Ab initio studies on photorelaxation

This work addresses relaxation mechanisms of photoexcited organic molecules of small and medium size, up to 62 atoms. For most systems it is investigated theoretically, how modifications, often in the form of substituents, influence the decay processes. The research in large parts is done in close collaboration with groups providing experimental data, which allows to formulate robust hypotheses and models. Four systems are discussed in this context. We find the formation of the dewar lesion in deoxyribonucleic acid (DNA) to only occur, when the nucleobase is embedded in the DNA backbone, which sterically hinders accessing alternative channels. Substituting hydroxy groups at certain points of thioindigo is shown to open up an efficient deactivation channel via excited state intramolecular proton transfer, and greatly enhance the photostability of the molecule. By substituting electron donating groups to the stilbene moiety of the hemithioindigo photoswitch and correlating their effect to their Hammett parameters, the isomerization speed of hemithioindigo is optimized. And lastly, when adding an aldehyde group to furan, an additional pathway is found for its derivatives furfural and β-furfural. Their relaxation is slowed down regardless. The effects on the excited state potential energy surfaces are described as general means, by which the surfaces can be influenced, and likely can be translated to other molecules as well. This eventually allows to predict properties and tailor molecules to yield desired behavior. In this context, for example for furan, furfural and β-furfural the structural implications of the aldehyde substituent on one conical intersection are deducted from the extended two-electron two-orbital model prior to any calculations or experiments. Alongside the system specific investigations, an interface for the on-the-fly dynamics package NewtonX to the quantum chemistry package Molpro was programmed. Non-adiabatic semiclassical on-the-fly dynamics are a powerful tool to simulate complete relaxation processes without constraints in the dimensionality. For the interface, which in its primary setup uses complete active space self consistent field theory calculations, a number of features has been implemented. Most notably, it enables non-adiabtatic dynamics on complete active space perturbation and ONIOM level of theory

Ultracold Molecules: The Effect of Electromagnetic Fields

There is great interest within the physics and chemistry communities in the properties of ultracold molecules. Electromagnetic fields can be used to create, trap, and modify the collisional dynamics of ultracold molecules, and thus the properties of ultracold molecules in electromagnetic fields is of growing importance. This thesis examines some of the effects of externally applied electromagnetic fields on ultracold molecules. Initially, magnetic Feshbach resonances in combined electric and magnetic fields are examined in the collisions of He($^1S$)+SO($^3\Sigma^-$). Through detailed quantum scattering calculations, it is then shown that the sympathetic cooling of NH($^3\Sigma^-$) molecules with Mg atoms has a good prospect of success, a first for a neutral molecular system. Detailed quantum scattering calculations are performed for a wide range of collision energies and magnetic field strengths and it is found that the ratio of elastic to inelastic collisions is large for temperatures below 10 mK, and increases as the collision energy and magnetic field strength decrease. The near threshold collision properties of Mg+NH have been examined using a multichannel quantum defect theory approach. A new type of conical intersection, that is a function of applied electromagnetic fields only, is also demonstrated. For states of opposite parity, brought into degeneracy with a magnetic field, the degeneracy can be resolved by the addition of an electric field, forming a conical intersection. A suitable arrangement of fields could thus be used to create a conical intersection in laboratory coordinates within an ultracold trapped gas. For a Bose-Einstein condensate, in the mean-field approximation, the resultant geometric phase effect induces stable states of persistent superfluid flow that are characterized by half-integer quantized angular momentum

Fock-Goncharov dual cluster varieties and Gross-Siebert mirrors

Cluster varieties come in pairs: for any $\mathcal{X}$ cluster variety there is an associated Fock-Goncharov dual $\mathcal{A}$ cluster variety. On the other hand, in the context of mirror symmetry, associated with any log Calabi-Yau variety is its mirror dual, which can be constructed using the enumerative geometry of rational curves in the framework of the Gross-Siebert program. In this paper we bridge the theory of cluster varieties with the algebro-geometric framework of Gross-Siebert mirror symmetry. Particularly, we show that the mirror to the $\mathcal{X}$ cluster variety is a degeneration of the Fock-Goncharov dual $\mathcal{A}$ cluster variety and vice versa. To do this, we investigate how the cluster scattering diagram of Gross-Hacking-Keel-Kontsevich compares with the canonical scattering diagram defined by Gross-Siebert to construct mirror duals in arbitrary dimensions. Consequently, we derive an enumerative interpretation of the cluster scattering diagram. Along the way, we prove the Frobenius structure conjecture for a class of log Calabi-Yau varieties obtained as blow-ups of toric varieties.Comment: 51 pages, revised version published in Journal f\"ur die reine und angewandte Mathematik (Crelles Journal

Photo initiated molecular processes elucidated by quantum chemistry and theoretical spectroscopy

Processes initiated by the interaction between light and matter are a fundamental step in various chemical, physical and biological phenomena. The present work investigates the photoinduced processes in artificial molecular machines and small molecules with the help of quantum chemical calculations. The research was performed in close collaboration with experimentalists, allowing an in-depth look at the underlying mechanisms of these ultrafast processes. The first part addresses the relaxation pathways after photoexcitation of the photoswitch hemithioindigo (HTI) and the artificial molecular motors, motor-1 and motor-2. The pho- tochromic compound HTI is a novel photoswitch capable of performing efficient isomerization upon irradiation with non-damaging visible light. Based on time-resolved absorption and emis- sion experiments and supported by high level quantum chemical calculations, a comprehensive reaction model for its photoisomerization, including the effects of different solvents as well as substitutions, is established. The structure of both molecular motors, motor-1 and motor-2, is based on the HTI moiety. By clever design, this switch was turned into a molecular motor, capable of unidirectional rotation. These motors are among the first light-powered molecular motors that operate under ambient and non-damaging conditions. The underlying processes for their multistep rotation was elucidated through multiscale broadband transient absorption mea- surements and quantum chemical investigations of their excited state potential energy surfaces. From these findings, pathways to improve the rotational speeds and efficiency of light-driven molecular motors in general could be developed. The second part of this work addresses the theoretical simulation of the ultrafast spec- troscopy technique known as attosecond transient absorption spectroscopy (ATAS). Attosecond pulses in the extreme ultraviolet (XUV) or X-ray region provide a powerful tool for investigating ultrafast nuclear and even electron dynamics in atoms, molecules and solids. Due to their high photon energy, they are able to create electron wave packets extremely well localized in time. This makes them an excellent choice for triggering photochemical reaction in a pump-probe scenario. Further, their broad bandwidth provides element, charge and electronic state sensitive insights by probing the inner-valence and core-level states of the excited molecules. To aid the interpretation of the experimental data and provide further insights into these complex inter- actions between light and matter, a comprehensive framework simulating XUV/X-ray transient absorption spectra is presented. Using ab initio non-adiabatic molecular dynamics (NAMD), the ultrafast processes of excited molecules after laser excitation is simulated, enabling the res- olution of both the changes in the electronic structure and the nuclear motion over time. Based on this information, the time-dependent XUV/X-ray transient absorption spectra are calculated by applying high-level multi-reference methods, namely restricted active space self-consistend field (RASSCF) and restricted active space perturbation theory (RASPT2). This framework is utilized in the two studies on the molecules vinyl bromide and trifluoroiodomethane. For both molecules the ultrafast coupled nuclear-electron dynamics after strong-field ionization could be explained in great detail

Bosonic Quantum Simulation in Circuit Quantum Electrodynamics

The development of controllable quantum machines is largely motivated by a desire to simulate quantum systems beyond the capabilities of classical computers. Investigating intrinsically multi-level model bosonic systems, using conventional quantum processors based on two-level qubits is inefficient and incurs a potentially prohibitive mapping overhead in the current near-term intermediate-scale quantum (NISQ) era. This motivates the development of hybrid quantum processors that contain multiple types of degrees of freedom, such that one can leverage an optimal one-to-one mapping between the model system and simulator. Circuit quantum electrodynamics (cQED) has emerged as a leading platform for quantum information processing owing to the immense flexibility of engineering high fidelity coherent interactions and measurements. In cQED, microwave photons act as bosonic particles confined within a nonlinear network of electromagnetic modes. Controlling these photons serves as the basis for a hardware efficient platform for simulation of naturally bosonic systems. In this thesis, we present two experiments that encapsulate this idea by simulating molecular dynamics in two different regimes of electronic-nuclear coupling: adiabatic and nonadiabatic. In the first experiment, we implement a boson sampling protocol for estimating Franck-Condon factors associated with photoelectron spectra. Importantly, we fulfill the scalability requirement by developing a novel single-shot number-resolved quantum non-demolition detector for microwave photons. In the second experiment, we develop and employ a model for simulating dissipative nonadiabatic dynamics through a conical intersection as a basis for modeling photochemical reactions. We directly observe branching of a coherent wave-packet upon passage through the conical intersection, revealing the competition between coherent evolution and dissipation in this system. The tools developed for the experiments in this thesis serve as a basis for implementing more complex bosonic simulations

Ab initio simulations of reactions occurring in molecular crystals

Although the solid state may not usually be thought of as an environment suitable for chemical reactions under mild conditions, a growing number of organic compounds are known to undergo interesting and, in many cases, practically useful chemistry in the molecular crystal phase. Of particular interest are photochemical reactions occurring in molecular crystals, which possess a number of characteristic features that make them attractive to study using the methods of theoretical chemistry. Firstly, molecular packing and steric effects strongly influence the mechanistic course of reactions in the crystal phase, which in some cases enables clean and controllable chemistry, including synthetic reactions as well as reversibly switchable isomerisations accompanied by a change of the macroscopic properties of the crystal, such as shape and colour. Secondly, in part due to their fast (subpicosecond) timescales and relatively low conversion rates (of the order of a few per cent), many of these reactions present challenges to experimental techniques, which computer simulation methods are uniquely positioned to overcome. Finally, these systems lend themselves well to simulation using a hybrid combination of two ab initio electronic structure methods, one of which is used to describe the electronic excitation of a reactive molecule while the other is applied to the surrounding bulk lattice. This thesis describes the computational modelling of two such reactions: the syn-anti photoisomerisation of 7-(2-pyridyl)indole and the reversible cis-enol⇄trans-keto photoisomerisation of N-salicylidene-2-chloroaniline. The solid-state mechanisms and rates of both reactions are computed using the TD-DFT/DFT hybrid method, in the latter case validating a previously postulated reaction mechanism. Furthermore, the thermal (ground-state) tautomerisation reaction in the photochromic and non-photochromic polymorphs of N-salicylidene-2-chloroaniline is investigated through calculations at the DFT level of theory. The results of these calculations indicate that both polymorphs are thermochromic, but tautomeric equilibrium in the non-photochromic polymorph is more sensitive to temperature than in the photochromic polymorph. Additionally, a critical assessment is presented of the accuracy of the various emphab initio methods employed throughout this work

Sequence Determinants of the Individual and Collective Behaviour of Intrinsically Disordered Proteins

Intrinsically disordered proteins and protein regions (IDPs) represent around thirty percent of the eukaryotic proteome. IDPs do not fold into a set three dimensional structure, but instead exist in an ensemble of inter-converting states. Despite being disordered, IDPs are decidedly not random; well-defined - albeit transient - local and long-range interactions give rise to an ensemble with distinct statistical biases over many length-scales. Among a variety of cellular roles, IDPs drive and modulate the formation of phase separated intracellular condensates, non-stoichiometric assemblies of protein and nucleic acid that serve many functions. In this work, we have explored how the amino acid sequence of IDPs determines their conformational behaviour, and how sequence and single chain behaviour influence their collective behaviour in the context of phase separation. In part I, in a series of studies, we used simulation, theory, and statistical analysis coupled with a wide range of experimental approaches to uncover novel rules that further explore how primary sequence and local structure influence the global and local behaviour of disordered proteins, with direct implications for protein function and evolution. We found that amino acid sidechains counteract the intrinsic collapse of the peptide backbone, priming the backbone for interaction and providing a fully reconciliatory explanation for the mechanism of action associated with the denaturants urea and GdmCl. We discovered that proline can engender a conformational buffering effect in IDPs to counteract standard electrostatic effects, and that the patterning those proline residues can be a crucial determinant of the conformational ensemble. We developed a series of tools for analysing primary sequences on a proteome wide scale and used them to discover that different organisms can have substantially different average sequence properties. Finally, we determined that for the normally folded protein NTL9, the unfolded state under folding conditions is relatively expanded but has well defined native and non-native structural preferences. In part II, we identified a novel mode of phase separation in biology, and explored how this could be tuned through sequence design. We discovered that phase separated liquids can be many orders of magnitude more dilute than simple mean-field theories would predict, and developed an analytic framework to explain and understand this phenomenon. Finally, we designed, developed and implemented a novel lattice-based simulation engine (PIMMS) to provide sequence-specific insight into the determinants of conformational behaviour and phase separation. PIMMS allows us to accurately and rapidly generate sequence-specific conformational ensembles and run simulations of hundreds of polymers with the goal of allowing us to systematically elucidate the link between primary sequence of phase separation