Constructed Ab Initio Ground Potential Energy Surface.

We employ coupled three-dimensional (3D) time dependent wave packet formalism in hyperspherical coordinates for reactive scattering problem on the newly constructed ab initio calculated ground adiabatic potential energy surface for the F + H2/D2 reaction. The convergence profiles for various reactive channels are depicted at low collision energy regimes with respect to the total angular momentum (J) quantum numbers. For two different reactant diatomic molecules (H2 and D2) initially at their respective ground roto-vibrational state (v = 0, j = 0), calculated state-to-state as well as total integral cross sections as a function of collision energy, temperature dependent rate constants, and the kinetic isotope effect for various reactivity profiles of F + H2 and F + D2 reactions are presented along with previous theoretical and experimental results.