Geometries of third-row transition-metal complexes from density-functional theory

A set of 41 metal-ligand bond distances in 25 third-row transition-metal complexes, for which precise structural data are known in the gas phase, is used to assess optimized and zero-point averaged geometries obtained from DFT computations with various exchange-correlation functionals and basis sets. For a given functional (except LSDA) Stuttgart-type quasi-relativistic effective core potentials and an all-electron scalar relativistic approach (ZORA) tend to produce very similar geometries. In contrast to the lighter congeners, LSDA affords reasonably accurate geometries of 5d-metal complexes, as it is among the functionals with the lowest mean and standard deviations from experiment. For this set the ranking of some other popular density functionals, ordered according to decreasing standard deviation, is BLYP > VSXC > BP86 approximate to BPW91 approximate to TPSS approximate to B3LYP approximate to PBE > TPSSh > B3PW91 approximate to B3P86 approximate to PBE hybrid. In this case hybrid functionals are superior to their nonhybrid variants. In addition, we have reinvestigated the previous test sets for 3d- (Buhl M.; Kabrede, H. J. Chem. Theory Comput. 2006, 2, 1282-1290) and 4d- (Waller, M. P.; Buhl, M. J. Comput. Chem. 2007,28,1531-1537) transition-metal complexes using all-electron scalar relativistic DFT calculations in addition to the published nonrelativistic and ECP results. For this combined test set comprising first-, second-, and third-row metal complexes, B3P86 and PBE hybrid are indicated to perform best. A remarkably consistent standard deviation of around 2 pm in metal-ligand bond distances is achieved over the entire set of d-block elements.PostprintPeer reviewe

Exchange Coupling Interactions from the Density Matrix Renormalization Group and N-Electron Valence Perturbation Theory: Application to a Biomimetic Mixed Valence Manganese Complex

The accurate description of magnetic level energetics in oligonuclear exchange-coupled transition-metal complexes remains a formidable challenge for quantum chemistry. The density matrix renormalization group (DMRG) brings such systems for the first time easily within reach of multireference wave function methods by enabling the use of unprecedentedly large active spaces. But does this guarantee systematic improvement in predictive ability and, if so, under which conditions? We identify operational parameters in the use of DMRG using as a test system an experimentally characterized mixed-valence bis-μ-oxo/μ-acetato Mn(III,IV) dimer, a model for the oxygen-evolving complex of photosystem II. A complete active space of all metal 3d and bridge 2p orbitals proved to be the smallest meaningful starting point; this is readily accessible with DMRG and greatly improves on the unrealistic metal-only configuration interaction or complete active space self-consistent field (CASSCF) values. Orbital optimization is critical for stabilizing the antiferromagnetic state, while a state-averaged approach over all spin states involved is required to avoid artificial deviations from isotropic behavior that are associated with state-specific calculations. Selective inclusion of localized orbital subspaces enables probing the relative contributions of different ligands and distinct superexchange pathways. Overall, however, full-valence DMRG-CASSCF calculations fall short of providing a quantitative description of the exchange coupling owing to insufficient recovery of dynamic correlation. Quantitatively accurate results can be achieved through a DMRG implementation of second order N-electron valence perturbation theory (NEVPT2) in conjunction with a full-valence metal and ligand active space. Perspectives for future applications of DMRG-CASSCF/NEVPT2 to exchange coupling in oligonuclear clusters are discussed.</p

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

What Can We Learn from a Biomimetic Model of Nature's Oxygen-Evolving Complex?

A recently reported synthetic complex with a Mn4CaO4 core represents a remarkable structural mimic of the Mn4CaO5 cluster in the oxygen-evolving complex (OEC) of photosystem II (Zhang et al., Science 2015, 348, 690). Oxidized samples of the complex show electron paramagnetic resonance (EPR) signals at g ≈ 4.9 and 2, similar to those associated with the OEC in its S2 state (g ≈ 4.1 from an S = 5/2 form and g ≈ 2 from an S = 1/2 form), suggesting similarities in the electronic as well as geometric structure. We use quantum-chemical methods to characterize the synthetic complex in various oxidation states, to compute its magnetic and spectroscopic properties, and to establish connections with reported data. Only one energetically accessible form is found for the oxidized "S2 state" of the complex. It has a ground spin state of S = 5/2, and EPR simulations confirm it can be assigned to the g ≈ 4.9 signal. However, no valence isomer with an S = 1/2 ground state is energetically accessible, a conclusion supported by a wide range of methods, including density matrix renormalization group with full valence active space. Alternative candidates for the g ≈ 2 signal were explored, but no low-spin/low-energy structure was identified. Therefore, our results suggest that despite geometric similarities the synthetic model does not mimic the valence isomerism that is the hallmark of the OEC in its S2 state, most probably because it lacks a coordinatively flexible oxo bridge. Only one of the observed EPR signals can be explained by a structurally intact high-spin one-electron-oxidized form, while the other originates from an as-yet-unidentified rearrangement product. Nevertheless, this model provides valuable information for understanding the high-spin EPR signals of both the S1 and S2 states of the OEC in terms of the coordination number and Jahn-Teller axis orientation of the Mn ions, with important consequences for the development of magnetic spectroscopic probes to study S-state intermediates immediately prior to O-O bond formation.Financial support by the Max Planck Society and by Project MANGAN (03EK3545) funded by the Bundesministeriums fü r Bildung und Forschung is gratefully acknowledged. N.C. acknowledges the support of the Australian Research Council (Grant FT140100834). D.A.P. acknowledges network support by the COST action CM1305 “Explicit Control Over SpinStates in Technology and Biochemistry (ECOSTBio)”

Exchange Coupling Interactions from the Density Matrix Renormalization Group and N-Electron Valence Perturbation Theory: Application to a Biomimetic Mixed Valence Manganese Complex

The accurate description of magnetic level energetics in oligonuclear exchange-coupled transition-metal complexes remains a formidable challenge for quantum chemistry. The density matrix renormalization group (DMRG) brings such systems for the first time easily within reach of multireference wave function methods by enabling the use of unprecedentedly large active spaces. But does this guarantee systematic improvement in predictive ability and, if so, under which conditions? We identify operational parameters in the use of DMRG using as a test system an experimentally characterized mixed-valence bis-μ-oxo/μ-acetato Mn(III,IV) dimer, a model for the oxygen-evolving complex of photosystem II. A complete active space of all metal 3d and bridge 2p orbitals proved to be the smallest meaningful starting point; this is readily accessible with DMRG and greatly improves on the unrealistic metal-only configuration interaction or complete active space self-consistent field (CASSCF) values. Orbital optimization is critical for stabilizing the antiferromagnetic state, while a state-averaged approach over all spin states involved is required to avoid artificial deviations from isotropic behavior that are associated with state-specific calculations. Selective inclusion of localized orbital subspaces enables probing the relative contributions of different ligands and distinct superexchange pathways. Overall, however, full-valence DMRG-CASSCF calculations fall short of providing a quantitative description of the exchange coupling owing to insufficient recovery of dynamic correlation. Quantitatively accurate results can be achieved through a DMRG implementation of second order N-electron valence perturbation theory (NEVPT2) in conjunction with a full-valence metal and ligand active space. Perspectives for future applications of DMRG-CASSCF/NEVPT2 to exchange coupling in oligonuclear clusters are discussed

Temporal dynamics of the neural representation of hue and luminance contrast

Hue and luminance contrast are the most basic visual features, emerging in early layers of convolutional neural networks trained to perform object categorization. In human vision, the timing of the neural computations that extract these features, and the extent to which they are determined by the same or separate neural circuits, is unknown. We addressed these questions using multivariate analyses of human brain responses measured with magnetoencephalography. We report four discoveries. First, it was possible to decode hue tolerant to changes in luminance contrast, and luminance contrast tolerant to changes in hue, consistent with the existence of separable neural mechanisms for these features. Second, the decoding time course for luminance contrast peaked 16-24 ms before hue and showed a more prominent secondary peak corresponding to decoding of stimulus cessation. These results are consistent with the idea that the brain uses luminance contrast as an updating signal to separate events within the constant stream of visual information. Third, neural representations of hue generalized to a greater extent across time, providing a neural correlate of the preeminence of hue over luminance contrast in perceptual grouping and memory. Finally, decoding of luminance contrast was more variable across participants for hues associated with daylight (orange and blue) than for anti-daylight (green and pink), suggesting that color-constancy mechanisms reflect individual differences in assumptions about natural lighting

Calcium Valence-to-Core X-ray Emission Spectroscopy: A Sensitive Probe of Oxo Protonation in Structural Models of the Oxygen-Evolving Complex

Calcium is an abundant, nontoxic metal that finds many roles in synthetic and biological systems including the oxygen-evolving complex (OEC) of photosystem II. Characterization methods for calcium centers, however, are underdeveloped compared to those available for transition metals. Valence-to-core X-ray emission spectroscopy (VtC XES) selectively probes the electronic structure of an element’s chemical environment, providing insight that complements the geometric information available from other techniques. Here, the utility of calcium VtC XES is established using an in-house dispersive spectrometer in combination with density functional theory. Spectral trends are rationalized within a molecular orbital framework, and Kβ_(2,5) transitions, derived from molecular orbitals with primarily ligand p character, are found to be a promising probe of the calcium coordination environment. In particular, it is shown that calcium VtC XES is sensitive to the electronic structure changes that accompany oxo protonation in Mn₃CaO₄-based molecular mimics of the OEC. Through correlation to calculations, the potential of calcium VtC XES to address unresolved questions regarding the mechanism of biological water oxidation is highlighted

Ammonia binding to the oxygen-evolving complex of photosystem II identifies the solvent-exchangeable oxygen bridge (μ-oxo) of the manganese tetramer

The assignment of the two substrate water sites of the tetra-manganese penta-oxygen calcium (Mn4O5Ca) cluster of photosystem II is essential for the elucidation of the mechanism of biological O-O bond formation and the subsequent design of bio-inspired water-splitting catalysts. We recently demonstrated using pulsed EPR spectroscopy that one of the five oxygen bridges (μ-oxo) exchanges unusually rapidly with bulk water and is thus a likely candidate for one of the substrates. Ammonia, a water analog, was previously shown to bind to the Mn4O5Ca cluster, potentially displacing a water/substrate ligand [Britt RD, et al. (1989) J Am Chem Soc 111(10):3522–3532]. Here we show by a combination of EPR and time-resolved membrane inlet mass spectrometry that the binding of ammonia perturbs the exchangeable μ-oxo bridge without drastically altering the binding/exchange kinetics of the two substrates. In combination with broken-symmetry density functional theory, our results show that (i) the exchangable μ-oxo bridge is O5 {using the labeling of the current crystal structure [Umena Y, et al. (2011) Nature 473(7345):55–60]}; (ii) ammonia displaces a water ligand to the outer manganese (MnA4-W1); and (iii) as W1 is trans to O5, ammonia binding elongates the MnA4-O5 bond, leading to the perturbation of the μ-oxo bridge resonance and to a small change in the water exchange rates. These experimental results support O-O bond formation between O5 and possibly an oxyl radical as proposed by Siegbahn and exclude W1 as the second substrate water