Single-molecule magnets (SMMs) have been proposed as a new generation of data storage materials and for qubit applications, because SMMs are magnetically bistable with spin reversal barriers (U). [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17] For many complexes, zero-field splitting (ZFS) parameters D and E govern magnetic anisotropy with the simplified spin Hamiltonian inside applied magnetic fields (Eq. 1):
𝐻 ̂𝑆 = 𝐷 (𝑆 ̂𝑧 2 -1 3 𝑆(𝑆 + 1)) + 𝐸 (𝑆 ̂𝑥 2 -𝑆 ̂𝑦 2 ) + 𝜇 𝐵 𝑔 𝑥 𝐵 𝑥 𝑆 ̂𝑥 + 𝜇 𝐵 𝑔 𝑦 𝐵 𝑦 𝑆 ̂𝑦 + 𝜇 𝐵 𝑔 𝑧 𝐵 𝑧 𝑆 ̂𝑧 (1) where 𝑆 ̂𝑧, 𝑆 ̂𝑦, 𝑆 ̂𝑥 = spin operators in the x, y, and z directions; μB = electron Bohr magneton; gx, gy, gz = g-factor components; B = (Bx, By, Bz), applied magnetic field vector. D, E, gx, gy, gz are called spin-Hamiltonian parameters.
ZFS refers to the splitting of the spin microstate degeneracy in S 1 compounds in the absence of an applied field. The 2S + 1 (= 4 for high-spin Co 2+ complexes, 3d 7 , S = 3/2) degeneracy is lifted in such systems mainly due to lowered molecular symmetry from cubic:
octahedral Oh or tetrahedral Td. 17,18 The degeneracy is removed when the ligand along the z-axis is different from those in the x, y directions, producing Kramers doublets (KDs) in compounds with odd numbers of unpaired electrons as a result of second-order spin-orbit coupling (SOC). 18 If D > 0, magnetization of the compound occurs along the x,y plane, and the anisotropy is called easy-plane. If D ˂ 0, magnetization is along the z axis, and the anisotropy is called easyaxis. For the former, quantum tunneling occurs more readily than for the latter, because the transitions within the ground KD (MS = ±1/2) is allowed. 19,20 Transverse or rhombic parameter E shows anisotropy between the x and y axes and manifests when the crystallographic symmetry of the metal site is lower than 3-fold (x ≠ y ≠ z). This further splits the KD, and consequently, mixes KDs, 21 leading to faster relaxation, which is typically not desirable in SMMs. Magnetic anisotropies in several types of materials have been studied. 15,[22][23][24][25][26][27][28][29][30][31][32][33][34][35][36] High-spin (S = 3/2) Co 2+ is a commonly investigated ion for SMM applications. 10,[37][38][39] In tetrahedral Co 2+ complexes, the ground electronic 4 F state of the free Co 2+ ion is split into 4 A2, 4 T2, and 4 T1, with the 4 A2 as the ground state (Figure 1). 40 This 4 A2 ground state serves as an ideal system for examining how deviations from perfect tetrahedral geometry influence magnetic anisotropy, owing to quenched orbital angular momentum of this state. In comparison, five and six-coordinate Co 2+ complexes may have an appreciable orbital contribution to their magnetic anisotropy, giving large magnetic anisotropy (e.g., hundreds of cm -1 ) and substantial g anisotropy. In tetrahedral complexes, D-values are typically small, and g-values are relatively isotropic (larger than 2.0), 18 because of the second-order SOC. [Co(SPh)4] 2-with an easy-axis anisotropy (D = -70 cm -1 ) reported by Long and coworkers 41 demonstrates slow relaxation without an applied field. Several pseudo-tetrahedral Co 2+ complexes show slow magnetic relaxation under applied fields with field-induced SMM behaviors. 23,[42][43][44][45] Dunbar and coworkers studied ligand effects on axial ZFS parameters of Co(quinolone)2I2 and Co(EPh3)2I2 (E = P, As), 34 showing an increase in D for those with heavier donor atoms, particularly between (E = P, As). 46 Some of us have studied Co(PPh3)2X2 (X = Cl, Br, I) (C2v) 33 and Co(AsPh3)2I2 (C2v) by both far-infrared magneto-spectroscopy (FIRMS) and inelastic neutron scattering (INS), observing transitions between KDs and determining spin-Hamiltonian parameters for the complexes. (NEt4)[Co(PPh3)X3] (X = Cl, Br) (C3v) has also been studied by DC and AC magnetometry and high-frequency and -field electron paramagnetic resonance (HFEPR) to determine their spin-Hamiltonian parameters. 47 These tetracoordinate Co(II) complexes, except [Co(SPh)4] 2-, are all heteroleptic with pnictogen (group 15) and halide (group 17) ligands. We focus here on simpler, homoleptic halide complexes [CoX4] 2-(X = Cl, crystallizing in different space groups, to elucidate how packing and symmetry govern magnetic anisotropy and relaxation, supported by advanced spectroscopic techniques that yield accurate transition energies and spin-relaxation parameters.
Single-crystal structures of Co-Cl, Co-I at 100(2) K, and Co-Br at 295(2) K have been determined in the current work. Two independent crystal structures of Co-Br at room temperature were reported in 2010. 78,80 We obtained a different Co-Br structure with a lower residual error (R = 4.76%) compared to the reported (6.73% 80 and 7.03% 78 ). We also collected single-crystal X-ray diffraction data of Co-Br at 100 K, but the structure at this low temperature was too disordered to be solved. We also collected single-crystal X-ray diffraction data of Co-Cl and Co-I at 295(2) K, but they were also too disordered to be solved. The crystal structures of Co-X, including a reported Co-Br (with R = 6.73%), 80 are summarized and compared in Figure 2 and Table 1, including selected bond angles and lengths for Co-X.
Both Co-Cl at 100 The six I-Co-I bond angles are different from each other in the 106.38(4)-114. 32(3) range with average of 109.43. The above-described crystal structures (Figure 2) provide metrics that can be used for ligand-field theory, specifically the angular overlap model (AOM). 72,85 For the AOM, Td. These structure-temperature correlations are consistent with previous studies. 86,87 Specifically, Nover and Schmidtke extensively investigated tetrahedral complexes, including (NEt4)2[CoX4] (Co-X), and found from a single-crystal optical spectroscopic measurement at 2 K that the anion is more distorted from tetrahedral geometry than at room temperature. 86
Direct-current (DC) susceptibility measurements of the compounds were taken at 0.1 T applied magnetic field in the range of 1.8 K to 300 K. These complexes are paramagnetic, giving values of χMT at room temperature of 2.56 (Co-Cl), 2.63 (Co-Br), and 2.70 (Co-I) cm 3 mol -1 K which are larger than the calculated spin-only value (χMT = 1.87 cm 3 mol -1 K, 3.87 B.M. for S = 3/2 with g = 2.0), but they are consistent with reported values for tetrahedral Co(II) complexes with orbital contributions to the magnetic moment. 88,89 The χMT plots (Figure 3) gradually decrease with temperature due to ZFS 90 and reach the smallest value at about 1.8 K, the lowest temperature possible in the magnetometer, in the three complexes. Fitting of the DC data using the PHI program yielded D, E, and g values listed in Table 2 with additional details such as zJ (mean-field intermolecular exchange interaction) and TIP (temperature-independent paramagnetism) data given in Table S2 in SI. 91,92 For 2.
HFEPR has been used extensively to probe molecular magnetism, 17,33,34,47,[93][94][95][96][97][98][99][100][101][102][103][104] including determining ZFS. The approximate energy range of HFEPR for this determination is 33 cm -1 in non-Kramers (S = integers) and 15 cm -1 in Kramers (S = half integers) complexes with the magnetic field of up to 16 T for the facilities at the US National High Magnetic Field Laboratory (NHMFL).
HFEPR spectra of these compounds were obtained using the EMR facility at NHMFL.
Simulations of the spectra using spin-Hamiltonian parameters in Table 2 reveal good fits to the experimental spectra. Complex Co-Cl (Figure 4a) measured at 4.5 K and 148 GHz shows a near-ZFS frequency of the inter-Kramers transition between the two lowest Kramers doublets, which immediately yields the approximate 2D value. This frequency corresponds to an energy of 4.9 cm -1 . Complex Co-Br (Figure 4b) also gave an excellent EPR response at 4.5 K and 310 GHz, which exactly corresponds to the frequency of the ZFS transition between the two lowest Kramers doublets. This frequency corresponds to an energy of 10.3 cm -1 , which immediately yields the approximate 2D value. There is a maximum E value of 1.505(10) cm -1 [|E/D| = 0.333(3)] for Co-Br, even though its crystal structure at 295(2) K is in a tetragonal space group with D2d point group symmetry (with two-fold degeneracy x = y). Since HFEPR was taken at 4.5 K, we believe there is a phase change(s) between room temperature and the liquid helium temperature, leading to significant deviations from the D2d symmetry and giving the rhombic ZFS parameter observed by HFEPR at 4.5 K. Serious distortion of the Co-Br structure at 100 (2) K from our single-crystal X-ray diffraction data, which we could not solve, supports this view.
The EPR response of Co-I was much weaker in terms of signal amplitude than those of its two congeners described above (Figure 4c). This is due to the extremely broad linewidth of the turning points, about an order of magnitude larger than those of the Co-Cl and Co-Br compounds. As a result, we were only able to register spectra at a few of the available frequency harmonics, specifically those that produced the most sub-THz wave power. For that reason, no field vs. frequency maps could be constructed, and the SH parameters are only estimates obtained from single-frequency spectra. The fitting of single-frequency spectra of all the compounds showed positive D values. No conventional (e.g., X-band) EPR spectra were recorded for any of the three Co-X complexes, given the availability of HFEPR and FIRMS. But effective g' values (i.e., S' = 1/2) were calculated using perturbation theory equations 105 and are given in Table S7. Simulated Xband (9.5 GHz, 77 K) EPR spectra are shown in Figure S16. The difference in spectral appearance between Co-Cl and Co-Br with perfectly rhombic ZFS and Co-I with essentially axial ZFS is readily apparent.
In INS spectroscopy, the sample is bombarded with incident neutrons, leading to magnetic and phonon excitations. 30,94,[106][107][108][109][110][111][112][113][114][115][116][117][118][119][120] Phonons here refer to both external (intermolecular) and internal (intramolecular) vibrational modes in the solid states. Internal modes are molecular vibrations in which the molecules maintain almost no displacement of the mass center. External modes are lattice vibrations, when molecules vibrate primarily as a whole with little internal distortion and typically with much lower frequencies than internal modes. Internal and external modes are often coupled as they originate from the same governing equations. Thus, we do not distinguish external and internal modes in the current work and refer to all vibrations as phonons. Variable-temperature (VT) INS spectra may distinguish magnetic from phonon transitions, as they have different temperature dependencies. Electrons (spin = 1/2) are fermions that follow the Boltzmann distribution (or Maxwell-Boltzmann statistics) at a given temperature. In contrast, phonons/vibrations (spin = 0) are bosons that follow Bose-Einstein statistics with 0 2 4 6 8 10 12 14 (a) d / dH (Arb. Unit) Exp D > 0 D < 0 2 4 6 8 10 12 14 (b) Exp Sim Magnetic Field (T) 2 4 6 8 10 12 14 (c) Exp D > 0 D < 0 temperature. In other words, magnetic and phonon peaks in VT INS spectra follow different temperature profiles. Bose correction of the INS spectra will bring phonon spectra at different temperatures to similar levels, thus helping reveal magnetic transitions. 94, 106 Unlike IR and Raman spectroscopies, each with different selection rules to give IR-allowed and Raman-allowed transitions, respectively, INS has no symmetry-based selection rules for phonons. Hence, all phonon transitions are allowed in INS. 95,121 INS experiments were conducted using Vibrational Spectrometer (VISION) at the Spallation Neutron Source (SNS), Oak Ridge National Laboratory (ORNL). 94,106 Variabletemperature INS can be used to distinguish between magnetic and phonon peaks due to their different temperature dependences. Bose correction of the VT INS spectra makes the intensities of phonon peaks relatively constant, helping to reveal magnetic peaks. Intensities of magnetic peaks decrease with increasing temperature, as the excited Kramers doublet in Figure 1 is increasingly thermally populated at the expense of the ground Kramers doublet. VISION is an indirect-geometry INS spectrometer with its schematic shown in Figure 5.
Such INS spectrometers have been reviewed. 94,106 An incident neutron beam (with energy Ei) with a broad range of energies (e.g., "white" beam) is used to irradiate the sample. The Ei is determined using the time the neutron reaches the detector through time of flight (TOF). Two banks of analyzers for forward-and backscattering of neutrons, respectively, are used to give spectra. Forward-scattering analyzers catch scattered neutrons with low Q (with respect to the incident neutron beam; Q = length of the vector of momentum transfer Q between the incident
Neutron beam with broad energies Sample neutrons and the sample). 94,106 Backscattering analyzers receive scattered neutrons with high Q.
Magnetic transitions are more pronounced in forward-scattering with low Q, because their intensities decrease with increasing Q. 106
AILFT calculations have been performed using ORCA 122
Results of the current AILFT calculations are summarized in Table S3 in SI. Additional AILFT calculations have also been performed on [CoBr4] 2-and [CoI4] 2-anions, giving results
summarized in SI (Table S6).
For ab initio ligand field theory (AILFT) analysis using NEVPT2 (Table S5).
The AILFT calculations on the [CoCl4] 2-fragment in the structure of (C13H12N3)2[CoCl4] by Vassilyeva et al. gave a small and positive D value (3.96 cm -1 ) with a moderate rhombic component (E/D = 0.12). 123 The ZFS obtained was small compared to that from experimental magnetometric determination, because it was based on a simple isolated ion model extracted from the ionic solid. 123 In current work, the overestimated D value of [CoCl4] 2-is likely associated with the high disorder in the crystal structure. However, E/D and g values show reasonable agreement with the experimental results. An attempt to obtain reasonable D value, the second d-shell, as (CAS 7,10) calculations were also done, in addition to using the Douglas-Kroll-Hess Hamiltonian (DKH) relativistic method. This still gave the same value as the one in Table 2. Thus, we think the overestimation of D is due to severe disorder in the crystal structure of Co-Cl.
The origin of ZFS in these compounds was also probed with the semi-empirical Angular Overlap Model (AOM) using the Ligfield program by J. Bendix, 124 and the locally written (J.
Telser) program DDN. 125 Nover and Schmidtke reported the NIR (near IR) spectra of the three compounds from single crystals at 2 K and assigned Kramers components of the three quartet excited states, which in Td are (in increasing energy): 4 T2(F), 4 T1(F), and 4 T1(P). These states are split by spin-orbit coupling (SOC) and lower symmetry in the crystal. Assignment of electronic levels was by comparison with results from AOM calculations performed for various sub-group symmetries. 86 In the D2d point group symmetry, the ground electronic state of Co-X is 4 B1, derived from the parent 4 A2(F) term in Td symmetry (e 4 t2 3 in strong-field notation). The quartet excited states are 4 T2(F) (e 3 t2 4 ), 4 T1(F) (e 2 t2 5 ), and 4 T1(P) (e 3 t2 4 ) in Td symmetry and each split into 4 B2 and 4 E for ( 4 T2) or 4 A2 and 4 E (for 4 T1) states. Transitions to the states derived from 4 T2 and those derived from 4 T1(F, P) are in the NIR and visible region, respectively, and have been reported from both experimental and theoretical perspectives. 86 These states are given in Figure 7a, showing the symmetry descent for the Co(II) ion from a free ion, first to a hypothetical tetrahedral [CoX4] 2-ion, and then to a hypothetical tetragonally compressed [CoX4] 2-ion in the present studies (ϴ1,2 > 54.5°) (Table S7a). The perturbation equation in Eq. 2, based on the second-order SOC and similar to the one given by Van Stapele et al., applies. 126
where ζ is the SOC constant for Co 2+ ion, E ( 4 B2 -4 B1) is the energy difference between the 4 B2 and 4 B1 states, and E ( 4 E -4 B1) is the energy difference between the 4 E and 4 B1 states.
Angular overlap model (AOM) parameters eσ and eπ for the Co-Cl and Co-Br complexes were taken directly from Benelli and Gatteschi. 85 For Co-I, eσ and eπ were not reported and were therefore determined in two ways: (a) eσ = 2800, eπ = 820 cm -1 were treated as adjustable parameters and optimized jointly with the SOC constant ζ to reproduce the experimental ZFS, while preserving the expected spectrochemical trend of a weaker ligand field for iodide; (b) eσ and eπ were extrapolated by scaling with the halide ionic radii (1.96 Å for Br -and 2.20 Å for I -; scaling factor = 1.122), which yields eσ I = 3478 cm -1 , eπ I = 870 cm -1 , using eσ Br = 3100 and eπ Br = 775 cm -1 . The Racah parameter B for Co-Br (695 cm -1 ) was adopted from Schmidtke, 86 whereas B for Co-Cl (700 cm -1 ) and Co-I (690 cm -1 ) was adjusted to reflect the expected nephelauxetic trend of decreasing interelectronic repulsion along Cl < Br < I; the corresponding C = ~4.3B values were then scaled, together with B, to approximately 70% of the Co 2+ free-ion value (B = 988.6 cm -1 ) 127 to account for overall metal-ligand covalency. Spinorbit coupling was included via effective one-electron SOC constants ζ, which were adjusted for each Co-X complex to reproduce the experimental ZFS parameters (Table 2); relative to the Co 2+ free-ion value (ζ free = 533 cm -1 ), 128 the fitted ζ values are 243 cm -1 (Co-Cl, 46%), 300 cm -1 (Co-Br, 56%), and 385 cm -1 (Co-I, 72%). These calculated ZFS values with a positive sign corroborate the HFEPR results for the compounds (Table 2). The ZFS values increase with an increase in the (second-order) SOC, a decrease in the crystal field parameters (Figure 7b), and the sigma bond strength (eσ) Cl > Br > I, which are in agreement with the spectrochemical series. 129 In addition to the sign and magnitude of ZFS, the calculations also gave the single dorbital energy splitting in Figure 7b. AOM parameters eσ and eπ obtained from AILFT by Buchhorn, Deeth, and Krewald were also employed as an independent theoretical reference set. 72 Using these AILFT-derived AOM parameters, together with the Racah parameters and ζ values defined above and the experimental geometries, leads to an overestimation of the axial ZFS parameter 2D. However, a good agreement with the experimental 2D was achieved by reducing ζ, such that the required ζ values amount to 38%, 47%, and 63% of the free-ion value (533 cm -1 ) for Co-Cl, Co-Br, and Co-I, respectively (Tables S7-S9). The systematic increase in the fitted SOC ζ from Cl to Br to I reflects the larger atomic spin-orbit coupling of the heavier halides and is consistent with their higher covalency, as expected from the nephelauxetic effect.
Spin-lattice relaxation refers to the process by which the spin system of magnetic ions or complexes equilibrates with the lattice vibrations (phonons) at thermal equilibrium, which may be influenced by the crystallographic symmetry of the material. A long relaxation time to spin reversal is desired for SMMs in data storage applications. The spin and lattice systems are the components of SMMs, and interactions between them are often termed spin-phonon couplings, leading to relaxations. 10 Eq. 3 shows the three types of spin-lattice relaxation mechanisms:
where the first term represents the direct process, the second term is Raman process, and the third term describes the thermally activated Orbach process. τ -1 = relaxation time; A = direct process constant; H = magnetic field; T = temperature; C = Raman constant; τ0 = relaxation rate;
Ueff = energy to spin reversal; kB = Boltzmann constant.
The dynamic magnetic properties of the compounds were probed by AC susceptibility studies at 10 kHz frequency under an applied 0.1 T DC field. The applied DC field is required to quench quantum tunneling and to give an observable out-of-phase signal, which is often used for Co(II) complexes. 130 The results showed that both Co-Cl and Co-Br exhibit SMM properties.
Due to the 10 kHz frequency limit for the current state-of-the-art SQUID instrument, Co-Cl shows three maxima points below 10 kHz (Figure 8a). Maxima points at two additional temperatures (2.4, 2.6 K) were also obtained based on the data <10 kHz using the CCFit2 program. 131,132 Since these two maxima points were essentially obtained through extrapolation, their use in Figure 8b should be viewed with caution. In addition, the temperature range of 1.8-2.6 K is small, potentially leading to large errors. The ln vs ln T plot in Figure 8b gives a linear fit (R 2 = 0.997) with C = 8.8(9) 10 3 s -1 and n2 = 2.41 (10). The relaxation dynamics is interpreted using the Raman mechanism, since the data points were obtained at lower temperatures. n2 is lower than 9 expected for the Raman pathway, but it is consistent with the presence of the phonon-bottleneck effect. Cole-Cole plots for Co-Cl are given in Figure S5a in the SI. However, Co-Br shows only one data point below 10 kHz (Figure S3), which is not sufficient to fit the Debye equation.
100 1000 10000 0.0 0.1 0.2 0.3 (a) M '' (cm 3 mol -1
) Frequency (Hz)
1.8 2.0 2.2 2.4 2.6 0.6 0.8 1.0 -11.5 -11.0 -10.5 (b) Slope = -2.41(10) Intercept = -9.08(8) R 2 = 0.993 ln (s) ln T (K) Exp Raman Fit Co-I (with the largest D value) does not show an out-of-phase signal in the AC measurements. Co-I crystallizes in the orthorhombic P21212 space group with the D2 point group symmetry (x ≠ y ≠ z), 133 while Co-Cl and Co-Br crystals are in the tetragonal space group S13 in SI). In other words, there are fewer phonon modes in Co-Cl and Co-Br due to their degeneracy than in Co-I. We speculate that, as a result, spin-phonon couplings are more likely in Co-I, leading to its magnetic relaxation.
FIRMS is far-IR spectroscopy inside magnetic fields, a crucial technique for investigating magnetic properties and spin-phonon interactions. In the experiments, far-IR spectra at different magnetic fields are collected, revealing how Zeeman splitting shifts magnetic transitions. 17,23,28,31,34,[135][136][137][138][139][140][141][142][143][144][145][146][147][148] In the present case, it provides direct measurements of 2D' values for S = 3/2 spin state, and may reveal spin-phonon couplings typically as avoided crossings, offering insight into the spin relaxation process. 94,86 Earlier research by Brackett, Richards, and coworkers demonstrated that transitions between ZFS states are magnetic dipole-allowed, with the transition moment operator (Rx, Ry, Rz). 149 Magnetic transitions of the three Co-X compounds (at 2D in Table 2) are either outside or at the low detection limit (typically 12 cm -1 ) of the FIRMS instrument at NHMFL. 34,94 Thus, FIRMS did not directly show the magnetic transitions in Co-X at 0 T. However, in the FIRMS of Co-I (Figure 9), several spin-phonon couplings were observed involving low-energy phonons.
Observation of these couplings, demonstrated as avoided crossings, is consistent with the faster spin-relaxation observed in Co-I than in Co-Cl and Co-Br by dynamic (AC) susceptibility. The MS = -1/2 to MS = +3/2 magnetic transition, which is extrapolated to 12.5 cm -1 at 0 T and labeled A in Figure 9, undergoes a blue-shift (i.e., shift to higher energies) with magnetic field increase. Due to the presence of transverse or rhombic anisotropy E leading to admixture of states shown in Figure 1, this transition has the MS = -1/2 → MS = -1/2 (MS = 0) component and is spin-allowed. In FIRMS of Co-Br (Figure S12 in SI), a similar MS = -1/2 to MS = +3/2 magnetic transition, extrapolated to 10.4 cm -1 at 0 T (2D), is also observed. This transition undergoes a blue shift with magnetic field increase, although no spin-phonon coupling is obvious in the plots (Figure S12).
In FIRMS of Co-I (Figure 9), the interaction of magnetic transitions (spin) with a phonon is observed as an avoided interaction with the magnetic transition taking up phonon character and the phonon becoming magnetic with an increase in field. When the energy of a phonon is close to the magnetic excitation, spin-phonon coupling occurs, in which the phonon peak appears to be "pushed" away from the magnetic peak. Such coupling is often expressed with a simple Hamiltonian in Eq. 4:
Understanding spin-phonon interaction is a crucial aspect of developing better SMMs.
This requires simulation of the interaction between magnetic transition and possible phonons which can be performed using the given Hamiltonian in Maple software. This method yields the diagonal matrix element corresponding to the expected shift in magnetic and phonon transitions with the field, and the off-diagonal element, , corresponding to the spin-phonon coupling constant.
In Co-I, four phonons, labeled B, C, D, and E in Figure 9, were found to interact with the magnetic transition, resulting in a 5 × 5 matrix representation in Eq. 5 under the assumption that there is no phonon-phonon interaction. Fitting Eq. 5 gives the simulated spin-phonon lines in Figure 9 and the four spin-phonon coupling constants ΛB-ΛE in Table 3. Phonon B at 25 cm⁻¹ initially shows magnetic field dependence until ~4 T, when it begins to exhibit avoided crossing behavior, acquiring magnetic character, while the magnetic transition correspondingly becomes phonon-like. This coupled state then continues as a magnetic excitation until it interacts with Phonon C at 30 cm⁻¹ at ~8 T, leading to another avoided crossing. C gradually becomes a phonon, while Phonon D takes more magnetic character, blue-shifting to the right. The process repeats at about 10 T, when D undergoes a third avoided crossing with Phonon E at 42 cm⁻¹.
[ A B C D E (a) VASP (Vienna Ab initio Simulation Package) calculations using density functional theory (DFT) 150 can provide the phonon symmetries and energies for a given compound as well as phonon movies. 26,27,30,33,150 The VASP calculations were only conducted on Co-I, as the NEt4 + cations in the crystal structures of both Co-Cl and Co-Br are too disordered to be used in the calculations. Calculated phonon symmetries and energies are listed in Table S14 in SI. Since B1, B2, and B3 modes are IR-active in D2 point group (Table S13) The calculated phonon at 25.99 cm -1 with B1 symmetry is close in energy to Phonon B.
This vibrational mode is primarily localized on the NEt4 + cations, particularly in the terminal CH₃ groups. Asymmetric C-H stretching and torsional motions are observed in CH₃ groups attached to C1 and C3 atoms, which twist in the same direction but with different magnitudes.
This contrasts with the CH₃ stretching of C7 and C11 atoms, which move in the opposite directions. The N-C framework exhibits slight bending toward the metal center. A wagging motion of the Co-I bonds is also evident, confirming that this mode involves distortion of the first coordination sphere around the Co center.
The calculated phonon at 30.76 cm -1 with B2 symmetry is close in energy to Phonon C.
In this vibration, the torsional and wagging of the CH₃ groups attached to C1 and C3 atoms are still the same as the phonon at 25.99 cm -1 , except that the CH3 groups of C9, C11, and C16 atoms are in the opposite directions with a larger amplitude. The wagging of the Co-I core is observable.
The calculated phonon at 35.85 cm -1 with B3 symmetry is close in energy to Phonon D.
This vibration represents a symmetric wagging of the ethyl groups on each of the NEt4 + cations, with opposing displacements at the two N centers. The Co-I stretching is weaker than that of phonon at 30.76 cm -1 .
The calculated phonon at 40.34 cm -1 with B2 symmetry is close in energy to Phonon E.
This molecular vibration involves the bending (scissor-like) motion of the alkyl substituents. The deformation propagates through the C-C and C-N framework, which acts as a hinge, resulting in collective NEt4 + distortion. The Co-I core has a minimal wagging motion.
The current work provides detailed studies of magnetism in the (NEt4
The complexes (NEt4)2[CoX4] (Co-X; X = Cl, Br, I) were prepared by the literature methods. 151 The UV-Vis spectra were recorded at room temperature in acetonitrile using an Agilent UV-visible spectrometer.
Single-crystal X-ray diffraction data were collected using a Bruker D8 Venture at 100 K with Mo Kα radiation using φ and ω scans. Data collection and integration were completed using APEX 4 programs, reduced using Bruker SAINT, and corrected for absorption using the SADABS multi-scan program. 152,153 Molecular structure models were solved using SHELXT and refined with SHELXL, using the OLEX2-1.5 interface. [154][155][156]
Magnetic measurements were performed using a vibrating sample magnetometer (VSM) of the Quantum Design MPMS SQUID-VSM system. Variable-temperature DC susceptibility data of these compounds were collected under a field of 0.10 T in the range of 1.8-300 K.
Alternating-current (AC) susceptibility measurements were carried out on a vibrating sample magnetometer (VSM) of Quantum Design PPMS system with an oscillating ac field of 1000 Oe for Co-Cl and Co-Br and 3000 Oe for Co-I, respectively, at frequencies ranging from 10 to 10000 Hz. All magnetic susceptibility data were corrected for the diamagnetic contributions of the sample holder as well as for the diamagnetism of the sample using Pascal's constants. 157 The DC and AC data were processed using the PHI program 91 and the CCFit2 program, 131,132 respectively.
HFEPR was performed at the EMR facility at NHMFL. The facility operates a transmission spectrometer described elsewhere, 158 which was modified by the use of Virginia Diodes Inc. (VDI, Charlottesville, VA, USA) sources, generating sub-THz radiation in the 50-640 GHz frequency range. The spectrometer is associated with a 15/17 T warm-bore superconducting magnet. The samples were measured both "as is" which allowed them to orient (torque) in the magnetic field, or as pellets mixed with n-eicosane. About 30-60 mg of the powder samples were used in each measurement.
FIRMS spectra were recorded at the National High Magnetic Field Laboratory (NHMFL) using a Bruker Vertex 80v FT-IR spectrometer with a 17.5 T superconducting magnet. A mercury lamp and a composite silicon bolometer served as the THz radiation source and detector. The radiation traveled through an evacuated optical beamline and a brass light pipe to minimize air absorption, reaching the sample at the field center. Samples, prepared as n-eicosane mulls with ~2 mg of powder, were cooled to ~5 K alongside the bolometer using helium gas.
Spectra were measured from 10 to 720 cm⁻¹ (0.3-21.6 THz) with 0.3 cm⁻¹ resolution, a 4-minute acquisition time, and a scanner speed of 20 kHz.
Variable and Co-I are given in Figure 6.
AILFT calculations were carried out using the ORCA software package (version 5.0.4). 159 Computational models were based on crystallographic structures of Co-Cl, Co-Br, and
Co-I obtained in the current work. Zora-def2-TZVP was used for Co and X = Cl, Br, while sarczora-def2 was used for I. The resolution of identity and chain of sphere (RIJCOSX) approximations 160 were applied in conjunction with the appropriate auxiliary basis sets. 161 The core orbitals were not frozen. For the three complexes, the CAS(7,5) active space and 10 quartets and 40 doublets were calculated. Dynamic electron correction was incorporated using N-electron valence state second-order perturbation theory (NEVPT2). 162 Parameters related to spin-orbit coupling (g-values and ZFS) were calculated by calling the SINGLE ANISO program.
LFT calculations were obtained using Ligfield software by J. Bendix 124 and the locally written DDN software by J. Telser. 125 The experimental data were satisfactorily fitted using the AOM parameters in SI. For simplification, halide ligands were considered equivalent across all compounds and were assumed to exhibit cylindrical π-donating interactions. The DDN software can incorporate the effects of an external magnetic field. Applying a magnetic field of 300 mT, like that used in conventional X-band EPR, helps reveal the spin states of the compounds and provides information about the sign of D, and can also get the g values from the slope of the lines with multiple fields.
The DDN software can also take as input the single electron d orbital energies (either as the five pure d orbitals or the 5 5 d orbital matrix) and these values were taken from the AILFT calculations to calculate ZFS in the Co-X series (Table S12).
Modeling by spin-polarized Density Functional Theory (DFT) was performed using the Vienna Ab initio Simulation Package (VASP). 163 The calculation used Projector Augmented Wave (PAW) method 164,165 to describe the effects of core electrons, with an energy cutoff of 800 eV for the plane-wave basis of the valence electrons. The lattice parameters and atomic coordinates from the CIF file, generated by the single-crystal X-ray diffraction measurement of Co-I at 100 K, were used as the initial structure. Given the relatively large unit cell (252 atoms),
the electronic structure was calculated on the Γ-point only. The total energy tolerance for electronic energy minimization was 10 -8 eV, and 10 -7 eV for structure optimization. The maximum interatomic force after relaxation was below 0.001 eV/Å. The optB86b-vdW functional 166,167 for dispersion corrections was applied, and a Hubbard U term of 3.32 eV 168 was applied to account for the localized 3d orbitals of Co. The vibrational eigenfrequencies and modes were then calculated using VASP and Phonopy. 169 The OClimax software 170 was used to convert the DFT-calculated phonon results to the simulated INS spectra.
The Supporting Information is available free of charge at
Author contributions, table of single-crystal X-ray diffraction, IR spectra of Co-X, electronic spectra of Co-X, additional DC and AC results, additional HFEPR results, INS spectra in the 10-4000 cm -1 range, additional FIRMS and far-IR results, additional results from the AILFT and LFT calculations, and calculated phonon modes in Co-I and their symmetries.
The authors declare no conflict of interest. scattering experiments were conducted at the Spallation Neutron Source, which is supported by the Scientific Users Facilities Division, Office of Basic Energy Sciences, U.S. Department of Energy under Contract DE-AC0500OR22725 with UT Battelle, LLC. This research used computing resources made available through the VirtuES project, funded by the Laboratory Directed Research and Development program and Compute and Data Environment for Science (CADES) at ORNL, as well as resources of the National Energy Research Scientific Computing Center (NERSC), a U.S. Department of Energy Office of Science User Facility located at Lawrence Berkeley National Laboratory, operated under Contract No. DE-AC02-05CH11231 using NERSC award ERCAP0024340. AAF and ZLX acknowledge the Infrastructure for Scientific Applications and Advanced Computing (ISAAC) at the University of Tennessee for computational resources. We thank Dr. Tianwei Wang, Nanjing University, China, for help with collection of the DC and AC magnetic susceptibility data, Prof. Jesper Bendix, University of Copenhagen, Denmark, for the Ligfield software, Prof. Daniel Aravena, University of Santiago, Chile, for help with the ORCA software, Dr. Andrew Ozarowski, NHMFL, for the SPIN software, and Dr. Adam T. Hand for the MatLab script for processing the FIRMS data. S2. Single-Crystal X-ray Diffraction Table S1. Summary of crystal data and structure refinement parameters Compound Co-Cl Co-Br Co-I Formula C16 H40 Cl4 Co N2 C16 H40 Br4 Co N2 C16 H40 I4 Co N2 FW (g/mol) 461.23 639.03 827.03 Temperature (K) 100(2) 295(2) 100(2) Space group Tetragonal P42/nmc (No. 137) Tetragonal P-421c (No. 114) Orthorhombic P21212 (No. 18) a (Å) 8.7426(3) 8.9864(13) 13.633(3) b (Å) 8.7426(3) 8.9864(13) 14.800(3) c (Å) 15.2212(6) 15.955(3) 13.683(3) α ( ∘ ) 90 90 90.00(3) β ( ∘ ) 90 90 90.00(3) γ ( ∘ ) 90 90 90.00(3) V (Å 3 ) 1163.40(9) 1288.5(4) 2761.0(10) Z / Z 2 / 0.125 2/0.25 4/1 Density (g/cm 3 ) 1.317 1.647 1.990 F(000) 490 634.0 1550 Crystal size (mm 3 ) 0.197 0.123 0.107 0.778 0.431 0.202 0.255 0.186 0.144 Radiation Mo Kα (0.71073) Mo Kα (0.71073) Mo Kα (0.71073) θ Range ( ∘ ) 2.6765-30.522 2.553-26.766 2.027-29.188 Reflections collected 29568 24752 70106 Independent reflections 1000 1376 6075 GOF 1.077 1.037 1.108 R [I > 2 sigma(I) ]/ wR 0.0609 / 0.1674 0.0476 / 0.1047 0.0163 / 0.0382 R (all data) / wR 0.0621 / 0.1689 0.0716 / 0.1199 0.0169 / 0.0385 Restraints / Parameters 45 / 96 0 / 58 0 / 229 a wR2 = [ w(Fo 2 -Fc 2 ) 2 / w(Fo 2 ) 2 ] 1/2 ; R = Fo -Fc / Fo; w = 1 / [ 2 (Fo 2 ) + (aP) 2 + bP]; P = [2Fc 2 + Max(Fo 2 ,0)] / 3 S-4 S3. IR Spectra of Co-X 500 1000 1500 2000 2500 3000 3500 4000 0.75 0.80 0.85 0.90 0.95 1.00 (a) Transmittance Wavenumber (cm -1 ) 500 1000 1500 2000 2500 3000 3500 4000 0.80 0.85 0.90 0.95 S-8
Table S2. Spin-Hamiltonian parameters and other parameters from fittings of DC susceptibility data by the PHI program a D (cm -1 ) |E| (cm -1 ) |E/D| g z J b TIP c Co-Cl +2.3(3) 0.4(5) 0.2(2) 2.257(1) -0.00195(5) 0.00169(1) Co-Br +4.7(4) d 1.3(3) 0.28(9) 2.299(1) -0.00244(6) 0.00112(2) Co-I +7.5(1) 0.11(10) 0.01(3) 2.295(2) -0.0535(14) 0.001033(18) a D, |E|, |E/D| and g values from Table 2 are re-listed here for completeness. S-11 10 100 1000 10000 0.0 0.1 0.2 0.3 M '' (cm 3 mol -1 ) Frequency (Hz) 0.0 kOe 0.2 0.4 0.6 0.8 1.0 1.5 2.0 2.5 3.0 (a) 10 100 1000 10000 0.0 0.1 0.2 0.3 M '' (cm 3 mol -1 ) Frequency (Hz) 0.0 kOe 0.2 0.4 0.6 0.8 1.0 1.5 2.0 2.5 3.0 (b) 10 100 1000 10000 -0.02 -0.01 0.00 M '' (cm 3 mol -1 ) Frequency (Hz) 0.0 kOe 0.4 1.0 1.5 (c) Figure S6. Isothermal field-sweep, out-of-phase AC susceptibilities (χM'') on polycrystalline gz gx gy gy gz gx (a) (b) (c) gz gx gy
Table S6. SH parameters for [CoX4] 2-(X = Br, I) from AILFT calculations [CoBr4] 2- CASSCF NEVPT2 HFEPR of (NEt4)2[CoBr4] (Co-Br) D (cm -1 ) -1.50 -1.15 4.515 E/D 0.00 0.00 0.333 gx gy gz 2.476 2.476 2.494 2.353 2.353 2.367 2.384 2.36 2.47 [CoI4] 2- CASSCF NEVPT2 HFEPR of (NEt4)2[CoI4] (Co-I) D (cm -1 ) +6.47 +3.50 +6.1 E/D 0.008 0.005 0.10 gx gy gz 2.509 2.588 2.589 2.359 2.400 2.400 2.55 2.55 2.35 Table S8c. Edited DDN output for Co-Cl with D2d symmetry having compressed geometry, with SOC and external field of 300 mT -----ELECTRONIC CONFIGURATION: d 7 -----SINGLE-ELECTRON SPIN-ORBIT COUPLING CONSTANT: zeta = -243.00 cm -1 STEVENS ORBITAL REDUCTION FACTORS: kx = 1.0000 ky = 1.0000 kz = 1.0000 RACAH INTER-ELECTRONIC PARAMETERS: B = 700.00 C = 3025.00 cm -1 ++++++++++++++++++++ AOM PARAMETERS ++++++++++++++++++++ LIGAND # 1 -X1 HAS BONDING ANGLES: theta= 58.790 phi= 0.000 psi= 0.000 DEGREES LIGAND # 2 -X2 HAS BONDING ANGLES: theta= 58.790 phi= 180.000 psi= 0.000 DEGREES LIGAND # 3 -X3 HAS BONDING ANGLES: theta= 121.210 phi= 90.000 psi= 0.000 DEGREES LIGAND # 4 -X4 HAS BONDING ANGLES: theta= 121.210 phi= 270.000 psi= 0.000 DEGREES LIGAND # 1-4 Bonding Parameters: e(sigma) = 3600 e(pi-s(y)) = 900 e(pi-s(x)) 900 ###### DIAGONALIZED d ORBITALS, ASCENDING ENERGY, ###### d ORBITAL EIGENVALUE (1)= 2257.3979 RELATIVE ENERGY= 0.00000 cm -1 0.0000000 eV d ORBITAL EIGENVECTOR, Re c(i)^2= 0.000000 0.000000 0.000000 0.000000 1.000000 dx2-y2 dxy dxz dyz dz2 d ORBITAL EIGENVALUE (2)= 2633.3760 RELATIVE ENERGY= 375.97806 cm -1 0.0466153 eV d ORBITAL EIGENVECTOR, Re c(i)^2= 0.000000 1.000000 0.000000 0.000000 0.000000 dx2-y2 dxy dxz dyz dz2 d ORBITAL EIGENVALUE (3)= 5111.6281 RELATIVE ENERGY= 2854.23013 cm -1 0.3538794 eV d ORBITAL EIGENVECTOR, Re c(i)^2= 0.000000 0.000000 1.000000 0.000000 0.000000 dx2-y2 dxy dxz dyz dz2 d ORBITAL EIGENVALUE (4)= 5111.6281 RELATIVE ENERGY= 2854.23013 cm -1 0.3538794 eV d ORBITAL EIGENVECTOR, Re c(i)^2= 0.000000 0.000000 0.000000 1.000000 0.000000 dx2-y2 dxy dxz dyz dz2 d ORBITAL EIGENVALUE (5)= 6485.9700 RELATIVE ENERGY= 4228.57202 cm -1 0.5242761 eV d ORBITAL EIGENVECTOR, Re c(i)^2= Table S10a. Edited Ligfield S7 and DDN S8 Calculations for Co-I These matrices were generated from the following terms: 4 P, 4 F, 2 P, 2 D1, 2 D2, 2 F, 2 G, and 2 H of d 7 in SLMSML-basis. Ligator theta (deg.) a phi (deg.) I 57.900 (57.88) 0.00 I 57.860 (57.88) 180 I 123.670 (122.12) 90 123.670 (122.12) 270 a The actual values are given, but for the idealized D2d model used for the AOM, the theta values in parentheses are used, which makes the model for Co-I correspond to those for Co-Cl and Co-Br. Parameter Value (cm -1 ), this work Value (cm -1 ), Buchhorn, et al. S9 Value (cm -1 ), Buchhorn, et al. S9 e(I) 2800 3478 2090 2090 2090 e(I) 820 870 630 630 630 Racah B 690 690 Same value as the left Same value as the left Same value as the left Racah C 2939 2939 Same value as the left Same value as the left Same value as the left Zeta 385 450 450 385 335 2D 12.347 12.392 19.995 15.608 12.366 Table S10c. Edited DDN output for Co-I with D2d symmetry having compressed geometry, with SOC and external field of 300 mT -----ELECTRONIC CONFIGURATION: d7 -----SINGLE-ELECTRON SPIN-ORBIT COUPLING CONSTANT: zeta = -385.00 cm -1 STEVENS ORBITAL REDUCTION FACTORS: kx = 1.0000 ky = 1.0000 kz = 1.0000 RACAH INTER-ELECTRONIC PARAMETERS: B = 690.00 C = 2939.00 cm -1 ++++++++++++++++++++ AOM PARAMETERS ++++++++++++++++++++ LIGAND # 1 -X1 HAS BONDING ANGLES: theta= 57.790 phi= 0.000 psi= 0.000 DEGREES LIGAND # 2 -X2 HAS BONDING ANGLES: theta= 57.860 phi= 180.000 psi= 0.000 DEGREES LIGAND # 3 -X3 HAS BONDING ANGLES: theta= 123.670 phi= 90.000 psi= 0.000 DEGREES LIGAND # 4 -X4 HAS BONDING ANGLES: theta= 123.670 phi= 270.000 psi= 0.000 DEGREES LIGAND # 1-4 Bonding Parameters: e(sigma) = 2800 e(pi-s(y)) = 820 e(pi-s(x)) 820 ###### DIAGONALIZED d ORBITALS, ASCENDING ENERGY, ###### d ORBITAL EIGENVALUE (1)= 2059.9662 RELATIVE ENERGY= 0.00000 cm-1 0.0000000 eV d ORBITAL EIGENVECTOR, Re c(i)^2= 0.000000 0.000000 0.000000 0.000000 1.000000 dx2-y2 dxy dxz dyz dz2 d ORBITAL EIGENVALUE (2)= 2352.7480 RELATIVE ENERGY= 292.78184 cm-1 0.0363003 eV d ORBITAL EIGENVECTOR, Re c(i)^2= 0.000000 1.000000 0.000000 0.000000 0.000000 dx2-y2 dxy dxz dyz dz2 d ORBITAL EIGENVALUE (3)= 4180.0950 RELATIVE ENERGY= 2120.12882 cm-1 0.2628625 eV d ORBITAL EIGENVECTOR, Re c(i)^2= 0.000000 0.000000 1.000000 0.000000 0.000000 dx2-y2 dxy dxz dyz dz2 d ORBITAL EIGENVALUE (4)= 4180.0950 RELATIVE ENERGY= 2120.12882 cm-1 0.2628625 eV d ORBITAL EIGENVECTOR, Re c(i)^2= 0.000000 0.000000 0.000000 1.000000 0.000000 dx2-y2 dxy dxz dyz dz2 d ORBITAL EIGENVALUE (5)= 4987.0958 RELATIVE ENERGY= 2927.12961 cm-1 0.3629178 eV d ORBITAL EIGENVECTOR, Re c(i)^2= 1.000000 0.000000 0.000000 0.000000 0.000000 dx2-y2 dxy dxz dyz S1) with D2 point group symmetry. S10 In other words, VASP-calculated phonons of Co-I have D2 point group symmetries. Character table for D2 is provided below to show that phonons with B1, B2, and B3 symmetries are IR-active.
x, Rx yz
Table S14. Calculated Phonon Modes in Co-I and Their Symmetries in D2 point Group Wavenumber (cm -1 ) Symmetries of the modes Wavenumber (cm -1 ) Symmetries of the modes 8.55 A 42.05 B1 12.76 B3 42.55 B3 14.22 B2 42.77 B2 14.71 B1 43.39 A 17.60 A 44.40 B1 19.92 A 46.85 B3 21.36 B3 48.94 B2 21.68 B1 49.09 B1 23.09 B2 49.13 B3 24.60 A 50.49 A 25.49 B2 50.83 A 25.72 B3 51.04 B1 25.99 B1 51.63 B2 27.96 B2 52.40 B3 28.72 B3 52.93 A 29.79 A 53.39 B2 30.76 B2 55.32 B2 31.29 B1 56.36 B3 32.23 B3 56.79 A 35.13 B2 57.55 B1 35.85 B3 58.07 B2 36.70 A 58.13 B3 36.80 B1 58.67 A 38.26 B1 59.73 B3 39.17 A 59.97 B1 40.34 B2 60.22 A 41.26 B3 60.60 B1 60.77 B2 87.19 B3 62.17 A 87.46 B2 62.27 B3 89.49 B1 62.38 B2 92.45 A 63.12 A 93.69 B2 65.19 B1 95.47 B3 65.44 B2 95.93 B2 66.41 B3 98.20 B1 66.73 B2 98.52 A 69.07 B1 98.69 B3 69.70 A 100.90 B2 70.02 B1 101.82 B3 70.59 B3 106.50 B3 73.83 B3 107.19 B1 74.43 B2 107.85 B2 76.05 A 108.30 B3 77.44 B1 108.83 A 77.79 A 111.39 B2 78.28 B1 114.88 B1 78.35 B3 115.16 A 80.05 B2 115.46 B2 80.26 A 117.21 B3 82.27 B3 117.86 A 83.22 B2 118.13 B1 85.37 B3 119.53 B3 85.69 B2 120.53 B2 86.28 B1 125.66 B1 127.27 A 195.27 B1 127.73 B2 196.96 A 128.99 B3 207.93 B1 145.85 B1 208.03 A 145.89 A 208.46 B1 152.56 A 209.25 A 153.34 B1 211.37 B1 159.79 B3 211.58 A 159.82 A 217.51 B2 162.21 B2 219.92 A 163.38 B1 220.17 B3 165.12 A 221.10 B1 165.34 B1 222.06 B1 185.07 B2 222.62 A 185.28 A 229.27 B1 185.66 B3 229.71 A 186.45 B1 231.59 B3 186.86 B3 231.68 A 186.90 B2 232.45 B2 187.61 A 233.79 B1 189.11 B1 236.81 B1 192.97 B2 236.94 A 193.15 B3 237.42 B3 194.01 B1 237.55 B2 194.13 B3 241.03 B1 194.44 B2 241.53 A 194.87 A 244.85 B3 S-44 244.91 B2 345.57 B1 249.91 B3 345.94 B2 250.40 B2 346.19 A 250.46 B3 346.39 B3 251.15 B2 349.41 B3 257.54 B2 349.68 B2 257.80 B3 349.83 A 293.48 B3 351.31 B1 293.84 B2 374.88 B1 294.25 B1 374.92 A 295.01 A 375.43 B1 300.20 B1 375.77 A 300.41 A 376.71 A 301.18 A 376.93 B1 301.31 B1 377.01 B3 326.35 B2 377.11 B2 326.85 A 382.25 B1 326.94 B1 382.35 A 327.06 B3 387.65 A 328.38 B3 388.22 B1 328.52 B2 404.95 B2 331.19 B3 405.45 B1 331.21 B2 405.61 B3 335.02 B2 406.52 A 335.07 B3 413.43 B3 342.43 B2 413.49 B2 342.46 B3 419.00 B1 S-45 420.95 A 668.27 B1 457.91 B2 669.36 A 457.92 B3 753.14 B1 461.08 B3 754.57 A 461.09 B2 754.80 B2 464.96 B2 754.99 B3 465.03 B3 760.74 B2 467.72 B3 760.84 B3 467.77 B2 763.02 B2 502.95 B3 763.03 B3 503.10 B2 763.42 A 503.87 A 764.93 B1 504.62 B1 765.85 B2 522.62 B3 765.99 B3 522.88 B2 770.33 A 523.91 A 770.94 B3 524.85 B1 771.09 B2 548.59 A 771.51 B2 548.62 B1 771.59 B3 550.56 A 772.16 B1 550.57 B1 773.56 B2 652.32 B1 773.77 B3 652.38 A 779.67 A 661.60 A 780.00 B1 661.64 B1 787.07 A 665.78 B3 787.09 B1 665.83 B2 793.05 B1 S-46 793.89 A 882.30 B3 798.14 B1 883.41 B2 798.47 A 883.71 B1 798.62 B1 885.33 A 799.47 A 974.75 B1 800.28 B2 974.95 A 800.50 B3 975.45 B2 865.78 A 975.93 B3 865.93 B1 984.66 B3 868.15 B3 985.05 B2 868.26 B2 986.06 A 868.66 A 986.16 B1 869.35 B1 987.37 A 869.83 A 989.65 B1 870.87 B1 992.41 A 873.31 B2 993.31 B1 873.53 B3 1003.41 B1 875.02 B3 1003.53 A 875.13 B2 1005.95 B3 875.93 A 1006.16 B2 876.46 B3 1009.08 A 877.02 B1 1010.24 B1 877.22 B2 1012.70 B1 877.98 B3 1013.28 B2 877.99 B2 1013.31 B3 879.43 B2 1014.04 A 880.61 B3 1014.88 B2 S-47 1014.94 B3 1066.54 B2 1020.58 B3 1066.88 B3 1020.76 B2 1071.73 B1 1026.92 B2 1072.43 A 1027.37 B3 1073.80 B3 1046.34 B2 1074.68 B2 1046.45 B3 1107.83 B2 1048.93 B1 1107.84 B3 1049.69 A 1109.55 B1 1050.01 A 1110.06 B1 1050.08 B3 1110.30 A 1050.78 B2 1110.56 A 1050.92 B1 1111.43 A 1055.10 A 1111.96 B1 1055.54 B1 1129.43 A 1057.09 B1 1129.70 B1 1057.20 A 1132.19 B1 1058.62 B3 1132.66 A 1058.94 B2 1133.71 B1 1061.32 A 1134.67 B2 1062.37 B2 1135.14 A 1062.58 B3 1135.34 B3 1063.64 B3 1148.97 B2 1063.81 B1 1149.61 B3 1063.81 B2 1151.12 B1 1064.53 B2 1152.71 A 1064.62 B3 1161.01 B2 S-48 1161.49 B3 1282.32 B3 1162.04 B3 1282.40 B2 1162.50 B2 1282.47 B1 1164.15 B3 1283.96 A 1164.72 B2 1284.07 B1 1165.63 B2 1285.42 A 1166.25 B3 1285.45 B2 1170.98 B1 1285.61 B3 1171.22 A 1286.38 B2 1172.93 B3 1286.45 B3 1173.20 B2 1291.61 B3 1173.28 A 1291.66 B2 1174.20 B1 1310.36 A 1174.20 A 1310.89 B3 1174.54 B3 1311.08 B1 1175.17 B2 1311.11 B2 1176.52 B1 1316.01 B3 1178.77 A 1316.32 A 1179.47 B1 1316.42 B2 1257.05 B1 1316.66 B1 1257.81 B2 1327.02 A 1258.10 A 1327.27 B1 1258.12 B3 1335.95 A 1274.96 B1 1336.07 B1 1275.33 A 1339.20 A 1277.05 B2 1339.45 B1 1277.16 B3 1342.85 A S-49 1344.25 B1 1366.64 B3 1345.13 B2 1367.04 B1 1345.79 B1 1367.30 B2 1345.87 B3 1368.39 A 1345.90 B2 1371.11 A 1345.97 B3 1371.85 B3 1346.32 A 1372.05 B2 1348.89 B3 1372.85 B1 1348.92 B2 1372.93 B1 1352.74 B3 1373.01 A 1352.76 B2 1373.39 A 1354.13 B3 1375.59 B1 1354.16 B2 1375.74 A 1354.89 A 1376.17 B2 1355.19 B3 1376.20 B3 1355.26 B2 1376.42 B1 1355.54 B1 1376.94 B1 1356.07 B3 1377.29 B2 1356.23 B2 1378.32 B3 1357.21 B1 1378.39 A 1357.83 A 1379.47 B1 1359.02 B1 1379.99 B3 1359.66 A 1380.36 A 1364.45 B1 1380.70 B2 1364.58 A 1381.33 B1 1366.07 B2 1382.39 B3 1366.21 B3 1382.43 A S-50 1383.50 B2 1428.03 B3 1384.66 B2 1428.15 B2 1386.07 B3 1428.84 B3 1400.93 B3 1428.90 B1 1401.60 B2 1429.09 B1 1404.51 A 1429.25 A 1405.09 B1 1430.40 B1 1410.88 A 1430.86 B2 1412.91 B3 1431.64 B2 1413.22 B2 1431.77 B3 1413.64 B1 1432.37 B2 1414.01 A 1432.60 B1 1415.21 B1 1433.94 B2 1415.83 A 1434.06 B3 1418.12 B1 1434.42 B1 1418.84 B2 1435.27 A 1419.32 B1 1435.90 B3 1419.32 B3 1436.33 A 1420.69 A 1436.35 B2 1423.99 B2 1436.61 B3 1424.08 B3 1437.56 B1 1424.66 B2 1437.91 B3 1425.08 B3 1438.16 B2 1426.64 B2 1438.33 A 1426.79 B3 1439.03 B1 1426.93 A 1440.32 B2 1427.97 A 1440.81 A S-51 1440.99 B3 1454.16 A 1441.01 B1 1454.21 B2 1442.22 A 1455.68 A 1442.70 B3 1458.96 B2 1443.13 B1 1459.02 B3 1443.98 B2 1459.15 B2 1445.11 A 1459.26 B3 1445.35 A 1461.35 B1 1445.96 B1 1461.64 B2 1446.46 B2 1462.65 B3 1446.58 B3 1464.68 A 1446.91 A 1464.98 B1 1447.25 B1 1467.62 B3 1448.31 B1 1467.85 B2 1448.40 B3 1467.88 A 1448.44 B2 1469.06 B1 1448.76 B3 1470.51 B3 1448.92 B2 1470.61 A 1448.98 A 1471.17 B2 1450.12 B3 1472.33 B1 1450.32 B2 1472.92 B1 1451.30 B1 1473.41 A 1452.07 A 2925.92 B2 1452.13 B1 2925.93 B3 1452.56 B3 2930.25 B1 1452.79 A 2930.28 A 1453.64 B1 2940.03 B1 S-52 2940.04 B2 2957.95 A 2940.28 B3 2958.07 B1 2940.33 A 2959.34 B3 2940.42 A 2959.34 B2 2940.47 B3 2962.74 B3 2940.71 B2 2962.96 A 2940.73 B1 2963.04 B1 2942.22 B2 2963.12 B2 2942.23 B3 2963.48 B2 2942.68 A 2963.59 A 2942.71 B1 2963.64 B1 2946.28 B2 2963.79 B3 2946.30 B3 2966.10 A 2946.94 B1 2966.12 B1 2946.98 A 2967.30 B3 2947.09 B3 2967.31 B2 2947.11 B2 2970.38 B2 2948.20 A 2970.53 B1 2948.26 B1 2970.54 B3 2949.86 B3 2970.61 A 2949.87 B2 2972.48 B2 2951.32 A 2972.53 B3 2951.33 B1 2973.13 A 2952.22 A 2973.14 B1 2952.24 B1 2976.32 B3 2952.35 B2 2976.33 B2 2952.41 B3 2976.67 A S-53 2977.08 B1 3006.80 B1 2984.49 B3 3007.00 A 2984.49 B2 3008.33 A 2985.05 A 3008.41 B2 2985.12 B1 3008.45 B1 2994.04 B1 3008.46 B3 2994.15 A 3008.81 A 2995.63 B2 3008.90 B1 2995.80 B3 3010.01 A 2997.63 B3 3010.04 B1 2997.69 B2 3010.15 B3 2997.69 B1 3010.17 B2 2997.84 A 3010.82 A 3001.12 B1 3010.92 B3 3001.14 A 3010.97 B2 3002.14 B3 3011.10 B1 3002.23 B2 3011.32 B1 3003.79 B2 3011.33 A 3003.89 B3 3011.63 B1 3003.96 A 3011.68 A 3004.37 B2 3011.75 B3 3004.38 B3 3011.75 B2 3004.38 B1 3012.92 B2 3005.10 B1 3012.95 B3 3005.13 A 3014.02 B3 3006.21 B3 3014.03 B2 3006.37 B2 3014.68 B2 S-54 3014.69 B3 3025.74 B2 3017.07 A 3027.42 A 3017.17 B1 3027.43 B1 3017.50 B1 3027.71 B3 3017.78 B3 3027.75 B2 3017.93 A 3029.96 B3 3018.00 B2 3030.00 A 3019.40 B2 3030.08 B1 3019.46 B1 3030.17 B2 3019.88 A 3030.72 A 3019.91 B3 3030.73 B1 3020.29 B3 3033.39 B2 3020.31 B2 3033.42 B3 3021.95 A 3033.42 B1 3022.00 B1 3033.46 A 3022.97 B2 3033.90 B2 3022.99 B3 3034.05 B1 3024.18 A 3034.06 B3 3024.19 B1 3034.06 A 3024.92 B2 3035.39 B3 3025.03 B3 3035.44 B2 3025.35 A 3038.23 A 3025.60 B3 3038.23 B1 3025.65 B1