Quantum Wave Packet Propagation Research Articles

Interacting trajectory representation of quantum dynamics: influence of boundary conditions on the tunneling decay of resonant states

We perform quantum trajectory simulations of the decay dynamics of initially localized resonant states. Quantum dynamics is represented by a swarm of interacting trajectories which maps the originally quantum problem into the motion of an equivalent (higher-dimensional) classical system. We address two model problems, in which the decay of the initial resonance leads to either spatially confined or asymptotically free wave-packet dynamics, specifically on a double well potential and on a potential plain. The traditional choice of fixed boundary conditions in the interacting trajectory representation (ITR), set at infinity, is found to have a moderate influence on the accuracy of the ITR of quantum trajectory dynamics, for the motion on a double well potential, i.e. the results of the trajectory-based scheme are in good correspondence with those obtained via quantum wave-packet propagation up to several fundamental vibrational periods. On the other hand, standard boundary conditions have negligible effect on the interacting trajectory dynamics of a decaying shape resonance, whose predictions reproduce quantum mechanical results at long times.

Intersystem crossing pathways in [5]-, [7]-, and [9]cycloparaphenylenes.

We analyze the energetics and internal conversion dynamics of singlet and triplet manifolds to identify the possible intersystem crossing pathways in odd-numbered [n]cycloparaphenylenes ([n]CPPs, n = 5, 7, and 9). Quantum wavepacket propagation calculations within the linear vibronic coupling framework suggest that both [5]- and [7]CPPs rapidly relax to S2 upon populating "bright" higher singlet excited states. The S2-S1 energy decreases with the increase in CPP size, and hence, [9]CPP exhibits a faster S2 → S1 internal conversion decay. Higher triplet states act as receiver states for the intersystem crossing happening either via S1 or S2. The wavepacket evolving on the receiver triplet state would decay to lower states via multiple conical intersections and reach T1. The estimated size-dependent fluorescence and emission energies are in good accord with the experiment.

Complex saddle trajectories for multidimensional quantum wave packet and coherent state propagation: Application to a many-body system.

A practical search technique for finding the complex saddle points used in wave packet and coherent state propagation is developed which works for a large class of Hamiltonian dynamical systems with many degrees of freedom. The method can be applied to problems in atomic, molecular, and optical physics and other domains. A Bose-Hubbard model is used to illustrate the application to a many-body system where discrete symmetries play an important and fascinating role. For multidimensional wave packet propagation, locating the necessary saddles involves the seemingly insurmountable difficulty of solving a boundary value problem in a high-dimensional complex space, followed by determining whether each particular saddle found actually contributes. In principle, this must be done for each propagation time considered. The method derived here identifies a real search space of minimal dimension, which leads to a complete set of contributing saddles up to intermediate times much longer than the Ehrenfest timescale for the system. The analysis also gives a powerful tool for rapidly identifying the various dynamical regimes of the system.

Quantum controlled fusion

Quantum-controlled motion of nuclei, starting from the nanometer-size ground state of a molecule, can potentially overcome some of the difficulties of thermonuclear fusion by compression of a fuel pellet or in a bulk plasma. Coherent laser control can manipulate nuclear motion precisely, achieving large phase space densities for the colliding nuclei. We combine quantum wavepacket propagation of D and T nuclei in a field-bound molecule with coherent control by a shaped laser pulse to demonstrate enhancement of nuclear collision rates. Atom-smashers powered by coherent control may become laboratory sources of particle bursts, and even assist muonic fusion.

Photodissociation dynamics of weakly bound HeH2+ in intense light fields

Photoinduced dynamics of a weakly bound triatomic molecule $\mathrm{He}{{\mathrm{H}}_{2}}^{+}$ exposed to electromagnetic radiation is investigated by time-dependent quantum wave-packet propagation. Adopting a two-dimensional linear H-H-He model, the three lowest-lying potential energy surfaces (PESs) and corresponding dipole moment surfaces are constructed. One of the two characteristic excited PESs of $\mathrm{He}{{\mathrm{H}}_{2}}^{+}$ leads to the charge-transfer reaction ${{\mathrm{H}}_{2}}^{+}+\mathrm{He}\ensuremath{\rightarrow}{\mathrm{H}}_{2}+\mathrm{H}{\mathrm{e}}^{+}$ and the other corresponds to the first excited state of ${{\mathrm{H}}_{2}}^{+}$ perturbed by the presence of He. When $\mathrm{He}{{\mathrm{H}}_{2}}^{+}$ is exposed to a femtosecond intense ultraviolet light pulse ($I=4\ifmmode\times\else\texttimes\fi{}{10}^{14}\phantom{\rule{4pt}{0ex}}\mathrm{W}\phantom{\rule{0.16em}{0ex}}\mathrm{c}{\mathrm{m}}^{\ensuremath{-}2}, \ensuremath{\lambda}=400\phantom{\rule{0.16em}{0ex}}\mathrm{nm}$), both of the two excited PESs are found to be coupled with the light field and a variety of reaction pathways become opened so that HeH, $\mathrm{He}{\mathrm{H}}^{+}, {\mathrm{H}}_{2},\phantom{\rule{0.16em}{0ex}}{{\mathrm{H}}_{2}}^{+},\phantom{\rule{0.16em}{0ex}}\mathrm{H},\phantom{\rule{0.16em}{0ex}}{\mathrm{H}}^{+}$, He, and $\mathrm{H}{\mathrm{e}}^{+}$ are produced. Simulations also show that the anharmonic coupling between the two stretching vibrational modes in $\mathrm{He}{{\mathrm{H}}_{2}}^{+}$ leads to the stabilization of the ${{\mathrm{H}}_{2}}^{+}$ moiety against the decomposition into $\mathrm{H}+{\mathrm{H}}^{+}$ compared with bare ${{\mathrm{H}}_{2}}^{+}$. The theoretical findings of the formation of $\mathrm{He}{\mathrm{H}}^{+}$ composed of the most abundant elements in the universe are also discussed in view of the theoretical modeling of the chemical reactions proceeding in the primordial gas and in the interstellar medium.

Mixed semiclassical initial value representation time-averaging propagator for spectroscopic calculations.

A mixed semiclassical initial value representation expression for spectroscopic calculations is derived. The formulation takes advantage of the time-averaging filtering and the hierarchical properties of different trajectory based propagation methods. A separable approximation is then introduced that greatly reduces (about an order of magnitude) the computational cost compared with a full Herman-Kluk time-averaging semiclassical calculation for the same systems. The expression is exact for the harmonic case and it is tested numerically for a Morse potential coupled to one or two additional harmonic degrees of freedom. Results are compared to full Herman-Kluk time-averaging calculations and exact quantum wavepacket propagations. We found the peak positions of the mixed semiclassical approximations to be always in very good agreement with full quantum calculations, while overtone peak intensities are lower with respect to the exact ones. Given the reduced computational effort required by this new mixed semiclassical approximation, we believe the present method to make spectroscopic calculations available for higher dimensional systems than accessible before.

Dynamic Symmetry Breaking Hidden in Fano Resonance of a Molecule: S1 State of Diazirine Using Quantum Wave Packet Propagation.

Fano resonance in the predissociation of the S1 state of diazirine was studied by applying a time-dependent wave packet propagation method, and dynamic symmetry breaking (DSB) around the stationary structure of S1 was disclosed in a detailed analysis of this theoretical result. The DSB was found to originate in coupling between the asymmetric C-N2 stretching and CH2 wagging modes, suggesting that there is a slight time gap between ring opening and the concurrent dragging of two H atoms of the CH2 moiety. Although the depth of the double well due to DSB is just 0.011 eV, its presence noticeably affects the early time dynamics and observed spectrum.

A Chebyshev expansion of hydrodynamical fields for ultrafast vibrational wave packet dynamics

A computational method based on the Chebyshev polynomial expansion of the hydrodynamical fields is applied to the quantum trajectory modeling of the one-dimensional vibrational dynamics. The spatial derivatives of the fields are computed using the Chebyshev polynomial recursion, and they are subsequently used to numerically integrate the equations of motion for the fluid particles. The performance of the proposed algorithm is assessed via the comparison with the analytical solutions for the time evolution of a Gaussian wave packet on harmonic potential, and with the results of quantum wave packet propagation on an anharmonic potential. The scheme is found to provide an accurate representation of both the molecular density and the quantum potential, even if low-order truncated expansions are used. The quantum trajectory propagation using the Chebyshev expansion method yields results in close agreement with the corresponding benchmarks, regarding both the time-dependent molecular distributions and the computed observables.

Semiclassical modelling of finite-pulse effects on non-adiabatic photodynamics via initial condition filtering: The predissociation of NaI as a test case.

Femtosecond-laser pulse driven non-adiabatic spectroscopy and dynamics in molecular and condensed phase systems continue to be a challenge for theoretical modelling. One of the main obstacles is the "curse of dimensionality" encountered in non-adiabatic, exact wavepacket propagation. A possible route towards treating complex molecular systems is via semiclassical surface-hopping schemes, in particular if they account not only for non-adiabatic post-excitation dynamics but also for the initial optical excitation. One such approach, based on initial condition filtering, will be put forward in what follows. As a simple test case which can be compared with exact wavepacket dynamics, we investigate the influence of the different parameters determining the shape of a laser pulse (e.g., its finite width and a possible chirp) on the predissociation dynamics of a NaI molecule, upon photoexcitation of the A(0(+)) state. The finite-pulse effects are mapped into the initial conditions for semiclassical surface-hopping simulations. The simulated surface-hopping diabatic populations are in qualitative agreement with the quantum mechanical results, especially concerning the subpicosend photoinduced dynamics, the main deviations being the relative delay of the non-adiabatic transitions in the semiclassical picture. Likewise, these differences in the time-dependent electronic populations calculated via the semiclassical and the quantum methods are found to have a mild influence on the overall probability density distribution. As a result, the branching ratios between the bound and the dissociative reaction channels and the time-evolution of the molecular wavepacket predicted by the semiclassical method agree with those computed using quantum wavepacket propagation. Implications for more challenging molecular systems are given.

Factors Affecting the Branching Ratio of Photodissociation: Thiophenol Studied through Quantum Wavepacket Dynamics.

The photodissociation dynamics of thiophenol (PhSH) excited to the 1(1) ππ* state was investigated by time-dependent quantum wavepacket propagation within two-dimensional (2D) space consisting of the S-H bond and -SH torsion. We systematically studied the dependence of the branching ratio (Ã/X(~)) between the two electronic states of the phenylthiyl radical (PhS(.) ) on several factors of the 2D potential energy surfaces (PESs). The effect of a reduced initial barrier to the first ππ*/πσ* conical intersection (CI) was found to be marginal, whereas the effects of a reduced torsional barrier of -SH on the excited ππ* state and the mitigated slope of the πσ* PES between the first (ππ*/πσ*) and the second (πσ*/S0 ) CIs were noticeable. The effect of the slope on the branching ratio has never been previously noticed. It was shown that the branching ratio can be sufficiently above unity without pre-excitation of the torsion mode of -SH, which has been assumed so far.

Controlling the transport of an ion: classical and quantum mechanical solutions

The accurate transport of an ion over macroscopic distances represents a challenging control problem due to the different length and time scales that enter and the experimental limitations on the controls that need to be accounted for. Here, we investigate the performance of different control techniques for ion transport in state-of-the-art segmented miniaturized ion traps. We employ numerical optimization of classical trajectories and quantum wavepacket propagation as well as analytical solutions derived from invariant based inverse engineering and geometric optimal control. The applicability of each of the control methods depends on the length and time scales of the transport. Our comprehensive set of tools allows us make a number of observations. We find that accurate shuttling can be performed with operation times below the trap oscillation period. The maximum speed is limited by the maximum acceleration that can be exerted on the ion. When using controls obtained from classical dynamics for wavepacket propagation, wavepacket squeezing is the only quantum effect that comes into play for a large range of trapping parameters. We show that this can be corrected by a compensating force derived from invariant based inverse engineering, without a significant increase in the operation time.

Branching Ratio between Proton Transfer and Electron Transfer Channels of a Bidirectional Proton-Coupled Electron Transfer.

Rigorous quantum dynamical study of concerted proton-coupled electron transfer (PCET) on the time scale of a few femtoseconds (fs) has been rarely reported. Herein, a time-dependent quantum wavepacket propagation method was applied to the dynamics of the charge-transfer excited electronic state of FHCl corresponding to F(+)HCl(-). The dynamics corresponds to a bidirectional PCET with two dissociation channels: the electron transfer (ET, generating FH+Cl) and proton transfer (PT, generating F+HCl) paths. The calculated branching ratio (Cl/F), 0.78, implies a surprising fact: PT prevails over ET. A detailed analysis of the proton movement and electron readjustment suggests that the proton movement starts ∼3 fs earlier than the electron movement, and the electron readjustment is triggered by the initial movement of the proton. The branching ratio drastically inverts to 1.24 because of a reduced nonadiabatic effect in the isotope-substituted system, FDCl.

When fast atom diffraction turns 3D

Fast atom diffraction at surfaces (FAD) in grazing incidence geometry is characterized by the slow motion in the direction perpendicular to the surface and fast motion parallel to the surface plane along a low index direction. It is established experimentally that for the typical surfaces the FAD reveals the 2D diffraction patterns associated with exchange of the reciprocal lattice vector perpendicular to the direction of fast motion. The reciprocal lattice vector exchange along the direction of fast motion is negligible. The usual approximation made in the description of the experimental data is then to assume that the effective potential leading to the diffraction results from the averaging of the 3D surface potential along the atomic strings forming the axial channel. In this work we use full quantum wave packet propagation calculations to study theoretically the possibility to observe the 3D diffraction in FAD experiments. We show that for the surfaces with large unit cell, such as can be the case for reconstructed or vicinal surfaces, the 3D diffraction can be observed. The reciprocal lattice vector exchange along the direction of fast motion leads to several Laue circles in the diffraction pattern.

Response of solid Ne upon photoexcitation of a NO impurity: A quantum dynamics study

The ultrafast geometrical rearrangement dynamics of NO doped cryogenic Ne matrices after femtosecond laser pulse excitation is studied using a quantum dynamical approach based on a multi-dimensional shell model, with the shell radii being the dynamical variables. The Ne-NO interaction being only weakly anisotropic allows the model to account for the main dynamical features of the rare gas solid. Employing quantum wave packet propagation within the time dependent Hartree approximation, both, the static deformation of the solid due to the impurity and the dynamical response after femtosecond excitation, are analysed. The photoinduced dynamics of the surrounding rare gas atoms is found to be a complex high-dimensional process. The approach allows to consider realistic time-dependent femtosecond pulses and the effect of the pulse duration is clearly shown. Finally, using the pulse parameters of previous experiments, pump-probe signals are calculated and found to be in good agreement with experimental results, allowing for a clear analysis of the ultrafast mechanism of the energy transfer into the solid.

Quantum Wave Packet Propagation Study of the Photochemistry of Phenol: Isotope Effects (Ph-OD) and the Direct Excitation to the 1πσ* State

An earlier time-dependent quantum wave packet propagation study of the photochemistry of Ph-OH [J. Chem. Phys. 2005, 122, 224315] is extended to investigate isotope effects (for Ph-OD) and the dynamics initiated by direct (vibronically induced) excitation to the (1)πσ* state. The isotope effect is significant only when the initially excited state is (1)ππ*, that is, there are noticeable changes not only in the time scale but also in the branching ratio (Ã/X̃) for the electronic states of the product Ph-O radical. In contrast, the isotope effect on the dynamics initiated by direct excitation to the (1)πσ* state is very small. Our most important observation for the dynamics initiated by direct excitation to the (1)πσ* state is that the initial excitation of the O-H stretch mode does not result in a noticeable enhancement of the product Ph-O radical in the à state, which corresponds to a dissociating H atom with low kinetic energy. The initial excitation of the CCOH torsion mode is the main reason for the enhancement of the product Ph-O radical in the à state that was observed in a vibrationally mediated two-photon experiment [J. Chem. Phys.2008, 128, 104307].

Study of the sticking of a hydrogen atom on a graphite surface using a mixed classical-quantum dynamics method

The sticking of one hydrogen atom chemisorbed on the (0001) graphite surface is investigated using a mixed classical-quantum method. The phonon modes of the system in the collinear scattering approach are included in the dynamics calculations. The vibrational degrees of freedom of the surface (phonons) are treated classically, while the H-surface motion is treated using a one-dimensional quantum wave packet propagation method. The sticking probabilities are calculated and the individual contributions of the phonon bands to the collision dynamics are analyzed for surface temperatures of 10, 150, and 300 K and hydrogen kinetic energies ranging from 0.13 to 1.08 eV. An analytical form of the sticking probability as a function of the surface temperature is also proposed.

Theory of the optical spatial separation of racemic mixtures of chiral molecules

We propose a practical way of spatially separating a ("racemic") mixture of left-handed (L) and right-handed (R) chiral molecules using optically induced forces. The enantioselectivity of the method emanates from the sign difference between the n<-->m electric-dipole matrix elements of enantiomers of opposite handedness, and the, uniquely chiral, "cyclic adiabatic passage" laser configuration. The combination of these two factors is shown to cause considerable differences in the magnitude and direction of the optically induced forces as felt by enantiomers of opposite handedness. Two arrangements, tested by performing quantum wave packet propagation and classical trajectories, are suggested. Both arrangements involve the intracavity interaction of the racemic mixture with three, partially overlapping, cw laser beams. The first arrangement is composed of trapped molecules at 1 mK interacting with standing wave lasers. The second configuration uses a tightly skimmed molecular beam of a racemic mixture, forming one arm of a four-sided cavity, intersecting at a small angle the three laser beams.

Communications: Spatial separation of enantiomers by coherent optical means

We show that it is possible to spatially separate a ("racemic") mixture of left-handed and right-handed chiral molecules using optically induced forces. The separation is affected by the irradiation of the racemic mixture with three spatially inhomogeneous and partially overlapping cw laser fields, giving rise to enantiomeric and vibrational dependent light-induced forces. Two experimental arrangements, one consisting of placing the racemate in 1 mK optical trap, the second composed of a tightly skimmed molecular beam of the racemic mixture, forming one arm of a four-sided cavity, are numerically tested by performing quantum wave packet propagation and classical trajectories. Both the classical and the quantum simulations show an essentially perfect spatial separation between enantiomers of several vibrational states.

Photochemistry of the water dimer: Time-dependent quantum wave-packet description of the dynamics at the S1-S conical intersection

The photoinduced electron-driven proton-transfer dynamics of the water-dimer system has been investigated by time-dependent quantum wave-packet calculations. The main nuclear degrees of freedom driving the system from the Frank-Condon region to the S(0)-S(1) conical intersection are the distance between the oxygen atoms and the displacement of the hydrogen atom from the oxygen-oxygen bond center. Two important coupling modes have been investigated: Rotation of the H-donating water dangling proton and asymmetric stretching of the H-accepting water dangling protons' O(a)H bonds. Potential energy surfaces of the ground and lowest excited electronic states have been constructed on the basis of ab initio calculations. The time-dependent quantum wave-packet propagation has been employed within the (2 + 1)-dimensional systems for the description of the nonadiabatic dynamics of water dimer. The effects of the initial vibrational state of the system on the electronic population transfer and dissociation dynamics are presented. To approximate the photochemical behavior of water dimer in bulk water, we add a boundary condition into the (2 + 1)-dimensional systems to simulate the existence of water bulk. The results provide insight into the mechanisms of excited state deactivation of the water-dimer system in gas phase and in bulk water through the electron-driven proton-transfer process.

Fingerprints of Delocalized Transition States in Quantum Dynamics

Reactions with delocalized transition states (plateau reactions) can be characterized statically by their energy profile along the reaction path, where they exhibit a broad, flat region instead of one or several well-defined saddle points on the potential energy surface. Employing our new, highly flexible quantum dynamics code to perform two-dimensional and effective four-dimensional quantum wave packet propagations on ab initio based model potentials, we show that plateau reactions can also be discerned from the other standard reaction types by their dynamics.