Volume 11, Issue 9 - Ultrashort pulses and free-electron lasers applications

We review our recent work on ab initio nonadiabatic molecular dynamics, based on linear-response timedependent density functional theory for the calculation of the nuclear forces, potential energy surfaces, and nonadiabatic couplings. Furthermore, we describe how nuclear quantum dynamics beyond the Born-Oppenheimer approximation can be performed using quantum trajectories. Finally, the coupling and control of an external electromagnetic field with mixed quantum/classical trajectory surface hopping is discussed.

Semiconductor quantum dots are ideal candidates for quantum information applications in solid-state technology. However, advanced theoretical and experimental tools are required to coherently control, for example, the electronic charge in these systems. Here we demonstrate how quantum optimal control theory provides a powerful way to manipulate the electronic structure of coupled quantum dots with an extremely high fidelity. As alternative control fields we apply both laser pulses as well as electric gates, respectively. We focus on double and triple quantum dots containing a single electron or two electrons interacting via Coulomb repulsion. In the two-electron situation we also briefly demonstrate the challenges of timedependent density-functional theory within the adiabatic local-density approximation to produce comparable results with the numerically exact approach.

In the present work, we develop a calculational method of solving the scattering equations for spherically symmetric potentials by expanding the solutions on Coulomb functions. We utilize a multistep integration scheme together with the standard partial wave analysis in a region where the potential term dominates. The method applies to any physical problem expressed as [∇ 2 + V(r) + k 2]ψ(r) = 0, while the extension of the method to more general scattering problems is briefly discussed. At present, we demonstrate a two-step Coulomb-fitted integration scheme by calculating the short-range scattering phase shifts for various potentials V (r).

A set of rate equations have been tested against a more robust set of Time-Dependent Density Matrix (TDDM) equations [D. P. W. Middleton, L. A. A. Nikolopoulos, J. Mod. Opti. 59, 1650 (2012)] by using them to determine the populations of ion species and autoionising states (AIS) in noble gas atoms when interacting with a strong external field. Two field shapes were tested here — sinusoidal and square — and a variety of pulse characteristics were examined, i.e. intensity, duration and photon energy, for the neon atomic system. It was found that the rate equations were sufficiently accurate only when the external field is way off-resonant with the AIS. Moreover, analytical solutions of the rate equations in the square pulse case agree with the numerical solutions for a time-dependent pulse containing many cycles. An attempt to model a stochastic field was also made and it was found that the use of such a field diminished and broadened the ion yield ratio due to the presence of an added bandwidth.

This paper adresses the problem of above-threshold ionization (ATI) of hydrogen interacting with an intense X-ray electromagnetic field. Two approaches have been used. In the first approach, we calculate generalized differential and total cross sections based on second-order perturbation theory for the electron interaction with a monochromatic plane wave, with the A 2 and A · P contributions from the nonrelativistic Hamiltonian (including retardation) treated exactly. In the second approach, we solve the time-dependent Schrödinger equation (TDSE) for a pulsed plane wave using a spectral approach with a basis of oneelectron orbitals, calculated with L 2-integrable B-spline functions for the radial coordinate and spherical harmonics Y lm for the angular part. Retardation effects are included up to O(1/c), they induce extra terms forcing the resolution of the TDSE in a three dimensional space. Relativistic effects [of O (1/c 2)] are fully neglected. The isoelectronic series of hydrogen is explored in the range Z = 1 − 5 in both TDSE and perturbative approaches. Photoelectron angular distributions are obtained for photon energies of 1 keV and 3 keV for hydrogen, and photon energy of 25 keV for the hydrogenic ion B4+. Perturbative and TDSE calculations are compared.

In this paper, we present theoretical results for the process of non-sequential two-photon double ionization of helium at the photon energy 42 eV. Our approach is based on solving the time-dependent Schrödinger equation in a B-spline based numerical framework. Information about the process is obtained by extracting the double-ionized component by means of uncorrelated final states. The total (generalized) cross section for the process is extracted, as well as differential cross sections resolved in electron energies and ejection angles. We focus on the impact the final-state correlation has on the accuracy of the cross sections.

Semi-empirical adiabatic potential energy curves of highly excited states of the KRb molecule are calculated as a function of the internuclear distance R over a wide range from 3 to 150 a 0. The diatomic molecule is treated as an effective two-electron system by using the large core pseudopotentials and core polarization potentials. All calculations are performed by using the nonrelativistic CASSCF/MRCI method with accurate basis set functions. The spectroscopic constants of the calculated electronic states agree well with experimental data, including the recent ones from Lee et al., and with available theoretical results.

We present four promising schemes for photoassociative formation of KLi molecule in its ground electronic state. Analysis is based on newly calculated adiabatic potentials supported by transition dipole moments and Franck-Condon factors.

We study the Mott scattering of charged spinless particles in the presence of an intense plane wave laser pulse with fixed propagation direction and arbitrary duration and shape. We derive two equivalent forms of the transition amplitude and we discuss the relation between the respective results obtained in the case of a laser pulse and the monochromatic case. We obtain the condition defining the boundaries of the “bright” domain (the domain of allowed values in the energy-direction space of the scattered particle) and we illustrate our results with numerical examples.

The main effects of an intense THz pulse on gas high harmonic generation are studied via trajectory analysis on the single atom level. Spectral and temporal modifications to the generated radiation are highlighted.

The six lowest lying electronic singlet states of 8-(pyrimidine-2-yl)quinolin-ol and 2-(4-nitropyrimidine-2-yl)ethenol have been studied theoretically using the complete active space self-consistent-field (CASSCF) and M’ller-Plesset second-order perturbation theory (MP2) methods. Both molecules can be viewed as consisting of a frame and a crane component. As a possible mechanism for the excited-state relaxation process an intramolecular hydrogen transfer promoted by twisting around the covalent bond connecting the molecular frame and crane moieties has been considered. Based on this idea we have attempted to derive abstracted photochemical pathways for both systems. Geometry optimizations for the construction of hypothetical reaction coordinates have been performed at the MP2 level of theory while the CASSCF approach has been employed for the calculation of vertical excitation energies along the pathways. The results of the calculations along the specific twisting displacements investigated in this study do not support the notion of substantial twisting activity upon excitation of any of the five excited states at the planar terminal structures of the torsion coordinates of both molecules. However, the present analysis should be considered only as a first, preliminary step towards an understanding of the photochemistry of the two candidate compounds. For example, we have not performed any excited state geometry optimizations so far and the estimates of vertical excitation energies do not take dynamical electron correlation into account. Further work on this subject is in progress.

An analysis of the charge transfer mechanism in the collision of multiply charged ions with molecular and biomolecular targets is performed, considering the non-adiabatic interactions between the molecular states involved. Collisions of doubly charged C 2+ ions on small molecular targets, CO and OH, have been investigated, together with the analysis of charge transfer between C 4+ ions on uracil and halouracil biomolecular targets. The process is studied theoretically by means of ab-initio molecular calculations followed by a semi-classical treatment of the collision dynamics. The influence of rotational couplings is discussed with regard to the collision energy. Strong anisotropic and vibration effects are pointed out.

We use an extension of the static-exchange density functional theory (DFT) method, previously reported in [E. Plésiat et al., Phys. Rev. A 2, 023409 (2012), E. Plésiat, P. Decleva, F. Martín, Phys. Chem. Chem. Phys. 31, 10853 (2012)], to evaluate vibrationally resolved (total and angular) K-shell photoelectron cross sections of methane. The calculated cross sections are in very good agreement with the existing experimental measurements at low photoelectron energies. We show that, in contrast with the rich interference patterns previously observed in molecular frame C(1s) photoelectron angular distributions of methane at both low and high photoelectron energy, no interference effects are observed in the calculated β parameters, even at high photon energies.