Embedded wavefunctions for 2D and 3D periodic molecular systems

尽管发展了不同的方法，在周期系统中使用相关波函数仍然是一个挑战。本应用旨在使用相关波函数方法精确描述周期性分子系统中的局部特性，例如分子晶体中的局部缺陷或有机半导体中的跳跃输运。虽然波函数方法提供了动态或静态相关所需的精度，但传统方法的计算成本随着系统尺寸的增加而显著增加，这尤其限制了波函数方法在实际中对分子固体和液体的应用。冷冻密度嵌入（FDE）可以实现子系统数量的准线性缩放，极大地促进了包括缺陷在内的局部性质的研究。在目前的应用中，使用局部高斯基的嵌入式波函数将用于二维和三维周期系统，并结合快速多极方法用于远程库仑贡献。冻融迭代用于在扰动或缺陷附近放松分子。所提出的方法特别允许避免缺陷的周期性重复，从而使用相关波函数提供对体相和表面的完全放松的自一致描述。这种方法能够描述局部激发态上的远距离静电效应，但除了简单的静电模型外，它还确保由于短距离的有效嵌入势而产生的斥力贡献，以便充分考虑分子内和分子间效应。新开发的方法特别适用于有机半导体材料，如四叠氮-苝（TAPPs），但也可用于研究溶质的局部性质。

Despite the development of different approaches, the use of correlated wave functions in periodic sys- tems is still a challenge. The present application aims to enable accurate description of local properties in periodic molecular systems, such as local defects in molecular crystals or hopping-based transport in or- ganic semiconductors, using correlated wavefunction methods. While wavefunction methods provide the required accuracy for dynamic or static correlation, the computational cost of conventional approaches scales significantly with system size, limiting in particular the application of wavefunction methods to molecular solids and liquids in practice. Frozen-density embedding (FDE) enables quasi-linear scaling with number of subsystems, greatly facilitating the study of local properties including defects. In the present application, embedded wavefunctions using a local Gaussian basis will be used in 2D and 3D periodic systems in combination with fast multipole methods for the long-range Coulomb contributions. Freeze-Thaw iterations are used to relax molecules in close proximity to perturbations or defects. The proposed approach allows in particular to avoid the periodic repetition of the defect, thus providing a fully relaxed self-consistent description of the bulk phase and surfaces using correlated wave functions. This approach is able to describe long-range electrostatic effects on e.g. local excited states, but in addition to simple electrostatic models it also ensures repulsion contributions due to the effective embedding poten- tial at short distances, so that both intramolecular and intermolecular effects are adequately accounted for. The newly developed methods are particularly applicable to organic semiconductor materials such as tetra-aza-peropyrenes (TAPPs), but can also be used to study local properties of solutes.