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The basic requirements for an appropriate representation of the properties of physical methods and knowledge are briefly described, and shown to be in distinct contrast to empiricist views. A comprehensive understanding of physics requires one to include metaphysical and sociological elements in addition to factual and procedural knowledge. The philosophical basis of physics is defined as a “constructive realism” that is subsequently specified and extended by a number of implicit or “tacit” assumptions. A preliminary explication of the conception of a theory is exemplified by Bohr’s theory. The method of consistent adjustment, which is of crucial importance to understanding the relations between theory and experience, is elucidated using a simple mathematical example.

Three broad classes of theories are distinguished, viz., descriptive, explanatory, and unifying or grand theories. The structure of kinematics as the paradigm of a descriptive theory will be elaborated in detail and is represented in an axiom-like form. Within a theory, there are two conceptual levels with the abstract theory frame and the scientific applications. The theory frame is abstract, in that it is system-independent and has no direct connection with experiments.

In summary of the two preceding chapters, the general structure of physical knowledge is presented. The analysis of representative examples of physical laws demonstrates that they can be neither discovered nor falsified by experiment alone. The subsequent definition of the concept of physical law enables its demarcation from empirical statements and hypotheses. Since the relationship between theory and experience is not unequivocal, there are various options available to react to discrepancies between theory and experiment. The scientific applications are the largest units subject to refutation in an actual comparison between theory and experiment, and they constitute the contribution of the theory to the empirical content. The methods of consistent adjustment are elucidated with several examples, emphasizing their variety in establishing the relations between theory and experience.

The relevance of causality, explanations, and the search for truth are discussed against the background that the key objectives of fundamental research in physics are gaining, structuring, and securing knowledge. Necessary conditions for the existence of causal connections are given which prove that causality plays at best a marginal role in physics. Eight types of explanations are defined, and their relevance for physics discussed. A concept of truth is developed that focuses on the capabilities of the physical methods and enables a reasonable definition of the concept of a true theory. Finally, various steps are elaborated which establish physical reality in such a way that this reality is a consistent combination of construction and discovery.

The structure of physical knowledge and methods comprises three domains, viz., an empirical one with predominantly inductive methods, a theoretical one with predominantly deductive methods, and the relations between theory and experience characterized by the methods of consistent adjustment. The various experimental methods establishing the empirical basis will be discussed in detail. This empirical basis consists among other things of reproducible events and representative objects instead of singular experiences and direct observations (“sense data”). The dissimilarities between empirical and theoretical methods of concept formation are elaborated and contrasted with each other. Theoretical orders are defined as the conceptual reproduction of structures of reality and as the epistemological kernel of reality cognition in physics. In this context it is shown that Newtonian mechanics is not a causal theory. The diverse meanings and uses of models in physics are classified and elaborated in detail.

The heat capacities of Al, Si ordered alkali feldspars of different Na, K compositions were calculated using the density functional theory. The effect of the Na, K distribution, if random, ordered or clustered, on the resulting heat capacity was investigated on different cells with Ab50Or50 composition. For all compositions and distributions studied, the excess heat capacity of mixing is positive at low temperatures with a maximum at ~60 K. This produces an increasing excess vibrational entropy that reaches a constant value above ~200 K. The amount of the excess heat capacity of Ab50Or50, however, depends on the Na, K distribution. Best agreement with measured excess heat capacities is achieved, if the distribution of Na and K is either ordered or clustered. The positive excess heat capacities can be attributed to a strong softening of the acoustic and the lowest optical modes related to a strong increase of Na–O bond lengths in samples with intermediate compositions. The softening of the lowest optical mode is, however, not reflected by thoroughly measured literature IR data. Comparing calculated and measured IR spectra suggests that the resolution of the measured spectra was insufficient for detecting the lowest IR-active modes. Electronic supplementary material The online version of this article (doi:10.1007/s00269-014-0715-8) contains supplementary material, which is available to authorized users.

The heat capacity, Cp, of five solid-solution members of the almandine(Alm)–spessartine(Sps) binary, consisting of three synthetic polycrystalline and two natural single-crystal samples, was measured in the temperature range between 2 and 300 K using relaxation calorimetry and between 282 and 764 K using DSC methods. All garnets exhibit a λ-type heat-capacity anomaly at low temperatures resulting from a paramagnetic to antiferromagnetic phase transition. The temperature of the magnetic transition in Fe-rich garnets occurs between those of the two end-members (i.e. 9.2 K for almandine and 6.2 K for spessartine), but lies at lower values between 3.5 and 4.5 K for more Sps-rich compositions with X Mn grt > 0.5 . The calorimetric entropy at 298 K shows mechanical-mixture behavior for Sps-rich garnets and a slight possible negative deviation from such behavior for Alm-rich compositions. At the 2σ level all data are, however, consistent with ideal mixing behavior and the Margules entropy interaction parameter, W S , FeMn grt , is zero for the Alm–Sps binary. Thermodynamic analysis of published high P and T phase-equilibrium Fe–Mn exchange experiments between garnet and ilmenite shows that the excess Gibbs free energy of mixing, ΔGex, for Fe–Mn in garnet is positive and asymmetric towards spessartine. Margules enthalpy interaction parameters of W H,FeMn grt = 4170 ± 518 J/cation⋅mol and W H, MnFe = 1221 ± 588 J/cation⋅mol are derived giving a maximum of Δ G ex ≈ 0.7 kJ/cation⋅mol at X Mn grt ≈ 0.6 . ΔHex obtained using autocorrelation analysis of published IR spectra of Alm–Sps solid solutions is in reasonable agreement with that derived from phase-equilibrium and calorimetry data. Previous diffraction and spectroscopic results on Alm–Sps garnets and quantum mechanical calculations made on almandine are used to interpret the macroscopic thermodynamic behavior from a microscopic basis. The relevance of the new garnet Fe–Mn mixing model for petrological calculations is demonstrated by incorporating it into the quaternary garnet mixing model of Berman (1990) . Thus, better agreement for temperatures calculated using Fe–Mn garnet-ilmenite and Fe–Mg garnet-biotite geothermometry could be achieved. Temperatures calculated for Mn-poor and Mn-rich garnet-bearing assemblages, applying garnet-biotite thermometry, are in better agreement taking Fe–Mn mixing into account.

The new method presented here reports on combining the advantages of diffraction and spectroscopy techniques by a sophisticated computer software: the Difference Electron Nanoscope (DEN). On the example of synthetic fayalite α-Fe2SiO4 the possibilities of the DEN are outlined, especially the derivation and display of the fundamental physical property here concerned, the electric field gradient EFG on the Fe bearing M1 site. It is shown within the difference electron densities of the crystal lattice and in connection with surrounding structural units, the distorted oxygen ion octahedra. By using low-temperature Mossbauer data published elsewhere, the angles between the EFG and the internal magnetic field at the Fe nucleus, H(0), can be taken to fully describe the magnetic ordering of synthetic fayalite in the antiferromagnetic state, with an accuracy normally provided by neutron diffraction. Even small details of the magnetic coupling involved can be detected on the DEN images.

Experimental and calculated structure factors from a previous synchrotron diffraction measurement on synthetic fayalite have been converted by an inverse Fourier transformation to difference electron (deformation) densities (DED). These were processed in a revised 3D-display program giving hyperareas of DED floating in space around the iron positions M1 and M2 within the fayalite unit-cell and spanning a cluster size of 6 and 4 A, respectively. These relatively wide limits are due to the different site symmetries and had been proposed by earlier DFT (density functional theory) calculations. From the different hyperareas the supposed charges were integrated in space and processed to electric field gradients (EFG) on M1 and M2 using a point-charge model. The two EFGs were compared with respect to the system of crystallographic axes with those obtained from published single-crystal Mossbauer measurements (experimental EFGs), yielding excellent agreement within ±5° and surpassing even the DFT results. This study reports the procedure and the conditions of success of the underlying semi-quantitative method, which is halfway between theory (DFT) and experiment (diffractometry) and is promising valuable results on many other compounds. The term “nanoscope” for the graphical representation may be justified due to its high spatial resolution.

A natural iron bearing omphacite with composition Ca0.49 Na0.525 Mg0.424 Al0.43 Fe0.0762+ Fe0.0563+Ti0.0024 Mn0.005 Si1.989 O6 from Syros, Greece, has been investigated by Mossbauer spectroscopy. The interpretation of the spectra is based on electronic structure calculations in the local spin density approximation. The calculations emphasize that large clusters, extending beyond the second coordination sphere of iron, are necessary for a reliable description. As suggested by the electronic structure calculations, different environments around the Fe2+ octahedra give rise to slightly different hyperfine parameters, especially affecting the quadrupole splitting. Hence, the measured spectrum has been evaluated based on quadrupole splitting distribution. The calculated values including the temperature dependence are in almost quantitative agreement with the experimentally derived values.

The magnetic structure of almandine has been investigated by electronic structure calculations in the local spin density approximation in order to arrive at a more detailed understanding of the magnetic structure and the exchange pathways. The calculations are based on experimentally determined geometrical data of the crystal structure at 100 K. The calculated quadrupole splittings, spin-allowed d–d transitions and magnetic moment for iron atoms are in reasonable agreement with the respective experimental values obtained by Mossbauer and absorption spectroscopy, and magnetization measurements demonstrating the reliability of the calculations. The spin structure is derived from the calculated coupling constants for the possible exchange pathways. The competing superexchange pathways exist via oxygen bridges between directly neighboured iron ions and via edges of silicon tetrahedra and aluminium octahedra connecting more distant iron dodecahedra. Careful consideration revealed that almandine structure contains two identical interpenetrative sublattices of Fe dodecahedra connected via Al octahedra and Si tetrahedra. The calculations provide the information about ferromagnetic interaction between the iron spins within each sublattice, whereas the coupling between two magnetic sublattices is weakly antiferromagnetic via Al octahedra and Si tetrahedra. This antiferromagnetic interaction of two identical magnetic sublattices is in good agreement with the experiments and explains the Mossbauer spectra of almandine below the Neel temperature. Since almandine belongs to most abundant crystallized silicates that are main constituents of the earth and main components of cosmic dust, these results have scientific importance of studying the universe.

Sogdianite, a double-ring silicate of composition $$ ( {\text{Zr}}_{0. 7 6} {\text{Ti}}_{0. 3 8}^{4 + } {\text{Fe}}_{0. 7 3}^{3 + } {\text{Al}}_{0.13} )_{\Upsigma = 2} \left( {\square_{ 1. 1 5} {\text{Na}}_{0. 8 5} } \right)_{\Upsigma = 2} {\text{K}}[{\text{Li}}_{ 3} {\text{Si}}_{ 1 2} {\text{O}}_{ 30} ] $$ from Dara-i-Pioz, Tadjikistan, was studied by the combined application of 57Fe Mossbauer spectroscopy and electronic structure calculations. The Mossbauer spectrum confirms published microprobe and X-ray single-crystal diffraction results that indicate that Fe3+ is located at the octahedral A-site and that no Fe2+ is present. Both the measured and calculated quadrupole splitting, ΔE Q, for Fe3+ are virtually 0 mm s−1. Such a value is unusually small for a silicate and it is the same as the ΔE Q value for Fe3+ in structurally related sugilite. This result is traced back to the nearly regular octahedral coordination geometry corresponding to a very symmetric electric field gradient around Fe3+. A crystal chemical interpretation for the regular octahedral geometry and the resulting low ΔE Q value for Fe3+ in the Mossbauer spectrum of sogdianite is that structural strain is largely “taken up” by weak Li–O bonds permitting highly distorted LiO4 tetrahedra. Weak Li–O bonding allows the edge-shared more strongly bonded Fe3+O6 octahedra to remain regular in geometry. This may be a typical property for all double-ring silicates with tetrahedrally coordinated Li.

This work reports on the evaluation of the electric field gradient (EFG) in natural chrysoberyl Al2BeO4 and sinhalite MgAlBO4 using two different procedures: (1) experimental, with single crystal Mossbauer spectroscopy (SCMBS) on the three principal sections of each sample and (2) a “fully quantitative” method with cluster molecular orbital calculations based on the density functional theory. Whereas the experimental and theoretical results for the EFG tensor are in quantitative agreement, the calculated isomer shifts and optical d–d-transitions exhibit systematic deviations from the measured values. These deviations indicate that the substitution of Al and Mg with iron should be accompanied by considerable local expansion of the coordination octahedra.

The electronic and magnetic structure of the chain silicate orthoferrosilite Fe22+Si2O6 has been investigated by electronic structure calculations in the local spin density approximation. All calculations are based on experimentally determined geometrical data at room temperature. The calculated spin-allowed d–d excitation energies and hyperfine parameters are in quantitative agreement with the respective experimental data from optical absorption and Mossbauer spectroscopy. Inside one ribbon that is parallel to the crystallographic c axis and contains two non-equivalent M1 and M2 sites, all iron spins are ferromagnetically coupled with coupling constants of about +16 cm−1. Between these ribbons within the (b, c)-plane a weak ferromagnetic coupling of about +2 cm−1 is obtained. Neighboured (b, c)-planes are coupled antiferromagnetically via chains of SiB-tetrahedra but ferromagnetically via chains of SiA-tetrahedra. Such a theoretically determined "double-plane antiferromagnetic" spin structure is at variance with an experimentally derived magnetic structure. This discrepancy is attributed to differences between the geometry at room temperature and at temperatures below the Neel temperature currently not available.

The electronic and magnetic structure of the chain silicate hedenbergite (CaFe2+Si2O6) has been investigated by a number of experimental methods (neutron diffraction, Mossbauer spectroscopy, low temperature magnetic measurements), as well as by electronic structure calculations for clusters of different size in the local spin density approximation. The calculated size-converged spectroscopic data (d-d excitation energies, hyperfine parameters) are in quantitative agreement with the respective experimental values. The calculated magnetic coupling constants are about +25 cm−1 and −4 cm−1 for intra-chain and inter-chain coupling, respectively. The latter value shows that weak superexchange via edges of silicon tetrahedra is well reproduced by the calculations, and it is in qualitative agreement with an observed metamagnetic transition at 4.2 K in an external magnetic field with an onset around 4 T but saturation is not achieved in fields up to 14.5 T. The large ferromagnetic intra-chain coupling is attributed to a nearly degenerate ground state. The ratio between the two magnetic coupling constants agrees with earlier estimates on similar compounds. Finally, it is demonstrated how the detailed discussion of the various exchange pathways contributes to an improved understanding of the connection between magnetic properties and the geometrical structure.

The full multicentre molecular Hamiltonian in local density approximation for a mononuclear transition metal complex is transformed into a single-centre Hamiltonian explicitly including overlap, covalency and ligand-field effects. The orbital interactions of the metal d-orbitals with the ligand orbitals appear as a repulsive pseudopotential yielding the dominant contribution to the ligand-field splitting. This repulsive pseudopotential exhibits the same angular dependence as the electrostatic potential from the ligands entering the Hamiltonian of ligand-field theory. For this reason, ligand-field theory very often yields the correct splitting pattern of the d-orbitals. The radial part, however, is considerably different from the simple expression of ligand-field theory. In particular, there is no general theoretical justification for a R − 5 -dependence of the ligand-field splitting even for complexes of cubic symmetry. The reliability and capability of this new approach is demonstrated by calculating the d-orbital splitting pattern for a number of selected systems.

Natural alexandrite Al2BeO4:Cr from Malyshevo near Terem Tschanka, Sverdlovsk, Ural, Russia, has been characterized by 57Fe Mossbauer spectroscopy, electron microprobe, X-ray single-crystal diffractometry and by electronic structure calculations in order to determine oxidation state and location of iron. The sample contains 0.3 wt% of total iron oxide. The 57Fe Mossbauer spectrum can be resolved into three doublets. Two of them with hyperfine parameters typical for octahedrally coordinated high-spin Fe3+ and Fe2+, respectively, are assigned to iron substituting for Al in the octahedral M2-site. The third doublet is attributed to Fe3+ in hematite. Electronic structure calculations in the local spin density approximation are in reasonable agreement with experimental data provided that expansion and/or distortion of the coordination octahedra are presumed upon iron substitution. The calculated hyperfine parameters of Fe3+ are almost identical for the M1 and M2 positions, but the calculated ligand-field splitting is by far too large for high-spin Fe3+ on M1.

A short historical outline of sulfosalts with respect to their mineralogical origin and their possible technical applications is given. The high number of more than 200 species results from their chemical and structural definition. The modular crystal structures of sulfosalt compounds base on superstructures of diverse construction units. Physical properties of mineral samples as well as deposited thin films show promising results with respect to photovoltaic application. As a proof of concept, first sulfosalt thin film solar cells were prepared. The efficiency of this cell is reported to be 1%. Further efforts will be done to improve efficiency.

The high-temperature partitioning of Fe2+ and Mg between the two nonequivalent octahedral M1 and M2 sites in synthetic olivine (Fa50) was studied by Mossbauer spectroscopy. Powder samples have been equilibrated in annealing experiments performed under reducing oxygen fugacity at temperatures between 500 and 800°C followed by rapid quenching in order to prevent redistribution of cations. M-site ordering with Fe2+ preferring M1, Mg preferring M2 sites increases continuously with rising equilibrium temperature. K D values increase from 1.21 at 500°C to 1.48 at 750°C. The results are consistent with both room temperature as well as in situ high temperature single crystal X-ray diffraction experiments of Heinemann et al. [8, 9].

Three natural lawsonites from Syke Rock, Mendocino Co., Reed Ranch, Marin Co., and Blake Gardens, Sonoma Co., all from the Coast Range Region in California, were studied by Fe-57 Mossbauer spectroscopy, electron microprobe analysis, and X-ray powder diffraction. The samples contain about 0.6, 1.0, and 1.4 wt% of total iron oxide, respectively. Fe-57 Mossbauer spectra are consistent with the assumption that high-spin Fe3+ substitutes for Al in the octahedrally coordinated site. The Mossbauer spectrum of lawsonite from Syke Rock exhibits a second doublet with Fe-57 hyperfine parameters typical for octahedrally coordinated high-spin Fe2+. Electronic structure calculations in the local spin density approximation yield quadrupole splittings for Fe3+ in quantitative agreement with experiment indicating, however, that substitution of Al by Fe3+ must be accompanied by local distortion around the octahedral site. Model calculations also reproduce the room temperature hyperfine parameters of ferrous high-spin iron assuming the substitution of Ca by Fe2+. However, it cannot be excluded that Fe2+ may occupy a more asymmetric site within the microstructural cavity occupied by Ca and a H2O molecule.

In this first systematic, theoretical study of the complete electric field gradient (EFG) tensor of 5 7 Fe Mossbauer spectroscopy as a function of chemistry and local structural distortion using electronic structure calculations, local EFG tensors were calculated at the central Fe 2 + sites in clusters of seven octahedra, where the neighbor octahedra were populated with a mixture of Mg 2 + and Al 3 + cations. The independent parameters of the EFG tensor-particularly the principal value V z z , the asymmetry parameter η, and the direction of the principal axis with regards to the octahedral sheet-were examined in detail as functions of octahedral flattening for each of the thirteen possible configurations of cations. We demonstrate that the argument that the EFG tensor at a particular site is largely determined by the point group symmetry of the corresponding crystallographic site is not correct. We find that in clusters with monoclinic or triclinic local point group symmetry, the value of V z z changes discontinuously from positive to negative as flattening increases. The principal axis changes from being in the plane of the octahedral sheet to being normal to it at this discontinuity, and the value of η reaches a maximum and begins to decline. This discontinuous behavior is caused by the continuous change of the EFG eigenvalues as the Fe(3d) character of the highest occupied spin-down orbital evolves with flattening. Taking EFG tensor results from all clusters, and using probabilities for the occurrence of each possible cation configuration in a chemically disordered octahedral sheet of a given bulk composition, we simulate averages and distributions of η, principal axis angles, and quadrupole splittings. While the value of η is broadly distributed from zero to one at all flattening angles and bulk compositions, there are two distinct populations of principal axes, normal to and in-plane with the octahedral sheet, as has been observed experimentally. We find these in-plane and normal populations of principal axes correspond exactly to populations with positive and negative values of V z z , respectively. Histograms representing quadrupole splitting distributions (QSDs) show features found in experimental QSDs, such as a constant high edge, a variable low edge, and a QSD width that changes dramatically with flattening. These results represent the first predictions relating average structural parameters, as would be obtained by X-ray diffraction, to characteristics of the Fe 2 + QSD, as obtained by 5 7 Fe Mossbauer spectroscopy, in a chemically disordered material.

Two fresnoitic glasses (2BaO–TiO2–2GeO2 and 2SrO–TiO2–2SiO2) are studied by high-resolution electron energy-loss spectroscopy in the transmission electron microscope. It is shown that coordination fingerprinting using the electron energy-loss near-edge structure (being widely used in crystalline compounds bearing transition metals) can also be applied to amorphous matter. In particular, respective ratios of fourfold, fivefold, and sixfold co-ordinated Ti4+ are verified for both glasses in comparison to earlier X-ray photoemission measurements. The results demonstrate that – sufficiently high spectral resolution given – electron energy-loss spectroscopy in the transmission electron microscope is an extremely promising and powerful technique for atomistic-structure studies of amorphous materials. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

We report ab initio electronic structure calculations that directly relate given local chemical and distortion environments to corresponding hyperfine electric field gradients (EFGs) in 5 7 Fe Mossbauer spectroscopy, thereby giving needed interpretive power to the technique in characterizing V I Fe 2 + environments in minerals. Changes of the EFG with various distortions were investigated on model clusters, including the bare octahedra FeO 1 0 - 6 and Fe(OH) 4 - 6 , and various seven-octahedra sections of an octahedral sheet, through self-consistent charge Xa ab initio calculations. Distortions examined for all clusters were flattening, counter-rotation, and bond scaling, as well as changes in neighbor bond lengths and the identity and ordering of neighbor cations for the seven-octahedra clusters. The evolution of the EFG with distortion was derived at T = 0 K and T= 300 K as a function of the distortion parameters. We find that the percent change in the EFG over the range of distortion parameters found in I M trioctahedral micas is greatest with flattening for the clusters compared, suggesting that flattening is the most important structural distortion in determining the EFG. The EFGs for the seven-octahedra cluster as a function of flattening were compared for thirteen configurations of Mg 2 + and Al 3 + cations in the first nearest-neighbor octahedra. The percent change in the EFG for flattening and cation substitution was found to be of similar magnitude. In comparing EFG vs. flattening curves with measured quadrupole splitting distributions (QSDs), the magnitudes of EFGs in the theoretical curves agree well with experiment. The sharp high quadrupole splitting edge is explained by the presence of a maximum in the EFG vs. flattening curve. These model calculations are a necessary first step in establishing a firmer link between local structural distortions in minerals and measured QSDs.

Based on cluster molecular orbital calculations, high-energy resolution (ΔE ∼ 0.4 eV) Ti–L2,3 electron energy loss near-edge structures of single-crystalline and glassy Ba2TiGe2O8 are interpreted. The finding that the Ti–L2,3 near-edge structure of the Ba2TiGe2O8 single crystal possesses less pronounced peaks than the glass under identical experimental conditions can be attributed to distinct distortions of the titanium environment caused by the very strong one-dimensional structural modulation hosted by the Ba2TiGe2O8 crystal lattice. As lattice periodicity is absent in the glass, the titanium environment is more regular in the vitreous surroundings. Moreover, the modulation in crystalline Ba2TiGe2O8 is responsible for the virtually indiscernible O–K near-edge structures of the glassy and crystalline samples.

The three binary garnet solid solutions (Fe3Al2Si3O12)-Al-II-(X3Al2Si3O12)-Al-II (X-II= Mg-II, Mn-II, Ca-II) have been investigated by Fe-57 Mossbauer spectroscopy at 298 and 77 K and by electronic structure calculations in the local spin density approximation. The spectra yield isomer shifts and quadrupole splittings that are typical for Fe-II in the dodecahedral X-site of 222 point symmetry and are similar for each of the three binaries recorded. Conversely, electronic structure calculations based on the experimental crystal structure of the different end-member garnets exhibit pronounced variations in some of the electronic properties of Fe-II that are not reflected in the spectroscopic data. These results are interpreted as indicating that the different X-O bonds in garnet solid solutions retain to a large degree the intrinsic lengths that they possess in their respective end members, and that the Fe-O bond does not change greatly as a function of composition. This is evidence for the state of alternating bonds and not for the virtual crystal approximation in describing the X-O bond types or lengths in aluminosilicate garnet solid solutions. The observed degree and behavior of the Fe-II doublet asymmetry in the Mossbauer spectra for the three solid solution series do not indicate major variations in the anisotropic recoil-free fraction of Fe-II. Variations in doublet asymmetry are more likely a result of complex next-nearest X-site neighbor interactions and/or some degree of short-range cation ordering, though doublets representing different local X-site cation configurations cannot be resolved or fitted to the experimental spectra.

The Fe end-members scorzalite [Fe2+Al23+(PO4)(2)(OH)(2)] and barbosalite [Fe2+Fe23+(PO4)(2)(OH)(2)] of the lazulite series have been investigated by Mossbauer and diffuse reflectance spectroscopy, and by electronic structure calculations in the local spin density approximation. The measured quadrupole splitting (DeltaE(Q) = -3.99 mm/s) in scorzalite is in quantitative agreement with the calculated value (DeltaE(Q) = -3.90 mm/s), as well as its temperature dependence. The optical spectrum of barbosalite can be resolved into three peaks at 8985 cm(-1), 10980 cm(-1), and 14110 cm-1. These positions correlate well with the two calculated spin-allowed d-d transitions at 8824 cm-1 and 11477 cm-1, and with an intervalence charge transfer transition at about 14200 cm-1. The calculated low-temperature magnetic structure of barbosalite is characterized by a strong antiferromagnetic coupling (J = -84.6 cm-1) within the octahedral Fe3+-chains, whereas a weak antiferromagnetic coupling within the trioctabedral subunit cannot be considered as conclusive. The analysis of the charge and spin densities reveals that more than 90% of the covalent part of the iron-ligand bonds arises from the Fe(4s,4p)-electrons. Clusters of at least 95 atoms are required to reproduce the available experimental data with quantitative accuracy.

The electronic structure of iron-rich epidote has been investigated by cluster molecular orbital calculations in local spin density approximation. Calculated quadrupole splittings for Fe(III) at both the M1 and M3 sites are in quantitative agreement with the experimental values obtained by Mossbauer spectroscopy. A detailed analysis of the theoretical results shows that a strong tetragonal compression of the M3 octahedron is responsible for the unusually large value of the quadrupole splitting of FeM3(III). The corresponding electric field gradient (efg) is dominated by the anisotropy of the valence shell of iron, whereas the ligands contribute only about 15% to the efg. The calculations emphasize that rather large clusters, extending beyond the second coordination sphere of iron, are necessary for a reliable description. Small clusters including only the first coordination sphere of iron generally yield misleading results due to unsaturated oxygen bonds and relatively large cluster charges.

The electronic and magnetic structure of the octahydrophosphate vivianite, Fe3(PO4)2·8H2O, has been investigated by cluster molecular orbital calculations in local spin density approximation. Optical and Mossbauer spectra are well reproduced by the calculations, and the differences between the two iron sites can be correlated with differences in the geometrical structure of the first coordination sphere. The spin structure within the crystallographic ac plane is derived and explained on the basis of different superexchange pathways via edges of the phosphate tetrahedra. The calculations demonstrate that quite large clusters (up to 118 atoms) are necessary to arrive at reliable results.

The different Fe2+ lattice sites in iron-rich chlorites have been characterized by Mossbauer spectroscopy and molecular orbital calculations in local density approximation. The Mossbauer measurements were recorded at 77 K within a small velocity range (±3.5 mm s−1) to provide high energy resolution. Additionally, measurements were recorded in a wider velocity range (±10.5 mm s−1) at temperatures of 140, 200, and 250 K in an applied field (7 T) parallel to the γ-beam. The zero-field spectra were analyzed with discrete Lorentzian-shaped quadrupole doublets to account for the Fe2+ sites M1, M2, and M3 and with a quadrupole distribution for Fe3+ sites. Such a procedure is justified by the results obtained from MO calculations, which reveal that different anion (OH−) distributions in the first coordination sphere of M1, M2, and M3 positions have more influence on the Fe2+ quadrupole splitting than cationic disorder. The spectra recorded in applied field were analyzed in the spin-Hamiltonian approximation, yielding a negative sign for the electric field gradient (efg) of Fe2+ in the M1, M2, and M3 positions. The results of the MO calculations are in quantitative agreement with experiment and reveal that differences in the quadrupole splittings (ΔE Q ), their temperature dependence and in the isomer shifts (δ) of Fe2+ in M1, M2, and M3 positions can theoretically by justified. Therefore, the combined Mossbauer and MO investigation shows that the three Fe2+ lattice sites in the chlorites investigated here can be discriminated according to their ΔE Q -δ parameter pairs. With the calculated average iron-oxygen bond strength, the MO study provides an explanation for the observed trend that the population of the three lattice sites by Fe2+ increases according to the relation M1 < M2 < M3.

The complex (6,13-bis(ethoxycarbonyl)-5,14-dimethyl-1,4,8,11-tetraazacyclotetradeca-4,6,12,14-tetraenato(2−))iron(III) iodide, 3 (chemical formula C18H26O4N4FeI·0.5 C7H8), has been characterized by X-ray crystallography (a = 16.063(3) A, b = 15.895(3) A, c = 19.703(4) A, β = 107.11(3)°; monocline; I2/a; Z = 8), EPR and Mossbauer spectroscopy, and temperature-dependent magnetic susceptibility as well as by MO calculations. The pentacoordinated iron atom is 0.34 A outside of the [N4] plane. The equatorial Fe−N distances (1.92 A for the N's in neighborhood of the methylated C-atoms and 1.88 A for the others) are not significantly different from those found in octahedral low-spin iron(III) complexes with the same macrocyclic [N42-] ligand. The magnetic moment (μeff = 4.19 μB up to 20 K; ϑ = −7.37 K), the EPR measurements (gyeff = 5.38, gxeff = 2.70, and gzeff = 1.74), and the Mossbauer data (δ = 0.18 mm/s, ΔEQ = 3.56 mm/s, T = 120 K) indicate a pure intermediate-spin state of S = 3/2. The MO calculations yiel...

Recent neutron scattering and nuclear magnetic resonance experiments have revealed that the low temperature phase of doped V_{2-y}O_3 is an itinerant antiferromagnet with a helical spin structure. We use a band structure calculation as the point of departure to show that these experiments are in agreement with mean field results for an Overhauser spin-density wave state. The influences of a finite life-time and of dilute magnetic impurities are discussed.

Three axially bis-ligated Fe(II) porphyrinates, [PFeL2], have been investigated by Mossbauer spectroscopy over the temperature range 4.2−230 K and in an applied field of 6 T. Relatively large differences in the quadrupole splitting ΔEQ were found among [TMPFe(2-MeImH)2] (1), [TMPFe(N-MeIm)2] (2), and [OEPFe(PMe3)2] (3) (1.61, 1.07, and 0.38 mm/s, respectively). Compound 3 exhibits significant line broadening above 150 K that indicates fluxional distortion and/or ligand rotation. Molecular orbital calculations in the local density approximation yield electric field gradients (efg) in good agreement with the measured quadrupole splittings, ΔEQ, and the measured sign of the efg. The observed differences in quadrupole splittings can be ascribed to distortions (ruffling) of the porphyrin core in 1 as compared to 2 and 3 and to the differences in covalent interactions of the axial nitrogen donors of 1 and 2 and phosphorous donors of 3. The observed temperature-dependent line broadening of 3 correlates with the ...

The present commentary focusses on the role of the axial ligand in peroxidase- and P450-type catalysis. Based on molecular orbital calculations and the experimental evidence available, it is argued that the ligand of a heme-containing enzyme may be a factor in setting the relative chance, although not the intrinsic capability, of the enzyme to catalyse a specific type of heme-based reaction chemistry. The ligand can do so by influencing the electrophilicity, i.e. the redox potential of the high-valency iron-oxo complex, and also by influencing the energy barrier for a reaction pathway through delocalization of valence electrons along the axial ligands, thereby, in the case of a cysteinate but not a histidine axial ligand, stabilizing oxygen transfer pathways.

We have prepared a series of 94.5%-enriched 57Fe(II) complexes of tetramesitylporphyrin and octaethylporphyrin having various bis- or mixed axial ligation and investigated them by both NMR and Mossbauer spectroscopy. The results obtained, and literature values for MbCO and cytochrome c, show a rough correlation between ΔEQ and δFe. This correlation suggested that the previously-reported chemical shifts of the complexes [TPPFeL2], L = pyridine-d5, and pyrrolidine (Nozawa, T.; Sato, M.; Hatano, M.; Kobayashi, N.; Osa, T. Chem. Lett. 1983, 1289) might be incorrect; we have thus used the rapid pulsing method of Schwenck to detect the signal of the bis-pyridine-d5 complex at 11 715 ppm, within its predicted chemical shift range, based upon the δFe vs ΔEQ correlation, and ∼4,400 ppm to lower shielding than originally reported. These findings emphasize the value of the Mossbauer−NMR correlation in aiding the detection of 57Fe NMR signals, as well as the perils of seeking these easily “folded” signals without suc...

The reaction mechanism for the hydroxylation of benzene and monofluorobenzene, catalysed by a ferryl-oxo porphyrin cation radical complex (compound) is described by electronic structure calculations in local spin density approximation. The active site of the enzyme is modelled as a six-coordinated (Por+)Fe(IV)O a2u complex with imidazole or H3CS– as the axial ligand. The substrates under study are benzene and fluorobenzene, with the site of attack in para, meta and ortho position with respect to F. Two reaction pathways are investigated, with direct oxygen attack leading to a tetrahedral intermediate and arene oxide formation as a primary reaction step. The calculations show that the arene oxide pathway is distinctly less probable, that hydroxylation by an H3CS––coordinated complex is energetically favoured compared with imidazole, and that the para position with respect to F is the preferred site for hydroxylation. A partial electron transfer from the substrate to the porphyrin during the reaction is obtained in all cases. The resulting charge distribution and spin density of the substrates reveal the transition state as a combination of a cation and a radical σ-adduct intermediate with slightly more radical character in the case of H3CS– as axial ligand. A detailed analysis of the orbital interactions along the reaction pathway yields basically different mechanisms for the modes of substrate–porphyrin electron transfer and rupture of the Fe–O bond. In the imidazole-coordinated complex an antibonding π*(Fe–O) orbital is populated, whereas in the H3CS––coordinated system a shift of electron density occurs from the Fe–O bond region into the Fe–S bond.

Values for the exchange-coupling constant J and the double-exchange parameter B have been estimated for dimeric and hexameric mixed-valence iron clusters. For sulfur-bridged species the range of J values is 300–450 cm–1, and B values vary between 320 and 400 cm–1. For an OH-bridged diiron cluster B is as large as 1300 cm–1.

The lattice location of Fe atoms in Fe-doped LiNbO3 is determined experimentally employing X-ray standing waves. At a bulk concentration of 7.48*1018 cm-3 Fe is found to occupy sites close to the ferroelectric Li position; shifted by 0.18 AA in the direction of the -c axis. Electronic structure calculations confirm this result insofar as computed spectroscopic data are more consistent with the respective experimental values for Fe located in the vicinity of the Li site than for Fe occupying the Nb lattice position.

The linear trinuclear iron complex Fe 3 (SPh) 6 (CO) 6 with bridging benzenethiolate ligands is the subject of temperature-and field-dependent Mossbauer studies and of temperature-dependent magnetic susceptibility studies. The results reveal the two terminal iron atoms to be diamagnetic Fe(II) and the central iron atom to be high-spin Fe(II). The latter exhibits an enhanced effective magnetic moment compared to the ( S = 2) spin-only value of 4.9 μ B , and its magnetic Mossbauer pattern is dominated by a positive (!) internal field. Complementary to the experimental studies also theoretical studies are performed. Local density molecular orbital and ligand-field calculations yield an orbitally degenerate ground state that accounts for the unusual electronic and spectroscopic properties. With these results inconsistencies in previously reported spectroscopic studies of Fe 3 (SPh) 6 (CO) 6 are resolved.

The pairing theory of superconductivity is applied to tightly bound electrons in narrow energy bands that interact via short-range Coulomb interactions. We depart from the model Hamiltonian proposed by Hirsch that emphasizes the role of the bond-charge repulsion for the attractive interaction between holes in the almost-filled pπ band of the planar O 2- anion lattice of the CuO 2 layer. Using the method of Appel and Kohn we cast the pairing theory for the pπ electrons into the atomic representation and construct the set of vertex equations on the two-dimensional square lattice that determine the transition temperature T c

mainly determined by ion-multipole interactions", while the covalent interactions in H+-azoles must be practically constant. The analysis of the protonation energy based on Mulliken's theory, presented above, shows, however, that the trend of basicities is determined mainly by the a-ionization potential rather than by the electrostatic interaction. Besides, the example of pyrazole given above points out the importance of polarization and charge transfer in the formation of the protonated azoles. This conclusion is consistent with what has been found in a previous study on the stability of iodine complexes with ammonia and pyridine.19

An analytical expression for the transfer integral HAB between the localized magnetic orbitals in superexchange-coupled dimers as a function of the type of atoms and geometry of the molecule has been derived by explicitly including orbital interactions. It is shown that HAB plays the key role for the magnetic coupling constant J in understanding magneto-structural correlations. The reliability and capability of this approach is confirmed by comparison with numerical electronic structure calculations in the local spin-density approximation on singly and doubly bridged Cu(II)-dimers with fluorine ligands. All results can be calculated and understood within the analytical formalism representing, therefore, a powerful tool for understanding the magneto-structural correlations and also for constructing magnetic orbitals analytically.

A general discussion of electronegativity and electronegativity equalization is presented as background for the concept of charge capacity; the latter is the ability of an atom to absorb or yield electronic charge. We have discussed charge capacity in relation to a variety of atomic and molecular properties, e.g. atomic polarizabilities and outer shell properties, electron affinities, dipole moments, electronic density distributions, dissociation energies, electrostatic potentials, spectroscopic measurements, acidities, etc. Significant increases in charge capacity and decreases in electronegativity in going from the first to subsequent rows of the periodic table are important in explaining (especially for columns IV–VII) the discontinuities in many physical and chemical properties that occur between these rows. It is demonstrated that both intrinsic electronegativities and charge capacities must be considered in order to understand the redistribution that occurs when atoms interact to form molecules. We discuss many seemingly anomalous observations of chemical behavior that are explained quite readily when both of these factors are taken into account.

The C-H bond dissociation energy of acetylene was computed by both ab initio approaches and density functional theory in a local density approximation (DFT-LDA). Structures and energies for acetylene and its dissociation products (the ethynyl and hydrogen radicals) are presented and compared. Using directly computed HCCH and HCC. energies and the exact H. value, the DFTLDA calculations are found to yield C-H dissociation energies ranging from 129 to 131 kcal/mol, in good agreement with recent experimental and the highest level theoretical results. The DFTLDA results show little dependence upon the computational procedure used to obtain geometries.