Spin-mixed states of ferric ion in complexes of tetragonal symmetry

Using a strong crystal field model for ferric ion complexes with tetragonal symmetry and allowing spin-orbit coupling between sextet, quartet, and doublet states, a mechanism is obtained whereby ferric ion can exist in four qualitatively different ground states: a sextet, a quartet, a doublet or a substantially spin-mixed state. We have delineated the regions in crystal field parameter space in which these various possible ground states prevail. Also, we have calculated the eigenfunctions and eigenvalues typical of each region. We discuss in detail the nature of the 5 lowest ferric ion functions in these different regions, particularly in the regions of spin-mixed states. With this model we obtain a picture of these various ferric ion states consistent with the behavior of known complexes of ferric ion, particularly of the ferric heme compounds. The results presented here will be used in a subsequent calculation of some of the observed properties of these compounds.

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Zusammenfassung Das Fe(III)-Ion wird in einem starken tetragonalen Ligandenfeld unter Berücksichtigung der Spin-Bahn-Kopplung behandelt. Je nach Größe des kubischen Ligandenfeldes, der beiden Parameter der tetragonalen Verzerrung und des Spin-Bahn-Kopplungsparameters ist der Grundzustand ein Sextett, ein Dublett, ein Quartett oder ein spin-gemischter Zustand. Eigenwerte und Eigenfunktionen der fünf untersten Zustände in Abhängigkeit von den Parameterwerten werden eingehend diskutiert. Die Parameter werden physikalisch interpretiert. Die hier gewonnenen Resultate werden in den folgenden Arbeiten zur Berechnung der Eigenschaften von Eisen-Hämin-Komplexen herangezogen.

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Résumé En utilisant un modèle de champ cristallin fort pour les complexes de l'ion ferrique á symétrie tétragonale et en tenant compte du couplage spin-orbite entre les états sextet, quartet et doublet, on obtient un mécanisme pour l'existence de l'ion ferrique dans quatre états fondamentaux qualitativement différents: un sextet, un quartet, un doublet et un état mixte. Nous avons délimité les zones de paramètre du champ cristallin où dominent ces différents états fondamentaux. Nous avons aussi calculé les fonctions et les valeurs propres typiques dans chaque zone. Nous discutons en détail la nature des cinq plus basses fonctions de l'ion ferrique dans ces différentes zones, en particulier dans les zones á états de spin mixtes. A l'aide de ce modèle nous obtenons une image de ces différents états de l'ion ferrique en accord avec le comportement des complexes ferriques connus, en particulier du type hémique. Les résultats présentés ici seront utilisés dans un calcul de propriétés observées de ces composés.

     

The EPR spectra of copper compounds with tetragonal symmetry in glasses

The conditions for the appearance of the additional absorption peak and its position in the EPR spectra of copper compounds with tetragonal symmetry in glasses have been analyzed. It has been found that the constants of the spin hamiltonians A and B should always have negative signs. The resulting theoretical conclusions have been compared with experimental results on the EPR of bis(salicylideneiminato)copper in various solvents and low-temperature glasses.     

Spin-mixing and the different spin states of ferric ion in tetragonal symmetry

We have used the wave functions generated from a strong crystal field model of ferric ion in complexes of tetragonal symmetry with spin-orbit coupling, to calculate the behavior of several localized properties of the ferric ion in parameter regions of different ground and low-lying ferric ion states. In the previous paper of this series we have shown with this model that ferric ion can exist in a doublet, sextet, quartet and substantially spin-mixed ground state. We have delineated such regions and described the changing nature of the wave functions. In the present study, we calculate the effective magnetic moments and their temperature dependence, the first order magnetic field energies, and the electric field gradients of ferric ion in these various spin states. Particular emphasis is placed on the properties of ferric ion in substantially spin-mixed states which have hitherto not been reported. Wherever possible, our results are compared with existing experimental data. In particular, with this model, we have been able to quantitatively account for the continuously varying values of magnetic moment for a series of 12 ferric hemoglobin derivatives, in the region from range of 5.92 to 2.26 Bohr magnetons.     

EPR parameters for spin 3/2 iron in a strong crystal field with axial and rhombic symmetry components

Calculations are presented for the eigenfunctions, energy eigenvalues, and EPR g values, expected for mid-spin (S = 2/3) iron in a strong crystalline field with axial (D) and rhombic (E) symmetry components. For E/D=1/3, a polycrystalline sample is expected to exhibit identical EPR resonances from the two Kramers doublets; consequently, the temperature dependence of the overall EPR intensity is independent of the zero-field splitting.     

Crystal field calculation of g values and zero-field splitting for high spin ferric complexes of rhombic character

For high spin ferric ions in rhombic symmetry, we have used a crystal field model to relate term splittings of the ⁴ T ₁, ² T ₂ and ⁴ T ₂ excited states to zerofield split energies and g values of the ⁶ A ₁ term. In this model five crystal field parameters were used, namely, one cubic parameter, two tetragonal parameters and second and fourth order rhombic parameters. In tetragonal symmetry with only three crystal field parameters, a simpler model including only the ⁴ T ₁ and ² T ₂ excited states is adequate to relate term energies to g values and zero-field split energies. However, we have demonstrated the importance of the ⁴ T ₂ state in rhombic crystalline fields. No higher lying terms other than ⁴ T ₂ can influence the ⁴ T ₁ term directly through the tetragonal or rhombic crystal field, Furthermore, we show that the fourth order rhombic crystal field parameter is a key parameter because the rhombic splitting of the dominant low lying ⁴ T ₁ term of high spin ferric complexes depends to first order on the fourth order crystal field potential. We have performed a computer diagonalization of the spin-orbit, electrostatic and crystal field perturbation matrix, and calculated g values and zero-field splittings in seventeen high spin ferric mixed crystalline species of varying rhombicities and for metmyoglobin and cytochrome P-450. The high spin and spin-mixed regions are developed completely to yield the crystal field term energies, zero-field splittings and basis functions together with g values.     

ENDOR investigation of the liganding environment of mixed-spin ferric cytochrome c'

The electronic structure of the 5-coordinate quantum-mechanically mixed-spin (sextet-quartet) heme center in cytochrome c' was investigated by electron nuclear double resonance (ENDOR), a technique not previously applied to this mixed-spin system. Cytochrome c' was obtained from overexpressing variants of Rhodobacter sphaeroides 2.4.3. ENDOR for this study was done at the g(//) = 2.00 extremum where single-crystal-like, well-resolved spectra prevail. The heme meso protons of cytochrome c' showed a contact interaction that implied spin delocalization arising from the heme (d(z)(2)) orbital enhanced by iron out-of-planarity. An exchangeable proton ENDOR feature appeared from the proximal His123 Ndelta hydrogen. This Ndelta hydrogen, which crystallographically has no hydrogen-bonding partner and thus belongs to a neutral imidazole, showed a larger hyperfine coupling than the corresponding hydrogen-bonded Ndelta proton from metmyoglobin. The unique residue Phe14 occludes binding of a sixth ligand in cytochrome c', and ENDOR from a proton of the functionally important Phe14 ring, approximately 3.3 A away from the heme iron, was detected. ENDOR of the nitrogen ligand hyperfine structure is a direct probe into the sigma-antibonding (d(z)(2)) and (d(x)(2)-d(y)(2)) orbitals whose energies alter the relative stability and admixture of sextet and quartet states and whose electronic details were thus elucidated. ENDOR frequencies showed for cytochrome c' larger hyperfine couplings to the histidine nitrogen and smaller hyperfine couplings to the heme nitrogens than for high-spin ferric hemes. Both of these findings followed from the mixed-spin ground state, which has less (d(x)(2)-d(y)(2)) character than have fully high-spin ferric heme systems.     

Zero-field splitting of Mn2+ ions in tetragonal and rhombic symmetry. The effect of excited state contributions

Zero-field splitting parameters D and E are derived by a complete crystal field and spin-orbit interaction calculation for the d⁵ configuration in fields of tetragonal and rhombic symmetry. The differences as compared to the results of approximate calculations are due to the combined effect of excited states on the splitting of the ground state.     

A seed-based structural model for constructing rhombic quasilattice with 7-fold symmetry

Structural Chemistry - A seed-based theoretical model with built-in local degree of freedom for constructing rhombic quasilattice with 7-fold symmetry is presented. This new approach mitigates a...     

Electronic structures of tetragonal nitrido and nitrosyl metal complexes

The standard oxidation states of central metal atoms in C _4v nitrido ([M(N)(L)₅] ^z ) complexes are four units higher than those in corresponding nitrosyls ([M(NO)(L)₅] ^z ) (L=CN: z = 3−, M = Mn, Tc, Re; z = 2−, M = Fe, Ru, Os; L = NH₃: z = 2+, M = Mn, Tc, Re; z = 3+, M = Fe, Ru, Os). Recent work has suggested that [Mn(NO)(CN)₅]³⁻ behaves electronically much closer to Mn(V)[b ₂(xy)]², the ground state of [Mn(N)(CN)₅]³⁻, than to Mn(I)[b ₂(xy)]²[e(xz,yz)]⁴. We have employed density functional theory and time-dependent density functional theory to calculate the properties of the ground states and lowest-lying excitations of [M(N)(L)₅] ^z and [M(NO)(L)₅] ^z . Our results show that [M(N)(L)₅] ^z and [M(NO)(L)₅] ^z complexes with the same z value have strikingly similar electronic structures.     

Electronic structure of ferric heme nitrosyl complexes with thiolate coordination

The effect of trans thiolate ligation on the coordinated nitric oxide in ferric heme nitrosyl complexes as a function of the thiolate donor strength, induced by variation of NH-S(thiolate) hydrogen bonds, is explored. Density functional theory (DFT) calculations (BP86/TZVP) are used to define the electronic structures of corresponding six-coordinate ferric [Fe(P)(SR)(NO)] complexes. In contrast to N-donor-coordinated ferric heme nitrosyls, an additional Fe-N(O) sigma interaction that is mediated by the dz2/dxz orbital of Fe and a sigma*-type orbital of NO is observed in the corresponding complexes with S-donor ligands. Experimentally, this is reflected by lower nu(N-O) and nu(Fe-N) stretching frequencies and a bent Fe-N-O moiety in the thiolate-bound case.     

A new smectic mesophase with two dimensional tetragonal symmetry from dialkyldimethylammonium bromides: ST

A series of N, N-di-n-alkyl-N,N-dimethylammonium bromides was synthesized and characterized. Its thermotropic liquid-crystalline behaviour was studied by differential scanning calorimetry, polarizing optical microscopy and X-ray diffraction. A novel smectic mesophase was thus identified, in which the lateral packing of the molecules within the layers is ordered and tetragonal in symmetry.     

Combined quantum mechanical/molecular mechanical study on the pentacoordinated ferric and ferrous cytochrome P450cam complexes

The pentacoordinated ferric and ferrous cytochrome P450(cam) complexes have been investigated by combined quantum mechanical/molecular mechanical (QM/MM) calculations in the presence of a protein/solvent environment and by QM calculations on the isolated QM regions with use of density functional theory. The B3LYP functional has been found more reliable than the BLYP and BHLYP functionals for estimating the relative state energies. The B3LYP/CHARMM calculations with an all-electron basis set for iron give high-spin ground states for the title complexes, in agreement with experiment. The comparison of the B3LYP/CHARMM results of the entire protein system with the B3LYP calculations on the naked QM regions shows that the amount of stabilization by the protein environment is largest for the intermediate-spin states, followed by the high-spin states of the complexes. The calculation of M?ssbauer parameters in the presence of the enzyme environment confirms the double occupation of the d(xz) orbital in the quintet spin state of the ferrous complex, consistent with the computed QM/MM energies in the enzyme environment, while the d(x)2(-)(y)2 orbital is doubly occupied in the gas-phase quintet state.     

New N-representability results with symmetry in molecular quantum chemistry

We prove a new type of N-representability result: given a totally symmetric density function ρ, we construct a wavefunction Ψ such that the totally symmetric part of $\rho \Psi $ (its projection over the totally symmetric functions) be equal to ρ, and, furthermore, such that Ψ belongs to a given class of symmetry associated to the symmetry group of a molecule. Our proof uses deformations of density functions and which are solutions of a “Jacobian problem”. This allows us to formalize rigorously an idea of A. Görling (Phys. Rev. A 47 (1993) 2783), for Density-Functional Theory in molecular quantum chemistry, by defining a density functional that takes into account the symmetry of the molecule under study.