Ab initio-based determination of lanthanoid-radical exchange as visualised by inelastic neutron scattering.

Magnetic exchange coupling can modulate the slow magnetic relaxation in single-molecule magnets. Despite this, elucidation of exchange coupling remains a significant challenge for the lanthanoid(iii) ions, both experimentally and computationally. In this work, the crystal field splitting and 4f-π exchange coupling in the erbium-semiquinonate complex [ErTp2dbsq] (Er-dbsq; Tp- = hydro-tris(1-pyrazolyl)borate, dbsqH2 = 3,5-di-tert-butyl-1,2-semiquinone) have been determined by inelastic neutron scattering (INS), magnetometry, and CASSCF-SO ab initio calculations. A related complex with a diamagnetic ligand, [ErTp2trop] (Er-trop; tropH = tropolone), has been used as a model for the crystal field splitting in the absence of coupling. Magnetic and INS data indicate antiferromagnetic exchange for Er-dbsq with a coupling constant of Jex = -0.23 meV (-1.8 cm-1) (-2Jex formalism) and good agreement is found between theory and experiment, with the low energy magnetic and spectroscopic properties well modelled. Most notable is the ability of the ab initio modelling to reproduce the signature of interference between localised 4f states and delocalised π-radical states that is evident in the Q-dependence of the exchange excitation. This work highlights the power of combining INS with EPR and magnetometry for determination of ground state properties, as well as the enhanced capability of CASSCF-SO ab initio calculations and purposely developed ab initio-based theoretical models. We deliver an unprecedentedly detailed representation of the entangled character of 4f-π exchange states, which is obtained via an accurate image of the spin-orbital transition density between the 4f-π exchange coupled wavefunctions.

Triggering single-molecule qubit spin dynamics via non-Abelian geometric phase effects.

We illustrate how macroscopic rotations can be utilised to trigger and control a spin dynamics within the ground doublet of both Kramers and non-Kramers-type molecular nanomagnets via the non-Abelian character of the time-evolution operator. For Kramers magnets, we show how this effect can be harnessed to realise single-qubit quantum gates and give the explicit example of a recently reported CoCl2(tu)4 single-molecule magnet (SMM). We demonstrate that gating operations could be performed on this magnet in as fast as 10 ps before the breakdown of adiabaticity, much faster than typical spin-lattice relaxation times. Based on this effect, we also suggest CoCl2(tu)4 as a quantum gyroscope for sensing yaw-axis rotations. For integer spin nanomagnets where non-axial crystal field interactions often lift ground state degeneracy, we show how spin dynamics from the non-Abelian geometric propagator can be recovered using non-adiabatic macroscopic rotations not-necessarily resonant with the tunnel splitting gap. Using the well-known TbPc2 single-ion magnet as a further example, we identify an experimentally plausible non-adiabatic rotation that induces a coherent superposition of tunnelling ground states, tantamount to preparing each member of a TbPc2 ensemble in the maximal angular momentum state |mJ = 6〉. The detection of an ensuing coherent oscillation of the macroscopic magnetisation polarised along the TbPc2 principal magnetic axis after the completed rotation could then proceed via time-resolved magnetisation measurements.

Direct observation of magnetoelastic coupling in a molecular spin qubit: new insights from crystal field neutron scattering data.

Single-molecule magnets are promising candidates for data storage and quantum computing applications. A major barrier to their use is rapid magnetic relaxation and quantum decoherence due to thermal vibrations. Here we report a reanalysis of inelastic neutron scattering (INS) data of the candidate qubit Na9[Ho(W5O18)2]·35D2O, wherein we demonstrate for the first time that magnetic relaxation times and mechanisms can be directly observed as crystal field (CF) peak broadening in INS spectra of a lanthanoid molecular system. The magnetoelastic coupling between the lower energy CF states and phonons (lattice vibrations) is determined by the simultaneous measurement of CF excitations and the phonon density of states, encoded within the same INS experiment. This directly results in the determination of relaxation coupling pathways that occur in this molecule. Such information is invaluable for the further advancement of SMMs and to date has only been obtained from techniques performed in external magnetic fields. Additionally, we determine a relaxation rate of quantum-tunnelling of magnetisation that is consistent with previously measured EPR spectroscopy data.

Inelastic Neutron Scattering Measurement of the Ground State Tunneling Gap in Tb and Ho Analogues of a Dy Field-Induced Single-Molecule Magnet.

Recent advances in single-molecule magnet (SMM) research have placed great value on interpretation of inelastic neutron scattering (INS) data for rare earth (RE)-containing SMMs. Here, we present the synthesis of several rare earth complexes where combined magnetic and INS studies have been performed, supported by ab initio calculations. The reaction of rare earth nitrate salts with 2,2'-bipyridine (2,2'-bpy) and tetrahalocatecholate (X4Cat2-, X = Br, Cl) ligands in methanol (MeOH) afforded two new families of compounds [RE(2,2'-bpy)2(X4Cat)(X4CatH)(MeOH)] (X = Br and RE = Y, Eu, Gd, Tb, Dy, Ho, Yb for 1-RE; X = Cl and RE = Y, Tb, Dy, Ho, and Yb for 2-RE). Addition of triethylamine (Et3N) to the reaction mixture delivered Et3NH[RE(2,2'-bpy)2(Br4Cat)2] (3-RE, RE = Er and Yb). Interestingly, cerium behaves differently to the rest of the series, generating (2,2'-bpyH)2[Ce(Br4Cat)3(2,2'-bpy)] (4-Ce) with tetravalent Ce(IV) in contrast to the trivalent metal ions in 1-3. The static magnetic properties of 1-RE (RE = Gd, Tb, Dy and Ho) were investigated in conjunction with INS measurements on 1-Y, 1-Tb, and 1-Ho to probe their ground state properties and any crystal field excitations. To facilitate interpretation of the INS spectra and provide insight into the magnetic behavior, ab initio calculations were performed using the single-crystal X-ray diffraction structural data of 1-RE (RE = Tb, Dy and Ho). The ab initio calculations indicate ground doublets dominated by the maximal angular momentum projection states of Kramers type for 1-Dy and Ising type for 1-Tb and 1-Ho. Dynamic magnetic susceptibility measurements indicate that 1-Dy exhibits slow magnetic relaxation in the presence of a small applied magnetic field mainly through Raman pathways. Inelastic neutron scattering spectra exhibit distinct transitions corresponding to crystal field-induced tunneling gaps between the pseudo-doublet ground state components for 1-Tb and 1-Ho, which is one of the first direct experimental measurements with INS of such tunneling transitions in a molecular nanomagnet. The power of high-resolution INS is demonstrated with evidence of two distinct tunneling gaps measurable for the two crystallographically unique Tb coordination environments observed in the single crystal X-ray structure.

Ab initio non-covalent crystal field theory for lanthanide complexes: a multiconfigurational non-orthogonal group function approach.

We present a multiconfigurational ab initio methodology based on non-orthogonal fragments for the calculation of crystal field energy levels and magnetic properties of lanthanide complexes, implementing a systematic description of non-covalent contributions to metal-ligand bonding. The approach consists of two steps. In the first step, appropriate ab initio wave functions for the various ionic fragments (lanthanide ions and coordinating ligands) are optimized separately, accounting for the influence of the surrounding environment within various approximations. In the second and final step, the scalar relativistic (DKH2) electrostatic Hamiltonian of the whole molecule is represented on the basis of the optimized metal-ligand multiconfigurational non-orthogonal group functions (MC-NOGFs), and reduced to an effective (2J + 1)-dimensional non-orthogonal configuration interaction (CI) problem via Löwdin-partitioning. Within the proposed formalism, the projected non-orthogonal CI Hamiltonian can be expanded to any desired order of perturbation theory in the fragment-localised excitations out of the degenerate space, and its eigenvalues and eigenfunctions provide systematic approximations to the crystal field energies and wave functions. We present here a preliminary implementation of the proposed MC-NOGF method developed for first-order degenerate perturbation theory within our own ab initio code CERES, and compare its performance both with the simpler non-covalent orthogonal ab initio approach, Fragment Ab Initio Model Potential (FAIMP) approximation, and the full CAHF/CASCI-SO method, accounting for metal-ligand covalency in a mean-field manner. We found that the energies and magnetic properties of 44 complexes obtained via an iteratively optimized version of our MC-NOGF first-order non-covalent method compare remarkably well with those obtained using the full CAHF/CASCI-SO method including metal-ligand covalency, thus exposing the predominantly electrostatic character of the metal-ligand interactions, and are superior to those obtained using the FAIMP approach, which in its iteratively optimised variant was believed to date to be the best ab initio description of non-covalent metal-ligand interactions.

Elucidation of LMCT Excited States for Lanthanoid Complexes: A Theoretical and Solid-State Experimental Framework.

Photophysical and magnetic properties arising from both ground and excited states of lanthanoid ions are relevant for numerous applications. These properties can be substantially affected, both adversely and beneficially, by ligand-to-metal charge-transfer (LMCT) states. However, probing LMCT states remains a significant challenge in f-block chemistry, particularly in the solid state. Intriguingly, the europium compounds [EuIII(18-c-6)(X4Cat)(NO3)]·MeCN (18-c-6 = 18-crown-6; X = Cl (tetrachlorocatecholate, 1-Eu) or Br (tetrabromocatecholate, 2-Eu) are distinctly darkly-colored, in marked contrast to the analogues with other lanthanoid ions in the 1-Ln and 2-Ln series (Ln = La, Ce, Nd, Gd, Tb, and Dy). Herein, we report a multi-technique investigation of these compounds that has allowed elucidation of the LMCT character of the relevant absorption bands using magnetometry, absorption and emission spectroscopies, and solid-state electrochemistry. To support experimental observations, we present a semi-quantitative multireference ab initio model that (i) captures the anomalously low-lying LMCT excited state observed in the visible spectrum of 1-Eu (and its absence in the other 1-Ln analogues); (ii) elucidates the contribution of the LMCT excitation to the crystal field split 7FJ ground-state wave functions; and (iii) identifies the crucial role played by radial dynamical correlation of the EuIII 4f electrons in the description of the LMCT excited state, modeled by the inclusion of 4f → 5f excitations in the optimized wave function. By providing a set of experimental and theoretical tools, this work establishes a framework for the elucidation of LMCT excited states in lanthanoid compounds in the solid state.

Study of the most relevant spin-orbit coupling descriptions of magnetic excitations in a series of lanthanide complexes.

We present a number of computationally cost-effective approaches to calculate magnetic excitations (i.e. crystal field energies and magnetic anisotropies in the lowest spin-orbit multiplet) in lanthanide complexes. In particular, we focus on the representation of the spin-orbit coupling term of the molecular Hamiltonian, which has been implemented within the quantum chemistry package CERES using various approximations to the Breit-Pauli Hamiltonian. The approximations include the (i) bare one-electron approximation, (ii) atomic mean field and molecular mean field approximations of the two-electron term, (iii) full representation of the Breit-Pauli Hamiltonian. Within the framework of the CERES implementation, the spin-orbit Hamiltonian is always fully diagonalized together with the electron repulsion Hamiltonian (CASCI-SO) on the full basis of Slater determinants arising within the 4f ligand field space. For the first time, we make full use of the Cholesky decomposition of two-electron spin-orbit integrals to speed up the calculation of the two-electron spin-orbit operator. We perform an extensive comparison of the different approximations on a set of lanthanide complexes varying both the lanthanide ion and the ligands. Surprisingly, while our results confirm the need of at least a mean field approach to accurately describe the spin-orbit coupling interaction within the ground Russell-Saunders term, we find that the simple bare one-electron spin-orbit Hamiltonian performs reasonably well to describe the crystal field split energies and g tensors within the ground spin-orbit multiplet, which characterize all the magnetic excitations responsible for lanthanide-based single-molecule magnetism.

Effect of magnetic anisotropy on direct chiral discrimination in paramagnetic NMR spectroscopy.

We present and analyse a complete analytic expression for the generalized shielding polarizability third-rank tensor Φαßγ, whose isotropic average, the pseudoscalar [capital Phi, Greek, macron], is proportional to a chiral macroscopic electric polarization P measurable in a pulsed nuclear magnetic resonance (NMR) experiment probing molecules with an arbitrarily degenerate ground state, in solution. We have recently predicted that [capital Phi, Greek, macron] can be measurable at room temperature in chiral paramagnetic molecules, and identified strong magnetic anistropy (as featured e.g. in lanthanide complexes) as a crucial molecular property to achieve room temperature chiral discrimination using NMR spectroscopy. As previously proposed, the components of Φαßγ are obtained as analytical third derivatives of the electronic free energy. Here we present the explicit calculation of these derivatives, which provide working expressions for the explicit accurate ab initio calculation of Φαßγ. We apply our theory by performing ab initio multiconfigurational calculations of all contributions to Φαßγ, for a set of ten DyIII complexes, characterized by a strongly axial ground Kramers doublet, but also by thermally accessible excited Kramers doublets at room temperature. The results show that the thermally populated excited state contributions, while generally reducing the value of [capital Phi, Greek, macron] calculated on the assumption of a thermally isolated ground state, still confirm the room temperature detectability of this property for all ten studied complexes. Trends on the relative sign of dominant contributions are then discussed on the basis of a crystal field model electrostatic potential splitting a ground spin-orbit multiplet, which provides an insight into the properties of the generalized shielding polarizability tensor for open shell species.

Design of annulene-within-an-annulene systems by the altanisation approach. A study of altan-[n]annulenes.

The altanisation strategy, devised to design molecules with large and paratropic perimeter circulations, is applied to the family of [n]annulenes to give, altan-[n]annulenes, i.e. [n,5]coronenes. Analytical expressions are obtained for the eigenvalues of the Hückel Hamiltonian for altan-[n]annulenes, and used in conjunction with selection rules derived from the ipsocentric approach to predict patterns of global ring current in these systems. Density-functional calculations performed on seven altan-[n]annulenes, three neutral and four charged, give current-density maps in essential agreement with the predictions obtained at the unperturbed Hückel level. All but one of the systems show patterns with the tropicities expected for isolated annulenes, in line with the altanisation concept. The apparent exception is altan-[11]annulene-, the only singlet system with a well defined open-shell character in the studied set. The key role of open-shell character can be accommodated by appropriate choice of the occupation numbers of the initial Hückel molecular orbitals, where the anion altan-[11]annulene- is considered as an [11]annulene inside the [22]annulene anion.

Observation of the asphericity of 4f-electron density and its relation to the magnetic anisotropy axis in single-molecule magnets.

The distribution of electrons in the 4f orbitals of lanthanide ions is often assigned a crucial role in the design of single-molecule magnets, which maintain magnetization in zero external field. Optimal spatial complementarity between the 4f-electron density and the ligand field is key to maximizing magnetic anisotropy, which is an important factor in the ability of lanthanide complexes to display single-molecule magnet behaviour. Here we have experimentally determined the electron density distribution in two dysprosium molecular complexes by interpreting high-resolution synchrotron X-ray diffraction with a multipole model. The ground-state 4f-electron density is found to be an oblate ellipsoid, as is often deduced from a simplified Sievers model that assumes a pure |±15/2> ground-state doublet for the lanthanide ion. The large equatorial asymmetry-determined by a model wavefunction-was found to contain considerable MJ mixing of |±11/2> and only 81% of |±15/2>. The experimental molecular magnetic easy axes were recovered, and found to deviate by 13.1° and 8.7° from those obtained by ab initio calculations.

Single-ion anisotropy and exchange coupling in cobalt(ii)-radical complexes: insights from magnetic and ab initio studies.

The concurrent effects of single-ion anisotropy and exchange interactions on the electronic structure and magnetization dynamics have been analyzed for a cobalt(ii)-semiquinonate complex. Analogs containing diamagnetic catecholate and tropolonate ligands were employed for comparison of the magnetic behavior and zinc congeners assisted with the spectroscopic characterization and assessment of intermolecular interactions in the cobalt(ii) compounds. Low temperature X-band (ν ≈ 9.4 GHz) and W-Band (ν ≈ 94 GHz) electron paramagnetic resonance spectroscopy and static and dynamic magnetic measurements have been used to elucidate the electronic structure of the high spin cobalt(ii) ion in [Co(Me3tpa)(Br4cat)] (1; Me3tpa = tris[(6-methyl-2-pyridyl)methyl]amine, Br4cat2- = tetrabromocatecholate) and [Co(Me3tpa)(trop)](PF6) (2(PF6); trop- = tropolonate), which show slow relaxation of the magnetization in applied field. The cobalt(ii)-semiquinonate exchange interaction in [Co(Me3tpa)(dbsq)](PF6)·tol (3(PF6)·tol; dbsq- = 3,5-di-tert-butylsemiquinonate, tol = toluene) has been determined using an anisotropic exchange Hamiltonian in conjunction with multistate restricted active space self-consistent field ab initio modeling and wavefunction analysis, with comparison to magnetic and inelastic neutron scattering data. Our results demonstrate dominant ferromagnetic exchange for 3+ that is of similar magnitude to the anisotropy parameters of the cobalt(ii) ion and contains a significant contribution from spin-orbit coupling. The nature of the exchange coupling between octahedral high spin cobalt(ii) and semiquinonate ligands is a longstanding question; answering this question for the specific case of 3+ has confirmed the considerable sensitivity of the exchange to the molecular structure. The methodology employed will be generally applicable for elucidating exchange coupling between orbitally-degenerate metal ions and radical ligands and relevant to the development of bistable molecules and their integration into devices.

Slow Magnetic Relaxation in Lanthanoid Crown Ether Complexes: Interplay of Raman and Anomalous Phonon Bottleneck Processes.

The combination of lanthanoid nitrates with 18-crown-6 (18-c-6) and tetrahalocatecholate (X4 Cat2- , X=Cl, Br) ligands has afforded two compound series [Ln(18-c-6)(X4 Cat)(NO3 )]⋅MeCN (X=Cl, 1-Ln; X=Br, 2-Ln; Ln=La, Ce, Nd, Gd, Tb, Dy). The 18-c-6 ligands occupy equatorial positions of a distorted sphenocorona geometry, whereas the charged ligands occupy the axial positions. The analogues of both series with Ln=Ce, Nd, Tb and Dy exhibit out-of-phase ac magnetic susceptibility signals in the presence of an applied magnetic field, indicative of slow magnetization relaxation. When diluted into a diamagnetic La host to reduce dipolar interactions, the Dy analogue exhibits slow relaxation up to 20 K in the absence of an applied dc field. Concerted magnetic measurements, EPR spectroscopy, and ab initio calculations have allowed elucidation of the mechanisms responsible for slow magnetic relaxation. A consistent approach has been applied to quantitatively model the relaxation data for different lanthanoid analogues, suggesting that the spin dynamics are governed by Raman processes at higher temperatures, transitioning to a dominant phonon bottleneck process as the temperature is decreased, with an observed T-6 rather than the usual T-2 dependence (T is temperature). This anomalous thermal dependence of the phonon bottleneck relaxation is consistent with anharmonic effects in the lattice dynamics, which was predicted by Van Vleck more than 70 years ago.

Metal Cluster Electrides: A New Type of Molecular Electride with Delocalised Polyattractor Character.

Electrides are ionic substances containing isolated electrons. These confined electrons are topologically characterised by a quasi-atom, that is, a non-nuclear attractor (NNA) of the electron density. The electronic structure of the octahedral 4 A1g Li6+ and 5 A1g Be6 species shows that these species have a large number of NNAs. These NNAs have highly delocalised electron densities and, as a result, the chemical bonding pattern of these systems is reminiscent of that in solid metals, in which metal cations are surrounded by a "sea" of delocalised valence electrons. We propose the term metal cluster electrides to refer to this new class of compounds. In this study, we establish a computational protocol to identify, characterize, and design metal cluster electrides and we elucidate the intricate bonding patterns of this particular type of species.

CERES: An ab initio code dedicated to the calculation of the electronic structure and magnetic properties of lanthanide complexes.

We have developed and implemented a new ab initio code, Ceres (Computational Emulator of Rare Earth Systems), completely written in C++11, which is dedicated to the efficient calculation of the electronic structure and magnetic properties of the crystal field states arising from the splitting of the ground state spin-orbit multiplet in lanthanide complexes. The new code gains efficiency via an optimized implementation of a direct configurational averaged Hartree-Fock (CAHF) algorithm for the determination of 4f quasi-atomic active orbitals common to all multi-electron spin manifolds contributing to the ground spin-orbit multiplet of the lanthanide ion. The new CAHF implementation is based on quasi-Newton convergence acceleration techniques coupled to an efficient library for the direct evaluation of molecular integrals, and problem-specific density matrix guess strategies. After describing the main features of the new code, we compare its efficiency with the current state-of-the-art ab initio strategy to determine crystal field levels and properties, and show that our methodology, as implemented in Ceres, represents a more time-efficient computational strategy for the evaluation of the magnetic properties of lanthanide complexes, also allowing a full representation of non-perturbative spin-orbit coupling effects. © 2017 Wiley Periodicals, Inc.

Ferrotoroidic ground state in a heterometallic {CrIIIDyIII6} complex displaying slow magnetic relaxation.

Toroidal quantum states are most promising for building quantum computing and information storage devices, as they are insensitive to homogeneous magnetic fields, but interact with charge and spin currents, allowing this moment to be manipulated purely by electrical means. Coupling molecular toroids into larger toroidal moments via ferrotoroidic interactions can be pivotal not only to enhance ground state toroidicity, but also to develop materials displaying ferrotoroidic ordered phases, which sustain linear magneto-electric coupling and multiferroic behavior. However, engineering ferrotoroidic coupling is known to be a challenging task. Here we have isolated a {CrIIIDyIII6} complex that exhibits the much sought-after ferrotoroidic ground state with an enhanced toroidal moment, solely arising from intramolecular dipolar interactions. Moreover, a theoretical analysis of the observed sub-Kelvin zero-field hysteretic spin dynamics of {CrIIIDyIII6} reveals the pivotal role played by ferrotoroidic states in slowing down the magnetic relaxation, in spite of large calculated single-ion quantum tunneling rates.

A full-pivoting algorithm for the Cholesky decomposition of two-electron repulsion and spin-orbit coupling integrals.

A significant reduction in the computational effort for the evaluation of the electronic repulsion integrals (ERI) in ab initio quantum chemistry calculations is obtained by using Cholesky decomposition (CD), a numerical procedure that can remove the zero or small eigenvalues of the ERI positive (semi)definite matrix, while avoiding the calculation of the entire matrix. Conversely, due to its antisymmetric character, CD cannot be directly applied to the matrix representation of the spatial part of the two-electron spin-orbit coupling (2e-SOC) integrals. Here, we present a computational strategy to achieve a Cholesky representation of the spatial part of the 2e-SOC integrals, and propose a new efficient CD algorithm for both ERI and 2e-SOC integrals. The proposed algorithm differs from previous CD implementations by the extensive use of a full-pivoting design, which allows a univocal definition of the Cholesky basis, once the CD δ threshold is made explicit. We show that 2δ is the upper limit for the errors affecting the reconstructed 2e-SOC integrals. The proposed strategy was implemented in the ab initio program Computational Emulator of Rare Earth Systems (CERES), and tested for computational performance on both the ERI and 2e-SOC integrals evaluation. © 2017 Wiley Periodicals, Inc.

Titanium(III) Member of the Family of Trigonal Building Blocks with Scorpionate and Cyanide Ligands.

The titanium(III) cyanide compound [Et4N][Tp*Ti(CN)3] ([Et4N] = tetraethylamonium; Tp* = 3,5-dimethyltrispyrazolylhydroborate) is reported, which exhibits a trigonally distorted geometry. Magnetic data and ab initio calculations verified that the molecule is an S = 1/2 paramagnet and that it exhibits significant temperature-independent paramagnetism.

Magnetic Excitations in Polyoxotungstate-Supported Lanthanoid Single-Molecule Magnets: An Inelastic Neutron Scattering and ab Initio Study.

Inelastic neutron scattering (INS) has been used to investigate the crystal field (CF) magnetic excitations of the analogs of the most representative lanthanoid-polyoxometalate single-molecule magnet family: Na9[Ln(W5O18)2] (Ln = Nd, Tb, Ho, Er). Ab initio complete active space self-consistent field/restricted active space state interaction calculations, extended also to the Dy analog, show good agreement with the experimentally determined low-lying CF levels, with accuracy better in most cases than that reported for approaches based only on simultaneous fitting to CF models of magnetic or spectroscopic data for isostructural Ln families. In this work we demonstrate the power of a combined spectroscopic and computational approach. Inelastic neutron scattering has provided direct access to CF levels, which together with the magnetometry data, were employed to benchmark the ab initio results. The ab initio determined wave functions corresponding to the CF levels were in turn employed to assign the INS transitions allowed by selection rules and interpret the observed relative intensities of the INS peaks. Ultimately, we have been able to establish the relationship between the wave function composition of the CF split LnIII ground multiplets and the experimentally measured magnetic and spectroscopic properties for the various analogs of the Na9[Ln(W5O18)2] family.

Relay-Like Exchange Mechanism through a Spin Radical between TbPc2 Molecules and Graphene/Ni(111) Substrates.

We investigate the electronic and magnetic properties of TbPc2 single ion magnets adsorbed on a graphene/Ni(111) substrate, by density functional theory (DFT), ab initio complete active space self-consistent field calculations, and X-ray magnetic circular dichroism (XMCD) experiments. Despite the presence of the graphene decoupling layer, a sizable antiferromagnetic coupling between Tb and Ni is observed in the XMCD experiments. The molecule-surface interaction is rationalized by the DFT analysis and is found to follow a relay-like communication pathway, where the radical spin on the organic Pc ligands mediates the interaction between Tb ion and Ni substrate spins. A model Hamiltonian which explicitly takes into account the presence of the spin radical is then developed, and the different magnetic interactions at play are assessed by first-principle calculations and by comparing the calculated magnetization curves with XMCD data. The relay-like mechanism is at the heart of the process through which the spin information contained in the Tb ion is sensed and exploited in carbon-based molecular spintronics devices.

Carbonate-Bridged Lanthanoid Triangles: Single-Molecule Magnet Behavior, Inelastic Neutron Scattering, and Ab Initio Studies.

Optimization of literature synthetic procedures has afforded, in moderate yield, homogeneous and crystalline samples of the five analogues Na11[{RE(OH2)}3CO3(PW9O34)2] (1-RE; RE = Y, Tb, Dy, Ho, and Er). Phase-transfer methods have allowed isolation of the mixed salts (Et4N)9Na2[{RE(OH2)}3CO3(PW9O34)2] (2-RE; RE = Y and Er). The isostructural polyanions in these compounds are comprised of a triangular arrangement of trivalent rare-earth ions bridged by a µ3-carbonate ligand and sandwiched between two trilacunary Keggin {PW9O34} polyoxometalate ligands. Alternating-current (ac) magnetic susceptibility studies of 1-Dy, 1-Er, and 2-Er reveal the onset of frequency dependence for the out-of-phase susceptibility in the presence of an applied magnetic field at the lowest measured temperatures. Inelastic neutron scattering (INS) spectra of 1-Ho and 1-Er exhibit transitions between the lowest-lying crystal-field (CF) split states of the respective J = 8 and (15)/2 ground-state spin-orbit multiplets of the Ho(III) and Er(III) ions. Complementary ab initio calculations performed for these two analogues allow excellent reproduction of the experimental magnetic susceptibility and low-temperature magnetization data and are in reasonable agreement with the experimental INS data. The ab initio calculations reveal that the slight difference in coordination environments of the three Ln(III) ions in each complex gives rise to differences in the CF splitting that are not insignificant. This theoretical result is consistent with the observation of multiple relaxation processes by ac magnetic susceptibility and the broadness of the measured INS peaks. The ab initio calculations also indicate substantial mixing of the MJ contributions to the CF split energy levels of each Ln(III) ion. Calculations indicate that the CF ground states of the Ho(III) centers in 1-Ho are predominantly comprised of contributions from small MJ, while those of the Er(III) centers in 1-Er are predominantly comprised of contributions from large MJ, giving rise to slow magnetic relaxation. Although no direct evidence for intramolecular RE···RE magnetic coupling is observed in either magnetic or INS studies, on the basis of the ab initio calculations, we find noncollinear magnetic axes in 1-Er that are coplanar with the erbium triangle and radially arranged with respect to the triangle's centroid; thus, we argue that the absence of magnetic coupling in this system arises from dipolar and antiferromagnetic superexchange interactions that cancel each other out.