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The Role of Anisotropic Exchange in Single Molecule Magnets: A CASSCF/NEVPT2 Study of the Fe4 SMM Building Block [Fe2(OCH3)2(dbm)4] Dimer

Alessandro Lunghi, Federico Totti

2016
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Inorganics
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The rationalisation of single molecule magnets' (SMMs) magnetic properties by quantum mechanical approaches represents a major task in the field of the Molecular Magnetism. The fundamental interpretative key of molecular magnetism is the phenomenological Spin Hamiltonian and the understanding of the role of its different terms by electronic structure calculations is expected to steer the rational design of new and more performing SMMs. This paper deals with the ab initio calculation of
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... ulation of isotropic and anisotropic exchange contributions in the Fe(III) dimer [Fe 2 (OCH 3 ) 2 (dbm) 4 ]. This system represents the building block of one of the most studied Single Molecule Magnets ([Fe 4 RC(CH 2 O) 3 ) 2 (dpm) 6 ] where R can be an aliphatic chain or a phenyl group just to name the most common functionalization groups) and its relatively reduced size allows the use of a high computational level of theory. Calculations were performed using CASSCF and NEVPT2 approaches on the X-ray geometry as assessment of the computational protocol, which has then be used to evinced the importance of the outer coordination shell nature through organic ligand modelization. Magneto-structural correlations as function of internal degrees of freedom for isotropic and anisotropic exchange contributions are also presented, outlining, for the first time, the extremely rapidly changing nature of the anisotropic exchange coupling. 19 proposed by Heisenberg in the 1928[1-3]. Although its widespread in both chemists and physicists 20 communities, the direct mapping of the different SH terms with quantum mechanical approaches is 21 still an actual research field and its integration into a solid theoretical framework has been achieved 22 only recently [4][5][6][7][8][9][10][11]. The combination of the spin Hamiltonian theory together with computational 23 methods allowed to access to microscopic insights from electronic structure theories, that can be used 24 as guide to both the interpretation of phenomena and the design of new materials. The possibility 25 to calculate spin Hamiltonian parameters from first principles is also of particular importance for all 26 those systems where the origin of a complex magnetic structure cannot be easily disentangled. In fact, 27 the inclusion of several spin Hamiltonian terms can rapidly lead to an over-parametrization problem 28 in the fitting of the experimental results. A remarkable example of a class of systems, showing very 29 rich flavours of complex magnetic properties, is represented by single molecule magnets (SMMs). 30 Many hopes are set on SMMs as possible active elements in several technological areas as spintronic 31 and quantum computing [12-15], just to name a few. Although many efforts have been devoted to 32 18 Preprints (www.preprints.org) | NOT PEER-REVIEWED | Posted: Peer-reviewed version available at Inorganics 2016, 4, 28; doi:10.3390/inorganics4040028 the study of various spin Hamiltonian terms that contribute to SMMs' magnetism, their usual multi 33 paramagnetic ion-nature made these attempts not fully successful. Among the spin Hamiltonian 34 parameters, the most elusive one is by far the anisotropic exchange interaction. Although this 35 interaction is generally neglected in the interpretation of experiments, this might not always be a 36 correct assumption and especially for those systems where single-ion anisotropies do not necessarily 37 dominate the low-lying part of the spin spectrum, this interaction might play a fundamental role, as 38 also recently reported [16]. As showed by the authors in a previous paper[17], a possible route to the 39 computation of the anisotropic exchange has been presented but unfortunately, a conclusive claim 40 about the goodness of its applicability has not been possible. The reason mainly lies in the lack of 41 benchmark references, both of experimental and computational origin. In order to get some more 42 insights on the importance of this interaction in SMMs the most valuable strategy would concern the 43 application of a higher level of theory with respect to the usually employed DFT, but unfortunately 44 this is not possible for systems as large as those of practical interest and the study must be restrained 45 to its most characteristic building block fragments. 46 Figure 1. Fe 2 (OCH 3 ) 2 (dbm) 4 X-ray structure. Fe, O, C, and H atoms are blue, red, green, and white colored, respectively. The leading interaction is the isotropic interaction J 12 whose value is 15.4 cm −1 . For symmetry 54 reasons single ion anisotropic terms are equal and of the easy plane kind. The anisotropic exchange 55 has been estimated to be of the same order of magnitude of the single ion term suggesting its 56 importance in the final contribution to the magnetic behaviour of this paramagnetic complex. We here 57 2 of 11 Preprints (www.preprints.org) | NOT PEER-REVIEWED | Posted: 109 possible to extract the isotropic exchange coupling constant from the energy splitting between the 110 S=10 and S=9 multiplet at the NEVPT2 level according to the formula 111 J 12 = (E(S) − E(S − 1))/S (5) Among the many S=9 solutions the one that should be considered for this purpose is the one 112 corresponding to two misaligned local s=5/2 spins i.e. the solution with the largest weight on the 113 determinant with all the active orbitals singly filled. 114 3. Computational Details 115 All the calculations have been done with ORCA [29] employing a def2-TZVP [30] basis set for 116 magnetic elements and their first neighbours (oxygen atoms), while def2-SVP basis set has been 117 used for all the other atoms. The RI-J approximation along with the def2-TZVP/J auxiliary basis 118 set[31] for all the elements has been used. Speaking in the ORCA notation, grids were set to 5 and 119 VeryTightSCF convergence criteria have been used. This set up has been tested in the context of 120 CASSCF method with respect to calculations done with the def2-TZVP basis set on every atomic kind 121 and no significant differences have been noted on the energy ladder of the CASSCF excited states. 122 The computation of the magnetic properties included only SOC as relativistic interactions, neglecting 123 for instance spin-spin coupling. Optimisation and normal mode calculations have been done at the 124 DFT level of theory employing the PBE functional [32]. 125 4. Results and Discussion 126 4.1. Method Assessment 127 X-ray Structure. The calculation of isotropic J 12 and anisotropic exchange D 12 coupling parameters 128 of a dimer of Fe(III) ions by ab initio methods can still be considered a challenging task. Indeed, 129 the energetics of these parameters goes from a few to a fraction of wavenumbers, demanding a very 130 high computational accuracy. In this regard, to verify the reliability of the proposed computational 131 protocol, we have decided not to include further sources of possible errors given by the optimisation 132 procedure or some modelization of the geometry. For such a reason the Fe 2 X-ray structure (1-Ph xray 133 from now on) has been used for the first benchmark calculation at the post-HF level. Both CASSCF 134 and NEVPT2 approaches have been applied and results are listed in Table 1. As expected[6,10,23,25], 135

doi:10.3390/inorganics4040028
fatcat:crbkyudd7zflhhki4dm3ujbltm