Density functional estimations of Heisenberg exchange constants in oligonuclear magnetic compounds: Assessment of density functional theory versus ab initio.

Modern density functionals were assessed for the calculation of magnetic exchange constants of academic hydrogen oligomer systems. Full-configuration interaction magnetic exchange constants and wavefunctions are taken as references for several H(n) model systems with different geometrical distributions from Ciofini et al. [Chem. Phys. 309, 133 (2005)]. Regression analyses indicate that hybrid functionals (B3LYP, O3LYP, and PBE0) rank among the best ones with a slope of typically 0.5, i.e., 100% overestimation with a standard error of about 50 cm(-1). The efficiency of the highly ranked functionals for predicting the correct "exact states" (after diagonalization of the Heisenberg Hamiltonian) is validated, and a statistical standard error is assigned for each functional. The singular value decomposition approach is used for treating the overdetermination of the system of equations when the number of magnetic centers is greater than 3. Further discussions particularly about the fortuitous success of the Becke00-x-only functional for treating hydrogenic models are presented.

Structure of the oxygen-evolving complex of photosystem II: information on the S(2) state through quantum chemical calculation of its magnetic properties.

Twelve structural models for the S(2) state of the oxygen-evolving complex (OEC) of photosystem II are evaluated in terms of their magnetic properties. The set includes ten models based on the 'fused twist' core topology derived by polarized EXAFS spectra and two related models proposed in recent mechanistic investigations. Optimized geometries and spin population analyses suggest that Mn(iii), which is most often identified with the manganese ion at site D, is always associated with a penta-coordinate environment, unless a chloride is directly ligated to the metal. Exchange coupling constants were determined by broken-symmetry density functional theory calculations and the complete spectrum of magnetic sublevels was obtained by direct diagonalization of the Heisenberg Hamiltonian. Seven models display a doublet ground state and are considered spectroscopic models for the ground state corresponding to the multiline signal (MLS) of the S(2) state of the OEC, whereas the remaining five models display a sextet ground state and could be related to the g = 4.1 signal of the S(2) state. It is found that the sign of the exchange coupling constant between the Mn centres at positions A and B of the cluster is directly related to the ground state multiplicity, implying that interconversion between the doublet and sextet can be induced by only small structural perturbations. The recently proposed quantum chemical method for the calculation of (55)Mn hyperfine coupling constants is subsequently applied to the S(2) MLS state models and the quantities that enter into the individual steps of the procedure (site-spin expectation values, intrinsic site isotropic hyperfine parameters and projected (55)Mn isotropic hyperfine constants) are analyzed and discussed in detail with respect to the structural and electronic features of each model. The current approach performs promisingly. It reacts sensitively to structural distortions and hence may be able to distinguish between different structural proposals. Thus it emerges as a useful contributor to the ongoing efforts that aim at establishing correlations between the body of spectroscopic data available for the various S(i) states of the OEC and their actual geometric features.

A new quantum chemical approach to the magnetic properties of oligonuclear transition-metal complexes: application to a model for the tetranuclear manganese cluster of photosystem II.

The reliable correlation of structural features and magnetic or spectroscopic properties of oligonuclear transition-metal complexes is a critical requirement both for research into innovative magnetic materials and for elucidating the structure and function of many metalloenzymes. We have developed a novel method that for the first time enables the extraction of hyperfine coupling constants (HFCs) from broken-symmetry density functional theory (BS-DFT) calculations on clusters. Using the geometry-optimized tetranuclear manganese complex [Mn(4)O(6)(bpy)(6)](4+/3+) as a model, we first examine in detail the calculation of exchange coupling constants J through the BS-DFT approach. Complications arising from the indeterminacy of experimentally fitted J constants are identified and analyzed. It is found that only the energy levels derived from Hamiltonian diagonalization are a physically meaningful basis for comparing theory and experiment. Subsequently, the proposed theoretical scheme is applied to the calculation of (55)Mn HFCs of the Mn(III,IV,IV,IV) state of the complex, which is similar to the S(2) state of the oxygen-evolving complex (OEC) in photosystem II of oxygenic photosynthesis. The new approach performs reliably and accurately, and yields calculated HFCs that can be directly compared with experimental data. Finally, we carefully examine the dependence of HFC on the J value and draw attention to the sensitivity of the calculated values to the exchange coupling parameters. The proposed strategy extends naturally to hetero-oligonuclear clusters of arbitrary shape and nuclearity, and hence is of general validity and usefulness in the study of magnetic metal clusters. The successful application of the new approach presented here is a first step in the effort to establish correlations between the available spectroscopic information and the structural features of complex metalloenzymes like OEC.

Ab initio and coupled-perturbed density functional theory estimation of zero-field splittings in MnII transition metal complexes.

The paper presents a method comparison for the prediction of zero-field splitting (ZFS) parameters in a series of Mn (II) coordination complexes. The test set consists of Mn (II) complexes that are experimentally well-characterized by X-ray diffraction and high-field electron paramagnetic resonance. Their ZFS parameters have been calculated using density functional theory (DFT) as well as complete active space self-consistent field (CASSCF) methods. It is shown that the recently introduced coupled-perturbed spin-orbit coupling (CP-SOC) approach [ Neese, F. J. Chem. Phys. 2007, 127, 164112 ] together with hybrid-DFT functionals leads to a slope of the correlation line (plot of experimental vs calculated D values) that is essentially unity provided that the direct spin-spin interaction is properly included in the treatment. This is different from our previous DFT study on the same series of complexes where a severe overestimation of the D parameter has been found [ Zein, S. ; Duboc, C. ; Lubitz, W. ; Neese, F. Inorg. Chem. 2008, 47, 134 ]. CASSCF methods have been used to evaluate the ZFS in an "ab initio ligand-field" type treatment. The study demonstrates that a substantial part of the relevant physics is lost in such a treatment since only excitations within the manganese d-manifold are accounted for. Thus, a severe underestimation of the D parameter has been found. Because the CASSCF calculations in combination with quasidegenerate perturbation theory treats the SOC to all orders, we have nevertheless verified that second-order perturbation theory is an adequate approximation in the case of the high-spin d (5) configuration.

Focusing the view on nature's water-splitting catalyst.

Nature invented a catalyst about 3Gyr ago, which splits water with high efficiency into molecular oxygen and hydrogen equivalents (protons and electrons). This reaction is energetically driven by sunlight and the active centre contains relatively cheap and abundant metals: manganese and calcium. This biological system therefore forms the paradigm for all man-made attempts for direct solar fuel production, and several studies are underway to determine the electronic and geometric structures of this catalyst. In this report we briefly summarize the problems and the current status of these efforts and propose a density functional theory-based strategy for obtaining a reliable high-resolution structure of this unique catalyst that includes both the inorganic core and the first ligand sphere.

A systematic density functional study of the zero-field splitting in Mn(II) coordination compounds.

This work presents a detailed evaluation of the performance of density functional theory (DFT) for the prediction of zero-field splittings (ZFSs) in Mn(II) coordination complexes. Eighteen experimentally well characterized four-, five-, and six-coordinate complexes of the general formula [Mn(L)nL'2] with L' = Cl, Br, I, NCS, or N3 (L = an oligodentate ligand) are considered. Several DFT-based approaches for the prediction of the ZFSs are compared. For the estimation of the spin-orbit coupling (SOC) part of the ZFS, it was found that the Pederson-Khanna (PK) approach is more successful than the previously proposed quasi-restricted orbitals (QRO)-based method. In either case, accounting for the spin-spin (SS) interaction either with or without the inclusion of the spin-polarization effects improves the results. This argues for the physical necessity of accounting for this important contribution to the ZFS. On average, the SS contribution represents approximately 30% of the axial D parameters. In addition to the SS part, the SOC contributions of d-d spin flip (alphabeta) and ligand-to-metal charge transfer excited states (betabeta) were found to dominate the SOC part of the D parameter; the observed near cancellation between the alphaalpha and betaalpha parts is discussed in the framework of the PK model. The calculations systematically (correlation coefficient approximately 0.99) overestimate the experimental D values by approximately 60%. Comparison of the signs of calculated and measured D values shows that the signs of the calculated axial ZFS parameters are unreliable once E/D > 0.2. Finally, we find that the calculated D and E/D values are highly sensitive to small structural changes. It is observed that the use of theoretically optimized geometries leads to a significant deterioration of the theoretical predictions relative to the experimental geometries derived from X-ray diffraction. The standard deviation of the theoretical predictions for the D values almost doubles from approximately 0.1 to approximately 0.2 cm-1 upon using quantum chemically optimized structures. We do not find any noticeable improvement in considering basis sets larger than standard double- (SVP) or triple-zeta (TZVP) basis sets or using functionals other than the BP functional.

Spin crossover phenomenon accompanying order-disorder phase transition in the ligand of [FeII(DAPP)(abpt)](ClO4)2 compound (DAPP = bis(3-aminopropyl)(2-pyridylmethyl)amine, abpt = 4-amino-3,5-bis(pyridin-2-yl)-1,2,4-triazole) and its successive self-grinding effect.

The spin crossover phenomenon of the recently described spin crossover complex [FeII(DAPP)(abpt)](ClO4)2 [DAPP = bis(3-aminopropyl)(2-pyridylmethyl)amine, abpt = 4-amino-3,5-bis(pyridin-2-yl)-1,2,4-triazole] accompanying an order-disorder phase transition of the ligand was investigated by adiabatic heat capacity calorimetry, far-IR, IR, and Raman spectroscopies, and normal vibrational mode calculation. A large heat capacity peak due to the spin crossover transition was observed at T(trs) = 185.61 K. The transition enthalpy and entropy amounted to Delta(trs)H = 15.44 kJ mol-1 and Delta(trs)S = 83.74 J K-1 mol-1, respectively. The transition entropy is larger than the expected value 60.66 J K-1 mol-1, which is contributed from the spin multiplicity (R ln 5; R: the gas constant), disordering of the carbon atom of the six-membered metallocycle in the DAPP ligand, and one of the two perchlorate anions (2R ln 2), and change of the normal vibrational modes between the high-spin (HS) and low-spin (LS) states (35.75 J K-1 mol-1). The remaining entropy would be ascribed to changes of the lattice vibrations and molecular librations between the HS and LS states. Furthermore, [Fe(DAPP)(abpt)](ClO4)2 crystals disintegrated and became smaller crystallites whenever they experienced the phase transition. This may be regarded as a successive self-grinding effect, evidenced by adiabatic calorimetry, DSC, magnetic susceptibility, and microscope observation. The relationship between the crystal size and the physical quantities is discussed.

Investigation of the two-step spin crossover complex Fe[5-NO2-sal-(1,4,7,10)] using density functional theory.

A quantum chemical study of the Fe[5-NO2-sal-(1,4,7,10)] ((1,10-bis(5-nitrosalicylaldehyde)-1,4,7,10-tetra-ezdecane-O,O',N,N',N' ',N' '')iron(II)) molecule was performed using density functional theory (DFT). Starting from the different X-ray crystallographic structures, geometry optimizations have been performed. These calculations confirmed the conformational isomerism of this complex in each spin states of the molecule ((1)A(1g) and (5)T(2g)). Each employed DFT method (B3LYP, B3LYP*, BP86, HCTH407) reproduced correctly the structural differences between the two calculated conformers when compared to the experimental structures. Furthermore, electronic polarizabilities have been calculated in each spin state and for each conformer. These calculations revealed a higher polarizability in the singlet state in agreement with the measured higher dielectric constant in this state.

Origin of the zero-field splitting in mononuclear octahedral dihalide MnII complexes: an investigation by multifrequency high-field electron paramagnetic resonance and density functional theory.

The synthesis, structural characterization, and electronic properties of a new series of high-spin six-coordinate dihalide mononuclear MnII complexes [Mn(tpa)X2] (tpa=tris-2-picolylamine; X=I (1), Br (2), and Cl (3)) are reported. The analysis of the crystallographic data shows that in all investigated complexes the manganese ion lies in the center of a distorted octahedron with a cis configuration of the halides imposed by the tpa ligand. By a multifrequency high-field electron paramagnetic resonance investigation (95-285 GHz), the electronic properties of 1-3 were determined (DI=-0.600, DBr=-0.360, DCl=+0.115 cm-1), revealing the important effect of (i) the nature of the halide and (ii) the configuration (cis/trans) of the two halides on the magnitude of D. The spin Hamiltonian parameters obtained by density functional theory calculations initiated from the crystal structure of 1-3 are in reasonable agreement with the experimental values. The absolute value of D is consistently overestimated, but the sign and the trend over the chemical series is well reproduced. Theoretical models (cis- and trans-[Mn(NH3)4X2], X=I, Br, Cl and F) have been used to investigate the different contributions to D and also to understand the origin of the experimentally observed changes in D within the series reported here. This study reveals that the spin-spin coupling contributions to the D tensor are non-negligible for the lighter halides (F, Cl) but become insignificant for the heavier halides (I, Br). The four different types of excitations involved in the spin-orbit coupling (SOC) part of the D tensor contribute with comparable magnitudes and opposing signs. The general trend observed for halide MnII complexes (DI>DBr>DCl) can be explained by the fact that the halide SOC dominates the D value in these systems with a major contribution arising from interference between metal- and halide-SOC contributions, which are proportional to the product of the SOC constants of Mn and X.

The catalytic Mn2+ sites in the enolase-inhibitor complex: crystallography, single-crystal EPR, and DFT calculations.

Crystals of Zn2+/Mn2+ yeast enolase with the inhibitor PhAH (phosphonoacetohydroxamate) were grown under conditions with a slight preference for binding of Zn2+ at the higher affinity site, site I. The structure of the Zn2+/Mn2+-PhAH complex was solved at a resolution of 1.54 A, and the two catalytic metal binding sites, I and II, show only subtle displacement compared to that of the corresponding complex with the native Mg2+ ions. Low-temperature echo-detected high-field (W-band, 95 GHz) EPR (electron paramagnetic resonance) and 1H ENDOR (electron-nuclear double resonance) were carried out on a single crystal, and rotation patterns were acquired in two perpendicular planes. Analysis of the rotation patterns resolved a total of six Mn2+ sites, four symmetry-related sites of one type and two out of the four of the other type. The observation of two chemically inequivalent Mn2+ sites shows that Mn2+ ions populate both sites I and II and the zero-field splitting (ZFS) tensors of the Mn2+ in the two sites were determined. The Mn2+ site with the larger D value was assigned to site I based on the 1H ENDOR spectra, which identified the relevant water ligands. This assignment is consistent with the seemingly larger deviation of site I from octahedral symmetry, compared to that of site II. The ENDOR results gave the coordinates of the protons of two water ligands, and adding them to the crystal structure revealed their involvement in a network of H bonds stabilizing the binding of the metal ions and PhAH. Although specific hyperfine interactions with the inhibitor were not determined, the spectroscopic properties of the Mn2+ in the two sites were consistent with the crystal structure. Density functional theory (DFT) calculations carried out on a cluster representing the catalytic site, with Mn2+ in site I and Zn2+ in site II, and vice versa, gave overestimated D values on the order of the experimental ones, although the larger D value was found for Mn2+ in site II rather than in site I. This discrepancy was attributed to the high sensitivity of the ZFS parameters to the Mn-O bond lengths and orientations, such that small, but significant, differences between the optimized and crystal structures alter the ZFS considerably, well above the difference between the two sites.

Assessment of the exchange-correlation functionals for the physical description of spin transition phenomena by density functional theory methods: all the same?

This study aims to assess present day density functionals in the description of spin crossover iron(II) complexes. Two recently synthesized spin crossover complexes were considered. Theoretical calculations were made using 53 of the most popular exchange-correlation density functionals with triple zeta plus polarization quality basis sets. The present work shows that even though different density functionals can lead to different energy gaps between spin states, most of them are very similar for these two compounds when a comparison between energy gaps is sought. The present work shows that even though different exchange correlations can lead to different energy gaps between spin states, the difference between these gaps calculated at different geometries and that calculated at a given reference geometry is surprisingly independent of the choice of functional. The reasons for the similarities and the differences among exchange and correlation functional combinations are discussed.

Energetics of binuclear spin transition complexes.

The electronic structures of five binuclear iron(II) complexes, four of which display spin transitions between the low-spin (LS) and high-spin (HS) electronic states, are studied by density functional theory (DFT) calculations. Three electronic states, corresponding to [LS-LS], [LS-HS], and [HS-HS] electronic configurations, are characterized. The nature of the ground state agrees with the experimentally observed magnetic state of complexes stabilized at low temperatures. The results of the calculations agree with the conclusion of the phenomenological model, that the enthalpy of the [LS-HS] state must be lower than the average enthalpy of the [LS-LS] and [HS-HS] states, to create conditions for a two-step spin transition. The exchange parameters between Fe(II) ions in the [HS-HS] states are evaluated. It is shown that all complexes are weakly antiferromagnetic and the synergy between two spin transition centers is mainly of elastic origin.

Quantum chemical study of three polymorphs of the mononuclear spin-transition complex [Fe(DPPA)(NCS)2].

The calculations of the high spin (HS) and low spin (LS) states of the [Fe(II)(DPPA)(NCS)(2)] complex have been performed at three experimentally observed geometries corresponding to three synthesized polymorphs with different spin-transition behavior. The structure optimization leads to a single molecular structure, suggesting that the existence of three geometries is not an intrinsic phenomenon but is induced by the crystal lattice. The structural difference between three forms can be reproduced by introducing the Madelung field of the crystal lattice. However, the calculations show that the differences in magnetic behavior of the three polymorphs cannot be attributed only to variations of the energy gap between two spin states.

Cooperative spin crossover and order-disorder phenomena in a mononuclear compound [Fe(DAPP)(abpt)](ClO(4))(2) [DAPP = [bis(3-aminopropyl)(2-pyridylmethyl)amine], abpt = 4-amino-3,5-bis(pyridin-2-yl)-1,2,4-triazole].

The synthesis and detailed characterization of the new spin crossover mononuclear complex [Fe(II)(DAPP)(abpt)](ClO(4))(2), where DAPP = [bis(3-aminopropyl)(2-pyridylmethyl)amine] and abpt = 4-amino-3,5-bis(pyridin-2-yl)-1,2,4-triazole, are reported. Variable-temperature magnetic susceptibility measurements and Mössbauer spectroscopy have revealed the occurrence of an abrupt spin transition with a hysteresis loop. The hysteresis width derived from magnetic susceptibility measurements is 10 K, the transition being centered at T(c) downward arrow = 171 K for decreasing and T(c) upward arrow = 181 K for increasing temperatures. The crystal structure was resolved in the high-spin (293 and 183 K) and low-spin (123 K) states. Both spin-state structures belong to the monoclinic space group P2(1)/n (Z = 4). The thermal spin transition is accompanied by the shortening of the mean Fe-N distances by 0.177 A. The two main structural characteristics of [Fe(DAPP)(abpt)](ClO(4))(2) are a branched network of intermolecular links in the crystal lattice and the occurrence of two types of order-disorder transitions (in the DAPP ligand and in the perchlorate anions) accompanying the thermal spin change. These features are discussed relative to the magnetic properties of the complex. The electronic structure calculations show that the structural disorder in the DAPP ligand modulates the energy gap between the HS and LS states. In line with previous studies, the order-disorder phenomena and the spin transition in [Fe(DAPP)(abpt)](ClO(4))(2) are found to be interrelated.