Supporting Data for: Multimer Embedding for Molecular Crystals Utilizing up to Tetramer Interactions

Molecular crystals possess a highly complex crystallographic landscape which in many cases results in the experimental observation of multiple crystal structures for the same compound. Accurate results can often be obtained for such systems by employing periodic density functional theory using hybrid functionals; however, this is not always computationally feasible. One possibility to circumvent these expensive periodic calculations is the utilization of multimer embedding methods. Therein, the fully periodic crystal is described at a lower level of theory, and subsequently monomer energies, dimer interaction energies, etc. are corrected via high-level calculations. In this paper, we further extend such a multimer embedding approach by one multimer order for all investigated properties, allowing us to compute lattice energies up to the tetramer embedding level, and atomic forces, the stress tensor, and harmonic phonons up to the trimer level.We test the significance of including these higher-order multimers by embedding PBE0+MBD multimers into periodic PBE+MBD calculations utilizing the X23 benchmark set of molecular crystals and comparing the results to explicit periodic PBE0+MBD calculations. We show that tetramer interactions systematically improve the lattice energy approximation and explore multiple possibilities for multimer selection. Furthermore, we confirm that trimer interactions are crucial for the description of the stress tensor, yielding cell volumes within 1 % of those of PBE0+MBD. Subsequently, this also results in an improvement of the description of vibrational properties, giving on average gamma point frequencies within 1.3 wave numbers and vibrational free energies within 0.3 kJ/mol of the PBE0+MBD results. See the included README.md file for more details on which data is available. The related preprint can be found at https://doi.org/10.48550/arXiv.2512.16877.分子晶体具有高度复杂的晶体学构型空间，多数情形下会导致同一化合物被实验观测到多种晶体结构。对于这类体系，采用搭载杂化泛函的周期性密度泛函理论（periodic density functional theory）通常可获得精准结果，但该方法在计算层面往往并非始终可行。规避这类计算成本高昂的周期性计算的一种可行方案，是采用多聚体嵌入方法（multimer embedding methods）。该方法中，完整周期性晶体将以较低理论精度进行描述，随后通过高精度计算对单体能量、二聚体相互作用能等物理量进行校正。 本文中，我们针对所有研究的物性将该多聚体嵌入方法的聚合阶数提升了一级，由此可将晶格能量的计算推进至四聚体嵌入层级，而原子受力、应力张量与简谐声子的计算则可推进至三聚体嵌入层级。我们借助分子晶体基准测试集X23，将PBE0+MBD多聚体嵌入周期性PBE+MBD计算框架中，并将所得结果与显式周期性PBE0+MBD计算结果进行对比，以此验证引入高阶多聚体的实际意义。研究表明，四聚体相互作用可系统性优化晶格能量的近似精度，同时我们还探索了多聚体选择的多种可行方案。此外，我们证实三聚体相互作用对于应力张量的精准描述至关重要，由此得到的晶胞体积与PBE0+MBD计算结果的偏差仅在1%以内。后续的振动物性描述也因此得到优化，所得伽马点频率的平均偏差仅为1.3波数，振动自由能的平均偏差则控制在0.3 kJ/mol以内，与PBE0+MBD的计算结果高度吻合。 如需了解可用数据集的更多细节，请参阅随附的README.md文件。相关预印本可通过以下链接获取：https://doi.org/10.48550/arXiv.2512.16877。