An efficient procedure for calculating the evolution of the wave function by fast Fourier transform methods for systems with spatially extended wave function and localized potential

In-line attosecond photoelectron holography for single photon ionization

The momentum distribution of photoelectrons in H2+ molecules subjected to an attosecond pulse is theoretically investigated. To better understand the laser-molecule interaction, we develop an in-line photoelectron holography approach that is analogous to optical holography. This approach is specifically suitable for extracting the amplitude and phase of the forward-scattered electron wave packet in a dissociating molecule with atomic precision. We also extend this approach to imaging the transient scattering cross-section of a molecule dressed by a near infrared laser field. This attosecond photoelectron holography sheds light on structural microscopy of dissociating molecules with high spatial-temporal resolution.

Nuclear–Electron Correlation Effects and Their Photoelectron Imprint in Molecular XUV Ionisation

The ionisation of molecules by attosecond XUV pulses is accompanied by complex correlated dynamics, such as the creation of coherent electron wave packets in the parent ion, their interplay with nuclear wave packets, and a correlated photoelectron moving in a multi-centred potential. Additionally, these processes are influenced by the dynamics prior to and during the ionisation. To fully understand and subsequently control the ionisation process on different time scales, a profound understanding of electron and nuclear correlation is needed. Here, we investigate the effect of nuclear–electron correlation in a correlated two-electron and one-nucleus quantum model system. Solving the time-dependent Schrödinger equation allows to monitor the correlation impact pre, during, and post-XUV ionisation. We show how an initial nuclear wave packet displaced from equilibrium influences the post-ionisation dynamics by means of momentum conservation between the target and parent ion, whilst the attosecond electron population remains largely unaffected. We calculate time-resolved photoelectron spectra and their asymmetries and demonstrate how the coupled electron–nuclear dynamics are imprinted on top of electron–electron correlation on the photoelectron properties. Finally, our findings give guidelines towards when correlation resulting effects have to be incorporated and in which instances the exact correlation treatment can be neglected.

Molecular hydrogen isotope separation by a graphdiyne membrane: a quantum-mechanical study

Graphdiyne (GDY) has emerged as a very promising two-dimensional (2D) membrane for gas separation technologies. One of the most challenging goals is the separation of deuterium (D₂) and tritium (T₂) from a mixture with the most abundant hydrogen isotope, H₂, an achievement that would be of great value for a number of industrial and scientific applications. In this work we study the separation of hydrogen isotopes in their transport through a GDY membrane due to mass-dependent quantum effects that are enhanced by the confinement provided by its intrinsic sub-nanometric pores. A reliable improved Lennard-Jones force field, optimized on accurate ab initio calculations, has been built to describe the molecule-membrane interaction, where the molecule is treated as a pseudoatom. The quantum dynamics of the molecules impacting on the membrane along a complete set of incidence directions have been rigorously addressed by means of wave packet calculations in the 3D space, which have allowed us to obtain transmission probabilities and, in turn, permeances, as the thermal average of the molecular flux per unit pressure. The effect of the different incidence directions on the probabilities is analyzed in detail and it is concluded that restricting the simulations to a perpendicular incidence leads to reasonable results. Moreover, it is found that a simple 1D model-using a zero-point energy-corrected interaction potential-provides an excellent agreement with the 3D probailities for perpendicular incidence conditions. Finally, D₂/H₂ and T₂/H₂ selectivities are found to reach maximum values of about 6 and 21 at ≈50 and 45 K, respectively, a feature due to a balance between zero-point energy and tunneling effects in the transport dynamics. Permeances at these temperatures are below recommended values for practical applications, however, at slightly higher temperatures (77 K) they become acceptable while the selectivities preserve promising values, particularly for the separation of tritium.

Molecular Free Electron Vortices in Photoionization by Polarization-Tailored Ultrashort Laser Pulses

Atomic and molecular free electron vortices (FEVs), characterized by their spiral-shaped momentum distribution, have recently attracted a great deal of attention due to their varied shapes and their unusual topological properties. Shortly after their theoretical prediction by the single-photon ionization (SPI) of He atoms using pairs of counterrotating circularly polarized attosecond pulses, FEVs have been demonstrated experimentally by the multiphoton ionization (MPI) of alkali atoms using single-color and bichromatic circularly polarized femtosecond pulse sequences. Recently, we reported on the analysis of the experimental results employing a numerical model based on the ab initio solution of the time-dependent Schrödinger equation (TDSE) for a two-dimensional (2D) atom interacting with a polarization-shaped ultrashort laser field. Here, we apply the 2D TDSE model to study molecular FEVs created by SPI and MPI of a diatomic molecule using polarization-tailored single-color and bichromatic femtosecond pulse sequences. We investigate the influence of the coupled electron-nuclear dynamics on the vortex formation dynamics and discuss the effect of CEP- and rotational averaging on the photoelectron momentum distribution. By analyzing how the molecular structure and dynamics is imprinted in the photoelectron spirals, we explore the potential of molecular FEVs for ultrafast spectroscopy.

Simulation of photo-electron spectrum and electron scattering by dual time propagation

A dual time propagation approach is introduced to describe electron scattering and ionization. The space is divided into two regions, a central region with a full time-dependent Hamiltonian and an outer region where the kinetic operator and the laser field dominate. The two regions are connected by a source term. Time-dependent density functional theory calculations of wave packet scattering on molecules and photoelectron spectrum due to circularly polarized laser are presented to illustrate the efficiency and applicability of the approach.

Interaction-Asymptotic Region Decomposition Method for an Insertion Reaction: Application to the S(1D) + H2 Reaction

With adjusting principal axes hyperspherical (APH) coordinate in the interaction region, and the Jacobi coordinates in the asymptotic regions, an efficient multidomain interaction-asymptotic region decomposition (IARD) method has been developed to solve the "coordinate problem" in a product-state-resolved reactive scattering calculation using the quantum wave packet method. Although the APH coordinate treats with all three channels equally, and is efficient for describing the interaction region for some direct reactions, it is inefficient for describing the insertion-type reaction due to the singularity problem, such as the S(¹D) + H₂ reaction. To deal with this issue, in this work, the channel-dependent Delves hyperspherical (DH) coordinate is proposed to describe the interaction region using the IARD method. The proposed DH-IARD method was applied to calculate the product-state-resolved reaction probabilities of the H + HD reaction, and the differential and integral cross sections of the typical insertion reaction S(¹D) + H₂. It is found that the new DH-IARD method is much more efficient than the previous APH-IARD method for dealing with insertion reactions. The partial wave resonance structures were observed in the integral cross section. It is found that at a low collision energy, the position of the initial wave packet has to be put far away. Otherwise, the partial wave resonance structures could not be correctly reproduced due to the reef well arising with a large total angular momentum J.

Helium Isotopes Quantum Sieving through Graphtriyne Membranes

We report accurate quantum calculations of the sieving of Helium atoms by two-dimensional (2D) graphtriyne layers with a new interaction potential. Thermal rate constants and permeances in an ample temperature range are computed and compared for both Helium isotopes. With a pore larger than graphdiyne, the most common member of the γ-graphyne family, it could be expected that the appearance of quantum effects were more limited. We find, however, a strong quantum behavior that can be attributed to the presence of selective adsorption resonances, with a pronounced effect in the low temperature regime. This effect leads to the appearance of some selectivity at very low temperatures and the possibility for the heavier isotope to cross the membrane more efficiently than the lighter, contrarily to what happened with graphdiyne membranes, where the sieving at low energy is predominantly ruled by quantum tunneling. The use of more approximate methods could be not advisable in these situations and prototypical transition state theory treatments might lead to large errors.

Time-dependent quantum mechanical wave packet dynamics

Starting from a model study of the collinear (H, H₂) exchange reaction in 1959, the time-dependent quantum mechanical wave packet (TDQMWP) method has come a long way in dealing with systems as large as Cl + CH₄. The fast Fourier transform method for evaluating the second order spatial derivative of the wave function and split-operator method or Chebyshev polynomial expansion for determining the time evolution of the wave function for the system have made the approach highly accurate from a practical point of view. The TDQMWP methodology has been able to predict state-to-state differential and integral reaction cross sections accurately, in agreement with available experimental results for three dimensional (H, H₂) collisions, and identify reactive scattering resonances too. It has become a practical computational tool in predicting the observables for many A + BC exchange reactions in three dimensions and a number of larger systems. It is equally amenable to determining the bound and quasi-bound states for a variety of molecular systems. Just as it is able to deal with dissociative processes (without involving basis set expansion), it is able to deal with multi-mode nonadiabatic dynamics in multiple electronic states with equal ease. We present an overview of the method and its strength and limitations, citing examples largely from our own research groups.

Photodesorption mechanism of water on WO3(001) - a combined embedded cluster, computational intelligence and wave packet approach

In this work we investigate the mechanism of photodesorption of water from a WO3(001) surface by theoretical calculations, applying an embedded cluster model. Using the CASSCF method, we have calculated both the ground state as well as the energetically preferred charge-transfer state in three degrees of freedom of the water molecule on the surface. The calculated potential energy surfaces were afterwards fitted with a neural network optimized by a genetic algorithm. A final quantum dynamic wave packet study provided insight into the photodesorption mechanism.

Imprints of the Molecular Electronic Structure in the Photoelectron Spectra of Strong-Field Ionized Asymmetric Triatomic Model Molecules

We examine the circular dichroism in the angular distribution of photoelectrons of triatomic model systems ionized by strong-field ionization. Following our recent work on this effect [Paul, Yue, and Gräfe, J. Mod. Opt. 64, 1104 (2017)JMOPEW0950-034010.1080/09500340.2017.1299883], we demonstrate how the symmetry and electronic structure of the system is imprinted into the photoelectron momentum distribution. We use classical trajectories to reveal the origin of the threefolded pattern in the photoelectron momentum distribution, and show how an asymmetric nuclear configuration of the triatomic system effects the photoelectron spectra.

Time-resolved photoelectron spectroscopy of IR-driven electron dynamics in a charge transfer model system

If the adiabatic approximation is valid, electrons smoothly adapt to molecular geometry changes. In contrast, as a characteristic of diabatic dynamics, the electron density does not follow the nuclear motion. Recently, we have shown that the asymmetry in time-resolved photoelectron spectra serves as a tool to distinguish between these dynamics [Falge et al., J. Phys. Chem. Lett., 2012, 3, 2617]. Here, we investigate the influence of an additional, moderately intense infrared (IR) laser field, as often applied in attosecond time-resolved experiments, on such asymmetries. This is done using a simple model for coupled electronic-nuclear motion. We calculate time-resolved photoelectron spectra and their asymmetries and demonstrate that the spectra directly map the bound electron-nuclear dynamics. From the asymmetries, we can trace the IR field-induced population transfer and both the field-driven and intrinsic (non-)adiabatic dynamics. This holds true when considering superposition states accompanied by electronic coherences. The latter are observable in the asymmetries for sufficiently short XUV pulses to coherently probe the coupled states. It is thus documented that the asymmetry is a measure for phases in bound electron wave packets and non-adiabatic dynamics.

Photodesorption of water from rutile(110): ab initio calculation of five-dimensional potential energy surfaces of ground and excited electronic states and wave packet studies

In this paper, we report on our results concerning the interaction of water with titanium dioxide in its rutile modification. The (110) surface is modelled by an embedded Ti9O18Mg7(14+) cluster. We present up to five-dimensional potential energy surfaces for the water molecule on this surface and include the dissociation of one hydrogen atom. The electronic ground state as well as one electronically excited state is included. To deal with the multi-configurational character of the wave function, we use the complete active space self-consistent field (CASSCF) approach. The resulting potential energy surfaces are fitted by means of an artificial neural network. As a first example of quantum dynamical studies based on our potential surfaces, we present results on the photodesorption of water from rutile(110).

Quantum dynamical study of femtosecond photodesorption of CO from TiO2(110)

The photodesorption of CO from TiO2(110) by femtosecond pulses is investigated with the Surrogate Hamiltonian approach. The aim of the study is to resolve the relaxation mechanism and forecast the lifetime of the exited state based on a microscopic description of the excitation and relaxation processes. The parameters characterizing the system are obtained from ab initio and Density Functional Theory-calculations with one parameter estimated from physical considerations and convergence studies. Two electronic states are considered and the relaxation is assumed to be due to the interaction of the excited adsorbate with electron hole pairs in the surface. Desorption probabilities and velocity distributions of the desorbing molecules are calculated and an exited state lifetime is predicted. Throughout this paper atomic units, i.e., ℏ = me = e = a0 = 1, have been used unless otherwise stated.

Binding energies of the ground triplet state a(3) Σ(u)(+) of Rb2 and Cs2 in terms of the generalized Le Roy-Bernstein near-dissociation expansion

Formulae of Le Roy-Bernstein near-dissociation theory are derived in a general isotope-invariant form, applicable to any term in the rotational expansion of a diatomic ro-vibrational term value. It is proposed to use the generalized Le Roy-Bernstein expansion to describe the binding energies (ro-vibrational term values) of the ground triplet state a(3) Σ(u)(+) of alkali metal dimers. The parameters of this description are determined for Rb2 and Cs2 molecules. This approach gives a recipe to calculate the whole variety of the binding energies with characteristic accuracies from ∼1 × 10(-3) to 1 × 10(-2) cm(-1) using a relatively simple algebraic equation.

Using GPUs to compute fast Fourier transforms for crystal structure solution and refinement

In the past few years, new hardware tools have become available for computing using the graphical processing units (GPUs) present in modern graphics cards. These GPUs allow efficient parallel calculations with a much higher throughput than microprocessors. In this work, fast Fourier transformation calculations used inSIR2011software algorithms have been carried out using the power of the GPU, and the speed of the calculations has been compared with that achieved using normal CPUs.

Joint analysis of the Cs2 a3Σu+ and 1g (3(3)Π1g) states

Sets of experimental data on the Cs(2) a(3)Σ(u)(+) and 1(g) (3(3)Π(1g)) states, including the bound-bound and bound-free fluorescence spectra, are analyzed simultaneously to produce the potential energy curves of both states in the form of the Morse long range multiparameter function. The attractive branch of the a(3)Σ(u)(+) state potential is improved relative to the one reported in our earlier work [F. Xie, V. B. Sovkov, A. M. Lyyra, D. Li, S. Ingram, J. Bai, V. S. Ivanov, S. Magnier, and L. Li, J. Chem. Phys. 130, 051102 (2009)], in which the data on this state alone were analyzed. Besides, the new potential of this state also includes the repulsive branch in the range spanned by the bound-free fluorescence spectra. We have not found experimental evidence of the double minimum character of the 3(3)Π(1g) state potential, predicted by ab initio calculations, at least up to v = 8. This fact testifies that the upper state observed is better described by the Hund coupling case (c), in which the case (a) electronic basis states are intermixed by the strong spin-orbit interaction.

Mixed quantum-classical theory for the collisional energy transfer and the rovibrational energy flow: application to ozone stabilization

A mixed quantum-classical approach to the description of collisional energy transfer is proposed in which the vibrational motion of an energized molecule is treated quantum mechanically using wave packets, while the collisional motion of the molecule and quencher and the rotational motion of the molecule are treated using classical trajectories. This accounts rigorously for quantization of vibrational states, zero-point energy, scattering resonances, and permutation symmetry of identical atoms, while advantage is taken of the classical scattering regime. Energy is exchanged between vibrational, rotational, and translational degrees of freedom while the total energy is conserved. Application of this method to stabilization of the van der Waals states in ozone is presented. Examples of mixed quantum-classical trajectories are discussed, including an interesting example of supercollision. When combined with an efficient grid mapping procedure and the reduced dimensionality approximation, the method becomes very affordable computationally.

Geometric phase effects in the coherent control of the branching ratio of photodissociation products of phenol

Optimal control simulation is used to examine the control mechanisms in the photodissociation of phenol within a two-dimensional, three-electronic-state model with two conical intersections. This model has two channels for H-atom elimination, which correspond to the (2)pi and (2)sigma states of the phenoxyl radical. The optimal pulse that enhances (2)sigma dissociation initially generates a wave packet on the S(1) potential-energy surface of phenol. This wave packet is bifurcated at the S(2)-S(1) conical intersection into two components with opposite phases because of the geometric phase effect. The destructive interference caused by the geometric phase effect reduces the population around the S(1)-S(0) conical intersection, which in turn suppresses nonadiabatic transitions and thus enhances dissociation to the (2)sigma limit. The optimal pulse that enhances S(0) dissociation, on the other hand, creates a wave packet on the S(2) potential-energy surface of phenol via an intensity borrowing mechanism, thus avoiding geometric phase effects at the S(2)-S(1) conical intersection. This wave packet hits the S(1)-S(0) conical intersection directly, resulting in preferred dissociation to the (2)pi limit. The optimal pulse that initially prepares the wave packet on the S(1) potential-energy surface (PES) has a higher carrier frequency than the pulse that prepares the wave packet on the S(2) PES. This counterintuitive effect is explained by the energy-level structure and the S(2)-S(1) vibronic coupling mechanism.

Two-dimensional surrogate Hamiltonian investigation of laser-induced desorption of NO∕NiO(100)

The photodesorption of NO from NiO(100) is studied from first principles, with electronic relaxation treated by the use of the surrogate Hamiltonian approach. Two nuclear degrees of freedom of the adsorbate-substrate system are taken into account. To perform the quantum dynamical wave-packet calculations, a massively parallel implementation with a one-dimensional data decomposition had to be introduced. The calculated desorption probabilities and velocity distributions are in qualitative agreement with experimental data. The results are compared to those of stochastic wave-packet calculations where a sufficiently large number of quantum trajectories is propagated within a jumping wave-packet scenario.

Photo-induced desorption of NO from NiO(100): calculation of the four-dimensional potential energy surfaces and systematic wave packet studies

The velocity distributions of the laser-induced desorption of NO molecules from an epitaxially grown film of NiO(100) on Ni(100) have been studied [Mull et al., J. Chem. Phys., 1992, 96, 7108]. A pronounced bimodality of velocity distributions has been found, where the NO molecules desorbing with higher velocities exhibit a coupling to the rotational quantum states J. In this article we present simulations of state resolved velocity distributions on a full ab initio level. As a basis for this quantum mechanical treatment a 4D potential energy surface (PES) was constructed for the electronic ground and a representative excited state, using a NiO5Mg(18+)13 cluster. The PESs of the electronic ground and an excited state were calculated at the CASPT2 and the configuration interaction (CI) level of theory, respectively. Multi-dimensional quantum wave packet simulations on these two surfaces were performed for different sets of degrees of freedom. Our key finding is that at least a 3D wave packet simulation, in which the desorption coordinate Z, polar angle theta and lateral coordinate X are included, is necessary to allow the simulation of experimental velocity distributions. Analysis of the wave packet dynamics demonstrates that essentially the lateral coordinate, which was neglected in previous studies [Klüner et al., Phys. Rev. Lett. 1998, 80, 5208], is responsible for the experimentally observed bimodality. An extensive analysis shows that the bimodality is due to a bifurcation of the wave packet on the excited state PES, where the motion of the molecule parallel to the surface plays a decisive role.

Time-Dependent Reactive Scattering for the System H- + D2 ↔ HD + D- and Comparison with H- + H2 ↔ H2 + H-

This work presents results of quantum mechanical calculations of reaction probabilities for the ion-neutral molecule collisions H- + D2 <--> HD + D-. Time-dependent wave packet propagations for total angular momentum J not equal to 0, including the full Coriolis coupling, are performed. The calculated state-to-state reaction probabilities using product Jacobi coordinates are compared with energy-resolved reaction probabilities calculated with the flux-operator using reactant Jacobi coordinates and with time-independent calculations. Differences between nearly converged integral cross sections and those using the J-shifting method and centrifugal sudden approximation and comparison with experimental results will be presented.

Wave packet dynamics of H2(v1=8-14)+H2(v2=0-2): the role of the potential energy surface on different reactive and dissociative processes

A time-dependent wave packet method has been used to study different competing products of H(2)+H(2) collisions: four center reaction, collision induced dissociation, reactive dissociation, and three-body complex formation. A three-degree-of-freedom reduced dimensionality model has been used for five different geometries of the colliding complex (parallel H, crossed X, collinear L, and two T-shaped geometries T(I) and T(II)), with reactants in selected vibrational states with one diatom vibrationally "hot" and the other one vibrationally "cold." Product probabilities have been calculated using two potential energy surfaces [J. Chem. Phys. 101, 4004 (1994); J. Chem. Phys. 116, 666 (2002)] in order to compare their performance in the dynamics. The regions of the potential energy surfaces responsible of the threshold behavior of the probabilities have been identified. Overall, we have found that the most recent potential energy surface is less anisotropic, provides a smaller propensity for insertion-type processes, and gives lower energy thresholds.

Speed-up collisions in strong-field double ionization

We compare quantum and classical models of double ionization (DI) for aligned-electron helium in strong laser fields, considering specifically the role of recollision processes in which the returning electron travels in the direction of the laser force. Quantum studies show that for the knee region in our model a small but persistent portion of the total DI occurs through these speed-up collisions.We show that classical modeling displays similar collisions and reveals that with-the-force doubly ionizing collisions typically involve two-particle trajectories in which both electrons can be said to have been bound or very nearly bound at the zero of the laser field just before the collision. Trajectories leading to the with-the-force doubly ionizing collisions can be classified into two categories-direct excitation, in which there is no unambiguous single ionization before the doubly ionizing collision, and recapture, in which an ionized electron returns to the core and is recaptured prior to the speed-up collision. Comparison of the classical and quantum situations for our laser parameters yields evidence that for our parameters the quantum system favors the direct-excitation pathway over the reattachment pathway.

The dissociation adiabaticity parameter and the strong field dissociation of HCl+

In earlier work on H2+, we showed how a dissociation adiabaticity parameter, gammaDv identical with (Dv/2Upm)(1/2) (Dv is the dissociation energy from vibrational state v and U(pm) is the molecular ion system's ponderomotive energy), proposed by Walsh et al., can be modified and be a useful indicator of the strong field dissociation regime for a homonuclear diatomic. In the case of H2+, the new adiabaticity parameter, gamma(mol), indicates when a dissociation process can be most easily described as multiphoton above-threshold dissociation (gamma(mol)>1) and when it is better described using barrier-suppressed dissociation (gamma(mol)<1). In the case of a heteronuclear diatomic like HCl+, different electronic states can lead to different dissociation product channels to which are ascribed different gamma(mol) values. We show for a wide range of laser wavelengths and intensities that this adiabaticity parameter successfully predicts the type of dissociation dynamics (multiphoton above-threshold dissociation versus barrier-suppressed dissociation) on each electronic potential curve. We also discover that the dynamics in one electronic state can influence the dynamics in another at the same laser wavelengths and intensities, overriding the predictive capability of an adiabaticity parameter defined for a particular electronic state. Reasonable physical explanations are provided for these overriding cases.