Classical and quantum magnetic response of the pentakis dodecahedron

The nearest-neighbor antiferromagnetic Heisenberg model describes interactions between spins of magnitude s, when a single spin is located on each point of a lattice or vertex of a molecule. For bipartite structures the magnetization increases smoothly in a magnetic field up to saturation when the spins are classical. For quantum spins s=1/2 the magnetization has a staircase form in a field, where the total spin changes only by S=1. It was shown that for specific frustrated molecules the magnetization (and susceptibility) is discontinuous at the classical level, while at the quantum level it can switch directly between sectors differing by S=2. This is unexpected for a model lacking magnetic anisotropy and originates in the frustrated connectivity, which at zero field does not allow simultaneous minimization of all nearest-neighbor interactions. The discontinuities are of significant interest, as they allow considerable magnetization changes with small variations of a field. A class of molecules with discontinuous magnetic response are the fullerenes, where frustration originates in their twelve pentagons. The classical jumps can be as many as eight for fullerenes of up to 180 vertices. Quantum fluctuations work against the discontinuities, and only fullerenes of icosahedral Ih symmetry were found to have magnetization changes of S=2 when s=1/2. For s=1 there are two magnetization jumps for the smallest Ih fullerene, the dodecahedron. Fullerene duals are molecules formed when each fullerene face transcribes to a vertex of its dual. They consist of triangles and inherit the symmetry of the parent fullerene. The Ih symmetry fullerene duals are strong candidates for non-continuous magnetization response, as their parent molecules have discontinuities at both the classical and quantum level. The smallest Ih-fullerene dual is the icosahedron, derived from the dodecahedron. It was shown to have a magnetization discontinuity when classical spins are mounted on its vertices. Here it is proposed to calculate the magnetization response of the next bigger Ih-symmetry fullerene dual, the pentakis dodecahedron, which has 32 vertices. Its parent molecule is the truncated icosahedron, whose structure corresponds to the most well-known fullerene, C60. It is of significant interest to calculate the magnetization response of the pentakis dodecahedron with the goal to find a molecule made up of triangles with discontinuous magnetic response, at the classical level and also for s=1/2 and the much more uncommon quantum discontinuities. The methods to calculate the magnetization response were extensively used in the past. At the classical level the spin angles are moved opposite their gradient direction until the energy minimum is reached. For quantum spins the Hamiltonian is block-diagonalized according to its spatial and spin symmetries. This research project is part of a program, where a classification of magnetic properties according to molecular structure within the framework of the antiferromagnetic Heisenberg model is sought. It is a first step for the calculation of magnetic response in molecular nanomagnets where electron correlations are important. Consideration of more complicated models such as the Hubbard model is the ultimate goal.