Quantum Dynamics Of Wave Packets Research Articles

Quantum dynamics of wave packets in a Morse potential: A dynamical system approach

Quantum dynamics of wave packets in a Morse potential: A dynamical system approach

Non-adiabatic interactions in H[formula omitted] + C[formula omitted] system: An ab initio study

Diabatic surfaces generated for the ground state 11Σ+(11A′) as well as for the first excited electronic state 21Σ+(21A′) have been quantified for the C3 collision with H+ system employing the MRCI/aug-cc-pVQZ method. These collisions are significant in understanding the mechanism of energy transfer in astrophysics and molecular physics. For studying the dynamics of the interaction between the charge transfer and inelastic processes, properties such as non-adiabatic coupling matrix elements, and mixing angle have been determined. The computed surface and their properties will be useful in studying charge partitioning between the inelastic and charge transfer channels by wave packet quantum dynamics.

Spin-vibronic mechanism at work in a luminescent square-planar cyclometalated tridentate Pt(II) complex: absorption and ultrafast photophysics.

The absorption spectrum of [Pt(dpybMe)Cl] (dpyb = 2,6-di-(2-pyridyl)benzene), representative of luminescent halide-substituted tridentate cyclometalated square planar Pt(II) neutral complexes, has been revisited by means of non-adiabatic wavepacket quantum dynamics. The early photophysics has been investigated on the basis of four singlet and five triplet excited states, namely nineteen "spin-orbit states", coupled with both vibronic and spin-orbit couplings, and includes eighteen normal modes. It is shown that in-plane scissoring and rocking normal modes of the cyclometalated tridentate ligand are responsible for the vibronic structure observed at around 400 nm in the experimental spectrum of the complex. The ultrafast decay of [Pt(dpybMe)Cl], within 1 ps, follows a spin-vibronic mechanism governed by excited state electronic characters, spin-orbit, and active tuning mode interplay. Both spin-orbit coupling and Pt(II) coordination sphere stretching modes and in-plane scissoring/rocking of the cyclometalated ligand activate the ultrafast decay within 20 fs of absorption. At longer time-scales (>100 fs) an asynchronous stretching of the Pt-C and Pt-N bonds activates the depopulation of the upper "reservoir" electronic states to populate the two lowest luminescent T1 and T2 electronic states. The in-plane rocking motion of the ligand controls the T1/T2 population exchange which is equilibrated at about 1 ps. Stabilization of the upper non-radiative metal-centered (MC) states by out-of-plane ligand distortion of low frequency is not competitive with the ultrafast spin-vibronic mechanism discovered here for [Pt(dpybMe)Cl]. Modifying the Pt-C covalent bond position and rigidifying the cyclometalated ligand will have a dramatic influence on the spin-vibronic mechanism and consequently on the luminescence properties of this class of molecules.

Engineering insulator-metal transition in a class of decorated aperiodic lattices: A quantum dynamical study

We investigate the quantum dynamics of wave packets in a class of decorated lattices, both quasiperiodic and random, where a nominal quasi-one dimensionality is introduced at local levels, bringing in a deterministic or even random variations in the distribution of the coordination number throughout the system. We show that certain correlations in the numerical parameters of the system Hamiltonian can cause a drastic change in the dynamical evolution of the wave packet, revealing a complete delocalization, independent of the energy of the travelling particle, even in the absence of any translational invariance. We use an exact decimation of a selected subset of the degrees of freedom, and an analysis of the commutation of the 2×2 transfer matrices on a renormalized version of the parent systems within a tight binding framework. An in-depth analysis of the mean square displacement, temporal autocorrelation function and the inverse participation ratio establishes the gross change in the behaviour of the wave packet dynamics. The consequence is the occurrence of a parameter-driven insulator-metal transition over the full (or a major) range of the energy spectrum in each case. In certain cases, inclusion of an external magnetic flux enables us to control the transition. The observation is general, and, to our mind, can inspire experiments involving photonics or matter wave localization.

Accurate quantum dynamics simulation of the photodetachment spectrum of the nitrate anion (NO3 -) based on an artificial neural network diabatic potential model.

The photodetachment spectrum of the nitrate anion (NO3 -) is simulated from first principles using wavepacket quantum dynamics propagation and a newly developed accurate full-dimensional fully coupled five state diabatic potential model. This model utilizes the recently proposed complete nuclear permutation inversion invariant artificial neural network diabatization technique [D. M. G. Williams and W. Eisfeld, J. Phys. Chem. A 124, 7608 (2020)]. The quantum dynamics simulations are designed such that temperature effects and the impact of near threshold detachment are taken into account. Thus, the two available experiments at high temperature and at cryogenic temperature using the slow electron velocity-map imaging technique can be reproduced in very good agreement. These results clearly show the relevance of hot bands and vibronic coupling between the X̃ 2A2 ' ground state and the B̃ 2E' excited state of the neutral radical. This together with the recent experiment at low temperature gives further support for the proper assignment of the ν3 fundamental, which has been debated for many years. An assignment of a not yet discussed hot band line is also proposed.

Quantum dynamics studies of isotope effects in the Mg+(3p) + HD \u2192 MgH+/MgD+ + D/H insertion reaction

The time-dependent wave packet quantum dynamics studies for the Mg+(3p) + HD → MgH+/MgD+ + D/H diabatic reaction are carried out for the first time on recently developed diabatic YHWCH potential energy surfaces [Phys. Chem. Chem. Phys., 2018, 20, 6638–6647]. The results of reaction probabilities and total integral cross sections show a dramatic preference to the formation of MgD+ over MgH+ owing to the insertion reaction mechanism in the title reaction. The MgD+/MgH+ branching ratio witnesses a monotonic decrease from 10.58 to 3.88 at collision energy range of 0.01 to 0.20 eV, and at the collision energy of 0.114 eV, it is close to the experimental value of 5. The rovibrational state-resolved ICSs of the two channels show the products MgD+ have higher vibrational excitation and hotter rotational state distributions. The opacity function P(J) suggests that the MgH+ + D channel and MgD+ + H channel are dominated by high-b and low-b collisions, respectively. Both forward and backward scattering peaks are found in the differential cross section curves, whereas the angle distributions of products are not strictly forward-backward symmetric because of the short lifetime of the complex in the reaction.

Recovery time in quantum dynamics of wave packets

A wave packet formed by a linear superposition of bound states with an arbitrary energy spectrum returns arbitrarily close to the initial state after a quite long time. A method in which quantum recovery times are calculated exactly is developed. In particular, an exact analytic expression is derived for the recovery time in the limiting case of a two-level system. In the general case, the reciprocal recovery time is proportional to the Gauss distribution that depends on two parameters (mean value and variance of the return probability). The dependence of the recovery time on the mean excitation level of the system is established. The recovery time is the longest for the maximal excitation level.

Quantum dynamics of wave packets in a non-stationary parabolic potential and the Kramers escape rate theory

At sufficiently low temperatures, the reaction rates in solids are controlled by quantum rather than by thermal fluctuations. We solve the Schrödinger equation for a Gaussian wave packet in a non-stationary harmonic oscillator and derive simple analytical expressions for the increase of its mean energy with time induced by the time-periodic modulation. Applying these expressions to the modified Kramers theory, we demonstrate a strong increase of the rate of escape out of a potential well under the time-periodic driving, when the driving frequency of the well position equals its eigenfrequency, or when the driving frequency of the well width exceeds its eigenfrequency by a factor of [Formula: see text]. Such regimes can be realized near localized anharmonic vibrations (LAVs), in which the amplitude of atomic oscillations greatly exceeds that of harmonic oscillations (phonons) that determine the system temperature. LAVs can be excited either thermally or by external triggering, which can result in strong catalytic effects due to amplification of the Kramers rate.

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.

Simulation of quantum dynamics of a wave packet in a semiclassical limit

A new algorithm for modeling quantum dynamics of wave packets in a semiclassical limit was formulated and justified. The algorithm is valid in the case of two-particle systems and in the case of a single particle in any arbitrary central potential. The profile of the wave packet depending on the time for a single wave packet evolving in a one-dimensional (1D) Morse potential was obtained by direct computer simulations using the new algorithm. The results were compared with the calculation which was previously performed using the Initial Value Representation (IVR) method.

A five-dimensional quantum dynamics study of the F(P2)+CH4 reaction

By applying the semirigid vibrating rotor target (SVRT) model to the title reaction, five-dimensional wave packet quantum dynamics calculations have been carried out on the new potential energy surface PES-2006 [Espinosa-Garcia et al., J. Phys. Chem. A 111, 2761 (2007)]. The reaction probabilities have been calculated for total angular momentum J up to 105 to obtain the converged integral cross sections over a collision energy range of 0.01-0.345 eV. With the polyatomic system initially in its ground rovibrational state |000>, no obvious resonance signature has been observed in the integral cross sections although it appears in the reaction probabilities for J < or = 40. However, when the umbrella mode of the collision system is initially excited to nu(alpha0) = 1 level, |001> state, there is resonance signature in both the reaction probabilities with J < or = 55 and the integral cross sections. In addition, rate constants are calculated by Boltzmann averaging of the |000> integral cross sections over collision energy and compared with both the previous kinetic calculations and the experimental measurements. A reasonable agreement has been achieved over the investigated temperature range of 180-400 K.

Time-Dependent Quantum Dynamics Study of the Ne + H2+ (v = 0−9) and D2+ (v = 0−12) Proton Transfer Reactions at Thermal Collision Energies

The Ne + H2+ and D2+ proton transfer reactions were studied (reaction probabilities (P) and cross sections (sigma)) using the time-dependent real wave packet quantum dynamics method at the centrifugal sudden level (CS-RWP method). This was made considering the influence of vibrational excitation of H2+ and D2+ on the dynamics ((v = 0-9, j = 0) and (v = 0-12, j = 0) vibrorotational states, respectively) at thermal collision energies (Ecol = 0.010 to 0.14 eV). The CS-RWP relative cross sections at thermal collision energy (300 K) for Ne + H2+ and Ne + D2+ are in good agreement with the experimental data. The present results suggest the adequacy of the approach used here in describing these and related systems at thermal collision energies and from low to high vibrational excitation of reactants.

Time dependent quantum dynamics study of the Ne+H2+(v=–4)→NeH++H proton transfer reaction

The Ne + H2+-->NeH+ + H proton transfer reaction was studied using the time dependent real wave packet quantum dynamics method at the helicity decoupling level, considering the H2+ molecular ion in the (v=0-4, j=0) vibrorotational states and a wide collision energy interval. The calculated reaction probabilities and reaction cross sections were in a rather good agreement with reanalyzed previous exact quantum dynamics results, where a much smaller collision energy interval was considered. Also, a quite good agreement with experimental data was found. These results suggested the adequacy of the approach used here to describe this and related systems.

Theoretical study of the simplest Xe-containing molecule: HXeH

The simplest metastable Xe-containing compound HXeH has been theoretically investigated using highly-accurate CASPT2-level electronic structure calculations taking the relativistic effects into account. A new three-dimensional global potential energy surface has been developed and time-dependent wave packet quantum dynamics calculations were then performed to obtain vibrational energy levels of the metastable states for the HXeH, HXeD and DXeD systems. It has been found that low-lying vibrational states below and just above the H + Xe + H dissociation limit have extremely long lifetimes in a nanosecond time scale. The present theoretical results suggest that these rare-gas containing molecules can experimentally be detected in the gas phase.

Quasiperiodic tilings in a magnetic field

We study the electronic properties of a two-dimensional quasiperiodic tiling, the isometric generalized Rauzy tiling, embedded in a magnetic field. Its energy spectrum is computed in a tight-binding approach using the recursion method. As for the square lattice, a rich band structure is obtained when the magnetic flux per elementary plaquette is varied. Then, we study the quantum dynamics of wave packets and discuss the influence of the magnetic field on the diffusion and spectral exponents. We show that contrary to the zero field case where the propagation is faster in a periodic structure than in a quasiperiodic one, the diffusion exponent may be larger in the Rauzy tiling than in the square lattice for some incommensurate fluxes. Finally, we consider a quasiperiodic superconducting wire network with the same geometry and we determine the critical temperature as a function of the magnetic field. A non-trivial cusp-like structure arises that reveals the real importance of the quasiperiodic order.

Manifestation of Arnol'd diffusion in quantum systems.

We study an analog of the classical Arnol'd diffusion in a quantum system of two coupled nonlinear oscillators one of which is governed by an external periodic force with two frequencies. In a classical model this very weak diffusion happens in a narrow stochastic layer along the coupling resonance and leads to an increase of the total energy of the system. We show that quantum dynamics of wave packets mimics, up to some extent, global properties of the classical Arnol'd diffusion. This specific diffusion represents a new type of quantum dynamics and may be observed, for example, in 2D semiconductor structures (quantum billiards) perturbed by time-periodic external fields.

Relativistic dynamics of wave packets for spin- 1/2 particles in an electromagnetic field

Classical and quantum dynamics of wave packets for spin- 1/2 particles are analysed in the presence of an electromagnetic field. An almost exact agreement is found between these two approaches, both in the strong and the weak coupling limits. The question of negative energy states is discussed. and it is shown that they are not produced in such an interaction. The divergence problem of the perturbation expansion of the particles wavefunction is discussed, the source of which is explained.

Quantum dynamics of wave packets on phase space cells in nonlinearly coupled oscillators

AbstractThe time evolution of harmonic oscillator coherent states (minimum uncertainty wave packet) | Ψμ located on regular and random von Neumann lattice points in phase space is analyzed for nonlinearly coupled anharmonic vibrational systems. The Henon–Heiles system is studied as an example. A quasiprobability measure \documentclass{article}\pagestyle{empty}\begin{document}$ \bar P_{\mu \mu '} $\end{document} is introduced to investigate the relative probabilities for the transition between phase space cells within a narrow energy range. The probability \documentclass{article}\pagestyle{empty}\begin{document}$ \bar P_{\mu \mu '} $\end{document}, as well as the information entropy Sμ, is studied as a function of energy. A smooth transition from regular to chaotic motion is found indicated by a change of the fluctuations of these quantities as a function of energy.

Quantum dynamics of the Henon–Heiles system

In this paper, we investigate the quantum dynamics of wave packets of bound states in the nonlinear Henon–Heiles (HH) system. The time evolution of a wave packet was separated into two processes involving (a) the motion of its first moments and (b) its spreading. On the time scale when wave packet spreading can be neglected, we were able to establish relations between wave packet quantum dynamics expressed in terms of the initial-state population probability P(t) and classical trajectory dynamics. We have demonstrated that the initial states, which are characterized by a periodic time evolution of P(t) over many periods, are related to the five elliptic periodic orbits in the HH system. The decay of P(t) over a few vibrational periods is related to the classical features of quasiperiodic trajectories and can be accounted for in terms of overlap reduction effects. When the center of the initial wave packet is moved further away from the classical periodic orbits, P(t) is characterized by a single initial peak followed by a ’’noisy’’ background. There is no qualitative distinction between the ’’short-time’’ behavior of a wave packet initiated in distant integrable regions and in classical stochastic regions. For long times, wave packet spreading effects set in. Quantum mechanical estimates for the spreading time τs, which depends on the initial conditions, were provided. For wave packets initiated on periodic trajectories, τs is very long, becoming shorter as one moves away from the fixed points. The quantum mechanical long time (t≫τs) behavior of P(t) exhibits small-amplitude noisy time dependence for all initial conditions. This behavior may be described as ’’quantum mechanical stochasticity’’ and is related to the universal feature of irregularity of the spectral resolution of all wave packets in a nonlinear system. From this point of view, all wave packets exhibit ’’quantum stochastic behavior,’’ but there are vast quantitative differences for different initial conditions that are manifested in terms of the values of τs and of the average noisy amplitude. It should be emphasized that this ’’quantum stochasticity’’ is not related to classical stochasticity phenomena.