# The interest for lanthanide and actinide complexes appeared

The interest for lanthanide and actinide complexes appeared again recently, due to their unique features in the design of Single Molecule Magnets (SMM). Lanthanide SMMs are interesting due to large their intrinsic magnetic anisotropy, but their core 4f orbitals minimally participate in exchange interactions. As a result, the large magnetic relaxation barriers found in some lanthanide complexes are attributable to single-ion behavior. In the synthesis of SMMs two parameters are important, first large anisotropies are needed and second significant interaction between highly anisotropic magnetic centers [2]. The last one is in general the most important problem in the case of lanthanide. In an effort to couple and induce significant magnetic moments interaction many new compounds have been synthesized in the last years [13], [14], [15], [16], [17]. One good candidate, due to the possible efficient overlap with the metal f orbitals, in the design of new systems are the cyclooctatetraenide rings and particularly organometallic complexes where the metals centers are bridged by this kind of ligands. During the last decades many new compounds with the former characteristics has been synthesized and characterized. Recently Murugesu et al. have established a synthesis strategy to produce multidecker 4f complexes with single ion magnets behavior and investigate their magnetic properties [8], [18], [19], [20], [21], [22], [23]. In 2007 Andersen et al. have done an experimental review of the cerocene molecule and have reported the possible interconversion of this molecule in a triple decker gap-27 Ce2(C8H8)3, the magnetic properties of these compounds were reported [24]. The solid state magnetic susceptibility data of these organocerium compounds show that behaves as a temperature independent paramagnet, while that of Ce2(COT)3 shows that the spin carriers are antiferromagnetic coupled below 10 K, and above this temperature the individual spins are uncorrelated and the fragment behaves as an isolated paramagnet. Also the EPR spectra reveal that for both molecules the ground state correspond to [24].
From the theoretical point of view some rationalizations can be done if the symmetry considerations are included in the calculations. When only configurations are considered all systems of , and symmetry may be treated as a purely axial () ligand field [25], [26]. It means that in the present case if we consider an idealized symmetry the cerocene system can be treated as a pseudoaxial molecule and at first order of perturbation it is possible consider that is a good quantum number. With the aim to facilitate the comprehension of the results in the present work we use the notation commonly used for axial molecules. Let us first consider the effect of the spin-orbit (SO) interaction on the configuration. This removes the degeneracy of the ground state and gives two states and characterized by and , respectively. The main effect of the crystal-field (CF) is to remove the degeneracy of the and states into doubly degenerate Kramers states and the second order mixing of the states with different values of J but the same value of [27], [28], [29]. In the present work the wavefunction based methods (CASSCF/MRCI) are employed to describe the magnetic properties of Ce2(COT)3. First the spin-Hamiltonian for this system is builded, and a relationship between the magnetic parameters for the binuclear molecule and homonuclear is founded. In the last part the magnetic coupling constant is calculated and the mechanism of the coupling is described using correlation methods like MRCI + CIS or DDCIn (n = 2, 3).

Computational details
All the calculations performed in the present work were done using the MOLCAS 8.2 suite of programs without any symmetry restriction [30], [31]. The reported crystallographic data was used for the geometry [24]. In a first step the CASSCF (Complete Active Space Self Consistent Field) [32] calculation is performed employing an active space consistent in two electrons in fourteen f orbitals CAS(2,14) and 49 triplets and singlets states were taken into account. The purpose of the CASSCF step is to obtain wave functions that can be thought of as corresponding to the atomic Russell-Saunders terms, whose degeneracies are weakly split by the presence of the ligand environment. For a Ln(III) complex whose formal configuration is , this is achieved by choosing the active space to consist of n electrons in the seven -like orbitals. These are spin-adapted configurational state functions (CSF) of definite spin quantum numbers S. For each spin manifold a number of CASSCF wave functions are then optimized. Spin-orbit coupling (SOC) is introduced in the second step by diagonalizing the SOC operator in the basis of the optimized CASSCF wave functions by the RASSI (Restricted Active Space States Interaction) method [33]. The resulting eigenvectors are then used to calculate expectation values of relevant operators, in particular the magnetic moment [34]. Scalar relativistic effects are taken into account by means of the Douglas-Kroll-Hess transformation [35] and the SO integrals are calculated using the AMFI (Atomic Mean Field Integrals) method [36]. In all cases the all-electron ANO-RCC basis set with TZP quality are employed as follow Ce: 8s7p4d3f2g1h, and C: 4s3p2d1f [37].