Photoinitiated processes are key to many relevant natural phenomena and play an essential role in emerging fields such as renewable energy, material design or nano-medicine. Excited state processes have been traditionally simulated from a static viewpoint, delivering in some cases a biased, incorrect or incomplete description. Dynamics simulations, which account for temporal evolution, are nowadays becoming widespread despite being more costly, and are fundamental to understand chemical and physical mechanisms and to the concrete way they link with experimental (often spectroscopic) measurable observables.

This school aims to introduce state-of-the-art methodologies for the simulation of excited state dynamics, following the evolution in time of photoinitiated reactions, which is one of the priority topics of this call. The school introduces tools to both efficiently and accurately model potential energy surfaces, as well as to propagate (quantum and semi-classical) nuclear dynamics relevant for a given photophysical or photochemical process.

Motivation

The school aims to provide the attendants with the basic tools and knowledge to simulate photoinduced processes, from conventional electronic spectroscopy to ultrafast laser-induced phenomena, enabling participants to apply these concepts to their own research interests. The school covers ab initio strategies, including electronic structure theory calculations using either time-dependent density functional theory or multiconfigurational methods, and dynamics simulations using different treatments for the nuclei, and ranging from full quantum dynamics to mixed quantum-classical nuclear propagations schemes.

The simulations covered form the basis to characterise excited state processes, which are essential to understand photophysical and/or photochemical events initiated upon radiation exposure, as well as their time evolution. These important processes cover areas ranging from biology/medicine to physical/material science and energy conversion, and the tools provided in this school are meant to aid the students in tackling them. This for example may include the development of new nano-materials profiting from efficient and reversible photochemical reactions (photoswitches, microreactors) or the monitoring of ultrafast (femto to attosecond) charge migration events in ionised systems, which have grown exponentially in the last two decades. Furthermore, complex photo-processes as those outlined above often feature multiple competing mechanisms, where the time-dependent models here introduced can provide relative yields and their associated timings that help discern them.

Moving beyond the excited state, other fundamental ground state processes such as dissociation, ionization or triplet state formation (i.e. reactivity in the atmosphere and in the interstellar space) usually involve open-shell electronic states that require computational protocols like those introduced in this course.

At the end of the school, the students will be able to apply the acquired abilities to their research projects covering any of the subjects mentioned above and others related to electronic and vibrationally excited states in complex molecular systems.

Goals

The overarching goal of the school is to provide students with the necessary tools and knowledge to understand how to perform dynamic simulations for studying processes triggered upon light absorption in molecular systems. Modelling complex photoinitiated events accurately is a timely effort which goes together with the emergence of ever shorter light sources in large-scale state-of-the-art facilities and with the wide rage of applications in which they are nowadays applied on: as we probe deeper more detail emerges related to the electron-nuclear motions triggered upon absorption which is however encoded in intricate spectral signals, and state-of-the-art models are crucial to translate those signals into their molecular counterparts to enable their understanding. 

To achieve this, a wide range of theoretical methods and tools is presented to the students, starting with those appropriate for static approaches to reactivity and spectroscopy. In a subsequent step, those methods are applied to dynamics simulations. At the end of the school, students are expected to:

1. Understand the main processes initiated upon light absorption in molecules: radiative (fluorescence, phosphorescence) and non-radiative (internal conversion, intersystem crossing, photochemistry…) decay and their competition.
2. Perform multiconfigurational (CASSCF/CASPT2) and single-reference (TD-DFT) calculations for excited states: simulation of vibrationally resolved electronic absorption spectra and characterisation of potential energy surfaces. 
3. Set up and run dynamics simulations: pump-probe spectroscopy and non-adiabatic dynamics.
4. Get acquainted with using several well-known computational packages and codes (OpenMolcas, Psi4/pySCF, FCClasses3, Newton-X).

These objectives are delivered through theoretical lessons taught by internationally recognized experts in the field, complemented with practical sessions (workshops) grouped in 3 interrelated blocks, which gradually introduce the necessary knowledge, starting from the basics to eventually provide the students with state-of-the-art simulation methods for photochemistry. Six sets of lectures (distributed over 3 different blocks and arranged in 11 sessions) are devised to provide a solid theoretical background, which is then applied during 5 workshops where students perform simulations under the instructors’ guidance.

Scientific content of the course

The school is split in 11 lectures and 5 hands-on workshops to take place in a computer lab. Lectures are 1.5 hours-long, and workshops last 3 hours. It is divided in three main blocks, which are carefully intertwined: i) computational photochemistry and spectroscopy; ii) quantum chemical methods for the excited state, and iii) excited state molecular dynamics.

The first block has an introductory character and offers an overview of photochemistry and spectroscopy from a computational standpoint. The second block focusses on the basics as well as the crucial differences between mono- and multi-configurational electronic structure methods for the description of electronic excited states and their reactivity. The last block covers molecular dynamics’ methodologies for the excited state. The school ends with an open round-table discussion (~3 hours) engaging students and lecturers on different state-of-the-art applications, limitations, model suitability, future perspectives and challenges of the different computational strategies covered; this provides participants with the chance to get bespoke feedback from renown experts on their particular scientific problems. A more specific list of contents is provided below:

1st Block (12 hours): Introduction to photochemistry and spectroscopy

1. Overview of modern electronic and vibrational spectroscopy [Javier Cerezo]. The Born-Oppenheimer approximation. Ground and excited potential energy surface topology and light-matter interaction. Franck-Condon principle. Theoretical approaches to simulate steady state spectra. Nuclear dynamics and its characterization through rotational and vibrational spectroscopy. Vibrational structure of electronic spectra, and introduction to the simulation of vibronic bands within the harmonic approximation: from classical to fully quantum mechanical approaches.
2. Introduction to Computational Photochemistry [Sandra Gómez]. Photophysics vs Photochemistry. Jablonski diagram. Radiation absorption: selection rules. Mapping potential energy surfaces: ground and excited state minima and conical intersections. Non-radiative decays: internal conversion and intersystem crossing. Emission: fluorescence and phosphorescence. Excited state applications.

2nd Block (7.5 hours): Quantum Chemical Methods in Photochemistry

1. Multiconfigurational methods: CASSCF/CASPT2 [Javier Segarra]. Single vs Multiconfigurational Methods. CASSCF and RASSCF. Active space selection. Single vs. state-averaged calculations. Introducing dynamic electron correlation: the CASPT2 method. Basis sets considerations. Intruder states: the level-shift approach. Multistate treatments to CASPT2. Reducing cost in CASPT2 simulations: the FNO-CASPT2 method.
2. Single-reference methods: Time-dependent density functional theory (TD-DFT) [Basile Curchod]. Introduction to Density Functional Theory (DFT). Local density (LDA) and generalised gradient (GGA) approximations. Linear response theory: TD-DFT. The Tamm-Dancoff approximation. Introduction to Jacob’s ladder of density functional approximations: LDA, GGA, Long-range corrected, hybrid and double-hybrid density functionals.  

3rd Block (12 hours): Dynamics in Photochemistry

1. Semiclassical excited state molecular dynamics [Basile Curchod]. Born-Oppenheimer and Ehrenfest dynamics. Nonadiabatic dynamics, Tully's surface hopping. Simulation of experimental observables connecting theory to experiment (time-resolved ultrafast spectroscopy and scattering methods, photolysis quantities, …).
2. Wave packet dynamics [Roger Bello]. Wave Packet propagations and mixed quantum classical dynamics. Time-evolution operator, propagation. Relaxation method, filtering method. Interaction with an electric field. Correlation functions, spectra and eigenfunctions. Pump-probe spectroscopy and control. 

Roundtable discussion (3 hours). Course overview: the photophysics of acrolein. Analysis of reference case studies: the cyclobutanone challenge. Known issues and cautionary tales for electronic structure methods in the excited state. Predicting the future of the field: what the next big discovery will be. Q&A.