ELECTRONIC SUPPLEMENTARY INFORMATION

There is nothing wrong with being soft: using sulfur ligands to increase

axiality in a Dy(III) Single-Ion Magnet†

Angelos B. Canaj,a Sourav Dey,b Oscar Cespedes,c Claire Wilsona, Gopalan Rajaraman*b and Mark

Murrie*a

a School of Chemistry, University of Glasgow, University Avenue, Glasgow, G12 8QQ, UK. E-mail:

Mark.Murrie@glasgow.ac.uk b Department of Chemistry, Indian Institute of Technology Bombay, Powai, Mumbai, Maharashtra,

400076, India. E-mail: rajaraman@chem.iitb.ac.in c School of Physics and Astronomy, University of Leeds, Leeds LS2 9JT, UK.

Electronic Supplementary Material (ESI) for ChemComm.This journal is © The Royal Society of Chemistry 2019

1. Materials and physical measurements

All experiments were carried out using standard Schlenk techniques with air and moisture sensitive

materials stored and handled in a glovebox. All solvents used were dried using a solvent purification

system. Elemental analyses (C, H, N) were performed by the University of Glasgow microanalysis

service. Variable-temperature, solid-state magnetic susceptibility data were collected on a Quantum

Design MPMS-XL SQUID magnetometer equipped with a 5 T magnet at the University of Glasgow and

on a Quantum Design SQUID-VSM magnetometer at the University of Leeds. Ac magnetic

susceptibility data were collected on a Quantum Design MPMS3 SQUID magnetometer at the

University of Glasgow. Polycrystalline samples were embedded in eicosane and diamagnetic

corrections were applied to the observed paramagnetic susceptibilities using Pascal’s constants.

Powder XRD measurements were collected on freshly prepared samples of

[DyIIILON3(C5H10NS2)2]⋅0.5THF (1) on a PANalytical X'Pert Pro MPD diffractometer (λ (CuKα1) = 1.5405 Å)

on a mounted bracket sample stage, at the University of Glasgow. Single Crystal X-Ray diffraction data

were collected using a Bruker D8 VENTURE diffractometer equipped with a Photon II CPAD detector,

with an Oxford Cryosystems N-Helix device mounted on an IμS 3.0 (dual Cu and Mo) microfocus

sealed tube generator at the University of Glasgow. 1H NMR spectra were recorded at 298 K on a

Bruker AVIII 500 MHz spectrometer at the University of Glasgow.

2. Synthesis and characterization

Synthetic strategy for HLON3: N-(3,5-di-tert-butyl-2-hydroxybenzyl)-N,N-bis(2-pyridylmethyl)amine:

The preparation of N-(3,5-di-tert-butyl-2-hydroxybenzyl)-N,N-bis(2-pyridylmethyl)amine was

performed following a similar protocol to that used in the literature.1 In a Schlenk flask containing 30

ml of dichloroethane, ~1.08 ml (5.96 mmol) of di-(2-picolyl)amine and 1.396 g (5.96 mmol) of 3,5-di-

tert-butyl-2-hydroxybenzaldehyde were transferred under argon. The reaction mixture was stirred

under argon overnight at room temperature. The gold color turns to oily green. 2.014 g (9.5 mmol) of

sodium triacetoxyborohydride were transferred into the reaction (in three parts), which was then left

stirring under argon for 48 hours at room temperature. 10 mmol of sodium bicarbonate were

dissolved in 60 ml of distilled water and then were transferred slowly to the reaction mixture creating

two layers. The layers (organic and aqueous) were left stirring for 1 h and then the organic layer was

extracted using CH2Cl2. All combined organic layers were dried using sodium sulfate and after

filtration the CH2Cl2 was removed using a rotary evaporator to yield a yellow oil. Yield: ~ 80 %. 1H NMR

in CDCl3: δ 8.48 (2H, d); 7.55 (2H, t); 7.30 (2H, d); 7.18 (1H, s); 7.10 (2H, t); 6.80 (1H, s); 3.80 (4H, s);

3.73 (2H, s); 1.38 (9H, s); 1.19 (9H, s).

Scheme S1. Synthesis of N-(3,5-di-tert-butyl-2-hydroxybenzyl)-N,N-bis(2-pyridylmethyl)amine, HLON3.

Synthetic strategy for 1:

A Schlenk flask containing N-(3,5-di-tert-butyl-2-hydroxybenzyl)-N,N-bis(2-

pyridylmethyl)amine (43 mg, 0.18 mmol) and Dy(CF3SO3)3 (55 mg, 0.09 mmol) was heated

under vacuum using a moderate Bunsen burner flame up to the point that the N-(3,5-di-tert-

butyl-2-hydroxybenzyl)-N,N-bis(2-pyridylmethyl)amine ligand (HLON3) was melted in the

presence of Dy(CF3SO3)3. The hot flask was allowed to reach room temperature under argon.

The brown precipitate was treated with 5 ml of dry THF. The clear brown solution formed was

stirred for 2h at room temperature. Evaporation of the brown THF solution under vacuum

afforded an oily precipitate. The precipitate was treated with 2 ml of anhydrous pyridine. The

clear brown pyridine solution was left stirring under argon for 24 h producing a yellow

precipitate. The precipitate was filtered and transferred into a Schlenk flask containing

diethyldithiocarbamic acid diethylammonium salt (28 mg, 0.125 mmol). 3 ml of dry THF was

added and the reaction was stirred at 45 °C for 1 h under argon. After 1 h the reaction was left

stirring until it reached room temperature. Single crystals of [DyIIILON3(C5H10NS2)2].0.5THF (1)

were isolated by slow diffusion of dry pentane into the THF solution.

Elemental Anal. calcd (found) for 1.0.3H2O: C 51.29 (51.33), H 6.45 (6.49), N 7.64 (7.68) %.

Crystallographic details

The structure of 1 was solved using ShelxT (SHELXT: Sheldrick, G. M. (2015). Acta Cryst. A71, 3-8.) and

refined using ShelXL (Sheldrick, G.M. (2015). Acta Cryst. C71, 3-8) within the program Olex2

(Dolomanov, O.V., Bourhis, L.J., Gildea, R.J, Howard, J.A.K. & Puschmann, H. (2009), J. Appl. Cryst. 42,

339-341). All non-hydrogen atoms were refined with anistropic atomic displacement parameters

(ADPs), except the partially occupied lattice THF molecule which was refined with isotropic adps.

Hydrogen atoms were placed in geometrically calculated positions and included as part of a riding

model or as a rigid rotor for Me groups. Disorder in one t-Butyl group was modelled with all Me

carbon over two partially occupied sites with occupancy 0.57:0.43 and a 0.5 occupied molecule of THF

was included with 3 atoms modelled over two 0.25 occupied sites, suitable distance restraints were

applied. Further details are given in the CI, deposited with the CCDC number 1950766 and the Table

below.

Table S1. Crystallographic data for complex 1.2

1

Formula C37H54DyN5OS4·0.5(C4H8O)

MW 911.64

Crystal System Monoclinic

Space group P21/c

a/Å 16.4260 (8)

b/Å 14.4027 (7)

c/Å 20.5958 (9)

α/o 90

β/o 111.107 (2)°

γ/o 90

V/Å3 4545.6 (4)

Z 4

T/K 150

λ/Å 0.71073

Dc/g cm-3 1.332

μ(Mo-Kα)/ mm-1 1.86

Meas./indep.(Rint) refl. 47454/10374 (0.024)

Obs. refl. [I>2σ(I)] 9509

wR(F2) 0.067

R[F2 > 2s(F2)] 0.023

S 1.04

Δρmax,min/ eÅ-3 0.85, -0.45

Table S2. Selected bond distances and angles for complex 1 (Å, º).2

Dy1—O1 2.1591 (16) Dy1—S1C 2.8133 (5)

Dy1—N1 2.5403 (18) Dy1—S2C 2.8567 (6)

Dy1—N2 2.5711 (17) Dy1—S3C 2.9647 (6)

Dy1—N3 2.5237 (18) Dy1—S4C 2.8407 (6)

O1—Dy1—N1 76.67 (6) N3—Dy1—S1C 143.51 (4)

O1—Dy1—N2 77.52 (6) N3—Dy1—S2C 85.22 (4)

O1—Dy1—N3 89.15 (6) N3—Dy1—S3C 73.91 (4)

O1—Dy1—S1C 102.04 (4) N3—Dy1—S4C 106.26 (5)

O1—Dy1—S2C 80.94 (4) S1C—Dy1—S2C 62.960 (16)

O1—Dy1—S3C 154.39 (5) S1C—Dy1—S3C 82.240(16)

O1—Dy1—S4C 144.43 (4) S1C—Dy1—S4C 84.570 (18)

N1—Dy1—N2 65.64 (6) S2C—Dy1—S3C 78.667 (17)

N1—Dy1—S1C 85.98 (4) S4C—Dy1—S2C 131.143 (18)

N1—Dy1—S2C 136.60 (4) S4C—Dy1—S3C 60.638 (16)

N1—Dy1—S3C 128.94 (4) N2—Dy1—S4C 80.37 (4)

N1—Dy1—S4C 68.90 (4) N3—Dy1—N1 130.51 (6)

N2—Dy1—S1C 151.11 (4) N3—Dy1—N2 65.04 (6)

N2—Dy1—S2C 143.14 (4) N2—Dy1—S3C 110.83 (4)

Fig. S1 Selected bond distances for complex 1 in Å.

Table S3. Shape measures of complex 1. The lowest CShMs value, is highlighted.3

Dy Symmetry Ideal polyhedron

OP-8 31.667 D8h Octagon

HPY-8 22.926 C7v Heptagonal pyramid

HBPY-8 17.490 D6h Hexagonal bipyramid

CU-8 12.071 Oh Cube

SAPR-8 2.803 D4d Square antiprism

TDD-8 2.790 D2d Triangular dodecahedron

JGBF-8 12.680 D2d Johnson gyrobifastigium J26

JETBPY-8 25.910 D3h Johnson elongated triangular bipyramid J14

JBTPR-8 2.950 C2v Biaugmented trigonal prism J50

BTPR-8 2.707 C2v Biaugmented trigonal prism

JSD-8 4.508 D2d Snub diphenoid J84

TT-8 12.546 Td Triakis tetrahedron

ETBPY-8 21.144 D3h Elongated trigonal bipyramid

Fig. S2 The powder X-ray diffraction pattern of 1 (Inset: diffraction of 1 from 5-300). The black line represents the simulated powder X-ray diffraction pattern generated from single-crystal data collected at 150 K, and the red line represents the experimental data measured at ambient temperature.

Fig. S3 Comparison of the calculated (with SHAPE3) and experimental biaugmented trigonal prism

coordination sphere for the Dy(III) ion in complex 1 . Dy, gold; N, dark blue; O, red; S, brown.

Fig. S4 (Upper) The crystal packing of 1 looking down the b axis, (Lower) with the shortest Dy···Dy

distance of 8.394 Å highlighted. Hydrogen atoms and disorder components are omitted for clarity. Dy,

yellow; N, dark blue; O, red; S, brown; C, grey.

3. Magnetic Properties

Fig. S5 χMT vs. T data for 1 in a field of 1000 Oe from 290 – 2 K. Inset: Magnetisation vs. Field

plot at temperatures 2, 4 and 6 K for 1 from 0.1-5 T.

Fig. S6 The Field cooled (FC) and Zero-Field cooled (ZFC) magnetic susceptibility of 1 at 1000 Oe.

Fig. S7 Powder magnetic hysteresis measurements for 1 at 2-8 K, with an average sweep rate of 20 mTs−1.

Fig. S8 Temperature dependence of the in-phase, χ′Μ (upper), and out-of-phase, χ″Μ (lower) ac

susceptibility, in zero dc field, for 1 with ac frequencies of 5−940 Hz.

Fig. S9 Frequency dependence of the in-phase ac susceptibility for 1 up to 40 K in zero dc field.

The solid lines correspond to the best fit.

Fig. S10 Frequency dependence of the out-of-phase ac susceptibility for 1 up to 40 K in zero dc

field. The solid lines correspond to the best fit.

Fig. S11 χ″Μ vs χ′Μ plot of the AC magnetic susceptibility of 1 in zero dc field. The solid lines

correspond to the best fit to Debye’s law.4

Fig. S12 Frequency dependence of the in-phase (upper) and out-of-phase (lower) susceptibility

at 15 K measured at different dc fields for complex 1. The solid lines correspond to the best fit.

(Upper Inset) Relaxation times (τ) as a function of the applied field (Oe) for 1, showing the

optimum dc field as 1200 Oe.

Fig. S13 Frequency dependence of the in-phase (upper) and out-of-phase (lower) susceptibility

at 30 K measured at different dc fields for complex 1. The solid lines correspond to the best fit.

(Upper Inset) Relaxation times (τ) as a function of the applied field (Oe) for 1, showing the

optimum dc field as 1200 Oe.

Fig. S14 Frequency dependence of the in-phase ac susceptibility for 1 up to 40 K under 1200

Oe dc field. The solid lines correspond to the best fit.

Fig. S15 Frequency dependence of the out-of-phase ac susceptibility for 1 up to 40 K under

1200 Oe dc field. The solid lines correspond to the best fit.

Fig. S16 χ″Μ vs χ′Μ plot of the AC magnetic susceptibility of 1 under 1200 Oe dc field. The solid

lines correspond to the best fit to Debye’s law.4

Fig. S17 Log-Log plot of the relaxation times, τ−1 versus T for 1 in zero dc field. The data were analysed

using the equation: τ−1= τQTM−1 + CTn + τ0

−1 exp(-Ueff/T). The best fit (red line) gives n = 3.24, C = 0.02

K−n s−1, τQTM = 0.017 s , τ0 = 2.99 x 10-12 s,5 and Ueff = 638 K.6

Fig. S18 Log-Log plot of the relaxation times, τ−1 versus T for 1 under 1200 dc field. The data were

analysed using the equation: τ−1= CTn + τ0−1 exp(-Ueff/T). The best fit (red line) gives n = 3.96, C =

3.95x10-5 K−n s−1, τ0 = 1.94 x 10-12 s,5 and Ueff = 656 K.6

4. Ab initio calculations

Computational Details:

To find the magnetic anisotropy of the metal centre in 1 and the model systems ab initio CASSCF+SO-RASSI calculations have been performed using the MOLCAS 8.2 7 program package on the X-ray crystal structures of 1. The relativistic effect of the Dy centre has been taken into account by the DKH Hamiltonian. Disk space for calculation of two-electron integrals has been reduced by the Cholesky decomposition technique.8 The basis set for all the atoms has been taken from the ANO-RCC library implemented in the MOLCAS 8.2 program package. The basis set of VTZP quality was used for Dy, O, N, S, Se, Te atoms. The basis set of VDZ quality was used for the C and H atoms. The active space for the Dy(III) ion contains nine electrons in seven orbitals; i.e. CAS (9.7). The sextet, quartet and doublet states of Dy(III) were optimised with 21, 224 and 490 roots respectively. The 21 sextets, 128 quartets and 130 doublets have been mixed via SO-RASSI to calculate the spin-orbit coupling of the Dy(III) center. Finally, the g tensors and blocking barriers were calculated using the SINGLE_ANISO program which uses the energy of the spin orbit states generated from RASSI-SO.9 The Dy-O/Se/Te and O/Se/Te-C distances in the first set of in silico models 1-O, 1-Se and 1-Te have been fixed from the literature values.10 The geometry optimization in the second set of in silico models (labeled Optimized model in Table S5) has been performed with the UB3LYP12 functional using Gaussian09.13 The Dy atom of 1 and its model systems has been substituted by Gd to simplify the calculation. We have used Ahlrichs split valence basis set (SVP) for C and H, triple-ξ plus polarization (TZVP) for O and N, triple-ξ basis set (TZV) for S,14 and LANL2DZ ECP with its corresponding basis set for Gd.15 We have also performed NBO11 analysis with the UB3LYP12 functional using the Gaussian0913 suite to investigate the covalency of 1 and the model systems.

It is important to note that optimization of the in silico models leads to a decrease in the Ucal values (see Table S5) as the effects of intermolecular interactions / crystal lattice effects are removed, leading to variations in the molecular structure.

In the following tables, the angle between the gzz axis of the ground and excited KDs are higher than ideal collinearity demands, however, it has been shown that inclusion of a dynamic correlation reduces this angle offering relatively a larger window for collinearity, as assumed here.16

Table S4. CASSCF+RASSI-SO computed relative energies of the eight low lying Kramers Doublets (KDs) along with g tensors and deviations from the principal magnetisation axis with respect to the first KD for complex 1. Ucal (K) is shown in bold.

E (K) gxx gyy gzz Angle (°) Composition of mJ levels

0 0.001 0.001 19.859 0.99|±15/2>

313.5 0.023 0.028 17.359 17.3 0.86|±13/2>+0.10|±11/2>

517.6 0.281 0.380 14.372 23.7 0.52|±11/2>+0.23|±9/2>+0.12|±13/2>

651.3 3.063 5.791 10.130 44.9 0.23|±9/2>+0.24|±7/2>+0.16|±5/2>

696.9 9.097 7.887 0.450 10.6 0.28|±5/2>+0.20|±7/2>+0.13|±1/2>

737.2 1.313 4.608 11.758 94.6 0.49|±3/2>+0.12|±9/2>

796.3 0.687 1.302 16.193 94.3 0.48|±1/2>+0.20|±3/2>

963.9 0.060 0.133 19.258 64.2 0.30|±7/2>+0.24|±5/2>

Table S5. CASSCF+RASSI-SO computed relative energies of the eight low lying Kramers Doublets (KDs) along with g tensors and deviations from the principal magnetisation axis with respect to the first KD for models 1-O, 1-Te and 1-Se respectively. Ucal (K) is shown in bold.

Model 1-O (changing axial S-atoms for O-atoms)

E (K) gxx gyy gzz Angle (°) Composition of mJ levels

0 0.002 0.002 19.820 0.99|±15/2>

314.6 0.076 0.111 17.168 19.3 0.86|±13/2>+0.10|±11/2>

528.1 1.645 3.409 12.489 10.3 0.56|±11/2>+0.12|±13/2>+0.15|±9/2>

616.1 0.649 4.260 12.127 61.0 0.26|±9/2>+0.16|±7/2>+0.20|±5/2>

725.8 3.547 5.009 9.551 78.8 0.20|±9/2>+0.24|±7/2>+0.20|±5/2>

819.8 1.198 2.205 14.519 97.4 0.31|±3/2>+0.32|±5/2>+0.16|±7/2>

885.5 0.219 0.630 17.132 92.6 0.56|±1/2>+0.27|±3/2>

1162.3 0.014 0.024 19.598 61.4 0.28|±7/2>+0.21|±9/2>+0.23|±5/2>

Optimized model 1-O (changing axial S-atoms for O-atoms)

E (K) gxx gyy gzz Angle (°)

0.0 0.004 0.004 19.943 302.7 0.049 0.112 17.530 22.0 463.8 1.137 2.380 16.898 79.0 507.2 0.076 4.072 11.151 27.7 608.3 4.146 6.787 10.448 89.1 717.4 1.194 2.099 14.012 80.5

843.6 0.424 0.707 17.510 83.7 1010.7 0.057 0.079 19.737 74.0

Model 1-Te (changing axial S-atoms for Te-atoms)

E (K) gxx gyy gzz Angle (°) Composition of mJ levels

0 0.001 0.001 19.970 0.99|±15/2>

329.4 0.010 0.012 17.520 18.8 0.84|±13/2>+0.11|±11/2>

555.7 0.115 0.153 14.554 25.8 0.46|±11/2>+0.14|±13/2>+0.23|±9/2>

718.1 1.403 2.380 12.003 47.2 0.29|±11/2>+0.19|±7/2>+0.22|±5/2>

768.9 1.513 4.326 14.457 88.9 0.43|±1/2>+0.17|±5/2>+0.13|±9/2>

811.6 1.337 4.896 11.823 95.3 0.38|±3/2>+0.23|±5/2>+0.16|±9/2>

874.3 1.317 2.678 15.702 93.1 0.42|±1/2>+0.19|±3/2>+0.10|±5/2>

1042.7 0.103 0.239 19.241 65.0 0.30|±7/2>+0.25|±5/2>+0.20|±9/2>

Optimized model 1-Te (changing axial S-atoms for Te-atoms)

E (K) gxx gyy gzz Angle (°)

0.0 0.001 0.001 19.979 274.5 0.014 0.015 17.371 11.8 499.2 0.029 0.045 14.604 17.4 657.2 0.896 1.238 12.272 30.4 729.1 0.921 2.592 12.823 67.2 749.2 9.270 7.605 2.095 0.0 804.7 1.137 2.809 14.623 81.7 940.3 0.105 0.275 19.083 67.8

Model 1-Se (changing axial S-atoms for Se-atoms)

E (K) gxx gyy gzz Angle (°) Composition of mJ levels

0 0.000 0.001 19.862 0.99|±15/2>

349.3 0.010 0.012 17.379 17.1 0.87|±13/2>+0.10|±11/2>

589.7 0.140 0.166 14.499 24.1 0.52|±11/2>+0.12|±13/2>+0.22|±9/2>

751.8 1.805 2.574 12.640 52.8 0.24|±11/2>+0.18|±7/2>+0.23|±5/2>

810.6 1.285 4.848 11.195 76.2 0.31|±1/2>+0.10|±5/2>+0.14|±3/2>

859.5 2.238 5.762 11.776 88.7 0.38|±3/2>+0.30|±5/2>+0.15|±9/2>

917.9 0.822 1.456 15.994 91.7 0.44|±1/2>+0.15|±7/2>+0.18|±3/2>

1053.8 0.138 0.340 18.952 66.7 0.29|±7/2>+0.26|±5/2>+0.18|±9/2>

Optimized model 1-Se (changing axial S-atoms for Se-atoms)

E (K) gxx gyy gzz Angle (°)

0.0 0.001 0.001 19.972 285.3 0.020 0.022 17.394 13.5 509.3 0.184 0.209 14.541 18.1 669.0 1.563 1.907 11.787 29.5 738.4 2.442 6.576 11.747 77.3 769.8 0.705 5.368 11.165 90.3 812.0 1.265 2.821 15.416 87.7 920.6 0.130 0.361 18.983 67.8

Table S6. LoProp charges of the atoms attached to the Dy center for complex 1 (See Fig. S13) and for models 1-O, 1-Se and 1-Te respectively.17

1-O 1-O(opt) 1 1-Te 1-Te(opt) 1-Se 1-Se(opt)

Dy1 2.5015 2.5010 2.3701 2.2842 2.2846 2.3528 2.3507

O2 -0.9287 -0.9227 -0.9290 -0.9305 -0.9349 -0.9288 -0.9309

N3 -0.3526 -0.3831 -0.3694 -0.3791 -0.3824 -0.3740 -0.3777

N4 -0.3189 -0.3025 -0.3220 -0.3241 -0.3139 -0.3222 -0.3101

N5 -0.3619 -0.3852 -0.3714 -0.3790 -0.3814 -0.3741 -0.3787

S67(O/S/Te/Se) -0.8277 -0.8353 -0.5616 -0.4950 -0.4891 -0.5304 -0.5749

S68(O/S/Te/Se) -0.8170 -0.8100 -0.5414 -0.4443 -0.4419 -0.5902 -0.5252

S69(O/S/Te/Se) -0.8580 -0.8468 -0.5285 -0.4511 -0.4414 -0.5468 -0.5326

S70(O/S/Te/Se) -0.8167 -0.7891 -0.5916 -0.4490 -0.4467 -0.5466 -0.5110

Table S7. The ab initio computed crystal field parameters for complex 1 and for models 1-O, 1-Te and 1-Se respectively.

k q Bkq (1-O) Bk

q (1) Bkq (1-Te) Bk

q (1-Se)

2

-2 -1 0 1 2

-1.02E+00 1.85E+00 -3.35E+00 -3.63E+00 2.56E+00

-4.01E-01 2.72E+00 -3.07E+00 -2.04E+00 1.24E+00

-1.00E+00 3.63E+00 -3.38E+00 -9.49E-01 1.14E+00

-3.43E-01 3.31E+00 -3.56E+00 -1.14E+00 1.28E+00

B20/av.

non-axial 1.48 1.92 2.01 2.34

4

-4 -3 -2 -1 0 1 2 3 4

-1.76E-03 4.16E-02 -8.54E-03 1.12E-03 -6.23E-03 1.64E-02 9.72E-03 -2.97E-02 -7.25E-03

7.17E-05 3.03E-02 -4.97E-03 -7.13E-03 -5.99E-03 1.19E-02 4.35E-03 -4.58E-03 -3.19E-03

-3.80E-03 1.76E-02 -4.61E-03 -1.22E-02 -6.57E-03 9.36E-03 2.49E-03 1.39E-02 -2.75E-03

-2.05E-03 2.29E-02 -5.82E-03 -9.71E-03 -6.58E-03 9.95E-03 2.85E-03 1.09E-02 -3.10E-03

6

-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

7.98E-05 3.23E-04 -9.96E-05 1.05E-06 1.30E-04 -2.61E-04 7.63E-06 7.09E-05 -7.68E-05 -1.49E-04 2.46E-05 -5.81E-04 5.19E-05

4.38E-05 5.56E-04 -5.17E-05 1.50E-05 1.19E-04 -2.09E-04 4.73E-06 1.56E-05 -2.30E-05 -8.17E-05 -3.78E-05 -2.24E-04 1.10E-04

-2.68E-05 5.68E-04 -3.00E-05 4.22E-05 1.23E-04 -2.36E-04 8.36E-06 -6.00E-05 1.36E-05 -7.18E-05 -6.39E-05 6.88E-05 1.21E-04

-2.24E-05 6.00E-04 -2.73E-05 4.04E-05 1.19E-04 -2.39E-04 7.20E-06 -4.88E-05 8.68E-06 -7.24E-05 -5.96E-05 2.45E-05 1.04E-04

Fig. S19 Ab initio SINGLE_ANISO computed ground state Kramers Doublet for complex 1. Colour code:

Dy, gold; O, red; N, blue; S, brown; C, grey; Hydrogens are omitted for clarity.

Fig. S20 LoProp charges of the atoms attached to the Dy(III) center for complex 1. Colour code: Dy,

gold; O, red; N, blue; S, brown; C, grey.

Fig. S21 Ab initio calculated relaxation dynamics for Models 1-O, 1-Te and 1-Se. The arrows show the

connected energy states with the number representing the matrix element of the transverse moment

(see text for details). Here, the black line indicates the KDs as function of magnetic moments. The red

dashed arrow represents QTM (QTM = quantum tunnelling of the magnetisation) via the ground state

and TA-QTM (TA-QTM = thermally assisted QTM) via excited states. The blue dashed arrow indicates

possible Orbach processes. The pink thick arrow indicates the mechanism of magnetic relaxation. The

numbers above each arrow represent corresponding transverse matrix elements for the transition

magnetic moments.

1-Te 1-Se

1-O

Fig. S22 Ab initio SINGLE_ANISO computed ground state Kramers Doublet for Models 1-O, 1-Te and 1-

Se. Colour code: Dy, gold; O, red; N, blue; Te, lavender; Se, blue-grey; C, grey.

1-Te 1-Se

1-O

Table S8. The composition of the co-ligand Gd-O/S/Se/Te bonds (Note that the Dy atom of 1 and its model systems has been substituted by Gd to simplify the calculations) as computed from natural bond orbital (NBO) analysis, confirming that the Ln-O bonds are strongly ionic and that the covalency increases significantly as we move from O to S, Se and Te.

Bond Contribution from the corresponding elements Gd-O67 0.93% Gd + 99.07% O Gd-O68 0.92% Gd + 99.08% O Gd-O69 0.41% Gd + 99.59% O Gd-O70 0.41% Gd + 99.59% O Gd-S67 13.69% Gd + 86.31% S Gd-S68 13.02% Gd + 86.98% S Gd-S69 11.34% Gd + 88.66% S Gd-S70 12.99% Gd + 87.01% S

Gd-Se67 15.00% Gd + 85.00% Se Gd-Se68 15.10% Gd + 84.90% Se Gd-Se69 15.90% Gd + 84.10% Se Gd-Se70 16.08% Gd + 83.92% Se Gd-Te67 18.39% Gd + 81.61% Te Gd-Te68 18.18% Gd+ 81.82% Te Gd-Te69 19.52% Gd + 80.48% Te Gd-Te70 19.15% Gd+ 80.85% Te

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