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Publication# Efficient ab initio semiclassical dynamics for linear and nonlinear electronic spectroscopy

Résumé

Molecular spectroscopy is an essential experimental technique in both fundamental physical sciences and applied research. For example, electronic spectroscopy, in which light induces a change in the electronic state of a molecule, is a powerful tool for studying light-matter interactions appearing in solar energy conversion and light-emitting devices. To explain experimental findings and compare them with theoretical predictions, scientists often compute properties that can only be inferred indirectly, rather than simulating the observed spectroscopic signals. This is partly due to challenges associated with the simulation of electronic spectra, which requires both an accurate description of the electronic structure and the quantum-dynamical treatment of the motion of atomic nuclei. As the exact methods to solve the underlying quantum-mechanical problem scale exponentially with the number of atoms, this task must be performed approximately for all but the smallest molecules.

In this thesis, we develop a set of methods to systematically study the effects of different approximations on the computed spectra. As our starting point, we consider a semiclassical method called the thawed Gaussian approximation, which has resurfaced in recent years as an efficient and robust alternative to simple but crude models or highly accurate but costly quantum dynamics methods. First, we present several practical improvements of the method, such as generalization to non-Condon effects or the efficient single-Hessian version, which enable a broader set of molecules to be studied. Second, we introduce a more fundamental modification of the methods - the inclusion of non-zero temperature effects. The underlying theory, which is inspired by the concept of so-called thermo-field dynamics, is exact and applies to any quantum dynamics method. Remarkably, within the thawed Gaussian approximation, the inclusion of non-zero temperature comes at nearly no additional computational cost.

These methods, developed originally for steady-state linear spectra, are then employed to compute state-of-the-art, time-resolved spectra, which are typically measured with ultrashort laser pulses. More precisely, we study how the anharmonicity of the potential energy surfaces and mode-mode (Duschinsky) couplings affect pump-probe and two-dimensional electronic spectra. This approach, based on the thawed Gaussian wavepacket propagation, is the first method that can exactly evaluate the nonlinear electronic spectra of many-dimensional, shifted, distorted, and Duschinsky-rotated harmonic potentials. As in the case of linear absorption and emission spectra, we again use the concept of thermo-field dynamics to include non-zero temperature effects in the simulation of two-dimensional electronic spectra. The resulting wavepacket picture of two-dimensional spectroscopy at arbitrary temperature could strongly impact how we interpret and simulate multidimensional spectra in the future.

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The function of biologically active molecules depends both on their structure and on their conformational dynamics. In solution, intramolecular interaction with the solvent will influence different biological processes, i.e. protein folding. However secondary structure (helices, sheets) is heavily influenced by intramolecular forces and hence it is important to isolate biological molecules in order to study their intrinsic behavior. Moreover, gas phase studies on biomolecules provide critical information that can serve as benchmarks to test the accuracy of theoretical predictions. The main focus of this thesis is the investigation of the potential energy surfaces of biomolecules in the gas phase. Biomolecular ions are produced in the gas phase via nano-electrospray, mass-selected and guided into a cold, 22-pole ion trap where they are cooled via collisions with cold helium. A variety of double-resonance techniques based on photofragmentation detection are then applied to obtain information on the molecule stable conformations, the potential barriers separating stable conformations and their connectivity. We applied these techniques on molecules of increasing size, starting with protonated phenylalanine and proceeding to the 7amino acid peptides, Ac-Phe-(Ala)5-LysH+ and the 12-residue peptide Ac-Phe-(Ala)3-(Gly)4-(Ala)3-LysH +. As a first step, electronic spectra and conformation-specific IR-UV double resonance spectra are measured. These measurements, in combination with DFT calculations, allow the assignment of two stable conformers in the case of the protonated phenylalanine and four in the case of the seven residue peptide. In the second part of this work we focused on the conformational isomerization of these molecules by performing infrared and ultraviolet hole-filling spectroscopy in the ion trap. We demonstrated that we can induce isomerization between stable conformers of each molecule via vibrational excitation. After energy dissipation, the excited molecules are redistributed among the initially identified conformers, but no new minima were detected. In the last part of this thesis, the fractional populations and the isomerization quantum yields are determined through infrared induced population transfer spectroscopy. Protonated phenylalanine reveals conformational selectivity in its isomerization while the relaxation of the infrared excitation leads to the equilibrium distribution in the case of the 12-residue glycine-containing peptide. The steps that occur during the energy dissipation are discussed in this thesis.

Tomislav Begusic, Julien Roulet, Jiri Vanicek

We present a methodology for computing vibrationally and time-resolved pump-probe spectra, which takes into account all vibrational degrees of freedom and is based on the combination of the thawed Gaussian approximation with on-the-fly ab initio evaluation of the electronic structure. The method is applied to the phenyl radical and compared with two more approximate approaches based on the global harmonic approximation the global harmonic method expands both the ground- and excited-state potential energy surfaces to the second order about the corresponding minima, while the combined global harmonic/on-the-fly method retains the on-the-fly scheme for the excited-state wavepacket propagation. We also compare the spectra by considering their means and widths, and show analytically how these measures are related to the properties of the semiclassical wavepacket. We find that the combined approach is better than the global harmonic one in describing the vibrational structure, while the global harmonic approximation estimates better the overall means and widths of the spectra due to a partial cancellation of errors. Although the full-dimensional on-the-fly ab initio result seems to reflect the dynamics of only one mode, we show, by performing exact quantum calculations, that this simple structure cannot be recovered using a one-dimensional model. Yet, the agreement between the quantum and semiclassical spectra in this simple, but anharmonic model lends additional support for the full-dimensional ab initio thawed Gaussian calculation of the phenyl radical spectra. We conclude that the thawed Gaussian approximation provides a viable alternative to the expensive or unfeasible exact quantum calculations in cases, where low-dimensional models are not sufficiently accurate to represent the full system. (C) 2018 Author(s).

The development of multinary nitrides materials has revolutionised the hard coatings industry over the last 20 years. Especially important materials systems in this matter have been TiAlN and CrAlN which shows higher hardness, better oxidation resistance and can perform at higher temperatures as compared to TiN. When synthesised through physical vapour deposition techniques these system form cubic rock salt structured Ti1-xAlxN and Cr1-xAlxN solid solutions as a metastable phase over a large part of the concentration range. One of the main objectives during the optimisation of the coatings has been to increase the amount of Al in the coating while still keeping the rock salt structure, avoiding phase separation and the formation of hexagonal wurtzite AlN. However, in Al-rich TiAlN coatings it was found that isostructural decomposition within the cubic phase was in fact beneficial for the coatings performance at working temperatures just below 1000 °C. The reason was that the formation of strained coherent c-AlN domains within the grains initiated a age-hardening of the coating. In the CrAlN coatings it is possible to solve a larger amount of Al in the cubic phase. Possibly connected to this fact is that no isostructural decomposition and in principle no age hardening has been observed in rock salt structured Cr1-xAlxN. Although large series of experimental investigations have been performed on these systems, no systematic theoretical study has yet been undertaken. This theoretical work is an attempt by means of first-principles calculations together with thermodynamics considerations within the framework of alloy theory, to close or decrease the knowledge gap between experimental observations of cutting performance of various coatings and the fundamental quantum mechanical and thermodynamics processes that governs it. We first consider the structural properties of the treated mixed nitride systems. The concept of atomic misfit or volume difference, which is well known in the community is studied and the physics that leads to a positive deviation from Vegard's rule is revealed. Then the TiAlN and CrAlN systems are studied in detail. A clear connection between the development of the electronic structure with composition and the mixing enthalpy of the alloys, and thus the tendency for decomposition, is found for TiAlN. The importance of magnetic effects on the thermodynamics of mixing in CrAlN is established leading to a qualitative lower tendency for decomposition. Since the nitrogen composition can deviate substantially from perfect stoichiometry in these systems, a study of the influence of nitrogen vacancies on the decomposition pattern of TiAlN in the cubic phase is performed. The results imply that a presence of nitrogen sub-stoichiometry in Al-rich TiAlN will enhance the tendency for isostructural decomposition. The achieved results including those for the systems ScAlN and HfAlN are compared and discussed especially by considering volume misfit and electronic bandstructure effects as driving forces for coherent and incoherent decomposition.