Two 6-hour lectures (A, B) will be proposed, each organized and given by a tandem of Lecturers including one experimentalist and one theoretician. Two 3-hour lectures (C,D) will be proposed on two selected topics. The first lecture (A) will be illustrated with an additional 4-hour numerical practical session.

(A) Time-resolved non-linear optical spectroscopy of molecular systems: theory and experiments

By Tomáš Mančal⁽¹⁾ and Donatas Zigmantas⁽²⁾

Non-linear optical spectroscopy is our main tool for obtaining information on electronic/vibronic structure and ultrafast processes in molecular systems. The nature of this methodology enables a unique synergy between the theory and experiment, and in our lectures we will cover both theoretical and experimental aspects of the topic. We will expose the perturbation response function theory of the non-linear spectroscopy technique using density matrix formalism and the diagramatic notation of the double-sided Feynman diagrams (DSFDs). These diagrams provide a common language for the discussions of spectroscopic signals by both experimentalists and theorists in the field. Using elementary open quantum systems theory and the Frenkel exciton model of molecular aggregates, we will construct the theory of the most important time-resolved spectroscopic techniques such as pump-probe and two-dimensional electronic spectroscopy (2DES). From the experimental perspective we will discuss the most common implementations of 2DES, and use of DSFSs to provide interpretation of the signals acquired with the help of this technique. The advantages afforded by polarization control in the experiments will be deliberated. Revealed synergy between theory and experiment will lead to understanding of what information about molecular systems and photoexcited dynamic processes can be obtained. Keywords: Non-linear spectroscopy, Time-resolved spectroscopy, Two-dimensional electronic spectroscopy, molecular aggregates, Frenkel excitons, energy transfer, anisotropy, open quantum systems

Practical session*: Calculating open system dynamics and non-linear spectra with Quantarhei 

By Vladislav Slama

* Participants should bring their own lap-top or team up with another participant. A preliminary online session will be organized to install the minimal required python environment.

(B) Probing the coupling of molecular vibrations and solvent fluctuations to electronic excitations with linear, non-linear and time-resolved spectroscopies

By David Picconi⁽¹⁾  and David McCamant⁽²⁾

David Picconi will discuss the theoretical treatment of multidimensional vibrational wavepacket dynamics, both within isolated potential energy surfaces and beyond the Born-Oppenheimer approximation (2h15). He will also present efficient computational methods for determining the evolution of multidimensional wavepackets, such as the multi-configurational time-dependent Hartree (MCTDH) approach. As an experimentalist, David McCamant, will complement Picconi’s theoretical treatments with an experimental perspective on the generation and detection of vibrational wavepackets (3h45). Practical considerations when designing and implementing laser systems to study molecular vibronic coupling will be addressed, as well as how one might implement experiments to probe the latest theoretical proposals. Throughout both lectures, a variety of spectroscopies that are sensitive to both electronic and vibrational dynamics will be considered and contrasted with each other.  Keywords: vibrational coherence, vibronic transitions, nonadiabatic dynamics, transient absorption/fluorescence, quantum beats, Raman spectroscopy, CARS (Coherent Anti-Stokes Spectroscopy), FSRS (Femtosecond Stimulated Raman Spectroscopy), impulsive stimulated Raman, wavepacket interferometry, IVR (intramolecular vibrational relaxation). 

(C) Probing elementary chemical events on the atto- and femto- second timescales with linear, nonlinear and time-resolved x-ray spectroscopies

By Prof.Linda Young

In “Generation and characterization of attosecond x-ray pulses” (1h30) Prof. Young will discuss the basics of accelerator-based x-ray free electron lasers for the production of attosecond x-ray pulses and compare with table-top methods based upon high harmonic generation for experimental studies of chemical dynamics. 

In “Advancing from linear to nonlinear x-ray spectroscopies” (1h30), Prof. Young will discuss how time-resolved x-ray spectroscopic probes, with their inherent elemental, chemical and spin selectivity, can be used to track photoinduced electronic and nuclear dynamics on the attosecond-Ångstrom scale.  

Keywords: x-ray free electron lasers, attosecond transient absorption spectroscopy, stimulated x-ray Raman, x-ray emission, photon correlation.

(D) Computational time-resolved X-ray spectroscopy of non-adiabatic molecular dynamics

By Dr. Daniel Keefer

1- Nuclear Quantum Dynamics in Excited States of Molecules (1h30).  The temporal evolution of molecular quantum systems is governed by the time-dependent Schrödinger equation (TDSE). In modern computational molecular science, a variety of numerical approaches are used to solve the TDSE or to approximate its exact solution, each with its own advantages. In this lecture, we will discuss grid-based quantum dynamics in reduced dimensionality, also known as nuclear wave packets. This method has the advantage of solving the TDSE exactly, and the drawback of requiring a reduction of the molecular system to a few (usually up to three) nuclear degrees of freedom. Basic and advanced concepts will be outlined, with a special focus on the excited states of molecules and their coupling by resonant laser pulses. We will discuss the simulation of conical intersection passages, which require the non-trivial implementation of non-adiabatic couplings. Keywords: time-dependent Schrödinger equation, numerical propagation scheme, conical intersection, laser excitation, non-adiabatic coupling


2-  Probing Elementary Chemical Events with Linear and Non-Linear (X-ray) Spectroscopy and Diffraction (1h30).  Ultrafast x-ray and electron pulses have emerged as a novel and powerful tool to probe molecular dynamics with unprecedented temporal, spectral and spatial resolution. We will discuss how these signals can be simulated. Based on nuclear quantum dynamics, as outlined in the first lecture, the signals are computed in a perturbative approach, where the quantum matter is subjected to n interactions with classical probe pulses, generating an n'th order polarization and an (n+1)-order wave mixing process. In the x-ray regime, these signals provide distinct advantages such as sensitivity to conical intersections and atom selectivity. Specific examples such as X-ray and electron diffraction, X-ray stimulated Raman and photoelectron spectroscopy will be discussed.  A minimal working example of how to calculate X-ray stimulated Raman (with approximations) on the model system from the first lecture will be given.
Keywords: conical intersection, vibronic coherence, x-ray vs electron diffraction, x-ray stimulated Raman, femto- & attoseconds