Tools for Predicting the Nature and Magnitude of Magnetic Anisotropy in Transition Metal Complexes: Application to Co(II) Complexes

Magneto-Structural Correlation of Five-Coordinate Trigonal Bipyramidal High Spin Cobalt(II) Complexes

Here, we combined magnetometry, multi-frequency electronic paramagnetic resonance, and wave function based ab initio calculations to investigate magnetic properties of two high spin Co(II) complexes Co(BDPRP) (BDPRP=2,6-bis((2-(S)-di(4-R)phenylhydroxylmethyl-1-pyrrolidi-nyl)methyl)pyridine, R=H for 8; R=tBu for 9). Complexes 8 and 9 featuring effective D3h symmetry were found to possess D=24.0 and 32.0 cm-1, respectively, in their S=3/2 ground states of1 e ' ' d x z / y z 4 1 e ' d x y / x 2 - y 2 2 1 a 1 ' d z 2 1 ${{\left(1{{\rm e}}^{{\rm { {^\prime}}}{\rm { {^\prime}}}}\right({d}_{xz/yz}\left)\right)}^{4}{\left(1{{\rm e}}^{{\rm { {^\prime}}}}\right({d}_{{xy/{x}^{2}-y}^{2}}\left)\right)}^{2}{\left(1{{\rm a}}_{1}^{{\rm { {^\prime}}}}\right({d}_{{z}^{2}}\left)\right)}^{1}}$ . Ligand field analyses revealed that the low-lying d-d excited states make either positive or vanishing contributions to D. Hence, total positive D values were measured for 8 and 9, as well as related D3h high spin Co(II) complexes. In contrast, negative D values are usually observed for C3v congeners. In-depth analyses suggested that lowering symmetry from D3h to C3v induces orbital mixing between1 e d x z / y z ${1{\rm e}\left({d}_{xz/yz}\right)}$ and2 e d x y / x 2 - y 2 ${2{\rm e}\left({d}_{{xy/{x}^{2}-y}^{2}}\right)}$ and admixes excited state4 A 2 1 e → 2 e ${{}^{4}{{\rm A}}_{2}\left(1e\to 2e\right)}$ into the ground state. Both factors turn the total D value progressively negative with the increasing distance (δ) of the Co(II) center out of the equatorial plane. Therefore, δ determines the sign and magnitude of final D values of five-coordinate trigonal bipyramidal S=3/2 Co(II) complexes as measured for a series of such species with varying δ.

Correlating Valence and 2p3d RIXS Spectroscopies: A Ligand-Field Study of Spin-Crossover Iron(II)

The molecular spin-crossover phenomenon between high-spin (HS) and low-spin (LS) states is a promising route to next-generation information storage, sensing applications, and molecular spintronics. Spin-crossover complexes also provide a unique opportunity to study the ligand field (LF) properties of a system in both HS and LS states while maintaining the same ligand environment. Presently, we employ complementing valence and core-level spectroscopic methods to probe the electronic excited-state manifolds of the spin-crossover complex [FeII(H2B(pz)2)2phen]0. Light-induced excited spin-state trapping (LIESST) at liquid He temperatures is exploited to characterize magnetic and spectroscopic properties of the photoinduced HS state using SQUID magnetometry and magnetic circular dichroism spectroscopy. In parallel, Fe 2p3d RIXS spectroscopy is employed to examine the ΔS = 0, 1 excited LF states. These experimental studies are combined with state-of-the-art CASSCF/NEVPT2 and CASCI/NEVPT2 calculations characterizing the ground and LF excited states. Analysis of the acquired LF information further supports the notion that the spin-crossover of [FeII(H2B(pz)2)2phen]0 is asymmetric, evidenced by a decrease in eπ in the LS state. The results demonstrate the power of cross-correlating spectroscopic techniques with high and low LF information content to make accurate excited-state assignments, as well as the current capabilities of ab initio theory in interpreting these electronic properties.

Spectroscopic and Magnetic Studies of Co(II) Scorpionate Complexes: Is There a Halide Effect on Magnetic Anisotropy?

The observation of single-molecule magnetism in transition-metal complexes relies on the phenomenon of zero-field splitting (ZFS), which arises from the interplay of spin-orbit coupling (SOC) with ligand-field-induced symmetry lowering. Previous studies have demonstrated that the magnitude of ZFS in complexes with 3d metal ions is sometimes enhanced through coordination with heavy halide ligands (Br and I) that possess large free-atom SOC constants. In this study, we systematically probe this "heavy-atom effect" in high-spin cobalt(II)-halide complexes supported by substituted hydrotris(pyrazol-1-yl)borate ligands (Tp^tBu,Me and Tp^Ph,Me). Two series of complexes were prepared: [Co^IIX(Tp^tBu,Me)] (1-X; X = F, Cl, Br, and I) and [Co^IIX(Tp^Ph,Me)(Hpz^Ph,Me)] (2-X; X = Cl, Br, and I), where Hpz^Ph,Me is a monodentate pyrazole ligand. Examination with dc magnetometry, high-frequency and -field electron paramagnetic resonance, and far-infrared magnetic spectroscopy yielded axial (D) and rhombic (E) ZFS parameters for each complex. With the exception of 1-F, complexes in the four-coordinate 1-X series exhibit positive D-values between 10 and 13 cm^-1, with no dependence on halide size. The five-coordinate 2-X series exhibit large and negative D-values between -60 and -90 cm^-1. Interpretation of the magnetic parameters with the aid of ligand-field theory and ab initio calculations elucidated the roles of molecular geometry, ligand-field effects, and metal-ligand covalency in controlling the magnitude of ZFS in cobalt-halide complexes.

Multiconfiguration Pair-Density Functional Theory for Chromium(IV) Molecular Qubits

Pseudotetrahedral organometallic complexes containing chromium(IV) and aryl ligands have been experimentally identified as promising molecular qubit candidates. Here we present a computational protocol based on multiconfiguration pair-density functional theory for computing singlet-triplet gaps and zero-field splitting (ZFS) parameters in Cr(IV) aryl complexes. We find that two multireference methods, multistate complete active space second-order perturbation theory (MS-CASPT2) and hybrid multistate pair-density functional theory (HMS-PDFT), perform better than Kohn-Sham density functional theory for singlet-triplet gaps. Despite the very small values of the ZFS parameters, both multireference methods performed qualitatively well. MS-CASPT2 and HMS-PDFT performed particularly well for predicting the trend in the ratio of the rhombic and axial ZFS parameters, |E/D|. We have also investigated the dependence and sensitivity of the calculated ZFS parameters on the active space and the molecular geometry. The methodologies outlined here can guide future prediction of ZFS parameters in molecular qubit candidates.

The Full d3-d5 Redox Series of Mononuclear Manganese Complexes: Geometries and Electronic Structures of [Mn(dgpy)2]n

Although manganese ions exhibit a rich redox chemistry, redox processes are often accompanied by structural reorganization and a high propensity for ligand substitution, so that no complete structurally characterized manganese(II,III,IV) complex series without significant ligand sphere reorganization akin to the manganese(II,III,IV) oxides exists. We present here the series of pseudo-octahedral homoleptic manganese complexes [Mn(dgpy)₂]ⁿ⁺ (n = 2-4) with the adaptable tridentate push-pull ligand 2,6-diguanidylpyridine (dgpy). Mn-N bond lengths and N-Mn-N bond angles change characteristically from n = 2 to n = 4, while the overall [MnN₆] coordination sphere is preserved. The manganese(III) complex [Mn(dgpy)₂]³⁺ exhibits a Jahn-Teller elongated octahedron and a negative D = -3.84 cm^-1. Concomitantly with the consecutive oxidation of [Mn(dgpy)₂]²⁺ to [Mn(dgpy)₂]⁴⁺, the optical properties evolve with increasing ligand-to-metal charge transfer character of the absorption bands culminating in the panchromatic absorption of the purple-black manganese(IV) complex [Mn(dgpy)₂]⁴⁺.

Field-induced mononuclear cobalt(II) single-molecule magnet (SMM) based on a benzothiadiazole-ortho-vanillin ligand

A unique π-conjugated benzothiadiazole-ortho-vanillin ligand (HL), characterized by single crystal X-ray diffraction and DFT calculations, has been prepared by condensation between 4-amino-benzothiadiazole (BTD) and ortho-vanillin. Its reaction with cobalt(II) acetate...

Tuning chain topologies and magnetic anisotropy in one-dimensional cobalt(II) coordination polymers via distinct dicarboxylates

Based on a terpyridine derivative and two different dicarboxylate ligands, two new cobalt(II) coordination polymers, namely [Co(pytpy)(DClbdc)]n (1) and [Co(pytpy)(ndc)]n (2) (pytpy = 4'-(4-Pyridyl)-2,2':6',2''-terpyridine, H2DClbc = 2,5-Dichloroterephthalic acid, and H2ndc...

Role of Coordination Number and Geometry in Controlling the Magnetic Anisotropy in FeII , CoII , and NiII Single-Ion Magnets

Since the last decade, the focus in the area of single-molecule magnets (SMMs) has been shifting constructively towards the development of single-ion magnets (SIMs) based on transition metals and lanthanides. Although ground-breaking results have been witnessed for Dy^III -based SIMs, significant results have also been obtained for some mononuclear transition metal SIMs. Among others, studies based on Co^II ion are very prominent as they often exhibit high magnetic anisotropy or zero-field splitting parameters and offer a large barrier height for magnetisation reversal. Although Co^II possibly holds the record for having the largest number of zero-field SIMs known for any transition metal ion, controlling the magnetic anisotropy in these systems are is still a challenge. In addition to the modern spectroscopic techniques, theoretical studies, especially ab initio CASSCF/NEVPT2 approaches, have been used to uncover the electronic structure of various Co^II SIMs. In this article, with some selected examples, the aim is to showcase how varying the coordination number from two to eight, and the geometry around the Co^II centre alters the magnetic anisotropy. This offers some design principles for the experimentalists to target new generation SIMs based on the Co^II ion. Additionally, some important Fe^II /Fe^III and Ni^II complexes exhibiting large magnetic anisotropy and SIM properties are also discussed.

Influence of ligand field on magnetic anisotropy in a family of pentacoordinate CoII complexes

A family of mononuclear penta-coordinated CoII complexes, [Co(L)Cl2]·CH3OH (1), [Co(L)Br2] (2) and [Co(L)(NCS)2] (3) (where L is 1-mesityl-N,N-bis(pyridin-2-ylmethyl)methanamine) were synthesized and characterized. In these complexes, the neutral non-planar ligand, L, binds to three coordination sites around the metal center while two others are bound by anionic halide/pseudo halide ligands. The coordination geometry of the complexes is dictated by the coordinated anionic ligands. Thus, the coordination geometry around the metal ion is distorted trigonal bipyramidal for complexes 1 and 3, while it is distorted square pyramidal for complex 2. Ab initio CASSCF/NEVPT2 calculations on the complexes reveal the presence of an easy plane magnetic anisotropy with the D and E/D values being, 13.3 and 0.14 cm-1 for 1; 36.1 and 0.24 cm-1 for 2 and ±8.6 and 0.32 cm-1 for 3. These values are in good agreement with the values that were extracted from the experimental DC data. AC magnetic measurements reveal the presence of a field-induced slow relaxation of magnetization. However, clear maxima in the out-of-phase susceptibility curves were not observed for 1 and 3. For complex 2, peak maxima were observed when the measurements were carried out under an applied field of 1400 Oe which allowed an analysis of the dynamics of the slow relaxation of magnetization. This revealed that the relaxation is mainly controlled by the Raman and direct processes with the values of the parameters found to be: B = 0.77(15) s-1 K-6.35, n = 6.35(12) and A = 3.41(4) × 10-10 s-1 Oe-4 K-1 and m = 4 (fixed). The ab initio calculation which showed the multifunctional nature of the electronic states of the complexes justifies the absence of zero-field SIM behaviour of the complexes. The magnitude and sign of the D and E values and their relationship with the covalency of the metal-ligand bonds was analysed by the CASSCF/NEVPT2 as well as AILFT calculations.

Magnetic Relaxation Studies on Trigonal Bipyramidal Cobalt(II) Complexes

We report the preparation and the full characterization of a novel mononuclear trigonal bipyramidal Co^II complex [Co(NS₃ ^iPr )Br](BPh₄ ) (1) with the tetradentate sulfur-containing ligand NS₃ ^iPr (N(CH₂ CH₂ SCH(CH₃ )₂ )₃ ). The comparison of its magnetic behaviour with those of two previously reported compounds [Co(NS₃ ^iPr )Cl](BPh₄ ) (2) and [Co(NS₃ ^tBu )Br](ClO₄ ) (3) (NS₃ ^tBu =N(CH₂ CH₂ SC(CH₃ )₃ )₃ ) with similar structures shows that 1 displays a single-molecule magnet behaviour with the longest magnetic relaxation time (0.051 s) at T=1.8 K, which is almost thirty times larger than that of 3 (0.0019 s) and more than three times larger than that of 2 (0.015 s), though its effective energy barrier (26 cm^-1 ) is smaller. Compound 1, which contains two crystallographically independent molecules, presents smaller rhombic parameters (E=1.45 and 0.59 cm^-1 ) than 2 (E=2.05 and 1.02 cm^-1 ) and 3 (E=2.00 and 0.80 cm^-1 ) obtained from theoretical calculations. Compounds 2 and 3 have almost the same axial (D) and rhombic (E) parameter values, but present a large difference of their effective energy barrier and magnetic relaxation which may be attributed to the larger volume of BPh₄ ^- than ClO₄ ^- leading to larger diamagnetic dilution (weaker magnetic dipolar interaction) for 2 than for 3. The combination of these factors leads to a much slower magnetic relaxation for 1 than for the two other compounds.

General framework for calculating spin-orbit couplings using spinless one-particle density matrices: Theory and application to the equation-of-motion coupled-cluster wave functions

Standard implementations of nonrelativistic excited-state calculations compute only one component of spin multiplets (i.e., M_s = 0 triplets); however, matrix elements for all components are necessary for deriving spin-dependent experimental observables. Wigner-Eckart's theorem allows one to circumvent explicit calculations of all multiplet components. We generate all other spin-orbit matrix elements by applying Wigner-Eckart's theorem to a reduced one-particle transition density matrix computed for a single multiplet component. In addition to computational efficiency, this approach also resolves the phase issue arising within Born-Oppenheimer's separation of nuclear and electronic degrees of freedom. A general formalism and its application to the calculation of spin-orbit couplings using equation-of-motion coupled-cluster wave functions are presented. The two-electron contributions are included via the mean-field spin-orbit treatment. Intrinsic issues of constructing spin-orbit mean-field operators for open-shell references are discussed, and a resolution is proposed. The method is benchmarked by using several radicals and diradicals. The merits of the approach are illustrated by a calculation of the barrier for spin inversion in a high-spin tris(pyrrolylmethyl)amine Fe(II) complex.

In-depth investigation of large axial magnetic anisotropy in monometallic 3d complexes using frequency domain magnetic resonance and ab initio methods: a study of trigonal bipyramidal Co(ii)

The magnetic properties of 3d monometallic complexes can be tuned through geometric control, owing to their synthetic accessibility and relative structural simplicity. Monodentate ligands offer great potential for fine-tuning the coordination environment to engineer both the axial and rhombic zero-field splitting (ZFS) parameters. In [CoCl3(DABCO)(HDABCO)] (1), the trigonal bipyramidal Co(ii) centre has two bulky axial ligands and three equatorial chloride ligands. An in-depth experimental and theoretical study of 1 reveals a large easy-plane magnetic anisotropy (+ve D) with a negligible rhombic zero-field splitting (E) due to the strict axial symmetry imposed by the C 3 symmetric ligand and trigonal space group. The large easy-plane magnetic anisotropy (D = +44.5 cm-1) is directly deduced using high-field EPR and frequency-domain magnetic resonance (FDMR) studies. Ab initio calculations reveal a large positive contribution to the D term arising from ground state/excited state mixing of the 4E'' states at ∼4085 cm-1 and a minor contribution from the spin-flip transition as well. The nature of the slow relaxation in 1 is elucidated through analysis of the rates of relaxation of magnetisation, taking into account Raman and direct spin-lattice relaxation processes and Quantum Tunnelling of the Magnetisation (QTM). The terms relating to the direct process and QTM were found based on the fit of the field-dependence of τ at 2 K. Subsequently, these were used as fixed parameters in the fit of the temperature-dependence of τ to obtain the Raman terms. This experimental-theoretical investigation provides further insight into the power of FDMR and ab initio methods for the thorough investigation of magnetic anisotropy. Thus, these results contribute to design criteria for high magnetic anisotropy systems.

Progress towards creating optically addressable molecular qubits

The emerging field of quantum information science promises to transform a diverse range of scientific fields, ranging from computation to sensing and metrology. The interdisciplinary scientific community laid the groundwork for the next generation of quantum technologies through key advances in understanding the fundamental unit of quantum information science, the qubit. Electronic spin is a promising platform for qubits, demonstrating suitably long coherence times, optical initialization, and single spin addressability. Herein, we discuss recent accomplishments and future progress from our group targeted at imbuing transition metal complexes with the aforementioned properties, creating a pathway to fusing spatial precision with long coherence times. A strong emphasis of this feature article is progressing towards single spin measurements via a chemical approach for imbuing molecular qubits with an optically-induced spin polarization mechanism.

Pseudotetrahedral cobalt(ii) complexes with PNP-ligands showing uniaxial magnetic anisotropy

Two mononuclear pseudotetrahedral cobalt(ii) complexes with the formula Co(PNP)X2, where X = Cl (1) or X = SCN (2) and PNP = bis(2-(diphenylphosphaneyl)-4-methylphenyl)amine, have been synthesised. Magnetic and high-frequency/field electron paramagnetic resonance (HF-EPR) spectroscopy and ab initio calculation studies reveal that both complexes show uniaxial magnetic anisotropy.

Effect of Low Spin Excited States for Magnetic Anisotropy of Transition Metal Mononuclear Single Molecule Magnets

Rational, fine tuning of magnetic anisotropy is critical to obtain new coordination compounds with enhanced single molecule magnet properties. For mononuclear transition metal complexes, the largest contribution to zero-field splitting is usually related to the excited states of the same spin as the ground level. Thus, the contribution of lower multiplicity roots tends to be overlooked due to its lower magnitude. In this article, we explore the role of lower multiplicity excited states in zero-field splitting parameters in model structures of Fe(II) and Co(II). Model aquo complexes with coordination numbers ranging from 2 to 6 were constructed. The magnetic anisotropy was calculated by state of the art ab initio methodologies, including spin-orbit coupling effects. For non-degenerate ground states, contributions to the zero-field splitting parameter (D) from highest and lower multiplicity roots were of the same sign. In addition, their relative magnitude was in a relatively narrow range, irrespective of the coordination geometry. For degenerate ground states, the contribution from lower multiplicity roots was significantly smaller. Results are rationalized in terms of general expressions for D and are expected to be reasonably transferable to real molecular systems.

Design of a Binuclear Ni(II) Complex with Large Ising-type Anisotropy and Weak Anti-Ferromagnetic Coupling

The preparation of a binuclear Ni(II) complex with a pentacoordinate environment using a cryptand organic ligand and the imidazolate bridge is reported. The coordination sphere is close to trigonal bipyramidal (tbp) for one Ni(II) and to square pyramidal (spy) for the other. The use of the imidazolate bridge that undergoes π-π stacking with two benzene rings of the chelating ligand induces steric hindrance that stabilizes the pentacoordinate environment. Magnetic measurements together with theoretical studies of the spin states energy levels allow fitting the data and reveal a large Ising-type anisotropy and a weak anti-ferromagnetic exchange coupling between the metal ions. The magnitude and the nature of the magnetic anisotropy and the difference in anisotropy between the two metal ions are rationalized using wave-function-based calculations. We show that a slight distortion of the coordination sphere of Ni(II) from spy to tbp leads to an Ising-type anisotropy. Broken-symmetry density functional calculations rationalize the weak anti-ferromagnetic exchange coupling through the imidazolate bridge.

Pentagonal Bipyramid FeII Complexes: Robust Ising-Spin Units towards Heteropolynuclear Nanomagnets

Pentagonal bipyramid Fe^II complexes have been investigated to evaluate their potential as Ising-spin building units for the preparation of heteropolynuclear complexes that are likely to behave as single-molecule magnets (SMMs). The considered monometallic complexes were prepared from the association of a divalent metal ion with pentadentate ligands that have a 2,6-diacetylpyridine bis(hydrazone) core (H₂ L^N3O2R ). Their magnetic anisotropy was established by magnetometry to reveal their zero-field splitting (ZFS) parameter D, which ranged between -4 and -13 cm^-1 and was found to be modulated by the apical ligands (ROH versus Cl). The alteration of the D value by N-bound axial CN ligands, upon association with cyanometallates, was also assessed for heptacoordinated Fe^II as well as for related Ni^II and Co^II derivatives. In all cases, N-coordinated cyanide ligands led to large magnetic anisotropy (i.e., -8 to -18 cm^-1 for Fe and Ni, +33 cm^-1 for Co). Ab initio calculations were performed on three Fe^II complexes, which enabled one to rationalize the role of the ligand on the nature and magnitude of the magnetic anisotropy. Starting from the pre-existing heptacoordinated complexes, a series of pentanuclear compounds were obtained by reactions with paramagnetic [W(CN)₈ ]^3- . Magnetic studies revealed the occurrence of ferromagnetic interactions between the spin carriers in all the heterometallic systems. Field-induced slow magnetic relaxation was observed for mononuclear Fe^II complexes (U_eff /k_B up to 53 K (37 cm^-1 ), τ₀ =5×10^-9  s), and SMM behavior was evidenced for a heteronuclear [Fe₃ W₂ ] derivative (U_eff /k_B =35 K and τ₀ =4.6 10^-10  s), which confirmed that the parent complexes were robust Ising-type building units. High-field EPR spectroscopic investigation of the ZFS parameters for a Ni derivative is also reported.

On balancing the QTM and the direct relaxation processes in single-ion magnets – the importance of symmetry control

Two mononuclear trigonal-planar Co(ii) complexes with a similar coordination environment except for the symmetries were reported to exhibit distinct relaxation dynamics due to the effect of the QTM and direct process.