Computation of Electronic Excitation Spectra of Large Biomolecular Systems

Abstract

This thesis presents the theoretical investigation of electronic excitation spectra and nonlinear responses of large biomolecular systems (e.g., proteins or deoxyribonucleic acid fragments), with a particular focus on the simulation of (electronic) circular dichroism (CD) spectra and first hyperpolarizabilities. <br /> In the past, a fully quantum mechanical (QM) treatment of biomolecular structures for optical property calculations was computationally unfeasible. Due to their sizes and complexity, simulations on biomolecules were limited to calculations of subsystems in fragmentation approaches or with some system-specific adjustments. Modern developments regarding ultra-fast excited states calculations enable to characterize systems beyond the nowadays limit of thousand atoms. One prominent development in this regard is the extended tight-binding (xTB) based method combined with the simplified time-dependent density functional theory (sTD-DFT), including both flavors: sTDA-xTB and sTD-DFT-xTB. The applicability or transferability of these methods to systems up to several thousand atoms is by far non-trivial and therefore thoroughly investigated in this work. <br /> For this purpose, the first part of this thesis describes a comprehensive benchmarking on the sTDA-xTB method, regarding the computation of electronic excitation spectra of large biomolecules. This is the first time that relevant biomolecular systems are treated within a full QM approach for the calculation of the excited state properties. Therefore, it is especially remarkable that the computed CD spectra are in excellent agreement with the experiment. The highly efficient sTDA-xTB also enables the computation of spectra averaged along structures from molecular dynamics (MD) simulations, which are often needed to cover non-equilibrium structure and conformational effects. The investigations confirm also the all-round applicability of the sTDA-xTB method, since almost no limitation to a certain spectral range or type of chromophore is observed. <br /> The original publication of the sTDA-xTB method only provided a set of parameters for the most important elements. Some metals, naturally occurring in proteins, were missing from this set. However, such metal-containing proteins play essential roles in many biological mechanisms and are of great interest for spectroscopic studies. This parameterization gap is closed in this thesis, and the missing parameters for the 4d and 5d metals, as well as for the 4p, 5p, and 6p element blocks, are obtained. Comparisons to theory and experiment show that sTDA-xTB provides similar good results as for the elements in the original publication with an average deviation of excitation energies of 0.3-0.5 eV. <br /> For the simulation of electronic excitation spectra, reasonable three-dimensional structures are as important as the calculation of the excited states itself. Therefore, it is of particular interest to apply an accurate and efficient structure method in tandem with the excited state method. The xTB variants for geometries, frequencies, and non-covalent interactions (GFN) are ideally suited in this regard and comprehensively tested in combination with the sTDA-xTB method in this work. Just as CD spectroscopy, second-harmonic imaging microscopy (SHIM) is widely used in medical research. The underlying physical effect for this imaging technique is the second-harmonic generation phenomenon, a scattering process in which the optical frequency of incident photons is doubled. Theoretical models can access this non-linear optical (NLO) phenomenon via the first hyperpolarizability. The second part of this thesis deals with the application of the sTD-DFT-xTB method to relevant biomolecular systems, i.e., a set of tryptophan-rich oligopeptides for SHIM applications. For the first time, a structure-property analysis of the first hyperpolarizability can be conducted, because of the recent development of efficient conformational sampling and a computationally efficient implementation to evaluate first hyperpolarizabilities at the sTD-DFT level of theory. Furthermore, the comparison to commonly-used higher levels of theory shows that the sTD-DFT-xTB method is capable of providing equally reliable second-harmonic generation values at 10^3-10^5 of the higher levels computational cost. <br> In summary, for the first time a full QM treatment of the simulation of CD spectra and NLO properties of large biomolecular systems is reported. For this purpose, all parts of an efficient computational workflow are comprehensively tested and successfully elaborated. An automatic black-box approach for the calculation of optical properties of large biomolecules is desirable and the findings of this work show that xTB-based methods are excellent candidates in this regard.