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 how they link with experimentally (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 propagate the (quantum and semi-classical) nuclear dynamics relevant for a given photophysical or photochemical process.

The techniques introduced in the school 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 and charge transfer 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.

Beyond the excited state, 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 for their study.

At the end of the school, the students will be able to discern which of the different methodologies covered may be appropriate for their research questions, and to apply them successfully to various problems related to photophysical and photochemical processes in molecular systems, including their own research portfolios.

Target audience

The school is well suited for MSc and PhD in the first years in Theoretical and Computatioanl Chemistry. It is also open to postgraduate students in other areas such as atomic and molecular physics as well as to more experienced (PhD, postdocs or early-career) researchers initiating in these types of computations.

Basic quantum chemistry knowledge is required to attend the school since we do provide introductory lessons in photochemistry and spectroscopy (see section 1.2; 1st block). In particular, basic knowledge of Hartree-Fock theory, one-electron basis sets, Configuration Interaction theory and the Born-Oppenheimer approximation is strongly desirable, even if some of these concepts may be reviewed throughout the different lessons.

Goals

The overarching goal of the school is to provide students with the necessary tools and knowledge to understand how to perform excited state simulations, including potential energy surface characterisation, spectroscopic harmonic models and non-adiabatic molecular dynamics simulations, for studying processes triggered upon light absorption in a molecular system. 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 expanded to include their time-dependence in 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. [section 1.2, 1st block]

2    Perform multiconfigurational (CASSCF/CASPT2) and LR-TDDFT calculations for excited states: simulation of vibrationally resolved electronic absorption spectra and characterisation of potential energy surfaces. [section 1.2, 2nd block]

3    Set up and run dynamics simulations: pump-probe spectroscopy and non-adiabatic dynamics.  [section 1.2, 3rd block]

4    Get acquainted with using several commercial and non-commercial well-known computational packages and codes (OpenMolcas, 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 (section 1.2), 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, see section 1.2) are devised to provide a solid theoretical background, which is then applied during 5 workshops (section 1.3) where students perform simulations under the instructors’ guidance.

Scientific Content

The school is organised in 11 lectures and 5 hands-on workshops to take place in a large seminar room. Lectures are 1.5 hours-long, and workshops last 3 hours, even though they have been split in 2 1.5-hour sessions to allow for flexilibity and for a short resting period. The materials are roughly 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 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.

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 (10.5 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. Theorems of TDDFT. Linear-response TDDFT. Casida equation and Tamm-Dancoff approximation. Introduction to Jacob’s ladder of density functional approximations: LDA, GGA, Long-range corrected, hybrid and double-hybrid density functionals. Examples.

3rd Block (12 hours): Dynamics in Photochemistry

1.    Mixed quantum/classical excited state molecular dynamics [Basile Curchod]. Time-dependent Schrödinger equation for a molecule. Full and ab initio multiple spawning. Mixed quantum/classical methods: Ehrenfest dynamics and trajectory surface hopping. Initial conditions. Simulation of experimental observables connecting theory to experiment (time-resolved ultrafast spectroscopy and scattering methods, photolysis quantities, …).

2.    Wave packet dynamics [Stefano Cavaletto]. Wave Packet propagations. Time-evolution operator, propagation. Relaxation and filtering methods. Interaction with an electric field. Correlation functions, spectra and eigenfunctions. Pump-probe spectroscopy and control. Alternative spectroscopic observables to monitor photochemical processes: from standard approaches to observing conical intersections in real time.