Quasiclassical Simulations Research Articles

Coherent electron phase-space manipulation by combined elastic and inelastic light-electron scattering

Abstract Photon-Induced Near-field Electron Microscopy (PINEM), Kapitza-Dirac (KD) gratings, and ponderomotive phase plates are examples of techniques in which the wave function of an electron in free space is manipulated using light fields: Free Electron Quantum Optics (FEQO). These effects are usually treated in separate theoretical frameworks. In this paper we present a unified, two-pronged framework that can be used to describe and numerically evaluate the performance of a number of FEQO-based electron-optical elements. The first part is an extension of an existing analytical treatment of PINEM, based on solving a relativistically corrected Schrödinger equation. The extension covers both second-order contributions to PINEM and the Kapitza-Dirac effect. The second, novel element of the approach is based on electron wavefront reconstruction by evaluating the quantum mechanical phase along a bundle of classical electron trajectories. The quasi-classical (but fully relativistic) approach lends itself to simulating a wide variety of FEQO devices, including the examples mentioned. We apply both approaches to a few specific experimental configurations: mirror-based first-order PINEM, second-order PINEM in very high laser intensity, and Kapitza-Dirac diffraction. The results show excellent agreement between the analytical results and the quasi-classical simulations. Finally, we propose a setup that combines KD and PINEM to allow for simultaneous coherent energy and transverse momentum shaping of an electron beam, and present simulation results thereof.

Quasi-classical simulations of resonance Raman spectra based on path integral linearization.

Based on a linearization approximation coupled with path integral formalism, we propose a method derived from the propagation of quasi-classical trajectories to simulate resonance Raman spectra. This method is based on ground state sampling followed by an ensemble of trajectories on the mean surface between the ground and excited states. The method was tested on three models and compared to a quantum mechanics solution based on a sum-over-states approach: harmonic and anharmonic oscillators and the HOCl molecule (hypochlorous acid). The method proposed is able to correctly characterize resonance Raman scattering and enhancement, including the description of overtones and combination bands. The absorption spectrum is obtained at the same time, and the vibrational fine structure can be reproduced for long excited state relaxation times. The method can also be applied to dissociating excited states (as is the case for HOCl).

Feasibility of a pulsed ponderomotive phase plate for electron beams

We propose a scheme for constructing a phase plate for use in an ultrafast Zernike-type phase contrast electron microscope, based on the interaction of the electron beam with a strongly focused, high-power femtosecond laser pulse and a pulsed electron beam. Analytical expressions for the phase shift using the time-averaged ponderomotive potential and a paraxial approximation for the focused laser beam are presented, as well as more rigorous quasiclassical simulations based on the quantum phase integral along classical, relativistic electron trajectories in an accurate, non-paraxial description of the laser beam. The results are shown to agree well unless the laser beam is focused to a waist size below a wavelength. For realistic (off-the-shelf) laser parameters the optimum phase shift of is shown to be achievable. When combined with RF-cavity based electron chopping and compression techniques to produce electron pulses, a femtosecond regime pulsed phase contrast microscope can be constructed. The feasibility and robustness of the scheme are further investigated using the simulations, leading to motivated choices for design parameters such as wavelength, focus size and polarization.

Prediction of Kinetic Product Ratios: Investigation of a Dynamically Controlled Case.

Of the various factors influencing kinetically controlled product ratios, the role of nonstatistical dynamics is arguably the least well understood. In this paper, reactions were chosen in which dynamics played a dominant role in product selection, by design. Specifically, the reactions studied were the ring openings of cyclopropylidene to allene and tetramethylcyclopropylidene to tetramethylallene (2,4-dimethylpenta-2,3-diene). Both reactions have intrinsic reaction coordinates that bifurcate symmetrically, leading to products that are enantiomeric once the atoms are uniquely labeled. The question addressed in the study was whether the outcomes─that is, which product well on the potential energy surface was selected─could be predicted from their initial conditions for individual trajectories in quasiclassical dynamics simulations. Hybrid potentials were developed based on cooperative interaction between molecular mechanics and artificial neural networks, trained against data from electronic structure calculations. These potentials allowed simulations of both gas-phase and condensed-phase reactions. The outcome was that, for both reactions, prediction of initial selection of product wells could be made with >95% success from initial conditions of the trajectories in the gas phase. However, when trajectories were run for longer, looking for "final" products for each trajectory, the predictability dropped off dramatically. In the gas-phase simulations, this drop off was caused by trajectories hopping between product wells on the potential energy surface. That behavior could be suppressed in condensed phases, but then new uncertainty was introduced because the intermolecular interactions between solute and bath, necessary to permit intermolecular energy transfer and cooling of the hot initial products, often led to perturbations of the initial directions of trajectories on the potential energy surface. It would consequently appear that a general ability to predict outcomes for reactions in which nonstatistical dynamics dominate remains a challenge even in the age of sophisticated machine-learning capabilities.

The quantum dynamics of H2 on Cu(111) at a surface temperature of 925K: Comparing state-of-the-art theory to state-of-the-art experiments.

We present results of our recently expanded static corrugation model (SCM) approach that included the relevant surface temperature effects, applied to the dissociative chemisorption reaction of H2 on a Cu(111) surface. The reaction and rovibrationally elastic scattering probabilities that we obtain at a quantum dynamical (QD) level, as an average of many statically distorted surface configurations, show great agreement with those of a dynamic surface model, which reinforces the validity of the sudden approximation inherent to the SCM. We further investigate several simple methods of binning the final rovibrational state of quasi-classical dynamics simulations, to find those best suited to reproduce the QD results for our system. Finally, we show that the SCM obtained results reproduce experimental dissociation curves very well, when the uncertainty in experimental saturation values is taken into account. Some indication of a slow channel, so far only observed in experiment, can also be found at low incidence energies, although more rigorous QD simulations are required to reduce the noise inherent to our propagation methods.

Chloride-Mediated Alkene Activation Drives Enantioselective Thiourea and Hydrogen Chloride Co-Catalyzed Prins Cyclizations.

The mechanism of chiral hydrogen-bond donor (HBD) and hydrogen chloride (HCl) co-catalyzed Prins cyclizations was analyzed through a combination of experimental and computational methods and revealed to involve an unexpected and previously unrecognized mode of alkene activation. Kinetic and spectroscopic studies support the participation of a catalytically active HCl·HBD complex that displays reduced Brønsted acidity relative to HCl alone. Nevertheless, rate acceleration relative to the HCl-catalyzed background reaction as well as high levels of enantioselectivity are achieved. This inverse Brønsted correlation is ascribed to chloride-mediated substrate activation in the rate-limiting and enantiodetermining cyclization transition state. Density functional theory (DFT) calculations, distortion-interaction analysis, and quasiclassical dynamics simulations support a stepwise mechanism in which rate acceleration and enantioselectivity are achieved through the precise positioning of the chloride anion within the active site of the chiral thiourea to enhance the nucleophilicity of the alkene and provide transition-state stabilization through local electric field effects. This mode of selective catalysis through anion positioning likely has general implications for the design of enantioselective Brønsted acid-catalyzed reactions involving π-nucleophiles.

Influence of Water and Enzyme on the Post-Transition State Bifurcation of NgnD-Catalyzed Ambimodal [6+4]/[4+2] Cycloaddition.

The enzyme NgnD catalyzes an ambimodal cycloaddition that bifurcates to [6+4]- and [4+2]-adducts. Both products have been isolated in experiments, but it remains unknown how enzyme and water influence the bifurcation selectivity at the femtosecond time scale. Here, we study the impact of water and enzyme on the post-transition state bifurcation of NgnD-catalyzed [6+4]/[4+2] cycloaddition by integrating quantum mechanics/molecular mechanics quasiclassical dynamics simulations and biochemical assays. The ratio of [6+4]/[4+2] products significantly differs in the gas phase, water, and enzyme. Biochemical assays were employed to validate computational predictions. The study informs how water and enzyme affect the bifurcation selectivity through perturbation of the reaction dynamics in the femtosecond time scale, revealing the fundamental roles of condensed media in dynamically controlling the chemical selectivity for biosynthetic reactions.

Vibrational mode-specific dynamics of the F(2P3/2) + C2H6 → HF + C2H5 reaction.

We investigate the competing effect of vibrational and translational excitation and the validity of the Polanyi rules in the early- and negative-barrier F(2P3/2) + C2H6 → HF + C2H5 reaction by performing quasi-classical dynamics simulations on a recently developed full-dimensional multi-reference analytical potential energy surface. The effect of five normal-mode excitations of ethane on the reactivity, the mechanism, and the post-reaction energy flow is followed through a wide range of collision energies. Promoting effects of vibrational excitations and interaction time, related to the slightly submerged barrier, are found to be suppressed by the early-barrier-induced translational enhancement, in contrast to the slightly late-barrier Cl + C2H6 reaction. The excess vibrational energy mostly converts into ethyl internal excitation while collision energy is transformed into product separation. The substantial reaction energy excites the HF vibration, which tends to show mode-specificity and translational energy dependence as well. With increasing collision energy, direct stripping becomes dominant over the direct rebound and indirect mechanisms, being basically independent of reactant excitation.

Quasiclassical simulations based on cluster models reveal vibration-facilitated roaming in the isomerization of CO adsorbed on NaCl.

The desire to better understand the quantum nature of isomerization led to recent experimental observations of the vibrationally induced isomerization of OC-NaCl(100) to CO-NaCl(100). To investigate the mechanism of this isomerization, we performed dynamics calculations using finite (CO-NaCl)n cluster models. We constructed new potential energy surfaces for CO-NaCl and CO-CO interactions using high-level ab initio data and report key properties of the bare CO-NaCl potential energy surface, which show much in common with the experiment. We investigated the isomerization dynamics using several cluster models and, in all cases, isomerization was seen for highly excited CO vibrational states, in agreement with experiments. A detailed examination of the reaction trajectories indicates that isomerization occurs when the distance between CO and NaCl is larger than the distance at the conventional isomerization saddle point, which is a strong indicator of 'roaming'.

Energy transfers in a weakly coupled gas-surface system: The scattering of CO from MgO(001)

This work reports on quasi-classical dynamics simulations of the non-reactive scattering of CO from a prototypical cubic ionic surface. We shed light on the role of the incidence energy, the initial ro-vibrational state of impinging CO, and the effect of surface atom motion on the scattering behaviour of the molecules. Our results rely on a novel high-dimensional potential energy surface, which is fitted using a modified reactive bond order force field to reproduce reference energy data obtained from periodic embedding density functional theory. The scattering process is found to be strongly influenced by the anisotropy of the potential for CO impinging either from the C-end or O-end of the molecule. The distinct scattering features are significant at low incidence energies when surface atom motion is included in the simulations. This suggests that modelling energy transfer to phonons is very important to describe the dynamics of such weakly interacting systems.

Controlling the nature of a charged impurity in a bath of Feshbach dimers

We theoretically study the dynamics of a trapped ion that is immersed in an ultracold gas of weakly bound atomic dimers created by a Feshbach resonance. Using quasi-classical simulations, we find a crossover from dimer dissociation to molecular ion formation depending on the binding energy of the dimers. The location of the crossover strongly depends on the collision energy and the time-dependent fields of the Paul trap. Deeply bound dimers lead to fast molecular ion formation, with rates approaching the Langevin collision rate $\Gamma'_\text{L}\approx4.8\times10^{-9}\,$cm$^3$s$^{-1}$. The kinetic energies of the created molecular ions have a median below $1\,$mK, such that they will stay confined in the ion trap. We conclude that interacting ions and Feshbach molecules may provide a novel approach towards the creation of ultracold molecular ions with applications in precision spectroscopy and quantum chemistry.

Topology of quantum coherence in singlet fission: Mapping out spin micro-states in quasi-classical nonadiabatic simulations.

Quantum coherence plays an important role in exciton dynamics such as singlet fission, which may be determined by molecular physical properties, including energy levels, electronic couplings, and electron-phonon couplings, and by geometric properties, including packing configuration and exciton delocalization. However, the global picture of quantum coherence in high-dimensional multistate systems is still blurred. Here, we perform nonadiabatic molecular dynamics simulation for singlet fission in tetracene clusters and demonstrate that the topology of quantum coherence in terms of the global structure of the coupled multistate system may significantly modulate fission dynamics. In particular, quantum coherence in the spin-specified models could be protected by its topological structure from external perturbations. Our work suggests that the topology of quantum coherence is indispensable in the understanding and control of quantum dynamics, which may find potential implementations to singlet fission and quantum computation.

Inelastic Scattering of N2 off W(001): Reconciling Experiment and Theory at Low Collision Energies

The inelastic scattering dynamics of N2 off W(001) has recently been the subject of theoretical investigations, which were found to be unable to describe low-collision-energy molecular beam experiments. This discrepancy was suggested to originate from the neglect of van der Waals interactions in the construction of the potential energy surface. By making use of a newly developed potential energy surface, accounting for such dispersion interactions, we show that quasi-classical dynamics simulations, including dissipation to surface electrons and phonons, lead to an adequate description of the low-collision-energy experiments and, more specifically, the trapping-desorption component of inelastic scattering. This work highlights the prominent influence of van der Waals forces on gas–surface dynamics observables in the low-collision-energy regime.

Quantum and quasi-classical collisional dynamics of O2-Ar at high temperatures.

A hypersonic vehicle traveling at a high speed disrupts the distribution of internal states in the ambient flow and introduces a nonequilibrium distribution in the post-shock conditions. We investigate the vibrational relaxation in diatom-atom collisions in the range of temperatures between 1000 and 10 000 K by comparing results of extensive fully quantum-mechanical and quasi-classical simulations with available experimental data. The present paper simulates the interaction of molecular oxygen with argon as the first step in developing the aerothermodynamics models based on first principles. We devise a routine to standardize such calculations also for other scattering systems. Our results demonstrate very good agreement of vibrational relaxation time, derived from quantum-mechanical calculations with the experimental measurements conducted in shock tube facilities. At the same time, the quasi-classical simulations fail to accurately predict rates of vibrationally inelastic transitions at temperatures lower than 3000 K. This observation and the computational cost of adopted methods suggest that the next generation of high fidelity thermochemical models should be a combination of quantum and quasi-classical approaches.

Collision-induced rotational excitation in N2 (+)((2)Σg (+),v=0)-Ar: Comparison of computations and experiment.

The collisional dynamics of N2 (+)((2)Σg (+)) cations with Ar atoms is studied using quasi-classical simulations. N2 (+)-Ar is a proxy to study cooling of molecular ions and interesting in its own right for molecule-to-atom charge transfer reactions. An accurate potential energy surface (PES) is constructed from a reproducing kernel Hilbert space (RKHS) interpolation based on high-level ab initio data. The global PES including the asymptotics is fully treated within the realm of RKHS. From several ten thousand trajectories, the final state distribution of the rotational quantum number of N2 (+) after collision with Ar is determined. Contrary to the interpretation of previous experiments which indicate that up to 98% of collisions are elastic and conserve the quantum state, the present simulations find a considerably larger number of inelastic collisions which supports more recent findings.

Dynamical Effects and Product Distributions in Simulated CN + Methane Reactions.

Dynamics of collisions between structured molecular species quickly become complex as molecules become large. Reactions of methane with halogen and oxygen atoms serve as model systems for polyatomic molecule chemical dynamics, and replacing the atomic reagent with a diatomic radical affords further insights. A new, full-dimensional potential energy surface for collisions between CN + CH4 to form HCN + CH3 is developed and then used to perform quasi-classical simulations of the reaction. Coupled-cluster energies serve as input to an empirical valence bonding (EVB) model, which provides an analytical function for the surface. Efficient sampling permits simulation of velocity-map ion images and exploration of dynamics over a range of collision energies. Reaction populates HCN vibration, and energy partitioning changes with collision energy. The reaction cross-section depends on the orientation of the diatomic CN radical. A two-dimensional extension of the cone of acceptance for an atom in the line-of-centers model appropriately describes its reactivity. The simulation results foster future experiments and diatomic extensions to existing atomic models of chemical collisions and reaction dynamics.

Experiment and Theory Elucidate the Multichannel Predissociation Dynamics of the HCl Trimer: Breaking Up Is Hard To Do

The breaking of hydrogen bonds in molecular systems has profound effects on liquids, e.g., water, biomolecules, e.g., DNA, etc., and so it is no exaggeration to assert the importance of these bonds to living systems. However, despite years of extensive research on hydrogen bonds, many of the details of how these bonds break and the corresponding energy redistribution processes remain poorly understood. Here we report extensive experimental and theoretical insights into the breakup of two or three hydrogen bonds in the dissociation of a paradigm system of a hydrogen-bonded network, the ring HCl trimer. Experimental state-to-state vibrational predissociation dynamics of the trimer following vibrational excitation were studied by using velocity map imaging and resonance-enhanced multiphoton ionization, providing dissociation energies and product state distributions for the trimer's breakup into three separate monomers or into dimer + monomer. Accompanying the experiments are high-level calculations using diffusion Monte Carlo and quasiclassical simulations, whose results validate the experimental ones and further elucidate energy distributions in the products. The calculations make use of a new, highly accurate potential energy surface. Simulations indicate that the dissociation mechanism requires the excitation to first relax into low-frequency motions of the trimer, resulting in the breaking of a single hydrogen bond. This allows the system to explore a critical van der Waals minimum region from which dissociation occurs readily to monomer + dimer.

ChemInform Abstract: Direct Chemical Dynamics Simulations: Coupling of Classical and Quasiclassical Trajectories with Electronic Structure Theory

AbstractReview: 123 refs.

Evidence for aT-Shape Break-Up Pattern in the Triple Photoionization of Li

We examine the angular distributions of all three electrons ionized from Li by a single photon near the triple ionization threshold using a fully quantum-mechanical treatment. We find strong evidence for a T-shape break-up pattern at a 5 eV excess energy as previously predicted by quasiclassical simulations [A. Emmanouilidou and J. M. Rost, J. Phys. B 39, 4037 (2006); A. Emmanouilidou, P. Wang, and J. M. Rost, Phys. Rev. Lett. 100, 063002 (2008)]. This finding is in conflict with the expected Wannier break-up dynamics of three electrons moving at mutual angles of 120°, which is expected to hold at energies a few eV above threshold. We use our quantum-mechanical approach to explore the physical mechanisms behind this unusual break-up configuration.

Surface temperature effects on the dynamics of N2 Eley-Rideal recombination on W(100)

Quasiclassical trajectories simulations are performed to study the influence of surface temperature on the dynamics of a N atom colliding a N-preadsorbed W(100) surface under normal incidence. A generalized Langevin surface oscillator scheme is used to allow energy transfer between the nitrogen atoms and the surface. The influence of the surface temperature on the N(2) formed molecules via Eley-Rideal recombination is analyzed at T = 300, 800, and 1500 K. Ro-vibrational distributions of the N(2) molecules are only slightly affected by the presence of the thermal bath whereas kinetic energy is rather strongly decreased when going from a static surface model to a moving surface one. In terms of reactivity, the moving surface model leads to an increase of atomic trapping cross section yielding to an increase of the so-called hot atoms population and a decrease of the direct Eley-Rideal cross section. The energy exchange between the surface and the nitrogen atoms is semi-quantitatively interpreted by a simple binary collision model.