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

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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.