The theoretical study of molecular excited states is a topic of growing interest due to its potential applications in many areas. The development of faster computers and new methodologies has allowed to study increasingly large systems and also to broaden the traditionally static perspective of these studies, tackling the time evolution of their excited states. This is an area of interest for many possible PhD or master students working not only in theory but also in experimental photochemistry or photophysics. In our experience, of more than 10 years teaching this subject at master or doctorate level, this subject requires combining theory and practice for the students to fully understand the concepts and methods.
Excited state modelling is probably the area of quantum chemistry that requires more training. These calculations can almost never be run as a "black box". In fact these calculations require the detailed selection of configurations and the careful analysis of their convergence. Thus, practical exercises are crucial to have an in depth insight into the methodology. For this reason, we believe that this topic perfectly suits the proposed structure of a course with an equal distribution of theory and practice.
The tutorial we propose on "Molecular Excited States" will be part of the European Master in Theoretical Chemistry and Computational Modelling (EMTCCM, see details at www.emtcccm.org) for first year Spanish Students, but this course is intended to be open to other participants not involved in the master. Our goal is to offer our teaching experience on this subject not only to the students doing the EMTCCM master in Spain, but also to other European master or doctorate students, favoring the reinforcement of the contacts with other masters and European initiatives.

The level of the course corresponds to master or doctorate students in the areas of physics and chemistry. For Spanish students of the EMTCCM master, this course will be a part of an optional subject. The tutorial will be organized for a maximum number of 40 students, from which 15 are expected to belong to the EMTCCM master. We have previous experience in the organization of similar schools in ZCAM in June 2011 and June 2012, sponsored by the master and the COST action CMT0702. To give an idea of the potential interest of this course 41 students from 12 different European countries attended the tutorial in 2011, while 24 students from 10 different countries were registered in 2012.

The course will be organized in 10 theoretical lectures (2 sessions of 2 hours per day) in the mornings and 5 practical sessions of 4 hours in the evenings (a total of 10 half days). In the practical sessions the stress will be given to applying the concepts seen in the theory and their application to real cases. Different programs, mainly Gaussian, Molcas and Octopus, will be used in the practical sessions, but the use of one or other is not crucial. Instead, the emphasis will be given to the interpretation of the results and the physics or chemistry behind the results. We do not intend the course to be a tutorial of a specific program.

Theoretical lectures

Lectures 1 and 2
Basic Concepts in Modern Molecular Photochemistry I and II.
Photophysics (The quantum nature of matter and light: Electromagnetic radiation, the Born-Oppenheimer approximation, the harmonic and anharmonic oscillator, electronic and vibronic states. Light absorption: the Lambert-Beer Law, electronic transitions in polyatomic molecules, probability of transitions, selection rules, the Franck-Condon Principle. Deactivation of excited states: Radiative and radiationless transitions, Excited state lifetimes). Photochemical reactivity (State correlation diagrams, stationary points, funnels: conical intersections, minimum energy paths).

Lectures 3 and 4
Quantum Chemistry Calculations of Excited States: Multiconfigurational Methods I and II.
Electron correlation in molecules. Electronic Structure methods for excited states. Monoconfigurational vs. multiconfigurational methods. CASSCF and RASSCF methods. Choice of the active space. Single vs. state-average calculations. Basis sets considerations. Introducing dynamical correlation: the CASPT2 method. CASPT2 problems and solutions: intruder states, avoided crossings and valence-Rydberg mixing. Examples. The level shift technique and Multistate-CASPT2.

Lectures 5 and 6
Quantum Chemistry Calculations of Excited States: TD-DFT Methods I and II.
DFT, Runge-Gross theorems, linear response TDDFT, propagation of the electronic density. Spectra calculation, approximation of xc-functionals, Examples.

Lectures 7 and 8
Dynamical Calculations: Wave Packet propagations I and II.
Time-evolution operator, Propagation, the relaxation method, the filtering method. Interaction with an electric field. Correlation functions, spectra and eigenfunctions. Diabatic and adiabatic representations. Pump-probe spectroscopy and control.

Lectures 9 and 10
TD-DFT for ultrafast dynamics I and II.
Ab initio molecular dynamics: Born-Oppenheimer and Ehrenfest dynamics. Nonadiabatic dynamics, Tully's surface hopping. Examples of nonadiabatic ab initio molecular dynamics. Addition of environmental effects: Electromagnetic fields and solvents.

Practical sessions

Practical session 1
Absorption electronic spectra calculations: CASSCF/RASSCF and CASPT2/RASPT2 (single vs. state average calculations, symmetry). Oscillator strengths. Excited state optimizations.

Practical session 2
Minimum energy path calculations. Crossings. Degeneracy points vs. Conical intersection optimizations.

Practical session 3
Wave-packet propagations.

Practical session 4
TD-DFT excited state dynamics simulations.

Practical session 5
Semiclassical dynamics simulations.