S1 Supplementary Information to accompany     Ab Initio Calculations as a Quantitative Tool in the Inelastic Neutron  Scattering Study of a Single‐Molecule Magnet Analogue    Michele Vonci, Marcus J. Giansiracusa, Robert W. Gable, Willem Van den Heuvel, Kay Latham,  Boujemaa Moubaraki, Keith S. Murray, Dehong Yu, Richard A. Mole,* Alessandro Soncini* and  Colette Boskovic*  Electronic Supplementary Material (ESI) for ChemComm. This journal is © The Royal Society of Chemistry 2015 S2 Table of Contents Experimental Section ........................................................................................................................ S3  Synthesis .......................................................................................................................................... S3  Measurements .................................................................................................................................. S5  Single crystal X-ray diffraction and structure solution ....................................................................... S5  Table S1............................................................................................................................................ S6  Powder X-ray Diffraction ................................................................................................................... S7  Inelastic Neutron Scattering Spectroscopy ....................................................................................... S7  INS Data Fitting ................................................................................................................................. S8  Magnetic Susceptibility Measurements ............................................................................................. S9  Other Measurements ........................................................................................................................ S9  Theoretical Calculations .................................................................................................................... S9  Fig. S1............................................................................................................................................. S12  Fig. S2............................................................................................................................................. S13  Fig. S3............................................................................................................................................. S14  Fig. S4............................................................................................................................................. S15  Fig. S5............................................................................................................................................. S15  Fig. S6............................................................................................................................................. S16  Fig. S7............................................................................................................................................. S16  Fig. S8............................................................................................................................................. S17  Fig. S9............................................................................................................................................. S18  Fig. S10........................................................................................................................................... S19  Fig. S11........................................................................................................................................... S19  Fig. S12........................................................................................................................................... S20  Table S2.......................................................................................................................................... S21  Table S3.......................................................................................................................................... S22  Table S4.......................................................................................................................................... S23  Fig. S13........................................................................................................................................... S24  Fig. S14........................................................................................................................................... S25  Fig. S15........................................................................................................................................... S26  Fig. S16........................................................................................................................................... S26  Fig. S17........................................................................................................................................... S27  Fig. S18........................................................................................................................................... S27  Table S5.......................................................................................................................................... S28 Table S6.......................................................................................................................................... S29 Fig. S19........................................................................................................................................... S30  Fig. S20........................................................................................................................................... S31  Fig. S21........................................................................................................................................... S32  Fig. S22........................................................................................................................................... S33  References ...................................................................................................................................... S34 S3 Experimental Section Synthesis All chemicals were used as purchased with no further purification. Na2WO4·2H2O (Strem, 99%), Y(NO3)3·6H2O (Strem, 99.9%), Tb(NO3)3·5H2O (Aldrich, 99.9%), glacial acetic acid (Chem-Supply, 99.7%), deuterium oxide (Sigma-Aldrich, 99.9%). The Na9[Ln(W5O18)2] (Ln = Tb and Y) compounds were synthesised by modification of literature methods.1 Samples with deuterated hydrate molecules for INS were synthesised and handled under nitrogen using standard Schlenk and glove-box techniques. Na9[Tb(W5O18)2]·xH2O (Tb). Solid Na2WO4·2H2O (14.84 g, 45.00 mmol) was dissolved in water (30 ml) and heated to 90° C. The pH was then adjusted to 7.2 with glacial acetic acid, while maintaining the tungstate solution at constant temperature. A solution of Tb(NO3)3·5H2O (1.958 g, 4.500 mmol) in hot water (4 ml), was added dropwise to the tungstate solution with vigorous stirring, affording a fine precipitate. After the addition was complete, the mixture was stirred for a further 5 minutes and then cooled at room temperature. The resulting fine precipitate was removed by filtration and the filtrate was stored at 5 °C for 24 hours. The resulting colourless crystalline product (13.1 g, 3.8 mmol, yield 85 %) was recrystallised from hot water, giving colourless crystals with a mixture of blade (Tb-a) and distorted hexagonal prismatic (Tb-b) shapes after 24 hours. Selected IR data (KBr, cm-1): 944 (m), 844 (s), 782 (m), 704 (s), 583 (w), 542 (m), 490 (w), 420 (s). It was possible to isolate a pure sample of Tb-a by slow recrystallization from H2O at room temperature, whereas the formation of Tb-b was favored by recrystallization from the minimum amount of hot H2O followed by cooling at 5º. Phase Tb-a is stable in contact with mother liquor and upon drying, although it loses crystallinity upon grinding. In the presence of mother liquor, phase Tb-b is metastable and slowly converts into Tb-a, while following isolation and drying it is deliquescent. S4 Na9[Tb(W5O18)2]·20D2O (TbD). A sample of Tb (3-4 g) was heated at 150 °C under reduced pressure (100 μmHg) for 6 h. The resulting amorphous powder was recrystallised from the minimum amount of D2O under an atmosphere of dry nitrogen. The mixture of colourless blade-shaped (Tb-aD) and distorted hexagonal prismatic-shaped (Tb-bD) crystals that were obtained after 24 h were filtered dried and stored under nitrogen. The deuteration was checked by ATR-IR through the diagnostic peaks of DHO and D2O bending modes around 1440 and 1210 cm-1 respectively (Fig. S1). Selected IR data (ATR-IR, cm-1): 1438 (w), 1209 (w), 967 (m), 922 (s), 830 (s), 776 (s), 699 (s), 582 (w), 540 (w), 482 (m), 413 (s). Elemental analysis for Na9[Tb(W5O18)2]·20D2O, D40Na9O56TbW10, calcd (found): D 2.52 (2.90), Tb 5.0 (4.6), Na 6.5 (6.6), W 58 (55.0). Thermogravimetric analysis confirmed the degree of hydration. A pure sample of Tb-aD was obtained as per the non-deuterated sample. Na9[Y(W5O18)2]·xH2O (Y). Synthesised as per Tb using Y(NO3)3·6H2O. The sample appears to be predominantly phase a. Selected IR data (KBr, cm-1): 938 (m), 844 (s), 777 (s), 710 (s), 544 (w), 492 (w), 427 (s), 414 (s). Na9[Y(W5O18)2]·20D2O (YD). Synthesised as per TbD. Selected IR data (ATR-IR, cm-1): 1435 (w), 1209 (w), 968 (m), 941 (m), 924 (s), 910 (m), 836 (s), 773 (s), 698 (s), 585 (w), 548 (w), 483 (w), 415 (s). Elemental analysis for Na9[Y(W5O18)2]·20D2O, D40Na9O56W10Y, calcd (found): H 2.57 (2.85), Y 2.9 (2.7), Na 6.65 (7.0), W 59 (53). S5 Measurements Single Crystal X-ray Diffraction and Structure Solution Diffraction measurements (Table S1) were performed on an Agilent Technologies SuperNova diffractometer using CuKα radiation (λ = 1.54184 Å) at 130 K. Gaussian absorption correction was applied for all compounds. The structures were solved by direct methods approach using SHELXT 2014 structure solution program and refined through full- matrix least-squares techniques on F2 by using the SHELXL 2014 crystallographic software package. For all structures all atoms in the [Ln(W5O18)2] 9- unit were refined anisotropically. For Y and Tb-a it was possible to also the refine the sodium cations and the oxygen atoms from the water molecule anisotropically, whereas in Tb-b these were refined isotropically. The positional disorder of the sodium cations and water molecules in Tb-b was modelled splitting atoms, using SUMP restraints and fixing the chemical occupancy of the oxygen atoms of the solvent. For all the three structures the H-atom parameters were not defined. Further details on the crystal structure investigations may be obtained from the Fachinformationszentrum Karlsruhe, 76344 Eggenstein-Leopoldshafen, Germany (fax: (+49)7247-808-666; e-mail: crysdata@fiz-karlsruhe.de), on quoting the depository numbers ICSD-429951, -429952, and -429953). S6 Table S1. Single Crystal X-ray Diffraction Data and Refinement Parameters for Tb-a, Tb-b and Y Tb-a Tb-b Y Empirical formula Na9O71TbW10H70 Na9O72TbW10H72 YNa9O71W10H70 Formula weight 3410.89 3428.90 3340.88 Temperature / K 130.0(1) 131.1(1) 130.0(1) Crystal system triclinic triclinic triclinic Space group P-1 P-1 P-1 a / Å 12.7251(4) 12.8949(5) 12.7357(5) b / Å 13.0624(4) 13.1098(5) 13.0732(4) c / Å 20.4974(7) 20.9057(7) 20.4565(8) α / ° 82.857(3) 76.956(3) 82.865(3) β / ° 74.521(3) 83.954(3) 74.492(4) γ / ° 88.927(3) 77.348(3) 88.859(3) Volume / Å3 3257.65(19) 3353.5(2) 3256.2(2) Z 2 2 2 ρcalc / gcm3 3.477 3.396 3.407 μ / mm-1 38.720 37.561 34.502 F(000) 3084.0 3104.0 3032.0 Crystal size / mm3 0.1723 × 0.1367 × 0.0300 0.1477 × 0.0402 × 0.0344 0.1586 × 0.0193 × 0.0127 Radiation CuKα (λ = 1.54184) CuKα (λ = 1.54184) CuKα (λ = 1.54184) 2Θ range for data collection / ° 6.82 to 143.432 7.038 to 142.998 6.814 to 148.164 Index ranges -15 ≤ h ≤ 15, -16 ≤ k ≤ 16, - 24 ≤ l ≤ 25 -15 ≤ h ≤ 15, -15 ≤ k ≤ 16, - 25 ≤ l ≤ 25 -13 ≤ h ≤ 15, -16 ≤ k ≤ 16, - 24 ≤ l ≤ 25 Reflections collected 22002 22609 23776 Independent reflections 12145 [Rint = 0.0454, Rsigma = 0.0425] 12708 [Rint = 0.0364, Rsigma = 0.0615] 12808 [Rint = 0.0437, Rsigma = 0.0747] Data / restraints / parameters 12145/0/820 12708/19/848 12808/0/820 Goodness-of-fit on F2 1.085 1.052 1.017 Final R indexes [I  2σ (I)] R1 = 0.0476, wR2 = 0.1329 R1 = 0.0353, wR2 = 0.0863 R1 = 0.0354, wR2 = 0.0822 Final R indexes [all data] R1 = 0.0501, wR2 = 0.1364 R1 = 0.0439, wR2 = 0.0912 R1 = 0.0446, wR2 = 0.0879 Largest diff. peak / hole / e Å-3 2.56/-3.03 4.49/-2.61 1.44/-2.39 S7 Powder X-ray Diffraction Data were acquired on a Bruker D4 ENDEAVOR X-ray diffractometer, fitted with a Lynx- Eye Position Sensitive Detector, and using a copper tube source (CuKα,  = 1.5406 Å), operated at 40 kV and 35 mA. Data was collected with 5-40 degree 2 theta angle range with a 0.02 degree step size and a 2 s per step dwell time. The loss of crystallinity of both phases and metastability of Tb-b makes it difficult to obtain finely ground microcrystalline samples, especially of pure Tb-b. Thus powder X-ray diffraction data were collected on coarsely ground, air-dried samples under ambient conditions, which are likely to exhibit some preferential orientation of the crystallites. This tends to alter the relative intensities of the peaks in the experimental patterns compared to those simulated from the single crystal X-ray diffraction data. As a result, although the powder diffraction data are consistent with the presence of two phases in the mixed TbD sample, it is not possible to quantitatively establish the relative proportions of the two phases on the basis of these data. Inelastic Neutron Scattering Spectroscopy Coarsely ground, crystalline samples (1.5-2.5 g) of TbD, Tb-aD, YD were analysed in a 1 mm annular Al can. The background due to the empty sample can was subtracted and the data normalised to a vanadium standard. All data manipulations were carried out using the large array manipulation program LAMP.2,3 The sample was cooled using a displex type cryostat and data collected at 5, 10, 15, 30, and 40 K for TbD and at 5, 15 and 40 K for Tb-aD. The data of YD were collected at 10 and 50 K. By opportune phasing of the choppers each sample was analysed with two different neutron wavelength (4.74 and 2.37 Å) then offering complementary information. Better resolution and better access to the neutron energy gain side of the spectrum, but a narrower overall energy transfer range (3.64 meV) is available at the higher neutron wavelength, while the lower wavelength gives access to a broader S8 energy transfer range (14.6 meV), allowing the observation of otherwise inaccessible transitions on the energy loss side of the spectrum, but with lower resolution. INS Data Fitting A minimal set of Extended Stevens Operators were used to set-up a simplified CF Hamiltonian, consisting of only three (Tb-a) or two (Tb-b) CFPs. The selection of the CFPs incorporated in this simple model Hamiltonian, and their correlation with the actual geometrical structure of the molecule, was solely guided by the ab initio results and the symmetry arguments given in the text. The experimental INS data for Tb-a and Tb-b were fit to the simplified CF Hamiltonian, optimising the selected three (Tb-a) or two (Tb-b) parameters (Table 2) of: , , where are the extended Stevens operators.4 The two sets of CF field parameters were optimised using the simannfit fitting module of the MCPHASE modelling suite,5 using the values of the CF parameters determined by ab initio calculations as a first guess. Many other sets of initial CF parameters were also employed and the fitting program either converged to the same solution or did not converge to any solution. The fitting strategy uses a simulated annealing algorithm to iteratively minimise the standard deviation between the simulated and the experimental INS spectra.6 During the iterative fitting procedure the spectrum of the theoretical INS transition probabilities is convoluted with Gaussian functions of appropriate FWHM (870 μeV for λ = 2.37 Å and 250 μeV for λ = 4.74 Å) to generate the simulated INS spectrum to be compared to the experimental one. The experimental data fitted were peaks Ia, IIa, IIIa, Iva and Va of Tb-a at 40 K and peaks Ib and IIb of Tb at 30 K. The 0.3 meV peak was present in all data at all temperatures and assigned as spurious. S9 Magnetic Susceptibility Measurements Variable temperature magnetic susceptibility measurements were performed with a Quantum Design MPMS-5 susceptometer, equipped with a 5 T magnet. Data were collected on powdered, dry crystals in a gelatin capsule. The diamagnetic susceptibility was measured for Y and found to be very similar to the diamagnetic correction calculated from Pascal's constants, which was employed to correct the magnetic susceptibility measured for Tb. Other Measurements Elemental analyses were performed by the Campbell Microanalytical Laboratory, University of Otago, New Zealand. Thermogravimetric analyses were performed on a Mettler Toledo thermal analyzer. Infrared spectra (KBr disk or ATR) were recorded on a Bruker Tensor 27 FTIR spectrometer. Theoretical Calculations The ab initio calculations were carried out using the commercial Molcas 8.0 software package.[7–9] The typical timeframe for a full calculation was 72-96 h. The structural inputs of calculations for Tb-a and Tb-b were the Cartesian coordinates of the isolated [Tb(W5O18)2] 9- anion obtained from high quality single crystal X- ray diffraction data at 130 K, with no addition of counterions to balance the charge (table S6a). The point symmetry for the isolated [Tb(W5O18)2] 9- anion used in the calculations is C1. The z axis of the Cartesian reference system was chosen to incorporate atoms Tb1 and W1 for Tb-a and W1 and W10 for Tb-b. The ab initio calculations do not take into account the electrostatic potential arising from the crystal, as they are done on the isolated C1 symmetry anion. From a computational point of view, the presence of the {W5O18} ligands makes any attempt to use a full basis to describe the heavy W atoms extremely demanding. In order to reduce the computational load all W atoms were represented with an ab initio S10 Model Potential (W.ECP.Casarrubios.13s10p9d5f.3s3p4d2f.12e-CG-AIMP), using the basis set contraction suggested by Molcas.10,11 For other elements ANO-RCC basis sets were employed, with a TZP quality basis set for Tb and DZP quality basis set for O. The well-established procedure that provides the full ab initio electrostatic and strongly spin-orbit coupled eigenvalues and eigenvectors, including the full treatment of static correlation effects via complete-active space methods, involves the use of different modules of Molcas 8.0 (SEWARD + RASSCF + RASSI). In the computation of the bi- electronic integrals performed by the SEWARD module the Cholesky decomposition with a threshold of 10-8 was used in order to save disk space. The spin-only wavefunctions corresponding to the spin multiplicity of 7, 5, 3, and 1 were optimised using the Complete Active Space Self-Consistent Field (CASSCF) method supplied by the module RASSCF, (Restricted Active Space Self Consistent Field) with the active space set as the 8 electrons of Tb(III) in the 4f orbitals.12 The module RASSI (Restricted Active Space State Interaction) was used to introduce the spin–orbit coupling with the restricted active space state interaction method.13 A selected number of different spin states (149) were allowed to interact in the RASSI module, namely 7 septets (out of 7), 84 quintets (out of 140) and 58 (out of 588) triplets. None of the 490 singlets were included in the calculations because of their high energy. The static magnetic properties, the components of the lowest lying ab initio wavefunctions projected onto a (2J+1)-dimensional pseudo-spin basis set (Table S3 and S4), and the crystal field parameters (Table S5) were finally calculated from the CASSCF/RASSI results employing a rigorous, well-established and widely used projection technique implemented in the SINGLE_ANISO module of Molcas 8.0.14 In the SINGLE_ANISO computation the reference frame used for the quantisation of the total angular momentum basis when projecting the full ab initio wavefunctions on to the effective spin-orbit ground multiplet (J = 6) of the Tb(III) ion corresponds to the three S11 principal magnetic axes of the calculated g-tensor for the lowest energy quasi-degenerate doublet (first excited doublet) with the origin of the reference system lying on the Tb(III) ion (Table S6b and Figure S19). The choice of the quantisation axis along the z component of the g tensor allows the projections of the lowest lying CASSCF/RASSI wavefunctions onto the (2J+1)-dimensional basis to have almost pure ±MJ components (Table S3 and S4). It turns out that the anisotropy axis, as determined from the g-tensor of the first excited pseudo doublet, is approximately coincident with the pseudo C4 axis of the molecule (Table S6b). The matrix elements of the all-electron spin and angular momentum operators between low-lying optimised ab-initio CASSF/RASSI wavefunctions corresponding to the crystal field levels were used to calculate transition probabilities (i.e. INS peak intensities) in the reported theoretical INS spectra. S12 Fig. S1 Top: Measured ATR-IR spectra for TbD (thin line) and YD (thick line). Bottom: Thermogravimetric analysis data for TbD 1800 1600 1400 1200 1000 800 600 400 0.5 0.6 0.7 0.8 0.9 1.0 T ra n sm itt a n ce Wavenumber / cm-1 0 500 1000 88 89 90 91 92 93 94 95 96 97 98 99 100 % m as s lo ss temperature / °C Fig. S2 T simulation f using the se dependenc for Tb-a (re ets of optim ce of the χ ed) and Tb- mised crysta χMT product -b (blue). D al field param S13 t in the 2-3 Dashed lines meters as d 300 K rang s: simulatio described in ge for Tb-a ons for Tb-a n the main te a. Solid line a (red) and ext. es: ab initio Tb-b (blue o ) Fig. S3 Bo (orange, 50 elastic line. ottom: INS s 0 K) and Tb Neutron w spectra for bD (black, 4 wavelength λ YD (orange 0 K). All sp λ = 4.74 Å ( S14 e, 10 K) and pectra integ left) and λ = d TbD (blac rated over a = 2.37 Å (rig ck, 10 K). T all Q range ght). Top: INS sp e and norma ectra for YD alised to the D e Fig. S4 S(Q Fig. S5 S(Q Q,ω) diagra Q,ω) diagra m of Tb at m of Tb at 5 K and λ = 30 K and λ S15 = 4.74 Å neu = 4.74 Å ne utron wavel eutron wave ength. elength. Fig. S6 S(Q Fig. S7 S(Q Q,ω) diagra Q,ω) diagra m of Tb at m of Tb at 5 K and λ = 30 K and λ S16 = 2.37 Å neu = 2.37 Å ne utron wavel eutron wave ength. elength. Fig. S8 Q d K) for TbD. range 0.9 ≤ ≤ 2.0 meV, binning inte interval = 0 dependence Theoretica ≤ E ≤ 1.1 me binning int erval = 0.3 .3 Å-1) e of scatter al F2(Q) fun eV, binning terval = 0.3 Å-1); d) pe ring intensit nction for Tb interval = 0 Å-1); c) pea eak IIb (λ = S17 ty at energy b(III) ion (so 0.2 Å-1); b) p ak IIa (λ = 2 2.37 Å, in y correspon olid line); a peak Ia (λ = 2.37 Å, inte tegration ra ding to pea a) peak Ib (λ = 2.37 Å, int egration ran ange 4.1 ≤ aks Ia, IIa, I λ = 4.74 Å tegration ra nge 2.4 ≤ E E ≤ 4.3 m b and IIb (5 , integration ange 1.2 ≤ E ≤ 3.2 meV meV, binning 5 n E V, g Fig. S9 Po Experiment owder X-ra tal for Tb. d ay diffractio d) Experime n patterns. ental for Tb- S18 . a) Simula -b. e) Simul ated for Tb ated for Tb b-a. b) Exp -b perimental ffor Tb-a. c c) Fig. S10 C molecular a (turquoise) are omitted Fig. S11 R pairs of pla O17/O19-L ideal value average Crystal pac axis of [Tb and WO6 u d. Representati anes O16-L Ln-O21 (Pa2 of 45º of th deviation king diagra (W5O18)2] 9-. units as poly ion of the fo n-O18/O19 2/Pb1), O15 he skew an from 45 ams for Tb- Water-coo yhedra (yell our acute d -Ln-O21 (P 5-Ln-O17/O ngle betwee 5º (AD(ϕ) S19 -a (left) an ordinated so low). Oxyge ihedral ang Pa1/Pb1), O O20-Ln-O22 en the two b )45) calcu ∑4 1 d Tb-b (rig odium catio en atoms of gles ϕ1, ϕ2, O16-Ln-O18 2 (Pa2/Pb2) bases of the ulated ove 45 4 ght) viewed ons are rep f Na-coordin ϕ3, and ϕ4 /O20-Ln-O2 ). The avera e antiprism er ϕ1, d along the presented a nating wate 4 generated 22 (Pa1/Pb rage deviati is here def ϕ2, ϕ3, pseudo C as space-fil er molecules d by the fou b2), O15-Ln on from the fined as the and ϕ4 4 ll s r - e e 4: Fig. S12 a multiplet ob low lying st initio calcul Hamiltonian obtained fr ground stat to these e literature va Hamiltonian ) Detail of btained from tates corres lation for Tb n with fitted om the sim te multiplet nergy leve alues for Tb n the energie m CASSCF/ sponding to b-b. c) J = d crystal fie mplified CF energies li ls were no b-a; crystal es of the low /RASSI ab i the J = 6 g 6 ground s eld paramet Hamiltonian terature va ot explicitly field param S20 w lying sta initio calcula ground state state multip ters for Tb n with fitted lues for Tb reported. meters (cm-1 .17 tes corresp ation for Tb e multiplet o plet energies -a. d) J = 6 d crystal fie -a, the crys 16 f) J = 6 ) = -36 ponding to t b-a. b) Deta obtained fro s obtained 6 ground s eld paramet stal field pa 6 ground st 6.8, = the J = 6 g il of the ene om CASSC from the si state multip ters for Tb- arameters th tate multipl -89.0, ground state ergies of the F/RASSI ab implified CF let energies -b. e) J = 6 hat give rise et energies = -5.2 with e e b F s 6 e s h S21 Table S2. CASSCF/RASSI spin-orbit energies for the low-lying multiplets of Tb-a and Tb-b. Tb-a Tb-b cm-1 meV cm-1 meV 7F6 1 0 0 0 0 2 18.466 2.28936 14.352 1.77932 3 25.147 3.11765 30.229 3.74771 4 81.752 10.13538 78.352 9.71386 5 94.735 11.74498 99.566 12.34391 6 200.811 24.89598 199.459 24.72837 7 201.413 24.97062 201.099 24.93169 8 358.782 44.48078 354.728 43.97818 9 358.941 44.5005 355.13 44.02802 10 527.501 65.39809 519.765 64.439 11 527.505 65.39859 519.772 64.43987 12 586.067 72.65894 580.385 71.9545 13 586.067 72.65894 580.385 71.9545 7F5 14 2209.368 273.91123 2209.583 273.93789 15 2230.01 276.47037 2226.291 276.0093 16 2231.993 276.71622 2231.31 276.63154 17 2269.215 281.3309 2259.784 280.16167 18 2269.967 281.42413 2267.341 281.09856 19 2271.702 281.63923 2270.141 281.4457 20 2294.313 284.44247 2298.68 284.98388 21 2306.181 285.91384 2304.035 285.64778 22 2307.285 286.05071 2308.036 286.14381 23 2576.219 319.39239 2569.276 318.53161 24 2576.24 319.39499 2569.33 318.53831 7F4 25 3596.143 445.8397 3593.763 445.54463 26 3602.897 446.67704 3604.69 446.89933 27 3643.502 451.71113 3642.266 451.5579 28 3644.484 451.83288 3642.869 451.63266 29 3738.093 463.43826 3733.899 462.9183 30 3741.218 463.82569 3739.921 463.66489 31 3810.095 472.36486 3792.573 470.19254 32 3836.758 475.67047 3831.79 475.05455 33 3850.225 477.34007 3858.478 478.36325 S22 Table S3. Complex amplitudes of the CASSCF/RASSI wavefunctions corresponding to the lowest atomic multiplet J = 6 on the basis of total angular momentum eigenstates |JM > for Tb-a. The reference system has the origin on the Tb(III) ion and is oriented along the main axes of the g- tensor calculated for the first excited pseudo-doublet of Tb-a. |JM > w.f. 1 w.f. 2 w.f. 3 w.f. 4 -6 -0.000031 -0.000002 -0.000167 0.000299 0.000447 0.000005 -0.000952 -0.001289 -5 -0.001099 0.000002 0.000293 0.004183 0.001910 -0.003914 -0.005202 0.003329 -4 -0.010118 0.009067 0.007381 -0.003644 -0.006176 -0.000140 -0.004284 -0.003992 -3 0.010763 0.003626 0.020538 -0.014014 0.015953 -0.023712 -0.002691 0.024183 -2 0.011448 0.035297 -0.006767 -0.021069 -0.021356 0.016082 0.439397 0.552293 -1 0.021599 -0.022673 -0.449709 -0.544248 0.109177 0.697029 -0.021499 -0.010748 0 0.032393 -0.996798 0.013610 0.023230 -0.035833 -0.000220 -0.016334 0.032367 1 0.020081 0.024027 0.254912 0.658380 -0.117719 0.695637 -0.021418 -0.010909 2 -0.013716 0.034479 -0.015071 -0.016204 -0.021157 -0.016343 -0.705305 -0.025365 3 0.010975 -0.002920 0.022267 -0.011065 -0.015661 -0.023906 0.017855 -0.016531 4 0.009508 0.009705 -0.006787 0.004657 -0.006177 0.000064 0.005756 0.001075 5 -0.001096 -0.000073 -0.003505 -0.002301 -0.001862 -0.003937 -0.000412 -0.006163 6 0.000031 0.000000 0.000342 0.000000 0.000447 0.000000 0.001603 0.000000 |JM > w.f. 5 w.f. 6 w.f. 7 w.f. 8 -6 0.000989 0.001324 -0.004571 -0.001969 -0.004547 -0.001930 -0.001672 -0.001202 -5 0.005323 -0.003317 0.000642 -0.003705 0.001114 -0.003791 -0.007125 0.039120 -4 0.005906 0.004841 -0.026064 0.010179 -0.026373 0.009748 0.317073 0.630078 -3 0.002493 -0.024554 -0.316411 0.631119 -0.314271 0.631179 -0.026320 -0.009656 -2 -0.439708 -0.551904 -0.007357 -0.023216 -0.009042 -0.023156 0.001344 0.006035 -1 0.024922 -0.006850 0.010199 -0.007336 -0.024508 0.025542 -0.006094 0.004362 0 -0.032999 -0.016534 -0.000051 0.000245 -0.016657 -0.003389 0.000284 -0.000881 1 -0.009433 -0.024064 0.006465 0.010772 0.012579 0.033088 -0.002402 -0.007099 2 -0.705313 -0.021792 0.015941 -0.018413 -0.017371 0.017782 -0.004614 0.004116 3 0.018175 -0.016697 -0.040945 -0.704805 0.042655 0.703800 -0.027008 -0.007521 4 0.007413 0.001832 0.019912 0.019659 -0.020467 -0.019279 -0.625212 0.326564 5 -0.000530 -0.006250 -0.000876 0.003656 0.000456 -0.003925 0.017047 -0.035924 6 0.001652 0.000000 0.004977 0.000000 -0.004939 0.000000 0.002059 0.000000 |JM > w.f. 9 w.f. 10 w.f. 11 w.f. 12 -6 0.001687 0.001201 0.037352 -0.132782 0.037365 -0.132785 -0.693147 -0.022122 -5 0.007028 -0.039144 -0.114731 -0.682804 -0.114700 -0.682803 0.126325 -0.054838 -4 -0.318411 -0.629252 0.028687 0.026447 0.028696 0.026436 -0.005402 0.005633 -3 0.026488 0.009278 -0.000168 -0.003212 -0.000091 -0.003391 0.001128 -0.005263 -2 -0.002287 -0.006006 0.006128 -0.001708 0.006350 -0.001754 -0.000937 0.001278 -1 0.005787 -0.004908 -0.003227 -0.002443 -0.003417 -0.002616 0.000326 -0.000450 0 -0.018293 -0.005847 0.000181 0.000239 0.000176 -0.000134 -0.000001 0.000065 1 -0.001867 -0.007355 0.001478 0.003768 -0.001592 -0.003998 0.000312 0.000460 2 -0.005346 0.003566 -0.003303 0.005437 0.003409 -0.005638 0.000896 0.001307 3 -0.026958 -0.007805 0.003046 0.001032 -0.003240 -0.001006 0.000959 0.005297 4 -0.624349 0.327919 0.017690 0.034776 -0.017674 -0.034784 0.005219 0.005803 5 0.016978 -0.035964 0.626225 0.295341 -0.626206 -0.295368 0.124511 0.058840 6 0.002071 0.000000 -0.137936 0.000000 0.137942 0.000000 0.693500 0.000000 |JM > w.f. 13 -- -6 0.693145 0.022124 -5 -0.126328 0.054845 -4 0.005405 -0.005627 -3 -0.001133 0.005291 -2 0.000933 -0.001230 -1 -0.000395 0.000582 0 0.000069 0.000001 1 0.000376 0.000594 2 0.000893 0.001259 3 0.000963 0.005324 4 0.005223 0.005796 5 0.124515 0.058847 6 0.693498 0.000000 S23 Table S4. Complex amplitudes of the CASSCF/RASSI wavefunctions corresponding to the lowest atomic multiplet J = 6 on the basis of total angular momentum eigenstates |JM > for Tb-b. The reference system has the origin on the Tb(III) ion and is oriented along the main axes of the g- tensor calculated for the first excited pseudo-doublet of Tb-b. |JM > w.f. 1 w.f. 2 w.f. 3 w.f. 4 -6 -0.000151 -0.000176 -0.000195 -0.000132 0.000059 0.000308 -0.000698 0.000791 -5 0.000326 0.000325 -0.004116 -0.004434 0.001857 0.005176 0.001235 0.002200 -4 0.012373 0.016214 -0.001104 0.002528 0.003757 -0.002602 -0.012718 -0.007041 -3 0.004232 -0.005344 0.035347 0.000518 -0.006108 0.059030 0.003793 -0.024392 -2 -0.047816 0.072362 0.023378 -0.009784 -0.020721 -0.007818 0.547354 0.443186 -1 -0.031135 0.006993 -0.247825 0.660523 0.482615 -0.512149 0.019029 -0.013250 0 0.413276 -0.900664 -0.007818 0.025476 -0.029322 -0.024196 0.066027 -0.029799 1 -0.015004 -0.028164 0.165359 -0.685832 0.411216 -0.571065 -0.022525 0.005504 2 -0.023675 0.083439 -0.013865 -0.021214 -0.011610 -0.018860 0.029770 -0.703651 3 -0.001291 0.006693 0.029553 0.019399 -0.056797 0.017203 -0.020801 -0.013292 4 -0.020361 0.001193 -0.000504 0.002712 -0.001841 0.004182 -0.003134 0.014195 5 0.000460 0.000035 -0.005894 0.001361 -0.005434 -0.000841 0.000833 0.002382 6 0.000232 0.000000 0.000236 0.000000 0.000313 0.000000 -0.001054 0.000000 |JM > w.f. 5 w.f. 6 w.f. 7 w.f. 8 -6 0.000655 -0.000878 -0.000671 -0.001989 -0.000623 -0.002058 -0.007521 -0.003971 -5 -0.001224 -0.002310 0.009462 -0.000617 0.010166 -0.001342 0.020507 -0.037507 -4 0.016893 0.009213 0.010857 0.027249 0.010082 0.027274 0.479502 0.516760 -3 -0.001778 0.025425 -0.701219 -0.081049 -0.696610 -0.091814 0.028838 -0.008353 -2 -0.566801 -0.414965 -0.016424 0.019462 -0.014554 0.022518 0.010502 0.010891 -1 -0.025492 0.007849 0.009379 0.001724 -0.067106 -0.010998 -0.001372 -0.002111 0 -0.043947 -0.087590 0.006092 0.004373 -0.002100 0.002829 -0.000609 -0.000151 1 -0.021530 0.015744 -0.004633 -0.008335 -0.029963 -0.061044 0.002199 -0.001227 2 0.006153 -0.702439 0.013187 -0.021785 -0.017338 0.020452 0.014372 -0.004728 3 -0.021445 -0.013773 0.301056 0.638469 -0.289638 -0.640160 -0.021602 -0.020850 4 -0.002712 0.019050 0.029290 0.001572 -0.029025 -0.001750 0.665297 -0.233116 5 0.001120 0.002362 -0.002442 -0.009163 0.001659 0.010119 -0.000624 -0.042742 6 -0.001095 0.000000 -0.002099 0.000000 0.002150 0.000000 -0.008505 0.000000 |JM > w.f. 9 w.f. 10 w.f. 11 w.f. 12 -6 -0.007547 -0.003960 -0.132911 -0.077459 -0.132921 -0.077455 0.302195 -0.620431 -5 0.020451 -0.037599 0.364139 -0.584558 0.364115 -0.584553 -0.136473 -0.071509 -4 0.479932 0.515859 -0.028105 -0.033694 -0.028186 -0.033727 -0.000831 0.000609 -3 0.028899 -0.008288 0.004971 -0.006625 0.005369 -0.006845 -0.000371 0.000286 -2 0.010024 0.013026 -0.001066 0.000964 -0.001030 0.000952 0.001432 0.000504 -1 0.000813 -0.003409 0.005795 0.000239 0.006231 0.000497 0.000303 -0.001290 0 -0.007289 0.029577 0.000879 0.000237 0.000464 -0.001718 -0.000009 0.000006 1 -0.000864 0.003396 -0.005127 -0.002711 0.005634 0.002708 -0.001292 -0.000293 2 -0.014929 0.006877 -0.000435 -0.001370 0.000410 0.001341 0.000174 -0.001509 3 0.021739 0.020767 -0.000959 -0.008226 0.001193 0.008618 0.000420 -0.000208 4 -0.664668 0.233799 -0.041248 0.014960 0.041334 -0.014949 -0.000911 0.000481 5 0.000639 0.042796 -0.020274 -0.688399 0.020292 0.688383 -0.004528 -0.154007 6 0.008523 0.000000 -0.153835 0.000000 0.153841 0.000000 0.690113 0.000000 |JM > w.f. 13 -- -6 -0.302191 0.620432 -5 0.136473 0.071517 -4 0.000835 -0.000607 -3 0.000311 -0.000220 -2 -0.001485 -0.000538 -1 -0.000324 0.001284 0 0.000118 0.000188 1 -0.001297 -0.000271 2 0.000167 -0.001571 3 0.000334 -0.000183 4 -0.000911 0.000485 5 -0.004536 -0.154010 6 0.690112 0.000000 Fig. S13 Va 0.8 Å-1< Q ariable tem < 2.4 Å-1 . perature IN NS spectra f S24 for Tb-aD. DData collecteed at λ = 4.774 Å, integrration range e Fig. S14 Va 0.8 Å-1< Q < ariable tem < 2.4 Å-1, b perature IN inning interv NS spectra f val 0.125 m S25 for Tb-aD. D meV. Data collecteed at λ = 2.337 Å, integrration range e Fig. S15 S( Fig. S16 S( (Q,ω) diagr (Q,ω) diagr ram of Tb-a ram of Tb-a D at 5 K and D at 40 K an S26 d λ = 4.74 Å nd λ = 4.74 Å neutron w Å neutron w wavelength. wavelengthh. Fig. S17 S( Fig. S18 S( (Q,ω) diagr (Q,ω) diagr ram of Tb-a ram of Tb-a D at 5 K and D at 40 K an S27 d λ = 2.37 Å nd λ = 2.37 Å neutron w Å neutron w wavelength. wavelengthh. S28 Table S5. CASSCF/RASSI B(k,q) crystal field parameters (meV) for the Extended Stevens Operators (ESO) as computed by the SINGLE_ANISO module of Molcas, with k the rank and q the component of the operator. The reference system has the origin on the Tb(III) ion and is oriented along the main axes of the g-tensor calculated for the first excited pseudo-doublet of Tb-a and Tb-b respectively. Tb-a Tb-b k q B(k,q) k q B(k,q) 2 -2 0.00364 2 -2 1.42972E-4 2 -1 0.05851 2 -1 -0.10409 2 0 0.71028 2 0 0.70018 2 1 -0.08244 2 1 0.02901 2 2 0.01852 2 2 0.04564 4 -4 -6.53997E-4 4 -4 0.00117 4 -3 0.00169 4 -3 2.58863E-5 4 -2 -3.79475E-5 4 -2 6.68707E-5 4 -1 1.09886E-4 4 -1 -6.64415E-4 4 0 -0.00122 4 0 -0.00119 4 1 -5.0348E-4 4 1 -1.58559E-4 4 2 -3.31725E-5 4 2 -1.0613E-4 4 3 1.95295E-4 4 3 -5.48863E-4 4 4 5.98773E-4 4 4 7.10936E-4 6 -6 -6.21112E-8 6 -6 2.28334E-8 6 -5 -2.93668E-6 6 -5 3.74757E-6 6 -4 3.21245E-6 6 -4 -4.35004E-6 6 -3 9.94548E-7 6 -3 3.64135E-6 6 -2 -2.52274E-7 6 -2 6.89233E-8 6 -1 -1.97598E-6 6 -1 -2.44123E-6 6 0 -7.51428E-6 6 0 -7.22833E-6 6 1 -1.7076E-6 6 1 -3.5608E-6 6 2 -3.75784E-7 6 2 -6.59497E-7 6 3 -2.49986E-6 6 3 2.32893E-6 6 4 -3.59595E-7 6 4 -3.86924E-6 6 5 -6.18049E-7 6 5 4.3616E-6 6 6 3.07338E-7 6 6 -1.04473E-9 S29 Table S6. Cartesian coordinates (Å) used as inputs in the CASSCF/RASSI/SINGLE_ANISO calculations for Tb-a and Tb-b (a) and orientation of the first excited pseudo doublet g-tensor axes in the molecular reference system for Tb-a and Tb-b (b). (a) Tb-a Tb-b O1 0.05225 -0.00323 7.11921 -0.19205 0.22269 -7.15046 O2 -1.25378 -1.33731 4.94483 1.06981 -1.23404 -5.09732 O3 -1.31545 1.30006 4.97095 1.256 1.39347 -5.00111 O4 1.32407 1.36924 4.95861 -1.34821 1.59979 -4.90387 O5 1.37649 -1.24149 4.92996 -1.58306 -1.01093 -5.00122 O6 0.04279 0.03474 3.12176 -0.09014 0.11791 -3.15935 O7 0.09006 -2.69385 3.11583 -0.30837 -2.54682 -3.25163 O8 -2.74217 -2.98706 3.10081 2.52561 -2.94153 -3.36041 O9 -2.63549 -0.0535 3.11431 2.5692 -0.10461 -3.26238 O10 -2.88419 2.78646 3.17968 2.99797 2.72191 -3.23684 O11 -0.03014 2.69736 3.14388 0.13227 2.80004 -3.08621 O12 2.79737 2.98367 3.09654 -2.66838 3.2308 -2.97012 O13 2.72311 0.09527 3.11903 -2.76627 0.33964 -3.0483 O14 2.96279 -2.74072 3.16752 -3.18033 -2.44946 -3.20784 O15 -1.39436 -1.4569 1.20204 1.29423 -1.48625 -1.35655 O16 -1.4372 1.43242 1.22415 1.51685 1.38702 -1.28229 O17 1.41136 1.47444 1.23743 -1.34984 1.58143 -1.18948 O18 1.50674 -1.39784 1.22648 -1.59521 -1.30612 -1.24353 O19 -0.00723 -2.04887 -1.25432 -0.00229 -2.05105 1.24491 O20 -2.00795 0.04105 -1.30679 2.05433 0.00107 1.23307 O21 0.05321 2.02274 -1.29618 0.02335 2.02333 1.23598 O22 2.05043 -0.05016 -1.239 -2.01944 0.00102 1.25773 O23 1.92637 -1.91653 -3.11626 -1.89083 -1.90886 3.15993 O24 -0.01698 -4.03044 -3.19739 0.04597 -4.0496 3.19042 O25 -1.87081 -1.8931 -3.20499 1.89525 -1.88564 3.13251 O26 -3.98366 0.05173 -3.28715 4.07155 -0.01534 3.16017 O27 -1.81261 1.92981 -3.22407 1.90461 1.90187 3.13061 O28 0.186 4.01348 -3.22855 -0.01768 4.05659 3.12996 O29 1.99695 1.8498 -3.13394 -1.90136 1.90581 3.12309 O30 4.12138 -0.10669 -3.08398 -4.04427 0.00851 3.14351 O31 0.06822 -0.02724 -3.1751 0.00606 -0.00284 3.14174 O32 0.0833 -1.89885 -5.01044 -6.10E-04 -1.86092 4.97603 O33 -1.76193 -0.0018 -5.05765 1.8935 0.01191 4.97375 O34 0.13273 1.80848 -5.02556 0.01753 1.89089 4.9615 O35 1.97844 -0.0645 -4.98087 -1.84995 -7.50E-04 4.96893 O36 0.15790 -0.05362 -7.17573 -0.00336 0.01093 7.10625 W1 0.00000 0.00000 5.3853 -0.15607 0.19455 -5.42122 W2 -1.58409 -1.69341 2.98583 1.40019 -1.65202 -3.13661 W3 -1.62991 1.61169 2.98991 1.68984 1.59866 -3.04521 W4 1.61709 1.69769 2.99304 -1.5674 1.88468 -2.93104 W5 1.69358 -1.57449 3.00088 -1.84933 -1.37053 -3.00649 W6 0.00352 -2.31222 -3.02346 0.0145 -2.31809 3.01526 W7 -2.2591 0.04166 -3.08377 2.32092 0.0124 3.00058 W8 0.08956 2.28963 -3.06131 0.00135 2.31112 3.00158 W9 2.37822 -0.05454 -2.98942 -2.31556 -0.01155 3.02915 W10 0.10732 -0.01888 -5.43697 0.00000 0.00000 5.38813 Tb 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 (b) Main magnetic axes of the first excited doublet g-tensor Tb-a Tb-b X -0.73912 0.67357 -0.00281 -0.84670 -0.53170 0.01985 Y -0.67354 -0.73912 -0.00705 0.53102 -0.84679 -0.03108 Z -0.00682 -0.00332 0.99997 0.03334 -0.01578 0.99932 Fig. S19 M tensor axes olecular int s (red) for T ternal refere Tb-a (right) a ence system and Tb-b (le S30 m (blue) and eft). d orientationn of the firstt pseudo do oublet g- Fig. S20 Fi a) Experim individual p optimised c probabilities itted and ca mental data peak contri crystal field s as calcula alculated IN with Gaus ibutions (bl d paramete ated from th S spectra o sian fitting lack line). ers as desc he ab initio m S31 of Tb-a at λ of magnet b) Simulate cribed in t model for T = 4.74 Å (l ic signals ( ed INS spe he main te Tb-a. eft) and λ = (orange line ectra (red ext. c) The = 2.37 Å (rig es) and co line) using eoretical IN ght) at 30 K nvolution o the set o S transition K. of of n Fig. S21 Fi a) Experime peak contri Theoretical itted and ca ental data w butions (bla l INS transit alculated IN with Gaussi ack). b) Sim tion probab NS spectra o an fitting of mulated INS ilities as ca S32 of Tb-a at λ f magnetic s S spectra (re lculated fro λ = 4.74 Å ( signals (ora ed) using th m the ab in (left) and λ ange) and co he set of op itio model fo = 2.37 Å (r convolution ptimised cry for Tb-a. right) at 5 K of individua ystal field. c K. al c) Fig. S22 Fi Experiment contribution optimised c transition p simulations itted and ca tal INS da ns (black). crystal field probabilities s a 70:30 m alculated IN ata with G b) Simulat and convo s as calcula olar ratio of NS spectra o Gaussian f ted INS sp lution of ind ated from a f Tb-a:Tb-b S33 of Tb at λ = fitting (ora pectra of Tb dividual pha ab initio re b was assum = 4.74 Å (lef nge) and b-a (red) a ases contrib sults for T med. ft) and λ = 2 convolutio and Tb-b (b butions (bla b-a (red) a 2.37 Å (righ n of indiv blue) using ack). c) The and Tb-b ( ht) at 5 K. a vidual peak g the set o oretical INS blue). 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