Comprehensive Studies of Magnetic Transitions and Spin–Phonon Couplings in the Tetrahedral Cobalt Complex Co(AsPh3)2I2

A combination of inelastic neutron scattering (INS), far-IR magneto-spectroscopy (FIRMS), and Raman magneto-spectroscopy (RaMS) has been used to comprehensively probe magnetic excitations in Co(AsPh3)2I2 (1), a reported single-molecule magnet (SMM). With applied field, the magnetic zero-field splitting (ZFS) peak (2D′) shifts to higher energies in each spectroscopy. INS placed the ZFS peak at 54 cm-1, as revealed by both variable-temperature (VT) and variable-magnetic-field data, giving results that agree well with those from both far-IR and Raman studies. Both FIRMS and RaMS also reveal the presence of multiple spin-phonon couplings as avoided crossings with neighboring phonons. Here, phonons refer to both intramolecular and lattice vibrations. The results constitute a rare case in which the spin-phonon couplings are observed with both Raman-active (g modes) and far-IR-active phonons (u modes; space group P21/c, no. 14, Z = 4 for 1). These couplings are fit using a simple avoided crossing model with coupling constants of ca. 1-2 cm-1. The combined spectroscopies accurately determine the magnetic excited level and the interaction of the magnetic excitation with phonon modes. Density functional theory (DFT) phonon calculations compare well with INS, allowing for the assignment of the modes and their symmetries. Electronic calculations elucidate the nature of ZFS in the complex. Features of different techniques to determine ZFS and other spin-Hamiltonian parameters in transition-metal complexes are summarized. © 2022 American Chemical Society

Magnetic Transitions in Iron Porphyrin Halides by Inelastic Neutron Scattering and Ab Initio Studies of Zero-Field Splittings

Zero-field splitting (ZFS) parameters of nondeuterated metalloporphyrins [Fe­(TPP)­X] (X = F, Br, I; H₂TPP = tetraphenylporphyrin) have been directly determined by inelastic neutron scattering (INS). The ZFS values are <i>D</i> = 4.49(9) cm^–1 for tetragonal polycrystalline [Fe­(TPP)­F], and <i>D</i> = 8.8(2) cm^–1, <i>E</i> = 0.1(2) cm^–1 and <i>D</i> = 13.4(6) cm^–1, <i>E</i> = 0.3(6) cm^–1 for monoclinic polycrystalline [Fe­(TPP)­Br] and [Fe­(TPP)­I], respectively. Along with our recent report of the ZFS value of <i>D</i> = 6.33(8) cm^–1 for tetragonal polycrystalline [Fe­(TPP)­Cl], these data provide a rare, complete determination of ZFS parameters in a metalloporphyrin halide series. The electronic structure of [Fe­(TPP)­X] (X = F, Cl, Br, I) has been studied by multireference ab initio methods: the complete active space self-consistent field (CASSCF) and the N-electron valence perturbation theory (NEVPT2) with the aim of exploring the origin of the large and positive zero-field splitting <i>D</i> of the ⁶A₁ ground state. <i>D</i> was calculated from wave functions of the electronic multiplets spanned by the d⁵ configuration of Fe­(III) along with spin–orbit coupling accounted for by quasi degenerate perturbation theory. Results reproduce trends of <i>D</i> from inelastic neutron scattering data increasing in the order from F, Cl, Br, to I. A mapping of energy eigenvalues and eigenfunctions of the <i>S</i> = 3/2 excited states on ligand field theory was used to characterize the σ- and π-antibonding effects decreasing from F to I. This is in agreement with similar results deduced from ab initio calculations on CrX₆^3– complexes and also with the spectrochemical series showing a decrease of the ligand field in the same directions. A correlation is found between the increase of <i>D</i> and decrease of the π- and σ-antibonding energies <i>e</i>_λ^X (λ = σ, π) in the series from X = F to I. Analysis of this correlation using second-order perturbation theory expressions in terms of angular overlap parameters rationalizes the experimentally deduced trend. <i>D</i> parameters from CASSCF and NEVPT2 results have been calibrated against those from the INS data, yielding a predictive power of these approaches. Methods to improve the quantitative agreement between ab initio calculated and experimental <i>D</i> and spectroscopic transitions for high-spin Fe­(III) complexes are proposed

Advanced Magnetic Resonance Studies of Tetraphenylporphyrinatoiron(III) Halides

High-Frequency and -Field EPR (HFEPR) studies of Fe(TPP)X (X = F, Cl, Br; I, TPP2−= meso-tetraphenylporphyrinate dianion) and far-IR magnetic spectroscopic (FIRMS) studies of Fe(TPP)Br and Fe(TPP)I have been conducted to probe magnetic intra- and inter-Kramers doublet transitions in these S = 5/2 metalloporphyrin complexes, yielding zero-field splitting (ZFS) and g parameters for the complexes: Fe(TPP)F, D =  +4.67(1) cm−1, E = 0.00(1) cm−1, g⊥ = 1.97(1), g|| = 2.000(5) by HFEPR; Fe(TPP)Cl, D =  +6.458(2) cm−1, E =  +0.015(5) cm−1, E/D = 0.002, g⊥ = 2.004(3), g|| = 2.02(1) by HFEPR; Fe(TPP)Br, D = +9.03(5) cm−1, E =  +0.047(5) cm−1, E/D = 0.005, giso = 1.99(1) by HFEPR and D = +9.05 cm−1, giso = 2.0 by FIRMS; Fe(TPP)I, D =  +13.84 cm−1, E =  +0.07 cm−1, E/D = 0.005, giso = 2.0 by HFEPR and D = +13.95 cm−1, giso = 2.0 by FIRMS (the sign of E was in each case arbitrarily assigned as that of D). These results demonstrate the complementary nature of field- and frequency-domain magnetic resonance experiments in extracting with high accuracy and precision spin Hamiltonian parameters of metal complexes with S > 1/2. The spin Hamiltonian parameters obtained from these experiments have been compared with those obtained from other physical methods such as magnetic susceptibility, magnetic Mössbauer spectroscopy, inelastic neutron scattering (INS), and variable-temperature and -field magnetic circular dichroism (VT-VH MCD) experiments. INS, Mössbauer and MCD give good agreement with the results of HFEPR/FIRMS; the others not as much. The electronic structure of Fe(TPP)X (X = F, Cl, Br, I) was studied earlier by multi-reference ab initio methods to explore the origin of the large and positive D-values, reproducing the trends of D from the experiments. In the current work, a simpler model based on Ligand Field Theory (LFT) is used to explain qualitatively the trend of increasing ZFS from X = F to Cl to Br and to I as the axial ligand. Tetragonally elongated high-spin d5 systems such as Fe(TPP)X exhibit D > 0, but X plays a key role. Spin delocalization onto X means that there is a spin–orbit coupling (SOC) contribution to D from X•, as opposed to none from closed-shell X−. Over the range X = F, Cl, Br, I, X• character increases as does the intrinsic SOC of X• so that D increases correspondingly over this range

Spin–phonon Couplings in Transition Metal Complexes with Slow Magnetic Relaxation

Spin–phonon coupling plays an important role in single-molecule magnets and molecular qubits. However, there have been few detailed studies of its nature. Here, we show for the first time distinct couplings of g phonons of CoII(acac)2(H2O)2 (acac = acetylacetonate) and its deuterated analogs with zero-field-split, excited magnetic/spin levels (Kramers doublet (KD)) of the S = 3/2 electronic ground state. The couplings are observed as avoided crossings in magnetic-field-dependent Raman spectra with coupling constants of 1–2 cm−1. Far-IR spectra reveal the magnetic-dipole-allowed, inter-KD transition, shifting to higher energy with increasing field. Density functional theory calculations are used to rationalize energies and symmetries of the phonons. A vibronic coupling model, supported by electronic structure calculations, is proposed to rationalize the behavior of the coupled Raman peaks. This work spectroscopically reveals and quantitates the spin–phonon couplings in typical transition metal complexes and sheds light on the origin of the spin–phonon entanglement

Slow Magnetic Relaxations in Cobalt(II) Tetranitrate Complexes. Studies of Magnetic Anisotropy by Inelastic Neutron Scattering and High-Frequency and High-Field EPR Spectroscopy

Three mononuclear cobalt­(II) tetranitrate complexes (A)₂[Co­(NO₃)₄] with different countercations, Ph₄P⁺ (<b>1</b>), MePh₃P⁺ (<b>2</b>), and Ph₄As⁺ (<b>3</b>), have been synthesized and studied by X-ray single-crystal diffraction, magnetic measurements, inelastic neutron scattering (INS), high-frequency and high-field EPR (HF-EPR) spectroscopy, and theoretical calculations. The X-ray diffraction studies reveal that the structure of the tetranitrate cobalt anion varies with the countercation. <b>1</b> and <b>2</b> exhibit highly irregular seven-coordinate geometries, while the central Co­(II) ion of <b>3</b> is in a distorted-dodecahedral configuration. The sole magnetic transition observed in the INS spectroscopy of <b>1</b>–<b>3</b> corresponds to the zero-field splitting (2­(<i>D</i>² + 3<i>E</i>²)^1/2) from 22.5(2) cm^–1 in <b>1</b> to 26.6(3) cm^–1 in <b>2</b> and 11.1(5) cm^–1 in <b>3</b>. The positive sign of the <i>D</i> value, and hence the easy-plane magnetic anisotropy, was demonstrated for <b>1</b> by INS studies under magnetic fields and HF-EPR spectroscopy. The combined analyses of INS and HF-EPR data yield the <i>D</i> values as +10.90(3), +12.74(3), and +4.50(3) cm^–1 for <b>1</b>–<b>3</b>, respectively. Frequency- and temperature-dependent alternating-current magnetic susceptibility measurements reveal the slow magnetization relaxation in <b>1</b> and <b>2</b> at an applied dc field of 600 Oe, which is a characteristic of field-induced single-molecule magnets (SMMs). The electronic structures and the origin of magnetic anisotropy of <b>1</b>–<b>3</b> were revealed by calculations at the CASPT2/NEVPT2 level

Slow Magnetic Relaxations in Cobalt(II) Tetranitrate Complexes. Studies of Magnetic Anisotropy by Inelastic Neutron Scattering and High-Frequency and High-Field EPR Spectroscopy

Three mononuclear cobalt­(II) tetranitrate complexes (A)₂[Co­(NO₃)₄] with different countercations, Ph₄P⁺ (<b>1</b>), MePh₃P⁺ (<b>2</b>), and Ph₄As⁺ (<b>3</b>), have been synthesized and studied by X-ray single-crystal diffraction, magnetic measurements, inelastic neutron scattering (INS), high-frequency and high-field EPR (HF-EPR) spectroscopy, and theoretical calculations. The X-ray diffraction studies reveal that the structure of the tetranitrate cobalt anion varies with the countercation. <b>1</b> and <b>2</b> exhibit highly irregular seven-coordinate geometries, while the central Co­(II) ion of <b>3</b> is in a distorted-dodecahedral configuration. The sole magnetic transition observed in the INS spectroscopy of <b>1</b>–<b>3</b> corresponds to the zero-field splitting (2­(<i>D</i>² + 3<i>E</i>²)^1/2) from 22.5(2) cm^–1 in <b>1</b> to 26.6(3) cm^–1 in <b>2</b> and 11.1(5) cm^–1 in <b>3</b>. The positive sign of the <i>D</i> value, and hence the easy-plane magnetic anisotropy, was demonstrated for <b>1</b> by INS studies under magnetic fields and HF-EPR spectroscopy. The combined analyses of INS and HF-EPR data yield the <i>D</i> values as +10.90(3), +12.74(3), and +4.50(3) cm^–1 for <b>1</b>–<b>3</b>, respectively. Frequency- and temperature-dependent alternating-current magnetic susceptibility measurements reveal the slow magnetization relaxation in <b>1</b> and <b>2</b> at an applied dc field of 600 Oe, which is a characteristic of field-induced single-molecule magnets (SMMs). The electronic structures and the origin of magnetic anisotropy of <b>1</b>–<b>3</b> were revealed by calculations at the CASPT2/NEVPT2 level

Slow Magnetic Relaxations in Cobalt(II) Tetranitrate Complexes. Studies of Magnetic Anisotropy by Inelastic Neutron Scattering and High-Frequency and High-Field EPR Spectroscopy

Three mononuclear cobalt­(II) tetranitrate complexes (A)₂[Co­(NO₃)₄] with different countercations, Ph₄P⁺ (<b>1</b>), MePh₃P⁺ (<b>2</b>), and Ph₄As⁺ (<b>3</b>), have been synthesized and studied by X-ray single-crystal diffraction, magnetic measurements, inelastic neutron scattering (INS), high-frequency and high-field EPR (HF-EPR) spectroscopy, and theoretical calculations. The X-ray diffraction studies reveal that the structure of the tetranitrate cobalt anion varies with the countercation. <b>1</b> and <b>2</b> exhibit highly irregular seven-coordinate geometries, while the central Co­(II) ion of <b>3</b> is in a distorted-dodecahedral configuration. The sole magnetic transition observed in the INS spectroscopy of <b>1</b>–<b>3</b> corresponds to the zero-field splitting (2­(<i>D</i>² + 3<i>E</i>²)^1/2) from 22.5(2) cm^–1 in <b>1</b> to 26.6(3) cm^–1 in <b>2</b> and 11.1(5) cm^–1 in <b>3</b>. The positive sign of the <i>D</i> value, and hence the easy-plane magnetic anisotropy, was demonstrated for <b>1</b> by INS studies under magnetic fields and HF-EPR spectroscopy. The combined analyses of INS and HF-EPR data yield the <i>D</i> values as +10.90(3), +12.74(3), and +4.50(3) cm^–1 for <b>1</b>–<b>3</b>, respectively. Frequency- and temperature-dependent alternating-current magnetic susceptibility measurements reveal the slow magnetization relaxation in <b>1</b> and <b>2</b> at an applied dc field of 600 Oe, which is a characteristic of field-induced single-molecule magnets (SMMs). The electronic structures and the origin of magnetic anisotropy of <b>1</b>–<b>3</b> were revealed by calculations at the CASPT2/NEVPT2 level

Slow Magnetic Relaxations in Cobalt(II) Tetranitrate Complexes. Studies of Magnetic Anisotropy by Inelastic Neutron Scattering and High-Frequency and High-Field EPR Spectroscopy

Three mononuclear cobalt­(II) tetranitrate complexes (A)₂[Co­(NO₃)₄] with different countercations, Ph₄P⁺ (<b>1</b>), MePh₃P⁺ (<b>2</b>), and Ph₄As⁺ (<b>3</b>), have been synthesized and studied by X-ray single-crystal diffraction, magnetic measurements, inelastic neutron scattering (INS), high-frequency and high-field EPR (HF-EPR) spectroscopy, and theoretical calculations. The X-ray diffraction studies reveal that the structure of the tetranitrate cobalt anion varies with the countercation. <b>1</b> and <b>2</b> exhibit highly irregular seven-coordinate geometries, while the central Co­(II) ion of <b>3</b> is in a distorted-dodecahedral configuration. The sole magnetic transition observed in the INS spectroscopy of <b>1</b>–<b>3</b> corresponds to the zero-field splitting (2­(<i>D</i>² + 3<i>E</i>²)^1/2) from 22.5(2) cm^–1 in <b>1</b> to 26.6(3) cm^–1 in <b>2</b> and 11.1(5) cm^–1 in <b>3</b>. The positive sign of the <i>D</i> value, and hence the easy-plane magnetic anisotropy, was demonstrated for <b>1</b> by INS studies under magnetic fields and HF-EPR spectroscopy. The combined analyses of INS and HF-EPR data yield the <i>D</i> values as +10.90(3), +12.74(3), and +4.50(3) cm^–1 for <b>1</b>–<b>3</b>, respectively. Frequency- and temperature-dependent alternating-current magnetic susceptibility measurements reveal the slow magnetization relaxation in <b>1</b> and <b>2</b> at an applied dc field of 600 Oe, which is a characteristic of field-induced single-molecule magnets (SMMs). The electronic structures and the origin of magnetic anisotropy of <b>1</b>–<b>3</b> were revealed by calculations at the CASPT2/NEVPT2 level