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.

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 (X₄Cat^2-, 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.

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...

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 [Eu^III(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 ⁷F_J ground-state wave functions; and (iii) identifies the crucial role played by radial dynamical correlation of the Eu^III 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 have studied the effect of thermally populated crystal field states on room temperature chiral discrimination in NMR spectroscopy.

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

Computations on neutral and charged [n]annulenes confirm the general effectiveness of altanisation to design paratropic perimeter circulations. An extension of the design strategy is required for open-shell singlet species.

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.

Coupling multitemporal remote sensing with geomorphology and hydrological modeling for post flood recovery in the Strymonas dammed river basin (Greece)

We present a case study of a long-term integrated monitoring of a flood event which affected part of the Strymonas dammed river basin, a transboundary river with source in Bulgaria, which flows then through Greece to the Aegean Sea. The event, which affected the floodplain downstream the Kerkini dam, started at the beginning of April 2015, due to heavy rain upstream of the monitored area, and lasted for several months, with some water pools still present at the beginning of September, due to the peculiar geomorphological conditions of the watershed. We collected a multi-temporal dataset consisting of a high-resolution, X-band COSMO-SkyMed, and several C-band Sentinel-1 SAR and optical Landsat-8 images of the area. The results allow following the event in time, sketching a multi-temporal map of the post-flood evolution, with relatively high temporal resolution. We then use hydrological modeling to mimic the dynamics of the flooded area against post event weather patterns and thus explain the observed flood extent evolution. We show how integrating remote sensing-derived maps of flooded areas, geomorphological analyses of the landscape and simplified hydrological modeling allows accurate inference about long-term dynamics of flooded areas, very important in the post event in anthropogenic highly modified areas, where recovery time after the flood event is considerable, and long term water persistence may lead to large consequences, carrying economic damages and medical emergencies.

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.

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.

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.

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.

Spin-communication channels between Ln(III) bis-phthalocyanines molecular nanomagnets and a magnetic substrate

Learning the art of exploiting the interplay between different units at the atomic scale is a fundamental step in the realization of functional nano-architectures and interfaces. In this context, understanding and controlling the magnetic coupling between molecular centers and their environment is still a challenging task. Here we present a combined experimental-theoretical work on the prototypical case of the bis(phthalocyaninato)-lanthanide(III) (LnPc₂) molecular nanomagnets magnetically coupled to a Ni substrate. By means of X-ray magnetic circular dichroism we show how the coupling strength can be tuned by changing the Ln ion. The microscopic parameters of the system are determined by ab-initio calculations and then used in a spin Hamiltonian approach to interpret the experimental data. By this combined approach we identify the features of the spin communication channel: the spin path is first realized by the mediation of the external (5d) electrons of the Ln ion, keeping the characteristic features of the inner 4 f orbitals unaffected, then through the organic ligand, acting as a bridge to the external world.

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

We propose an ab initio method that simplifies the CASSCF/RASSI–SO approach for crystal field levels and magnetic properties of lanthanide complexes.

Ab initio calculations as a quantitative tool in the inelastic neutron scattering study of a single-molecule magnet analogue

Ab initio calculations of the electronic structure of Na₉[Tb(W₅O₁₈)₂] have allowed interpretation of the inelastic neutron scattering spectra, revealing the subtle relationship between molecular geometry and magnetic properties of two isostructural species.

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.

NMR chemical shift as analytical derivative of the Helmholtz free energy

We present a theory for the temperature-dependent nuclear magnetic shielding tensor of molecules with arbitrary electronic structure. The theory is a generalization of Ramsey's theory for closed-shell molecules. The shielding tensor is defined as a second derivative of the Helmholtz free energy of the electron system in equilibrium with the applied magnetic field and the nuclear magnetic moments. This derivative is analytically evaluated and expressed as a sum over states formula. Special consideration is given to a system with an isolated degenerate ground state for which the size of the degeneracy and the composition of the wave functions are arbitrary. In this case, the paramagnetic part of the shielding tensor is expressed in terms of the g and A tensors of the electron paramagnetic resonance spin Hamiltonian of the degenerate state. As an illustration of the proposed theory, we provide an explicit formula for the paramagnetic shift of the central lanthanide ion in endofullerenes Ln@C(60), with Ln = Ce(3+), Nd(3+), Sm(3+), Dy(3+), Er(3+), and Yb(3+), where the ground state can be a strongly spin-orbit coupled icosahedral sextet for which the paramagnetic shift cannot be described by previous theories.

Communication: paramagnetic NMR chemical shift in a spin state subject to zero-field splitting

We derive a general formula for the paramagnetic NMR nuclear shielding tensor of an open-shell molecule in a pure spin state, subject to a zero-field splitting (ZFS). Our findings are in contradiction with a previous proposal. We present a simple application of the newly derived formula to the case of a triplet ground state split by an easy-plane ZFS spin Hamiltonian. When kT is much smaller than the ZFS gap, thus a single non-degenerate level is thermally populated, our approach correctly predicts a temperature-independent paramagnetic shift, while the previous theory leads to a Curie temperature dependence.

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.

NMR chemical shift in an electronic state with arbitrary degeneracy

We present a theory of nuclear magnetic resonance shielding tensors for electronic states with arbitrary degeneracy. The shieldings are here expressed in terms of generalized Zeeman (g((k))) and hyperfine (A((k))) tensors, of all ranks k allowed by the size of degeneracy. Contrary to recent proposals [T. O. Pennanen and J. Vaara, Phys. Rev. Lett. 100, 133002 (2008)], our theory is valid in the strong spin-orbit coupling limit. Ab initio calculations for the fourfold degenerate Γ(8) ground state of lanthanide-doped fluorite crystals CaF(2):Ln (Ln=Pr(2+), Nd(3+), Sm(3+), and Dy(3+)) show that previously neglected contributions can account for more than 50% of the paramagnetic shift.

Visualising aromaticity of bowl-shaped molecules

Superposition of slices (planar maps of induced current density calculated within the ipsocentric pseudo-π model of electronic response to a magnetic field) gives a simple route to visual diagnosis of ring-current aromaticity in bowl-shaped molecules. Results are presented for currents in the recently synthesized indenocorannulene precursors of [60]fullerene.

Mechanisms of spin-mixing instabilities in antiferromagnetic molecular wheels

The microscopic theory of field-induced spin-mixing instabilities in antiferromagnetic molecular wheels CsFe8 is proposed. The basic features of magnetic torque measurements [O. Waldmann, Phys. Rev. Lett. 96, 027206 (2006)] are well explained by the interplay of three basic ingredients: the spin-mixing vibronic interaction with field-dependent vibronic constants, cooperative elastic interactions, and spin-mixing interactions independent from vibrations. The main contribution to spin mixing comes from second-order zero-field splitting mechanisms. At variance with previous interpretations, we find that the observed anomalies are not associated with a phase transition.

Effect of the metal environment on the ferromagnetic interaction in the Co-NC-W pairs of octacyanotungstate(V)-Cobalt(II) three-dimensional networks

State of the art CASSCF and CASPT2 calculations have been performed to elucidate the nature of ferromagnetism of CoII-NC-WV pairs in the three-dimensional compound [[WV(CN)2]2[(micro-CN)4CoII(H2O)2]3.4H2O]n, which has been recently synthesized and investigated by a number of experimental techniques (Herrera, J. M.; Bleuzen, A.; Dromzée, Y.; Julve, M.; Lloret, F.; Verdaguer, M. Inorg. Chem. 2003, 42, 7052-7059). In this network, the Co ions are in the high-spin (S = 3/2) state, while the single unpaired electron on the W centers occupies the lowest orbital of the dz2 type of the 5d shell. In agreement with the suggestion made by Herrera et al., we find that the ferromagnetism is due to a certain occupation scheme of the orbitals from the parent octahedral t2g shell on CoII sites, in which the orbital accommodating the unpaired electron is orthogonal to the dz2 orbitals of the surrounding W ions. We investigate the stabilization of such an orbital configuration on the Co sites and find that it cannot be achieved in the ground state of isolated mononuclear fragments [CoII(NC)4(OH2)2]2- for any conformations of the coordinated water molecules and Co-N-C bond angles. On the other hand, it is stabilized by the interaction of the complex with neighboring W ions, which are simulated here by effective potentials. The calculated exchange coupling constants for the CoII-NC-WV binuclear fragments are in reasonable agreement with the measured Curie-Weiss constant for this compound. As additional evidence for the inferred electronic configuration on the Co sites, the ligand-field transitions, the temperature-dependent magnetic susceptibility, and the field-dependent low-temperature magnetization, simulated ab initio for the mononuclear Co fragments, are in agreement with the available data for another compound [WIV[(micro-CN)4-CoII(H2O)2]2.4H2O]n containing diamagnetic W and high-spin Co ions in an isostructural environment.

Effect of the Metal Environment on the Ferromagnetic Interaction in the Co−NC−W Pairs of Octacyanotungstate(V)−Cobalt(II) Three-Dimensional Networks

State of the art CASSCF and CASPT2 calculations have been performed to elucidate the nature of ferromagnetism of CoII-NC-WV pairs in the three-dimensional compound [[WV(CN)2]2[(micro-CN)4CoII(H2O)2]3.4H2O]n, which has been recently synthesized and investigated by a number of experimental techniques (Herrera, J. M.; Bleuzen, A.; Dromzée, Y.; Julve, M.; Lloret, F.; Verdaguer, M. Inorg. Chem. 2003, 42, 7052-7059). In this network, the Co ions are in the high-spin (S = 3/2) state, while the single unpaired electron on the W centers occupies the lowest orbital of the dz2 type of the 5d shell. In agreement with the suggestion made by Herrera et al., we find that the ferromagnetism is due to a certain occupation scheme of the orbitals from the parent octahedral t2g shell on CoII sites, in which the orbital accommodating the unpaired electron is orthogonal to the dz2 orbitals of the surrounding W ions. We investigate the stabilization of such an orbital configuration on the Co sites and find that it cannot be achieved in the ground state of isolated mononuclear fragments [CoII(NC)4(OH2)2]2- for any conformations of the coordinated water molecules and Co-N-C bond angles. On the other hand, it is stabilized by the interaction of the complex with neighboring W ions, which are simulated here by effective potentials. The calculated exchange coupling constants for the CoII-NC-WV binuclear fragments are in reasonable agreement with the measured Curie-Weiss constant for this compound. As additional evidence for the inferred electronic configuration on the Co sites, the ligand-field transitions, the temperature-dependent magnetic susceptibility, and the field-dependent low-temperature magnetization, simulated ab initio for the mononuclear Co fragments, are in agreement with the available data for another compound [WIV[(micro-CN)4-CoII(H2O)2]2.4H2O]n containing diamagnetic W and high-spin Co ions in an isostructural environment.

Current-density maps as probes of aromaticity: Global and Clar π ring currents in totally resonant polycyclic aromatic hydrocarbons

Calculation and visualisation of induced current density are important aids to the study of both aromaticity and observable molecular magnetic response properties. The ipsocentric method offers an accurate and economical approach to calculation of induced current density, and a physical interpretation in terms of occupied-orbital contributions. In monocyclic systems, these contributions allow rationalisation of the existence, sense, and strength of ring current using simple symmetry and node-counting arguments. Here we show maps computed with the model pseudo-pi version of the ipsocentric theory for large polycyclic aromatic hydrocarbons (PAH) of the Clar type. Maps are presented for D(6h)-symmetric systems with up to 438 carbon centres; a full ab initio calculation for an isomer of C114H30 confirms that the success of the pseudo-pi method for small PAH carries over to these larger systems. The computed maps follow a generic overall pattern that can be understood with a natural extension of the orbital arguments to a 'band theory' of totally resonant PAH. All show pi current densities that combine a Clar-sextet structure of localised benzenoid diatropic ring currents (contributed by just four HOMO electrons) with a global perimeter diatropic ring current contributed by the remaining pi electrons. Both currents are explained in the ipsocentric model: the localised currents arise from excitations from the HOMO; the perimeter current from excitations from the rest of the HOMO-band.