The recent development of novel light sources like x-ray free-electron lasers and table-top lasers for high-harmonic generation, which are capable of delivering controllable sequences of intense sub-femtosecond ionizing pulses, has opened the way to monitor and control electron dynamics in atoms and molecules at its natural time scale, the attosecond (Chem. Rev. 2017, DOI: 10.1021/acs.chemrev.6b00453). The description of the coherent superposition of electronic continuum states that the interaction of such pulses with molecules generates goes beyond the capabilities of standard quantum-chemistry packages, which have been designed to describe the lowest bound states. Furthermore, stationary state-based pictures based on lowest-order perturbation theory are, in most cases, inapplicable. The purpose of this school is to introduce state-of-the-art ab-initio, hybrid and TDDFT numerical methods that can cope with ultra-fast dynamics in the electronic continuum of molecules, with an emphasis on unbound states in strong-fields and on the need to go beyond single-active-electron models to properly account for electron correlation. The course is directed to advanced master students, PhD students and young post-doctoral researchers in atomic and molecular physics, theoretical chemistry and applied mathematics, with an interest in developing new software for coherent control of electronic dynamics in systems of chemical interest.
The tutorial will be organized in 5 theoretical sessions and 4 practical sessions in the computer lab. Both theoretical and practical sessions will be of 4 hours. The school comprises four didactic blocks. The first block has an introductory character. It offers an overview of the field and a tutorial on strong field physics. The following three blocks focus on systems of increasing complexity and will be devoted to the description and use of new computational methods for fast time evolution in correlated systems in non-perturbative conditions (see description below). The school will end with a comprehensive overview of state-of-the-art results in attosecond pump-probe and strong field molecular science obtained with ab initio “exact” simulations in small systems, on the one side, and with TD-DFT effective-field simulations, capable of coping with larger systems, on the other side. The future perspectives, challenges and mutual interaction of these two complementary approaches will be discussed.
Theoretical Session 1st Block: Overview of strong-field and attosecond physics with a tutorial on analytical models for ionization and high-harmonic generation as well as a presentation of the most recent discoveries.
Theoretical Session 2nd Block:
Extreme ionization, static ionization rates and the breakdown of the "states" concept. Numerical and theoretical challenges associated to the description of strongly-driven electrons in the continuum, with the introduction of infinite-range Exterior Complex Scaling (ir-ECS) as a perfectly-matched-layer technique for time-dependent problems and the role of correlation in strongly-driven two-electron systems. Introduction of the time-dependent surface-flux method (t-SURFF) for the spectral analysis of many-body time-dependent wave functions.
Theoretical Session 3rd Block: Merging quantum chemistry packages with scattering theory methods: electronic structure calculations in the ionization continuum. Computational packages for strong-field ionization of molecules with correlated electrons: i) the molecular Ammosov-Delone-Krainov tunneling method (MO-ADK), ii) the time-dependent resolution in ionic states method (TD-RIS), and iii) the exterior-complex-scaling Möller-Plesset 2 method (ECS-MP2). Computational packages for weak-field ionization of molecules with correlkated electrons: (iv) the time-dependent all-B-spline method (MOLTWO code), and (v) the hybrid Gaussian/B-spline multi-reference CI method (XCHEM).
Theoretical Session 4th Block. Part1: ab-initio calculation of pump-probe light absorption and electron emission spectra in molecules. Part 2: Overview of time-dependent density-functional theory (TDDFT) and its application to non-linear response of strongly-driven quantum systems. Introduction to the OCTOPUS software. Description of current functionals accounting for electron correlation in strong-field multiple ionization (e.g., functional with derivative discontinuity) and of methods to extract ionization rates, photoelectron distributions, absorption spectra and high-harmonic generation from explicit time propagations.
Closing Lectures: Seminars on state-of-the-art results of attosecond molecular processes with ab-initio and effective-field time-dependent methods.
The speakers participating in this training will be: Alberto Castro (BIFI, Zaragoza), Mikhail Ivanov (Max Born Institute, Berlin), Fernando Martín (Autonomous University of Madrid), Alicia Palacios (Autonomous University of Madrid), Serguei Patchkovskii (Max Born Institute, Berlin), Ángel Rubio (Max Planck Institute SD, Hamburg), Armin Scrinzi (Ludwig-Maximilians University Munich), and Olga Smirnova (Max Born Institute, Berlin).