Periodic Reporting for period 1 - VibMolCryst (Vibrational Spectroscopy for Molecular Crystals via Quantum-Mechanical Embedding Methods)
Reporting period: 2020-07-01 to 2022-06-30
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.
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.
First, a comparably large benchmark set containing 30 representative molecular dimers was created and benchmark CCSD(T) calculations with a large basis set were performed for harmonic and Morse oscillators, and different variants of VPT2. We found that VPT2 yields very good results for many vibrational modes compared to experimental data, by far surpassing the accuracy of the harmonic approximation and Morse oscillators. However, within VPT2 low-frequency modes with large-amplitude motions – basically resembling hindered rotors – are highly problematic. Therefore, we developed an approach to approximately treat them with a simple one-dimensional hindered rotor model, which lead to a very good agreement with available reference data. Next, we tested a variety of different density functional approximations against the CCSD(T) VPT2 results using the created benchmark set. We found that the typically used functionals for molecular crystals applying the generalized-gradient approximation (GGA) show a large error in harmonic frequencies compared to CCSD(T), but more expensive hybrid functionals can significantly improve the description.
Furthermore, we extended a quantum-mechanical embedding approach from available first derivatives of the energy to vibrational properties and also trimer interactions for energetics. The performance of this embedding approach was then tested for 23 representative molecular crystals. The implemented embedding method was able to reproduce harmonic vibrational frequencies obtained from explicit periodic hybrid functional results within a narrow wave number range by only utilizing a much cheaper GGA functional for the periodic system and up to dimer corrections with the hybrid functional. This is a crucial step, since we need at least the accuracy of hybrid functionals for harmonic calculations. This development will then enable the incorporation of anharmonic effects via VPT2 calculations for monomers and relevant dimers within the molecular crystal. In addition, we already utilized the above-mentioned embedding approach in the most recent blind test for organic crystal structure prediction methods.
This work has resulted so far in two submitted papers, one manuscript close to submission, one open-source software package, two data sets, and was presented at six international conferences by oral presentations and posters.
Furthermore, we extended a quantum-mechanical embedding approach from available first derivatives of the energy to vibrational properties and also trimer interactions for energetics. The performance of this embedding approach was then tested for 23 representative molecular crystals. The implemented embedding method was able to reproduce harmonic vibrational frequencies obtained from explicit periodic hybrid functional results within a narrow wave number range by only utilizing a much cheaper GGA functional for the periodic system and up to dimer corrections with the hybrid functional. This is a crucial step, since we need at least the accuracy of hybrid functionals for harmonic calculations. This development will then enable the incorporation of anharmonic effects via VPT2 calculations for monomers and relevant dimers within the molecular crystal. In addition, we already utilized the above-mentioned embedding approach in the most recent blind test for organic crystal structure prediction methods.
This work has resulted so far in two submitted papers, one manuscript close to submission, one open-source software package, two data sets, and was presented at six international conferences by oral presentations and posters.
We have introduced a new, large benchmark set for vibrational frequencies of molecular dimers with high-level CCSD(T) results available for harmonic frequencies as well as VPT2 frequencies. This enables a rigorous testing of the accuracy of vibrational frequencies for dimers using existing methods or during the development of novel methods, since CCSD(T) is considered the gold standard in chemistry. Since also all calculated force constants are openly available, this might also aid the development of better approaches for dealing with large-amplitude motions or the development of new machine-learning models.
Furthermore, we have developed and newly implemented a multimer embedding approach for molecular crystals up to vibrational properties. The resulting source code is openly available. This methodology already allows the usage of hybrid functionals for vibrational properties of molecular crystals at a much lower cost compared to the canonical method. Since vibrational frequencies are also crucial for the calculation of free energies, this methodology is expected to increase the accuracy of calculated relative stabilities, which would be very beneficial for the field of crystal structure prediction. In fact, we have already participated in the most recent crystal structure prediction blind test organized by the Cambridge Crystallographic Data Centre using this methodology, which will bring it to the attention of the community. All these developments will enable the incorporation of anharmonic effects – calculated for monomers and relevant dimers – into the periodic calculation of molecular crystals. Such calculations are still affordable for relevant molecular crystals and we expect that they will significantly facilitate peak assignments and the interpretation of low-frequency THz spectra, used for instance for drug development or the detection of explosives.
Furthermore, we have developed and newly implemented a multimer embedding approach for molecular crystals up to vibrational properties. The resulting source code is openly available. This methodology already allows the usage of hybrid functionals for vibrational properties of molecular crystals at a much lower cost compared to the canonical method. Since vibrational frequencies are also crucial for the calculation of free energies, this methodology is expected to increase the accuracy of calculated relative stabilities, which would be very beneficial for the field of crystal structure prediction. In fact, we have already participated in the most recent crystal structure prediction blind test organized by the Cambridge Crystallographic Data Centre using this methodology, which will bring it to the attention of the community. All these developments will enable the incorporation of anharmonic effects – calculated for monomers and relevant dimers – into the periodic calculation of molecular crystals. Such calculations are still affordable for relevant molecular crystals and we expect that they will significantly facilitate peak assignments and the interpretation of low-frequency THz spectra, used for instance for drug development or the detection of explosives.