The fact that molecules show characteristic vibrations around their most stable structure is utilized for instance in infrared (IR) spectroscopy. Such IR radiation leads mainly to localized vibrations within certain structural features (functional groups), which are used to identify present functional groups or the measured molecule itself. Nowadays, accurate vibrational spectra can also be obtained for the terahertz (THz)/far-IR region of the electromagnetic spectrum. In this frequency range, one observes characteristic collective, delocalized intermolecular modes. Such spectra can for instance be used for molecular crystals to distinguish between different crystal-packing arrangements of the same molecule (polymorphs) in a non-destructive way. Therefore, THz spectra are an invaluable tool for the design and production of pharmaceuticals or the detection of drugs and explosives in security screenings. Knowledge about polymorphs is also important for society since different polymorphs of the same pharmaceutical can exhibit quite diverse drug efficacies or bioavailabilities.
Due to the complex nature of such THz spectra, insights from accurate quantum-mechanical simulations are needed for the interpretation of specific spectra and for getting a better understanding of this important frequency region in general. However, an accurate theoretical description of such intermolecular modes faces several challenges. First, the gold-standard method of quantum chemistry - CCSD(T) – cannot directly be applied to periodic systems without substantial approximations. Hence, density functional theory (DFT) has become the method of choice for molecular crystals. But even there, high-level calculations utilizing hybrid density functionals are very often already prohibitively expensive for relevant molecular crystals. Next, due to the computational complexity, the calculation of periodic vibrational spectra is mainly limited to the simplest approximations – the harmonic or the quasi-harmonic approximation. Therein, all vibrations are described independent of each other and modeled by a simple parabola and in the quasi-harmonic case the thermal expansion of the crystal is approximated by performing several harmonic calculations at difference cell volumes. However, an accurate description of THz spectra would require more sophisticated anharmonic approaches. While efforts are being made to utilize molecular dynamics approaches and vibrational self-consistent field methods to describe anharmonicities in THz spectra, we are working towards achieving this by utilizing second-order vibrational perturbation theory (VPT2) in combination with quantum-mechanical embedding methods. This means that the periodic system is treated at the much cheaper harmonic level while anharmonicities are calculated for single molecules and molecular dimers, which are subsequently incorporated into the periodic system.
Therefore, the main objectives of this project are the assessment of the accuracy of VPT2 for intermolecular vibrations and the development of a corresponding embedding approach up to the calculation of anharmonic vibrational properties for molecular crystals.
