Time-dependent Quantum Dynamics Research Articles

A seven-degree-of-freedom, time-dependent quantum dynamics study on the energy efficiency in surmounting the central energy barrier of the OH + CH3 → O + CH4 reaction.

A time-dependent, quantum reaction dynamics calculation with seven degrees of freedom was carried out to study the energy efficiency in surmounting the approximate center energy barrier of OH + CH3. The calculation shows the OH vibration excitations greatly enhance the reactivity, whereas the vibrational excitations of CH3 and the rotational excitations hinder the reactivity. On the basis of equal amount of total energy, although this reaction has a slight early barrier, it is the OH vibrational energy that is the dominate force in promoting the reactivity, not the translational energy. The studies on both the forward O + CH4 and reverse OH + CH3 reactions demonstrate, for these central barrier reactions, a small change of the barrier location can significantly change the energy efficacy roles on the reactivity. The calculated rate constants agree with the experimental data.

Nonadiabatic couplings and charge transfer study in H + CS+ collision using time-dependent quantum dynamics

Experiments have reported the high stability of HCS+ ion and inhibit to decompose over the range of collision energies. In this study, the various energy transfer channels of atomic H collision with CS+ molecular ion has been performed by ab initio computations at the multireference configuration interaction/aug-cc-pVQZ level of theory. The ground and several low-lying excited electronic state potential energy surfaces in three different molecular orientations, namely, two collinear configurations with, (1) H approaching the S atom (γ = 0°), (2) H approaching the C atom (γ = 180°) and one perpendicular configuration, (3) H approaching the centre of mass of CS (γ = 90°) with the diatom fixed at the equilibrium bond length, have been obtained. Nonadiabatic effects with Landau–Zener coupling leading to avoided crossings are observed between the ground- and the first-excited states in γ = 90° orientation, and also between the first- and second-excited states in γ = 180° orientation. Quantum dynamics have been performed to study the charge transfer using time-dependent wave packet method on the diabatic potential energy surfaces. The probability of charge transfer is found to be highest with 42% in γ = 180°. The high charge transfer probability result in the formation of H+ + CS channel which ascertains the high stability of HCS+ ion.

Probing time-ordering in two-photon double ionization of helium on the attosecond time scale

We show that time ordering underlying time-dependent quantum dynamics is a physical observable accessible by attosecond streaking. We demonstrate the extraction of time ordering for the prototypical case of time-resolved two-photon double ionization of helium by an attosecond XUV pulse. The Eisenbud–Wigner–Smith time delay for the emission of a two-electron wavepacket and the time interval between subsequent emission events can be unambiguously determined by attosecond streaking. The delay between the two emission events sensitively depends on the energy, pulse duration, and angular distribution of the emitted electron pair. Our fully-dimensional ab initio quantum mechanical simulations provide benchmark data for experimentally accessible observables.

Photodissociation Dynamics of Homonuclear Diatomic Molecules in Helium Nanodroplets. The Case of Cl₂@(⁴He)N.

To investigate the photodissociation dynamics of diatomic homonuclear molecules in helium nanodroplets, a hybrid quantum mechanical theoretical method that combines time dependent density functional theory (helium) and quantum dynamics (molecule) has been developed. This method has been applied to investigate the Cl2 photodissociation arising from the B ← X electronic transition, considering Cl2(v = 0,X)@((4)He)N nanodroplets with N = 50, 100, 200, 300, and 500 (initial configuration for the dynamics). A time scale of a few picoseconds has been determined, and the time required for the dissociating atoms to reach the nanodroplet surface increases with N. Moreover, at the high velocities involved (orders of magnitude above the Landau's critical velocity), an efficient energy exchange between the chlorine atoms and the helium takes place, releasing up to 91% of the energy of the excited diatomics for the bigger nanodroplet considered; and the energy exchange mechanism is the same for all the nanodroplets. Finally, simple (linear) relations for the average Cl final velocity and the (small) number of evaporated He atoms with respect to the radius of the droplets have been reported, together with the existence of confinement resonances. We hope that these results will encourage the experimentalists to investigate this kind of systems.

Space- and time-dependent quantum dynamics of spatially indirect excitons in semiconductor heterostructures.

We study the unitary propagation of a two-particle one-dimensional Schrödinger equation by means of the Split-Step Fourier method, to study the coherent evolution of a spatially indirect exciton (IX) in semiconductor heterostructures. The mutual Coulomb interaction of the electron-hole pair and the electrostatic potentials generated by external gates and acting on the two particles separately are taken into account exactly in the two-particle dynamics. As relevant examples, step/downhill and barrier/well potential profiles are considered. The space- and time-dependent evolutions during the scattering event as well as the asymptotic time behavior are analyzed. For typical parameters of GaAs-based devices, the transmission or reflection of the pair turns out to be a complex two-particle process, due to comparable and competing Coulomb, electrostatic, and kinetic energy scales. Depending on the intensity and anisotropy of the scattering potentials, the quantum evolution may result in excitation of the IX internal degrees of freedom, dissociation of the pair, or transmission in small periodic IX wavepackets due to dwelling of one particle in the barrier region. We discuss the occurrence of each process in the full parameter space of the scattering potentials and the relevance of our results for current excitronic technologies.

Born-Oppenheimer and Renner-Teller coupled-channel quantum reaction dynamics of O((3)P) + H2(+)(X(2)Σg(+)) collisions.

We present Born-Oppenheimer (BO) and Renner-Teller (RT) time dependent quantum dynamics studies of the reactions O((3)P) + H2(+)(X(2)Σg(+)) → OH(+)(X(3)Σ(-)) + H((2)S) and OH(X(2)Π) + H(+). We consider the OH2(+) X[combining tilde](2)A'' and Ã(2)A' electronic states that correlate with a linear (2)Π species. The electronic angular momenta operators L[combining circumflex] and L[combining circumflex](2) are considered in nonadiabatic coupled-channel calculations, where the associated RT effects are due to diagonal V(RT) potentials that add up to the PESs and to off-diagonal C(RT) couplings between the potential energy surfaces (PESs). Initial-state-resolved reaction probabilities PI, integral cross sections σI, and rate constants kI are obtained using recent ab initio PESs and couplings and the real wavepacket formalism. Because the PESs are strongly attractive, PI have no threshold energy and are large, σI decrease with collision energy, and kI depend little on the temperature. The X[combining tilde](2)A'' PES is up to three times more reactive than the Ã(2)A' PES and H2(+) rotational effects (j0 = 0, 1) are negligible. The diagonal V(RT) potentials are strongly repulsive at the collinearity and nearly halve all low-energy observables with respect to the BO ones. The off-diagonal C(RT) couplings are important at low partial waves, where they mix the X[combining tilde](2)A'' and Ã(2)A' states up to ∼20%. However, V(RT) effects predominate over the C(RT) ones that change at most by ∼19% the BO values of σI and kI. The reaction O((3)P) + H2(+)(X(2)Σg(+)) → OH(+)(X(3)Σ(-)) + H((2)S) is probably one of the most reactive atom + diatom collisions because its RT rate constant at room temperature is equal to 2.26 × 10(-10) cm(3) s(-1). Within the BO approximation, the present results agree rather well with recent quasiclassical and centrifugal-sudden data using the same PESs.

Influence of collision energy on the dynamics of the reaction H (2S) + NH (X3Σ−) → N (4S) + H2 (X1Σ g + ) by the state-to-state quantum mechanical study

State-to-state time-dependent quantum dynamics calculations have been carried out to study the abstraction processes in the title reaction for the first time. The ab initio potential energy surface of the lowest quartet electronic state of the system recently reported by Zhai et al. (J Chem Phys 135:104314/1–104314/7, 2011) is employed in this investigation. Influences of the collision energy on the product state-resolved differential cross sections (DCSs) are calculated and discussed. For low collision energies, we find that reactive collisions along the collinear pathway result in the H2 product backward scattering. In the case of high collision energy, the stripping collisions with larger impact parameters tend to produce sideways scattering and furnish a high internal excitation of the H2. The product H2 is found to have an inverted rotational distribution and no inversion in vibrational distributions. Moreover, the state-to-state DCSs provide a global perspective of the reaction mechanisms and their contribution to the final H2 internal energy states. A reaction model is built and works well for our calculated results.

Time-dependent quantum dynamics calculations of product photofragment cross-sections

A time-dependent quantum dynamics theory has been presented to interpret product partial cross-sections of the photofragmentation of triatomic molecule by treating correctly the coupling of angular momenta and taking fully into account the vector properties of the transition dipole moment and electric field of the exciting radiation. A model system of [Formula: see text] has been used to study the nuclear motion of N 2 photofragments through the asymptotic dissociation channels which relies upon the transition dipole vector either lies parallel on the molecular plane (1A′→1A′) or perpendicular to the molecular plane (1A′→1A′′).

Taming the escape dynamics of nonadiabatic time-periodically driven quantum dissipative system within the frame of Wigner formalism

Escape under the action of the external modulation constitutes a nontrivial generalization of an conventional Kramers rate because the system is away from thermal equilibrium. A derivation of this result from the point of view of Langevin dynamics in the frame of Floquet theorem in conjunction with the Kapitza–Landau time window (that leads to an attractive description of the time-dependent quantum dynamics in terms of time-independent one) has been provided. The quantum escape rate in the intermediate-to-high and very-high damping regime so obtained analytically using the phase space formalism associated with the Wigner distribution and path-integral formalism bears a quantum correction that depends strongly on the barrier height. It is shown that an increase of (amplitude/frequency) ratio causes the system to decay faster, in general. The crossover temperature between tunneling and thermal activation increases in the presence of field so that quantum effects in the escape are relevant at higher temperatures.

Carrier envelope phase retrieval of a multi-cycle pulse by heterodyne mixing of a pulse containing a few cycles

We present a theoretical routine for carrier envelope phase (CEP) retrieval of a multi-cycle femtosecond pulse by heterodyne mixing with a CEP-known few-cycle pulse using the time-dependent wavepacket quantum dynamics method. Our study is based on the CEP measuring technique and the dependence of high-order harmonic generation (HHG) spectra on CEP. After heterodyne mixing, half-cycle cutoffs (HCOs) in HHG spectra become distinct when the CEPs of multi-cycle and few-cycle pulses are well matched. The well-matched CEP of the heterodyne mixing field has a significant effect on the HHG spectra. Moreover, both quantum analysis and classical calculations are performed to demonstrate our theoretical results. The extension of CEP measurement from few-cycle pulses to multi-cycle pulses strengthens the controllability of laser parameters for femtosecond pulses.

Electronic transport and quantum localization effects in organic semiconductors

We explore the charge transport mechanism in organic semiconductors based on a model that accounts for the thermal intermolecular disorder at work in pure crystalline compounds, as well as extrinsic sources of disorder that are present in current experimental devices. Starting from the Kubo formula, we develop a theoretical framework that relates the time-dependent quantum dynamics of electrons to the frequency-dependent conductivity. The electron mobility is then calculated through a relaxation time approximation that accounts for quantum localization corrections beyond Boltzmann theory, and allows us to efficiently address the interplay between highly conducting states in the band range and localized states induced by disorder in the band tails. The emergence of a "transient localization" phenomenon is shown to be a general feature of organic semiconductors, that is compatible with the bandlike temperature dependence of the mobility observed in pure compounds. Carrier trapping by extrinsic disorder causes a crossover to a thermally activated behavior at low temperature, which is progressively suppressed upon increasing the carrier concentration, as is commonly observed in organic field-effect transistors. Our results establish a direct connection between the localization of the electronic states and their conductive properties, formalizing phenomenological considerations that are commonly used in the literature.

Floquet analysis of real-time wave functions without solving the Floquet equation

We propose a method to obtain Floquet states---also known as light-induced states---and their quasi-energies from real-time wavefunctions without solving the Floquet equation. This is useful for the analysis of various phenomena in time-dependent quantum dynamics if the Hamiltonian is not strictly periodic, as in short laser pulses, for instance. There, the population of the Floquet states depends on the pulse form and is automatically contained in the real-time wavefunction but not in the standard Floquet approach. Several examples in the area of intense laser-atom interaction are exemplarily discussed: (i) the observation of even harmonics for an inversion-symmetric potential with a single bound state; (ii) the dependence of the population of Floquet states on (gauge) transformations and the emergence of an invariant, observable photoelectron spectrum; (iii) the driving of resonant transitions between dressed states, i.e., the dressing of dressed states, and (iv) spectral enhancements at channel closings due to the ponderomotive shift of above-threshold ionization peaks.

Design of optimal laser pulses to control molecular rovibrational excitation in a heteronuclear diatomic molecule#

Optimal control theory in combination with time-dependent quantum dynamics is employed to design laser pulses which can perform selective vibrational and rotational excitations in a heteronuclear diatomic system. We have applied the conjugate gradient method for the constrained optimization of a suitably designed functional incorporating the desired objectives and constraints. Laser pulses designed for several excitation processes of the HF molecule were able to achieve predefined dynamical goals with almost 100% yield. State selective control of vibrational and rotational molecular dynamics in HF by optimally designed laser pulses with high yields is reported.

Quantum Instanton Evaluations of the Thermal Rate Constants for Complex Systems

Quantum instanton (QI) approximation is recently proposed for the evaluations of the chemical reaction rate constants with use of full dimensional potential energy surfaces. Its strategy is to use the instanton mechanism and to approximate time-dependent quantum dynamics to the imaginary time propagation of the quantities of partition function. It thus incorporates the properties of the instanton idea and the quantum effect of partition function and can be applied to chemical reactions of complex systems. In this paper, we present the QI approach and its applications to several complex systems mainly done by us. The concrete systems include, (1) the reaction of H+CH4→H2+CH3, (2) the reaction of H+SiH4→H2+SiH3, (3) H diffusion on Ni(100) surface; and (4) surface-subsurface transport and interior migration for H/Ni. Available experimental and other theoretical data are also presented for the purpose of comparison.

Exciton Dissociation at Thiophene/Fullerene Interfaces: The Electronic Structures and Quantum Dynamics

Exciton dissociation at donor–acceptor heterojunctions is one of the key processes that determine the energy conversion efficiency of organic solar cells. Here, we theoretically investigate the exciton dissociations at oligothiophene/C60 donor–acceptor heterojunctions by using the long-range corrected time-dependent density functional theory and quantum dynamics calculations. We analyze the absorption spectra, electronic structures in adiabatic and diabatic representations, vibronic coupling, and dynamics of the exciton dissociations. The coupling strength and relative energy between the exciton and charge transfer (CT) states depend sensitively on the donor–acceptor distance and the stacking structure, which in turn affects the absorption spectra and the dynamics of exciton dissociations. Our quantum dynamics calculations exhibit ultrafast exciton dissociations owing to the strong coupling between the exciton and CT states, as observed in the time-resolved spectroscopies of the donor–acceptor interfaces of conjugated polymers and fullerenes.

Transient localization in crystalline organic semiconductors

A relation derived from the Kubo formula shows that optical conductivity measurements below the gap frequency in doped semiconductors can be used to probe directly the time-dependent quantum dynamics of charge carriers. This allows to extract fundamental quantities such as the elastic and inelastic scattering rates, as well as the localization length in disordered systems. When applied to crystalline organic semiconductors, an incipient electron localization caused by large dynamical lattice disorder is unveiled, implying a breakdown of semiclassical transport.

PERFECT POPULATION TRANSFER IN PULSE-DRIVEN QUANTUM CHAINS

The quantum dynamics of a pulse-driven finite-dimensional quantum chain with only nearest-neighbor coupling is studied. We extend the concept of Rabi oscillations from two-level quantum systems to the multi-level quantum chains. The time-dependent quantum dynamics and solutions producing perfect population transfer are obtained for up to five-level quantum chains. The Gröbner basis analysis technique is used to generalize the results and get all analytical solutions for perfect population transfer. Explicit formulas for the solutions up to nine levels are presented. These results could be used to design control strategies for general finite-dimensional quantum systems.

Dynamics of a two-level system coupled to a quantum oscillator: transformed rotating-wave approximation

For studying the dynamics of a two-level system coupled to a quantum oscillator we have presented an analytical approach, the transformed rotating-wave approximation, which takes into account the effect of the counter-rotating terms but still keeps the simple mathematical structure of the ordinary rotating-wave approximation. We have calculated the energy levels of ground and lower-lying excited states, as well as the time-dependent quantum dynamics. It is obvious that the approach is quite simple and can be easily extended to more complicated situation. Besides, the results are compared with the numerically exact ones to show that for weak and intermediate coupling and moderate detuning our analytic calculations are quantitatively in good agreement with the exact ones.

Converged quantum dynamics with modified Shepard interpolation and Gaussian wave packets

A new hybrid method is presented in which modified Shepard interpolation of a potential energy surface is combined with time-dependent quantum dynamics calculations. The propagation of a wave packet composed of fixed-width Gaussian functions allows a one-to-one mapping between the quantum dynamics results and a small number of quantum trajectories, allowing electronic structure theory calculations to be performed preferentially in dynamically-important regions. The method is designed for demonstrable convergence of the quantum dynamics results from ab initio calculations. The photodissociation of NOCl is used as a test case.

Time-dependent quantum dynamics of the He + H+He reaction

Time-dependent quantum-mechanical wave packet calculations have been carried out to calculate the reaction probabilities and cross sections for the proton transfer reaction, He + H+He → HeH+ + He, in a collision energy range 0.0–0.5 eV. A global analytical potential energy surface developed by Panda and Sathyamurthy (2003 J. Phys. Chem. A 107 7125) has been used for the purpose. The probability curves are characterized by numerous oscillatory structures attributed to the presence of resonances. The calculated reaction probabilities are found to be weakly dependent on vibrational and rotational excitations of the diatom for total angular momentum (J) = 0. For higher J values, rotational excitation results in a decline in probability values for j = 1 followed by enhancements for j = 2 and 3. The oscillations seen in reaction probabilities are not fully washed out in the integral cross sections. The dependence of cross section on initial orientations of the reactants is also studied.