Advanced spectroscopic techniques have given us detailed pictures of molecular structure and properties, and served as the driving force for the development of new theories and approximations for quantum dynamics. Novel techniques have enabled the study of a large variety of compounds, ranging from small molecules to metal complexes, organometallic compounds, and biorelevant ions. Yet, at the moment, there is no theoretical method capable of exactly reproducing spectroscopic experimental results fully from first principles; each method makes a more or less severe approximation to the Schrödinger equation.¹ It is of fundamental importance to understand if and how approximated theory can still meet experiment.

Infrared (IR) and rotational spectroscopies provide traditional approaches to study molecular geometries. The field is expanding quickly and these traditional methods are being implemented into an apparatus of different spectroscopic techniques. Since free-electron laser (FEL) user facilities became available, optical spectroscopy has been coupled to FEL and mass spectrometry, as in the Infrared Multiphoton Dissociation (IRMPD) spectroscopy.^2,3 Special chemical physical conditions can be set up for spectroscopic experiments,⁴ as in the case of helium nanodroplet isolation infrared spectroscopy,⁵ which is able to investigate the structure of individual molecules at their ground rovibrational state, interactions within molecular clusters, and supramolecular aggregation at 0.37 K. Theoretical simulations can, in principle, reproduce all such experiments.^6-12 However, limitations exist due to the imperfect accuracy of the potential energy surface and quantum dynamics; only an experimental validation can  provide the necessary assessment.

Vibrationally resolved electronic spectra, while typically less resolved due to broadening,¹³ pose other challenges, including the necessity to describe excited electronic states, normal-mode displacement, distortion, and rotation (Duschinsky effect). A traditional way for computing vibronic spectra is the harmonic method.¹⁴ Many research groups nowadays account for the anharmonicity with vibrational perturbation theory^15,16 or with semiclassical trajectory-based approaches combined with on-the-fly ab initio evaluation of the potential energy surface.^17-20 As of recently, temperature effects²¹ and non-Condon effects²² can be easily included in these calculations. Other participants of the workshop made important contributions to the treatment of solvent effects on condensed-phase spectra.^23-25

Time-resolved spectroscopy has become a hot topic ever since the Nobel prize in chemistry was awarded to Zewail. While pump-probe spectroscopies of different flavors are becoming almost routine, more recently, 2D spectroscopies interrogating both nuclear²⁶ and electronic motion have come to the lime-light. Anharmonicities as well as the coupling between vibrational modes can be monitored, whereas linear spectroscopies do not easily reveal microscopic details of the underlying processes in the condensed phase. The fifth-order two-dimensional Raman spectroscopy is a tool for identifying certain modes in photophysical processes.²⁷ While theoretical simulations of two-dimensional vibrational spectra often employ classical molecular dynamics, recent experiments employing hybrid two-dimensional Raman-terahertz spectroscopy identified strong nuclear quantum effects in hydrogen-bonding liquids, e.g., in liquid water.²⁸ In the visible part of the spectrum, one of the most intensely studied systems is the Fenna–Matthews–Olson complex that plays a major role in the light harvesting process²⁹; 2D electronic spectroscopy of this system attempts to explain whether the highly efficient excitation transport is dominantly of quantum nature.³⁰