Detailed ab initio first-Principles study of the magnetic anisotropy in a family of trigonal pyramidal iron(II) pyrrolide complexes

A theoretical, computational, and conceptual framework for the interpretation and prediction of the magnetic anisotropy of transition metal complexes with orbitally degenerate or orbitally nearly degenerate ground states is explored. The treatment is based on complete active space self-consistent field (CASSCF) wave functions in conjunction with N-electron valence perturbation theory (NEVPT2) and quasidegenerate perturbation theory (QDPT) for treatment of magnetic field- and spin-dependent relativistic effects. The methodology is applied to a series of Fe(II) complexes in ligand fields of almost trigonal pyramidal symmetry as provided by several variants of the tris-pyrrolylmethyl amine ligand (tpa). These systems have recently attracted much attention as mononuclear single-molecule magnet (SMM) complexes. This study aims to establish how the ligand field can be fine tuned in order to maximize the magnetic anisotropy barrier. In trigonal ligand fields high-spin Fe(II) complexes adopt an orbitally degenerate ⁵E ground state with strong in-state spin–orbit coupling (SOC). We study the competing effects of SOC and the ⁵E⊗ε multimode Jahn–Teller effect as a function of the peripheral substituents on the tpa ligand. These subtle distortions were found to have a significant effect on the magnetic anisotropy. Using a rigorous treatment of all spin multiplets arising from the triplet and quintet states in the d⁶ configuration the parameters of the effective spin-Hamiltonian (SH) approach were predicted from first principles. Being based on a nonperturbative approach we investigate under which conditions the SH approach is valid and what terms need to be retained. It is demonstrated that already tiny geometric distortions observed in the crystal structures of four structurally and magnetically well-documented systems, reported recently, i.e., [Fe(tpa®)]⁻ (R = tert-butyl, Tbu (1), mesityl, Mes (2), phenyl, Ph (3), and 2,6-difluorophenyl, Dfp (4), are enough to lead to five lowest and thermally accessible spin sublevels described sufficiently well by S = 2 SH provided that it is extended with one fourth order anisotropy term. Using this most elementary parametrization that is consistent with the actual physics, the reported magnetization data for the target systems were reinterpreted and found to be in good agreement with the ab initio results. The multiplet energies from the ab initio calculations have been fitted with remarkable consistency using a ligand field (angular overlap) model (ab initio ligand field, AILFT). This allows for determination of bonding parameters and quantitatively demonstrates the correlation between increasingly negative D values and changes in the σ-bond strength induced by the peripheral ligands. In fact, the sigma-bonding capacity (and hence the Lewis basicity) of the ligand decreases along the series 1 > 2 > 3 > 4

Zero field splitting of the chalcogen diatomics using relativistic correlated wave-function methods.

International audienceThe spectrum arising from the (π*)(2) configuration of the chalcogen dimers, namely, the X(2)1, a2, and b0(+) states, is calculated using wave-function theory based methods. Two-component (2c) and four-component (4c) multireference configuration interaction (MRCI) and Fock-space coupled cluster (FSCC) methods are used as well as two-step methods spin-orbit complete active space perturbation theory at 2nd order (SO-CASPT2) and spin-orbit difference dedicated configuration interaction (SO-DDCI). The energy of the X(2)1 state corresponds to the zero-field splitting of the ground state spin triplet. It is described with high accuracy by the 2- and 4-component methods in comparison with experiment, whereas the two-step methods give about 80% of the experimental values. The b0(+) state is well described by 4c-MRCI, SO-CASPT2, and SO-DDCI, but FSCC fails to describe this state and an intermediate Hamiltonian FSCC ansatz is required. The results are readily rationalized by a two-parameter model; Δε, the π* spinor splitting by spin-orbit coupling and K, the exchange integral between the π(1)* and the π(-1)* spinors with, respectively, angular momenta 1 and -1. This model holds for all systems under study with the exception of Po(2)

Systematic theoretical study of the zero-field splitting in coordination complexes of Mn(III). Density functional theory versus multireference wave function approaches

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Theoretical determination of the zero-field splitting in copper acetate monohydrate.

International audienceThe zero-field splitting of the copper acetate monohydrate complex is studied using wave function based calculations. The anisotropy parameters extracted from highly correlated methods are in excellent agreement with the most accurate experimental results; in particular, the negative sign of the axial anisotropy parameter D is reproduced. During several decades, the interpretation of experimental data based on an analytical expression derived from perturbation theory led to a positive D-value. Although the validity of this expression is confirmed, it is explained that the incorrect attribution of a positive D is related to the assumption of an antiferromagnetic coupling between excited states. We have found in the present work that this coupling is actually ferromagnetic. The analysis of the various contributions to the anisotropy parameters shows that both spin-spin and spin-orbit couplings participate in the magnetic anisotropy of this complex. Although the anisotropy arising from the spin-spin coupling is essentially independent of the level of calculation, the zero-field-splitting parameters resulting from the spin-orbit coupling are strongly sensitive to the effects of dynamic correlation. This works provides important new insights into the physical origin of the zero-field-splitting parameters in copper dimers

The resolution of the identity approximation for calculations of spin-spin contribution to zero-field splitting parameters

In this work, the resolution of the identity (RI) approximation is developed for the calculation of the electron-electron spin-spin coupling (SSC) interaction that is a central component of the zero-field splitting (ZFS) term in the effective spin Hamiltonian. The approximated integrals are then used in large-scale multireference configuration interaction treatments of the SSC interaction. The SSC contribution to the ZFS is treated using the Breit-Pauli spin-spin Hamiltonian in conjunction with first-order perturbation theory. Test calculations on a set of diatomic molecules reveal that the error of the RI approximation does not exceed 0.01 cm(-1) even if standard auxiliary basis sets are used. This error of less than 1% is considered to be negligible compared to the presently achievable accuracy of the SSC calculations relative to experimental data. The present development allows the correlated ab initio calculation of ZFS parameters of larger systems such as linear polyenes and linear polyacenes. The basis set convergence of the calculated ZFS values was investigated, and the effect of electronic correlation on the calculated ZFS parameters is discussed

Visualization as a Service for Scientific Data

One of the primary challenges facing scientists is extracting understanding from the large amounts of data produced by simulations, experiments, and observational facilities. The use of data across the entire lifetime ranging from real-time to post-hoc analysis is complex and varied, typically requiring a collaborative effort across multiple teams of scientists. Over time, three sets of tools have emerged: One set for analysis, another for visualization, and a final set for orchestrating the tasks. This trifurcated tool set often results in the manual assembly of analysis and visualization workflows, which are one-off solutions that are often fragile and difficult to generalize. To address these challenges, we propose a serviced-based paradigm and a set of abstractions to guide its design. These abstractions allow for the creation of services that can access and interpret data, and enable interoperability for intelligent scheduling of workflow systems. This work results from a codesign process over analysis, visualization, and workflow tools to provide the flexibility required for production use. Finally, this paper describes a forward-looking research and development plan that centers on the concept of visualization and analysis technology as reusable services, and also describes several realworld use cases that implement these concepts

Exchangeable oxygens in the vicinity of the molybdenum center of the high-pH form of sulfite oxidase and sulfite dehydrogenase

The electron spin echo envelope modulation (ESEEM) investigation of the high- pH (hpH) form of sulfite oxidase (SO) and sulfite dehydrogenase (SDH) prepared in buffer enriched with H(2)(17)O reveals the presence of three types of exchangeable oxygen atoms at the molybdenum center. Two of these oxygen atoms belong to the equatorial OH ligand and the axial oxo ligand, and are characterized by (17)O hyperfine interaction (hfi) constants of about 37 MHz and 6 MHz, respectively. The third oxygen has an isotropic hfi constant of 3-4 MHz and likely belongs to a hydroxyl moiety hydrogen-bonded to the equatorial OH ligand. This exchangeable oxygen atom is not observed in the ESEEM spectra of the Y236F mutant of SDH, where the active site tyrosine has been replaced by phenylalanine