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.

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.

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.

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.

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.

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.

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.

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.

Room Temperature Chiral Discrimination in Paramagnetic NMR Spectroscopy.

A recently proposed theory of chiral discrimination in NMR spectroscopy based on the detection of a molecular electric polarization P rotating in a plane perpendicular to the NMR magnetic field [A. D. Buckingham, J. Chem. Phys. 140, 011103 (2014)] is generalized here to paramagnetic systems. Our theory predicts new contributions to P, varying as the square of the inverse temperature. Ab initio calculations for ten Dy^{3+} complexes, at 293 K, show that, in strongly anisotropic paramagnetic molecules, P can be more than 1000 times larger than in diamagnetic molecules, making paramagnetic NMR chiral discrimination amenable to room temperature detection.

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.

Configuration-averaged 4f orbitals in ab initio calculations of low-lying crystal field levels in lanthanide(iii) complexes.

A successful and commonly used ab initio method for the calculation of crystal field levels and magnetic anisotropy of lanthanide complexes consists of spin-adapted state-averaged CASSCF calculations followed by state interaction with spin-orbit coupling (SI-SO). Based on two observations valid for Ln(iii) complexes, namely: (i) CASSCF 4f orbitals are expected to change very little when optimized for different states belonging to the 4f electronic configuration, (ii) due to strong spin-orbit coupling the total spin is not a good quantum number, we show here via a straightforward analysis and direct calculation that the CASSCF/SI-SO method can be simplified to a single configuration-averaged HF calculation and one complete active space CI diagonalization, including spin-orbit coupling, on determinant basis. Besides its conceptual simplicity, this approach has the advantage that all spin states of the 4f(n) configuration are automatically included in the SO coupling, thereby overcoming one of the computational limitations of the existing CASSCF/SI-SO approach. As an example, we consider three isostructural complexes [Ln(acac)3(H2O)2], Ln = Dy(3+), Ho(3+), Er(3+), and find that the proposed simplified method yields crystal field levels and magnetic g-tensors that are in very good agreement with those obtained with CASSCF/SI-SO.

Complete spectrum of the infinite-U Hubbard ring using group theory.

We present a full analytical solution of the multiconfigurational strongly correlated mixed-valence problem corresponding to the N-Hubbard ring filled with N-1 electrons, and infinite on-site repulsion. While the eigenvalues and the eigenstates of the model are known already, analytical determination of their degeneracy is presented here for the first time. The full solution, including degeneracy count, is achieved for each spin configuration by mapping the Hubbard model into a set of Hückel-annulene problems for rings of variable size. The number and size of these effective Hückel annulenes, both crucial to obtain Hubbard states and their degeneracy, are determined by solving a well-known combinatorial enumeration problem, the necklace problem for N-1 beads and two colors, within each subgroup of the CN-1 permutation group. Symmetry-adapted solution of the necklace enumeration problem is finally achieved by means of the subduction of coset representation technique [S. Fujita, Theor. Chim. Acta 76, 247 (1989)], which provides a general and elegant strategy to solve the one-hole infinite-U Hubbard problem, including degeneracy count, for any ring size. The proposed group theoretical strategy to solve the infinite-U Hubbard problem for N-1 electrons is easily generalized to the case of arbitrary electron count L, by analyzing the permutation group CL and all its subgroups.

Dirac cones in the spectrum of bond-decorated graphenes.

We present a two-band model based on periodic Hückel theory, which is capable of predicting the existence and position of Dirac cones in the first Brillouin zone of an infinite class of two-dimensional periodic carbon networks, obtained by systematic perturbation of the graphene connectivity by bond decoration, that is by inclusion of arbitrary π-electron Hückel networks into each of the three carbon-carbon π-bonds within the graphene unit cell. The bond decoration process can fundamentally modify the graphene unit cell and honeycomb connectivity, representing a simple and general way to describe many cases of graphene chemical functionalization of experimental interest, such as graphyne, janusgraphenes, and chlorographenes. Exact mathematical conditions for the presence of Dirac cones in the spectrum of the resulting two-dimensional π-networks are formulated in terms of the spectral properties of the decorating graphs. Our method predicts the existence of Dirac cones in experimentally characterized janusgraphenes and chlorographenes, recently speculated on the basis of density functional theory calculations. For these cases, our approach provides a proof of the existence of Dirac cones, and can be carried out at the cost of a back of the envelope calculation, bypassing any diagonalization step, even within Hückel theory.

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.

PHI: a powerful new program for the analysis of anisotropic monomeric and exchange-coupled polynuclear d- and f-block complexes.

A new program, PHI, with the ability to calculate the magnetic properties of large spin systems and complex orbitally degenerate systems, such as clusters of d-block and f-block ions, is presented. The program can intuitively fit experimental data from multiple sources, such as magnetic and spectroscopic data, simultaneously. PHI is extensively parallelized and can operate under the symmetric multiprocessing, single process multiple data, or GPU paradigms using a threaded, MPI or GPU model, respectively. For a given problem PHI is been shown to be almost 12 times faster than the well-known program MAGPACK, limited only by available hardware.