## Introduction

Two-dimensional (2D) Fourier transform (FT) nuclear magnetic resonance (NMR) spectroscopic technique was introduced in the late 70s by Ernst,[1] revolutionizing the field of structural biology. In the last four decades, 2D-NMR has been source of inspiration for the development of other multidimensional spectroscopic techniques. The 2D-FT spectroscopy has been extended to the optical frequency domain using ultrashort light pulses,[2, 3] with first applications in the infrared (IR) spectral range, resonant with vibrational transitions.[4] Today, 2DIR is a mature spectroscopic technique that provided transformative insights into structure and dynamics of complex molecules, liquids, surfaces, and proteins by direct mapping of vibrational couplings.[2, 5-9] Recent advances in ultrafast optical techniques[10, 11] allowed for the extension of 2D spectroscopy to the visible range, targeting electronic transitions in such frequency domain. In the past decade, applications of 2D electronic spectroscopy (2DES) in the visible yielded fundamental insights into energy-transfer processes in photosynthetic systems.[12-15] Extension of 2DES to the UV domain (2DUV) is extremely attractive, as many biomolecules display strong absorption bands in the UV; however, it has been so far hampered by technical difficulties, including attainment of interferometric-phase stability and sufficient laser bandwidth. After recent progresses,[16, 17] a limited number of 2DUV experiments have been reported in the last two years,[18-20] investigating electronic excitations in DNA nucleobases[18, 19] and chemical reaction dynamics.[20]

By spreading the information content of the nonlinear signal on two frequency axes, 2DES (UV or visible) provides a wealth of novel information on molecular structure and dynamics with respect to the signal collected in 1D pump-probe experiments. However, the interpretation of 2D electronic spectra is challenging and theoretical methods necessary to interpret experimental spectra and disentangle the information contained in the nonlinear optical response of the sample. In particular, theoretical methods based on exciton models (EMs) have been used to interpret 2DIR spectra[5] and 2DES spectra in the visible.[5, 12, 21] In such context, the development of computational strategies for simulations of 2DES spectra based on accurate characterization of the electronic structure of multichromophoric systems is crucial. *Ab initio* quatum chemistry methods allow for quatitative description of electronic energy levels in multichromophoric systems, going beyond approximate EMs. Time-dependent density functional theory and molecular dynamics (MD) have been used to simulate 2DUV spectra of amide and aromatic side chains models, providing a crude approximation of the coherent signals in which double-excitation states and environmental effects have been neglected.[22] State-of-the-art wavefunction methods, such as complete active space self-consistent field (CASSCF) and second-order multireference perturbation theory (CASPT2) techniques, allow for determination of single- and double- excitation states with high accuracy and reasonable computational cost. Accurate simulations of 2DES spectra requires inclusion of environmental effects (solvent, protein embedding, etc.) and quatitative reproduction of the signal broadening due to thermal fluctuations of the multichromophoric system. Thus, advanced wavefunction methods have to be used in conjunction with a hybrid quatum mechanics/molecular mechanics (QM/MM) scheme for a realistic description of the multichromophoric system environment. Signal broadening and linewidths can be estimated by sampling the configurational space with MD techniques.

In this perspective, we show how first-principle simulations of 2DUV spectra of an oligopeptide containing two interacting aromatic side chains can be performed using state-of-the-art wavefunction methods within a hybrid QM/MM scheme. Only static environmental effects have been considered by selecting a representative configuration of the peptidic system, disregarding the effects of thermal fluctuations on signal broadening and linewidths. The results serve as proof of concept for extension of this methodology to larger proteic systems with inclusion of dynamical environmental effects and provide the first reported *ab initio* simulations of 2DUV spectra that include two-excitation states and static environmental effects.