Extension and application of vibrationally-resolved electronic spectroscopy for the study of molecular properties

Because of the complexity of the environment and the molecular structure, experimental spectra contain rich information, which makes their analysis complicated without the proper tools. Computational spectroscopy has become an essential instrument in complement to experiments, to help separate the many contributions to the recorded signals and understand their origin. A constant conundrum of computational protocols has been finding a good balance between accuracy and feasibility. The most advanced theoretical methods can provide results comparable to state-of-the-art experiments, but they are limited to very small systems. Cheaper methods can be devised with the introduction of some degree of simplification. While this gives the possibility to treat larger and more complex structures, the built-in approximations may limit the validity of such approaches. This is the case for electronic spectroscopy, where the response of a system upon an electronic transition can be treated explicitly, by looking at its evolution with time, or statically. The latter requires some analytic description of the potential energy surfaces (PESs) corresponding to the electronic states involved in the transition(s), as well as the corresponding electronic transition moments of the properties probed by the spectroscopy. Simplifications introduced at this level have limited the so-called vibrationally-resolved electronic spectroscopy, sometimes shortened as vibronic spectroscopy to rigid molecules. Building upon previous works to extend such methodologies to semi-rigid systems, this thesis explores more complex structural deformations related to electronic transitions. In parallel, new developments have extended the existing framework built for the prediction of one-photon vibronic spectra to new spectroscopies. With the development of electronic structure calculation methods, such as timedependent density functional theory (TD-DFT), which makes it possible to simulate the PES of electronic excited states, the use of computational models and software able to simulate electronic spectra including the vibrational information has grown. At present, for the computations of vibrationally-resolved spectra, generally, at least two PESs need to be taken into account (initial and final states). For such calculations to be computationally feasible, PESs are assumed harmonic. The parabolic shape can only match a very narrow region of the real PESs, too small to cover the parts typically involved in electronic spectra. As a result, different methods of extrapolation of the final-state PES have been proposed, which can be classified as two models: the Adiabatic Model and the Vertical Model. For those two models, the connection between the initial- and final-state normal coordinates is described by the Duschinsky transformation. Currently, Adiabatic and Vertical models still face a number of challenges in the calculation of the vibronic spectra. The most prominent challenge is the mode mixing, which often leads to excessively broad band-shapes and generally occurs in flexible molecules. Using Cartesian coordinates to describe vibrations makes this problem more evident. In this situation, choosing a correct set of internal coordinates significantly reduces the couplings between the vibrational modes. This is a fundamental step to handle systems that exhibit some degree of flexibility. Indeed, the structure deformation generally affects only a handful of modes, which end up strongly shifted and cannot be described with methods reached into the harmonic-oscillator approximation. Isolating and removing these large amplitude motions (LAMs) from the root of the system becomes critical. Indeed, the removal of strongly displaced LAMs provides a more correct picture, since their actual contribution to experimental spectra is often low, but becomes overestimated within the harmonic approximation. However, discarding these modes can only be done properly if they are fully disconnected from the other modes. In practice, this is rarely true, and some mixing is observed. A careful selection of coordinates is required to minimize these couplings and construct a model that closely approximates the real system. Such calculations have been done within an existing computational tool to generate different kinds of one-photon spectra, however, considering always an isotropic average of the structures. Such techniques are commonly used in experiments, but cannot provide details for instance on the individual components of the probed molecular properties. This is possible through linear dichroism (LD), a technique that uses a preferential orientation of molecules, proteins or assemblies, generally by a deposit on a polymeric surface, which is then probed by linearly polarized light. This makes it possible to study specific components of the electric dipole transition moment of oriented compounds. Therefore, LD can probe precise information on specific directions, help detect easily and understand better subtle structural changes. Since LD spectra are obtained from the subtraction of two signals, oriented parallel and perpendicularly to the depositing surface, it bears some similarities with electric circular dichroism (ECD), sharing a higher sensitivity compared to the standard absorption spectrum. Moreover, because of the anisotropy of the signal and the specific orientation, the electronic transition moments of the electric quadrupole and magnetic dipole can also contribute to the experimental spectrum. To obtain a more accurate description of the optical properties, their inclusion needs to be considered. In a simplified picture, a typical LD experiment can be divided into two main steps. The first step involves orienting the sample within a reference plane, followed by measuring the absorbance of the oriented sample using linearly polarized electromagnetic fields. Therefore, the implementation includes some parameters to match precisely the experimental setup, such as the definition of the polarized reference plane, molecular orientation, the direction of the polarized electric field. Those features make it simple for users to reproduce the experimental conditions in their simulations. Until now, the discussion has focused on the linear response of light-sample interactions, where the resulting transition signals are typically associated with equilibrium states. However, to gain insight into the dynamics of these transitions, multiple light pulses are often employed to capture rapid processes, which falls under the realm of nonlinear spectroscopy. For example, pump-probe (PP) two-dimensional vibrational-electronic (2DVE) spectroscopy utilizes an ultrafast infrared (IR) pulse to excite vibrational modes, followed by an ultraviolet (UV) pulse to probe the coupling between the vibrational and electronic states. By controlling the delay time between the IR and UV pulses, this technique can uncover the relaxation pathways of vibrational modes, energy transfer between vibrational modes, and electron transfer mechanisms in donor-acceptor systems. Unlike linear spectroscopy, 2DVE involves multiple interactions between light and matter, making simulations particularly complex. To address these challenges, we have introduced several reasonable approximations. First, we assume that the pump and probe pulses are sufficiently separated, allowing us to apply the doorway-window model, which divides the entire process into excitation, evolution, and probing stages. Additionally, we assume a very short pump pulse duration to ensure that it excites a single vibrational state without influencing other vibrational modes. This approximation enables us to investigate efficiently the interaction between the pre-excited vibrational mode and the electronic state.