Irreducible tensor operator techniques and point-group symmetries for molecular magnetism

对于足够小的自旋系统，数值精确和完全对角化的哈密顿量是最终选择的方法来评估和讨论所有静态，动态和热力学性质，例如磁性分子。然而，由于希尔伯特空间的巨大维度，这种计算经常受到严格的限制。在最近开发了使用全自旋-转动（即SU（2））对称性和一般点群对称性的精确对角化方法之后[1]，我们在这个项目中有三个主要目标。首先，我们希望与我们的化学合作伙伴合作，研究最新的分子化合物的磁性。其次，我们计划进一步发展一个方案，通过结合转动带的思想以及对称性参数来近似获得大量的低能量本征值。第三，我们希望在两个方面改进和进一步发展数值程序：它将被公开，并将开发一个能够处理更大自旋系统的高级版本。这个项目最好由罗曼·施纳勒（Roman Schnalle）来完成，他在博士学位时开发了这个方法。

For small enough spin systems numerical exact and complete diagonalization of the Hamiltonian is the ultimate method of choice to evaluate and discuss all static, dynamic, and thermodynamic properties, e.g. of magnetic molecules. Nevertheless, such calculations are very often severely restricted due to the huge dimension of the underlying Hilbert space. After having recently developed exact diagonalization methods using the full spin-rotational, i.e. SU(2), symmetry together with general point-group symmetries [1] we aim at three major objectives in this project. Firstly, we would like to investigate very recent molecular compounds for their magnetic properties in collaboration with our chemical partners. Secondly, we plan to further develop a scheme to approximately obtain a large number of low-lying energy eigenvalues by combining the idea of rotational bands as well as symmetry arguments. Thirdly, we want to improve and further develop the numerical program in two aspects: it shall be made public and an advanced version that is capable to treat even larger spin systems shall be developed. Preferably, the project should be carried out by Roman Schnalle, who developed the method in his Ph. D.