We investigate the spectroscopic magnetic excitations in molecular magnets with complex intermediate structure among the magnetic ions. Our approach consists in introducing a modified spin Hamiltonian that allows for discrete coupling parameters accounting for all energetically favorable spatial distributions of the valence electrons along the exchange bridges connecting the constituent magnetic ions. We discuss the physical relevance of the constructed Hamiltonian and derive its eigenvalues. The model is applied to explore the magnetic excitations of the tetrameric molecular magnet Ni 4 Mo 12 . Our results are in a very good agreement with the available experimental data. We show that the experimental magnetic excitations in the named tetramer can be traced back to the specific geometry and complex chemical structure of the exchange bridges leading to the splitting and broadness of the peaks centered about 0.5 meV and 1.7 meV.

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We develop a structured theoretical framework used in our recent articles (2019 Eur. Phys. J. B 92 93 and 2020 Phys. Rev. B 101 094427) to characterize the unusual behavior of the magnetic spectrum, magnetization and magnetic susceptibility of the molecular magnet Ni4Mo12. The theoretical background is based on the molecular orbital theory in conjunction with the multi-configurational self-consistent field method and results in a post-Hartree–Fock scheme for constructing the corresponding energy spectrum. Furthermore, we construct a bilinear spin-like Hamiltonian involving discrete coupling parameters accounting for the relevant spectroscopic magnetic excitations, magnetization and magnetic susceptibility. The explicit expressions of the eigenenergies of the ensuing Hamiltonian are determined and the physical origin of broadening and splitting of experimentally observed peaks in the magnetic spectra is discussed. To demonstrate the efficiency of our method we compute the spectral properties of a spin-one magnetic dimer. The present approach may be applied to a variety of magnetic units based on transition metals and rare Earth elements.

We study the behavior of the magnetization and the magnetic susceptibility of molecular magnets with complex bridging structure. Our computations are based on a post-Hartree-Fock method accounting for the intricate network of interatomic bonds and an effective spin-like Hamiltonian that captures the essential magnetic features of magnetic molecules. The devised method and the constructed Hamiltonian are further employed to characterize the magnetic properties of the molecular magnet Ni 4 Mo 12 . The obtained results reproduce both quantitatively and qualitatively the main features of the magnetic spectrum. Furthermore, the computations for the magnetization and the low-field susceptibility are in very good agreement with their experimental counterparts. In this respect, they improve upon the results obtained with conventional Heisenberg models.

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4 + guest ions are presented and discussed in the region of the stretching modes m 3 and m 1 of the sulfate ions and in the region of the asymmetric bending modes m 4 of the NH 4 + ions. The SO 4 2À ions matrix-isolated in the selenate matrices (approximately 5 mol%) exhibit three bands for m 3 and one band for m 1 in agreement with the low site symmetry C 1 of the SeO 4 2À host anions. The NH 4 + guest ions included in the potassium matrices are characterized also with three site symmetry components of m 4 (C 1 site symmetry of the K + cations). The spectral regions of m 4 and m 2 of the SO 4 2À guest ions as well as those of m 1 , m 3 and m 2 of the NH 4 + guest ions could not be analyzed precisely due to the overlapping of these motions with motions of other entities in the structures (for example, the normal modes of water molecules and water librations).The extent of energetic distortion of the isomorphously included ions as deduced from the values of Dm 3 and Dm 4 (site-group splitting for the SO 4 2À and NH 4 + guest ions, respectively) and Dm max (the difference between the highest and the lowest components of the stretching modes for the sulfate ions) are commented. The spectroscopic experiments show that the degree of energetic distortion of the guest ions is not affected by the guest ion concentration up to 20 mol%. It has been established that the SO 4 2À guest ions are stronger distorted in (NH 4 ) 2 Mg(SeO 4 ) 2 Á6H 2 O than in K 2 Mg(SeO 4 ) 2 Á6H 2 O (Dm 3 have values of 34 cm À1 in the potassium matrix and 45 cm À1 in the ammonium one; samples containing about 5 mol% sulfate ions, respectively). The formation of hydrogen bonds between the SO 4 2À guest ions and NH 4 + host ions increases the electrostatic field strength at the lattice sites where the guest ions are located, thus leading to a larger extent of energetic distortion of the sulfate ions included in (NH 4 ) 2 Mg(SeO 4 ) 2 Á6H 2 O. The NH 4 + guest ions are stronger distorted in K 2 Mg(SO 4 ) 2 Á6H 2 O than in K 2 Mg(SeO 4 ) 2 Á6H 2 O (Dm 4 have values of 73 cm À1 in the former compound and 66 cm À1 in the latter one) owing to the smaller unit-cell volume of the sulfate than that of the selenate (repulsion potential of the lattice). The analysis of the spectra reveals that the band positions of the water librations in the host compounds are affected by the included NH 4 + guest ions. The formation of hydrogen bonds between the NH 4 + guest ions and the XO 4 2À host ions leads to a decrease in the proton acceptor capabilities of the anions (anti-cooperative or proton acceptor competitive effect) and as a result the hydrogen bonds weaken on going from the neat potassium compounds to mixed crystals K 1.8 (NH 4 ) 0.2 Mg(SO 4 ) 2 Á6H 2 O and K 1.8 (NH 4 ) 0.2 Mg(SeO 4 ) 2 Á6H 2 O (the bands corresponding to water librations broaden and shift to lower frequencies).