Synthesis and single-molecule magnet properties of a trimetallic dysprosium metallocene cation†

The dimetallic fulvalene-bridged dysprosium complex [{Dy(Cp*)(μ-BH4)}2(Fvtttt)] (1, Cp* = C5Me5) is converted into the trimetallic borohydride-bridged species [{Dy(Cp*)(Fvtttt)}2Dy(μ-BH4)3] (2). In turn, 2 is reacted with a silylium electrophile to give [{Dy(Cp*)(μ-BH4)(Fvtttt)}2Dy][B(C6F5)4] ([3][B(C6F5)3]), the first trimetallic dysprosocenium cation. Compound [3][B(C6F5)3] can also be formed directly from 1 by adding two equivalents of the electrophile. A three-fold enhancement in the effective energy barrier from 2 to 3 is observed and interpreted with the aid of ab initio calculations.


X-ray crystallography
Single-crystal X-ray diffraction measurements were carried out on an Agilent Gemini Ultra diffractometer with an Enhance Ultra (Cu Kα), equipped with an Eos CCD area detector, operating in  scanning mode to fill the Ewald sphere. Control, integration and absorption corrections were processed with the CrysAlis Pro software. Crystals were mounted on MiTiGen loops from dried vacuum oil that had been kept over 4 Å molecular sieves in a glovebox under argon. Data were solved in Olex2 with SHELXT, using intrinsic phasing, and were refined with SHELXL using least squares minimisation. [2][3][4] The SQUEEZE program of PLATON was employed to deal with the disordered solvent molecules of compound 2. Table S1. Crystal data and structure refinement for 2 and [3][B(C 6 F 5 ) 3 ].

Magnetic property measurements
Magnetic susceptibility measurements were recorded on a Quantum Design MPMS-XL7 SQUID magnetometer equipped with a 7 T magnet. The samples were restrained in eicosane and sealed in 7 mm NMR tubes. Direct current (DC) magnetic susceptibility measurements were performed on crystalline samples in the temperature range 1.9-300 K using an applied field of 1000 Oe. The AC susceptibility measurements were performed in zero DC field. Diamagnetic corrections were made with Pascal's constants for all the constituent atoms. 5
The temperature-dependence of the molar magnetic susceptibility ( M ) for 2 and [3][B(C 6 F 5 ) 4 ] was measured in an applied DC field of 1000 Oe and in the temperature range 2-300 K. The values of  M T at 290 K were determined to be 40.5 cm 3 K mol -1 and 39.6 cm 3 K mol -1 , respectively, both of which are slightly lower than the theoretical value of 42.51 cm 3 K mol -1 for three weakly coupled Dy 3+ ions. On decreasing the temperature, a gradual decrease in  M T was observed, followed by a more noticeable drop below 10 K. The behaviour of  M T(T) for both compounds is indicative of weak exchange coupling between the dysprosium ions, with thermal depopulation of the excited crystal field levels evident at the lowest measurement temperatures.
S23 Fig. S17. Cole-Cole plots for the AC susceptibilities in zero DC field for [3][B(C 6 F 5 ) 4 ] from 12-60 K. Solid lines represent fits to the data using equations S1 and S2.   [3][B(C 6 F 5 ) 4 ]. The data were collected at 1.9 K using an average field sweep rate of 29 Oe s -1 .

Computational details
The geometries of 2 and [3][B(C 6 F 5 ) 4 ] were extracted from the crystal structure. Solvent molecules and the non-coordinated counter ion of [3][B(C 6 F 5 ) 4 ] were removed from the structure. The positions of hydrogen atoms were optimized using density functional theory (DFT) while the positions of heavier atoms were kept frozen to their crystal-structure coordinates.
The geometry optimization was carried out using the ADF2019 code version 1.03. 6 The pure GGA exchangecorrelation functional PBE 7 was used along with the DFT-D3 dispersion correction 8 utilizing the Becke-Johnson damping function. 9 Scalar relativistic effects were treated with the zeroth-order regular approximation (ZORA). 10 All-electron Slater-type basis sets of triple-ζ quality with two sets of polarization functions (TZ2P) were used in the optimizations. 11 Static electron correlation effects were simulated by using fractional occupation numbers in the 4f orbitals. In practice this means that the two 4f β electrons of each Dy(III) ion were evenly distributed over the seven 4f orbitals giving a total of 21 β orbitals with an occupation of 0.2857. The "NumericalQuality" keyword in ADF was set to "Good" and the geometry convergence criteria were set to 10 -4 , 10 -4 , 10 -3 and 10 -1 atomic units for energy, gradient, bond distance and bond angles, respectively.
A set of multireference calculations were then carried out for each of the three ions in 2 and [3][B(C 6 F 5 ) 4 ] using the OpenMolcas quantum chemistry software version 20.10. 12 The remaining ions were replaced by the diamagnetic Y(III) ion. The calculations were carried out using state-averaged complete active space selfconsistent field (SA-CASSCF) approach. 13 The active space consisted of the seven 4f orbitals and the nine 4f electrons. All 21 sextet, 224 quartet and 490 doublets were solved for in three separate SA calculations. Spinorbit coupling (SOC) was then introduced using the standard spin-orbit restricted active space state interaction (SO-RASSI) approach. 14 All 21 sextets and the lowest 128 quartets and 130 doublets corresponding to an energy cutoff of 50,000 cm -1 were included in the SO-RASSI treatment. The SOC operator was constructed using the atomic mean-field integral (AMFI) formalism 15 and diagonalized to yield the final spin-orbit coupled states. The local magnetic properties (g-tensors, crystal-field decomposition and effective local barrier) were calculated using the SINGLE_ANISO module. 16,17 Relativistically contracted atomic natural orbital (ANO-RCC) basis sets were used in all multireference calculations. 18 A valence-polarized triple-ζ quality basis set was used for the Dy(III) ions whereas valencepolarized double-ζ quality basis sets were used for the remaining atoms. Scalar relativistic effects were introduced using the scalar exact two-component (X2C) transformation. 19 Integrals were stored using the Cholesky decomposition with a threshold of 10 -8 atomic units.
The dipolar interations were calculated using the POLY_ANISO module. 17,20 The 16 lowest states of each Dy(III) ion corresponding to the ground J = 15/2 multiplet were used as an exchange basis. The reported exchange parameters correspond to the Ising-type pseudospin Hamiltonian (1) where the indices 1, 2 and 3 correspond to the same indices of the Dy(III) ions used in the crystal structure. The operators act on the projection of pseudospin states that describe the local ground KD of each Dy(III) ion. The exchange parameters J 12 , J 13 and J 23 were determined from the energy difference between the exchange eigenstates. Note that while we follow the usual practice and label the parameters J 12 , J 13 and J 23 as exchange parameters and the resulting eigenstates as exchange eigenstates, the parameters describe dipolar coupling and not any exchange interaction. The angle between the principal magnetic axis of the given doublet and the that of the ground doublet. The angle between the principal magnetic axis of the given doublet and the that of the ground doublet. The angle between the principal magnetic axis of the given doublet and the that of the ground doublet. The angle between the principal magnetic axis of the given doublet and the that of the ground doublet. The angle between the principal magnetic axis of the given doublet and the that of the ground doublet. The angle between the principal magnetic axis of the given doublet and the that of the ground doublet.   S38 Table S16. Local ab initio CF parameters (in cm -1 ) calculated for the Dy2 ion of 3 given in the S40 Table S17. Local ab initio CF parameters (in cm -1 ) calculated for the Dy3 ion of 3 given in the S43 Table S20. Squared magnitudes of projections of the local ab initio CF eigenstates calculated for the Dy3 ion of 2 onto pseudospin eigenstates with pseudospin J = 15/2 and projection M.   Table S22. Squared magnitudes of projections of the local ab initio CF eigenstates calculated for the Dy2 ion of 3 onto pseudospin eigenstates with pseudospin J = 15/2 and projection M.        Stronger arrows indicate larger absolute value of the transition magnetic moment matrix elements between the respective states. Transitions involving higher-energy states not involved in the relaxation mechanism are omitted for clarity.