Biophotons: New Experimental Data and Analysis.

Biophotons are an ultra-weak emission of photons in the visible energy range from living matter. In this work, we study the emission from germinating seeds using an experimental technique designed to detect light of extremely small intensity. The emission from lentil seeds and single bean was analyzed during the whole germination process in terms of the different spectral components through low pass filters and the different count distributions in the various stages of the germination process. Although the shape of the emission spectrum appears to be very similar in the two samples used in our experiment, our analysis can highlight the differences present in the two cases. In this way, it was possible to correlate the various types of emissions to the degree of development of the seed during germination.

Crucial Development: Criticality Is Important to Cell-to-Cell Communication and Information Transfer in Living Systems.

In the fourth paper of this Special Issue, we bridge the theoretical debate on the role of memory and criticality discussed in the three earlier manuscripts, with a review of key concepts in biology and focus on cell-to-cell communication in organismal development. While all living organisms are dynamic complex networks of organization and disorder, most studies in biology have used energy and biochemical exchange to explain cell differentiation without considering the importance of information (entropy) transfer. While all complex networks are mixtures of patterns of complexity (non-crucial and crucial events), it is the crucial events that determine the efficiency of information transfer, especially during key transitions, such as in embryogenesis. With increasing multicellularity, emergent relationships from cell-to-cell communication create reaction-diffusion exchanges of different concentrations of biochemicals or morphogenetic gradients resulting in differential gene expression. We suggest that in conjunction with morphogenetic gradients, there exist gradients of information transfer creating cybernetic loops of stability and disorder, setting the stage for adaptive capability. We specifically reference results from the second paper in this Special Issue, which correlated biophotons with lentil seed germination to show that phase transitions accompany changes in complexity patterns during development. Criticality, therefore, appears to be an important factor in the transmission, transfer and coding of information for complex adaptive system development.

Symmetry Breaking in Solution-Phase [Cu(tsc)2(H2O)2]2+: Emergent Asymmetry in Cu-S Distances and in Covalence.

The structure of aqueous Cu(II)-bis-thiosemicarbazide, [Cu(tsc)2]2+, is reported following EXAFS and MXAN analyses of the copper K-edge X-ray absorption (XAS) spectrum. The rising K-edge feature at 8987.1 eV is higher energy than those of crystalline models, implying unique electronic and structural solution states. EXAFS analysis (k = 2-13 Å-1; 2 × Cu-N = 2.02 ± 0.01 Å; 2 × Cu-S = 2.27 ± 0.01 Å; Cu-Oax = 2.41 ± 0.04 Å) could not resolve 5- versus 6-coordinate models. However, MXAN fits converged to an asymmetric broken symmetry 6-coordinate model with cis-disposed TSC ligands (Cu-Oax = 2.07 and 2.54 Å; Cu-N = 1.94 Å, 1.98 Å; Cu-S = 2.20 Å, 2.41 Å). Transition dipole integral evaluation of the sulfur K-edge XAS 1s → 3p valence transition feature at 2470.7 eV yielded a Cu-S covalence of 0.66 e-, indicating Cu1.34+. The high Cu-S covalence and short Cu-S bond in aqueous [Cu(tsc)2(H2O)2]2+ again contradict the need for a protein rack to explain the unique structure of the blue copper active site. MXAN models of dissolved Cu(II) complex ions have invariably featured broken centrosymmetry. The potential energy ground state for dissolved Cu(II) evidently includes the extended solvation field, providing a target for improved physical theory. A revised solvation model for aqueous Cu(II), |[Cu(H2O)5]·14H2O|2+, is presented.

Biophotons and Emergence of Quantum Coherence-A Diffusion Entropy Analysis.

We study the emission of photons from germinating seeds using an experimental technique designed to detect light of extremely small intensity. We analyze the dark count signal without germinating seeds as well as the photon emission during the germination process. The technique of analysis adopted here, called diffusion entropy analysis (DEA) and originally designed to measure the temporal complexity of astrophysical, sociological and physiological processes, rests on Kolmogorov complexity. The updated version of DEA used in this paper is designed to determine if the signal complexity is generated either by non-ergodic crucial events with a non-stationary correlation function or by the infinite memory of a stationary but non-integrable correlation function or by a mixture of both processes. We find that dark count yields the ordinary scaling, thereby showing that no complexity of either kinds may occur without any seeds in the chamber. In the presence of seeds in the chamber anomalous scaling emerges, reminiscent of that found in neuro-physiological processes. However, this is a mixture of both processes and with the progress of germination the non-ergodic component tends to vanish and complexity becomes dominated by the stationary infinite memory. We illustrate some conjectures ranging from stress induced annihilation of crucial events to the emergence of quantum coherence.

Dynamic multiple-scattering treatment of X-ray absorption: Parameterization of a new molecular dynamics force field for myoglobin.

We present a detailed analysis of the X-ray absorption near-edge structure (XANES) data on the Fe K-edge of CO Myoglobin based on a combined procedure of Molecular Dynamics (MD) calculations and MXAN (Minuit XANes) data analysis that we call D-MXAN. The ability of performing quantitative XANES data analysis allows us to refine classical force field MD parameters, thus obtaining a reliable tool for the atomic investigation of this important model system for biological macromolecules. The iterative procedure here applied corrects the greatest part of the structural discrepancy between classical MD sampling and experimental determinations. Our procedure, moreover, is able to discriminate between different heme conformational basins visited during the MD simulation, thus demonstrating the necessity of a sampling on the order of tens of nanoseconds, even for an application such X-ray absorption spectroscopy data analysis.

[Cu(aq)]2+ is structurally plastic and the axially elongated octahedron goes missing.

High resolution (k = 18 Å-1 or k = 17 Å-1) copper K-edge EXAFS and MXAN (Minuit X-ray Absorption Near Edge) analyses have been used to investigate the structure of dissolved [Cu(aq)]2+ in 1,3-propanediol (1,3-P) or 1,5-pentanediol (1,5-P) aqueous frozen glasses. EXAFS analysis invariably found a single axially asymmetric 6-coordinate (CN6) site, with 4×Oeq = 1.97 Å, Oax1 = 2.22 Å, and Oax2 = 2.34 Å, plus a second-shell of 4×Owater = 3.6 Å. However, MXAN analysis revealed that [Cu(aq)]2+ occupies both square pyramidal (CN5) and axially asymmetric CN6 structures. The square pyramid included 4×H2O = 1.95 Å and 1×H2O = 2.23 Å. The CN6 sites included either a capped, near perfect, square pyramid with 5×H2O = 1.94 ± 0.04 Å and H2Oax = 2.22 Å (in 1,3-P) or a split axial configuration with 4×H2O = 1.94, H2Oax1 = 2.14 Å, and H2Oax2 = 2.28 Å (in 1,5-P). The CN6 sites also included an 8-H2O second-shell near 3.7 Å, which was undetectable about the strictly pyramidal sites. Equatorial angles averaging 94° ± 5° indicated significant departures from tetragonal planarity. MXAN assessment of the solution structure of [Cu(aq)]2+ in 1,5-P prior to freezing revealed the same structures as previously found in aqueous 1M HClO4, which have become axially compressed in the frozen glasses. [Cu(aq)]2+ in liquid and frozen solutions is dominated by a 5-coordinate square pyramid, but with split axial CN6 appearing in the frozen glasses. Among these phases, the Cu-O axial distances vary across 1 Å, and the equatorial angles depart significantly from the square plane. Although all these structures remove the dx2-y2 , dz2 degeneracy, no structure can be described as a Jahn-Teller (JT) axially elongated octahedron. The JT-octahedral description for dissolved [Cu(aq)]2+ should thus be abandoned in favor of square pyramidal [Cu(H2O)5]2+. The revised ligand environments have bearing on questions of the Cu(i)/Cu(ii) self-exchange rate and on the mechanism for ligand exchange with bulk water. The plasticity of dissolved Cu(ii) complex ions falsifies the foundational assumption of the rack-induced bonding theory of blue copper proteins and obviates any need for a thermodynamically implausible protein constraint.

Coherent structural trapping through wave packet dispersion during photoinduced spin state switching.

The description of ultrafast nonadiabatic chemical dynamics during molecular photo-transformations remains challenging because electronic and nuclear configurations impact each other and cannot be treated independently. Here we gain experimental insights, beyond the Born-Oppenheimer approximation, into the light-induced spin-state trapping dynamics of the prototypical [Fe(bpy)3]2+ compound by time-resolved X-ray absorption spectroscopy at sub-30-femtosecond resolution and high signal-to-noise ratio. The electronic decay from the initial optically excited electronic state towards the high spin state is distinguished from the structural trapping dynamics, which launches a coherent oscillating wave packet (265 fs period), clearly identified as molecular breathing. Throughout the structural trapping, the dispersion of the wave packet along the reaction coordinate reveals details of intramolecular vibronic coupling before a slower vibrational energy dissipation to the solution environment. These findings illustrate how modern time-resolved X-ray absorption spectroscopy can provide key information to unravel dynamic details of photo-functional molecules.

Characterization of a Poly-4-Vinylpyridine-Supported CuPd Bimetallic Catalyst for Sonogashira Coupling Reactions.

CuPd bimetallic solvated metal atoms (SMA) synthesized by metal vapor synthesis (MVS) technique and supported on poly-4-vinylpyridine (PVPy) resin, showed significantly higher catalytic activity in Sonogashira-type carbon-carbon coupling reactions than the corresponding monometallic Cu and Pd systems as well as their physical mixture. The analysis of the bimetallic catalyst combining transmission electron microscopy techniques and X-ray absorption fine structure (XAFS) spectroscopy revealed the presence of small Pd nanoparticles (dm =2.5 nm) while the analysis of the X-ray absorption data, at the Cu K-edge suggests the formation of thin and incomplete Cu oxide layers around the Pd-rich cores.

Solvation structure of the halides from x-ray absorption spectroscopy.

Three-dimensional models for the aqueous solvation structures of chloride, bromide, and iodide are reported. K-edge extended X-ray absorption fine structure (EXAFS) and Minuit X-ray absorption near edge (MXAN) analyses found well-defined single shell solvation spheres for bromide and iodide. However, dissolved chloride proved structurally distinct, with two solvation shells needed to explain its strikingly different X-ray absorption near edge structure (XANES) spectrum. Final solvation models were as follows: iodide, 8 water molecules at 3.60 ± 0.13 Å and bromide, 8 water molecules at 3.40 ± 0.14 Å, while chloride solvation included 7 water molecules at 3.15 ± 0.10 Å, and a second shell of 7 water molecules at 4.14 ± 0.30 Å. Each of the three derived solvation shells is approximately uniformly disposed about the halides, with no global asymmetry. Time-dependent density functional theory calculations simulating the chloride XANES spectra following from alternative solvation spheres revealed surprising sensitivity of the electronic state to 6-, 7-, or 8-coordination, implying a strongly bounded phase space for the correct structure during an MXAN fit. MXAN analysis further showed that the asymmetric solvation predicted from molecular dynamics simulations using halide polarization can play no significant part in bulk solvation. Classical molecular dynamics used to explore chloride solvation found a 7-water solvation shell at 3.12 (-0.04/+0.3) Å, supporting the experimental result. These experiments provide the first fully three-dimensional structures presenting to atomic resolution the aqueous solvation spheres of the larger halide ions.

Equilibrium between 5- and 6-Fold Coordination in the First Hydration Shell of Cu(II).

The hydration structure dynamics of Cu(II) ion is characterized by a combination of classical molecular dynamics simulation and X-ray absorption near-edge spectroscopy. Previous experimental data have been analyzed on the basis of 5- or 6-fold first hydration structure, with a quite well-established equatorial structure. This 4-fold equatorial geometry has been our starting point to develop a simple but effective in silico model, which provides ab initio theoretical X-ray absorption spectra in very good agreement with the experimental data. Our results point out two equally populated 6- and 5-fold hydration structures with remarkable different water residence times of 5 and 98 ps, respectively, and a low free energy barrier between first and second hydration shell.

A high-resolution XAS study of aqueous Cu(II) in liquid and frozen solutions: pyramidal, polymorphic, and non-centrosymmetric.

High-resolution EXAFS (k = 18 Å(-1)) and MXAN XAS analyses show that axially elongated square pyramidal [Cu(H2O)5](2+) dominates the structure of Cu(II) in aqueous solution, rather than 6-coordinate JT-octahedral [Cu(H2O)6](2+). Freezing produced a shoulder at 8989.6 eV on the rising XAS edge and an altered EXAFS spectrum, while 1s → 3d transitions remained invariant in energy position and intensity. Core square pyramidal [Cu(H2O)5](2+) also dominates frozen solution. Solvation shells were found at ∼3.6 Å (EXAFS) or ∼3.8 Å (MXAN) in both liquid and frozen phases. However, MXAN analysis revealed that about half the time in liquid solution, [Cu(H2O)5](2+) associates with an axially non-bonding 2.9 Å water molecule. This distant water apparently organizes the solvation shell. When the 2.9 Å water molecule is absent, the second shell is undetectable to MXAN. The two structural arrangements may represent energetic minima of fluxional dissolved aqueous [Cu(H2O)5](2+). The 2.9 Å trans-axial water resolves an apparent conflict of the [Cu(H2O)5](2+) core model with a dissociational exchange mechanism. In frozen solution, [Cu(H2O)5](2+) is associated with either a 3.0 Å axial non-bonded water molecule or an axial ClO4(-) at 3.2 Å. Both structures are again of approximately equal presence. When the axial ClO4(-) is present, Cu(II) is ∼0.5 Å above the mean O4 plane. This study establishes [Cu(H2O)5](2+) as the dominant core structure for Cu(II) in water solution, and is the first to both empirically resolve multiple extended solution structures for fluxional [Cu(H2O)5](2+) and to provide direct evidence for second shell dynamics.

Probing the electronic and geometric structure of ferric and ferrous myoglobins in physiological solutions by Fe K-edge absorption spectroscopy.

We present an iron K-edge X-ray absorption study of carboxymyoglobin (MbCO), nitrosylmyoglobin (MbNO), oxymyoglobin (MbO2), cyanomyoglobin (MbCN), aquomet myoglobin (metMb) and unligated myoglobin (deoxyMb) in physiological media. The analysis of the XANES region is performed using the full-multiple scattering formalism, implemented within the MXAN package. This reveals trends within the heme structure, absent from previous crystallographic and X-ray absorption analysis. In particular, the iron-nitrogen bond lengths in the porphyrin ring converge to a common value of about 2 Å, except for deoxyMb whose bigger value is due to the doming of the heme. The trends of the Fe-Nε (His93) bond length is found to be consistent with the effect of ligand binding to the iron, with the exception of MbNO, which is explained in terms of the repulsive trans effect. We derive a high resolution description of the relative geometry of the ligands with respect to the heme and quantify the magnitude of the heme doming in the deoxyMb form. Finally, time-dependent density functional theory is used to simulate the pre-edge spectra and is found to be in good agreement with the experiment. The XAS spectra typically exhibit one pre-edge feature which arises from transitions into the unoccupied dσ and dπ - πligand* orbitals. 1s → dπ transitions contribute weakly for MbO2, metMb and deoxyMb. However, despite this strong Fe d contribution these transitions are found to be dominated by the dipole (1s → 4p) moment due to the low symmetry of the heme environment.

X-ray absorption spectroscopic investigation of the electronic structure differences in solution and crystalline oxyhemoglobin.

Hemoglobin (Hb) is the heme-containing O2 transport protein essential for life in all vertebrates. The resting high-spin (S = 2) ferrous form, deoxy-Hb, combines with triplet O2, forming diamagnetic (S = 0) oxy-Hb. Understanding this electronic structure is the key first step in understanding transition metal-O2 interaction. However, despite intense spectroscopic and theoretical studies, the electronic structure description of oxy-Hb remains elusive, with at least three different descriptions proposed by Pauling, Weiss, and McClure-Goddard, based on theory, spectroscopy, and crystallography. Here, a combination of X-ray absorption spectroscopy and extended X-ray absorption fine structure, supported by density functional theory calculations, help resolve this debate. X-ray absorption spectroscopy data on solution and crystalline oxy-Hb indicate both geometric and electronic structure differences suggesting that two of the previous descriptions are correct for the Fe-O2 center in oxy-Hb. These results support the multiconfigurational nature of the ground state developed by theoretical results. Additionally, it is shown here that small differences in hydrogen bonding and solvation effects can tune the ground state, tipping it into one of the two probable configurations. These data underscore the importance of solution spectroscopy and show that the electronic structure in the crystalline form may not always reflect the true ground-state description in solution.

The x-ray absorption spectroscopy model of solvation about sulfur in aqueous L-cysteine.

The environment of sulfur in dissolved aqueous L-cysteine has been examined using K-edge x-ray absorption spectroscopy (XAS), extended continuum multiple scattering (ECMS) theory, and density functional theory (DFT). For the first time, bound-state and continuum transitions representing the entire XAS spectrum of L-cysteine sulfur are accurately reproduced by theory. Sulfur K-edge absorption features at 2473.3 eV and 2474.2 eV represent transitions to LUMOs that are mixtures of S-C and S-H σ∗ orbitals significantly delocalized over the entire L-cysteine molecule. Continuum features at 2479, 2489, and 2530 eV were successfully reproduced using extended continuum theory. The full L-cysteine sulfur K-edge XAS spectrum could not be reproduced without addition of a water-sulfur hydrogen bond. Density functional theory analysis shows that although the Cys(H)S⋯H-OH hydrogen bond is weak (∼2 kcal) the atomic charge on sulfur is significantly affected by this water. MXAN analysis of hydrogen-bonding structures for L-cysteine and water yielded a best fit model featuring a tandem of two water molecules, 2.9 Å and 5.8 Å from sulfur. The model included a S(cys)⋯H-O(w1)H hydrogen-bond of 2.19 Å and of 2.16 Å for H(2)O(w1)⋯H-O(w2)H. One hydrogen-bonding water-sulfur interaction alone was insufficient to fully describe the continuum XAS spectrum. However, density functional theoretical results are convincing that the water-sulfur interaction is weak and should be only transient in water solution. The durable water-sulfur hydrogen bond in aqueous L-cysteine reported here therefore represents a break with theoretical studies indicating its absence. Reconciling the apparent disparity between theory and result remains the continuing challenge.

The X-ray absorption spectroscopic model of the copper(II) imidazole complex ion in liquid aqueous solution: a strongly solvated square pyramid.

Cu K-edge extended X-ray absorption fine structure (EXAFS) and Minuit X-ray absorption near-edge structure (MXAN) analyses were combined to evaluate the structure of the copper(II) imidazole complex ion in liquid aqueous solution. Both methods converged to the same square-pyramidal inner coordination sphere [Cu(Im)(4)L(ax)](2+) (L(ax) indeterminate) with four equatorial nitrogen atoms at EXAFS, 2.02 ± 0.01 Å, and MXAN, 1.99 ± 0.03 Å. A short-axial N/O scatterer (L(ax)) was found at 2.12 ± 0.02 Å (EXAFS) or 2.14 ± 0.06 Å (MXAN). A second but very weak axial Cu-N/O interaction was found at 2.9 ± 0.1 Å (EXAFS) or 3.0 ± 0.1 Å (MXAN). In the MXAN fits, only a square-pyramidal structural model successfully reproduced the doubled maximum of the rising K-edge X-ray absorption spectrum, specifically excluding an octahedral model. Both EXAFS and MXAN also found eight outlying oxygen scatterers at 4.2 ± 0.3 Å that contributed significant intensity over the entire spectral energy range. Two prominent rising K-edge shoulders at 8987.1 and 8990.5 eV were found to reflect multiple scattering from the 3.0 Å axial scatterer and the imidazole rings, respectively. In the MXAN fits, the imidazole rings took in-plane rotationally staggered positions about copper. The combined (EXAFS and MXAN) model for the unconstrained cupric imidazole complex ion in liquid aqueous solution is an axially elongated square-pyramidal core, with a weak nonbonded interaction at the second axial coordination position and a solvation shell of eight nearest-neighbor water molecules. This core square-pyramidal motif has persisted through [Cu(H(2)O)(5)](2+), [Cu(NH(3))(4)(NH(3),H(2)O)](2+), (1, 2) and now [Cu(Im)(4)L(ax))](2+) and appears to be the geometry preferred by unconstrained aqueous-phase copper(II) complex ions.

Structural characterization of a high affinity mononuclear site in the copper(II)-α-synuclein complex.

Human α-Synuclein (aS), a 140 amino acid protein, is the main constituent of Lewy bodies, the cytoplasmatic deposits found in the brains of Parkinson's disease patients, where it is present in an aggregated, fibrillar form. Recent studies have shown that aS is a metal binding protein. Moreover, heavy metal ions, in particular divalent copper, accelerate the aggregation process of the protein. In this work, we investigated the high affinity binding mode of truncated aS (1-99) (aS99) with Cu(II), in a stoichiometric ratio, to elucidate the residues involved in the binding site and the role of copper ions in the protein oligomerization. We used Electron Paramagnetic Resonance spectroscopy on the Cu(II)-aS99 complex at pH 6.5, performing both multifrequency continuous wave experiments and pulsed experiments at X-band. The comparison of 9.5 and 95 GHz data showed that at this pH only one binding mode is present. To identify the nature of the ligands, we performed Electron Spin Echo Envelope Modulation, Hyperfine Sublevel Correlation Spectroscopy, and pulsed Davies Electron-Nuclear Double Resonance (Davies-ENDOR) experiments. We determined that the EPR parameters are typical of a type-II copper complex, in a slightly distorted square planar geometry. Combining the results from the different pulsed techniques, we obtained that the equatorial coordination is {N(Im), N(-), H(2)O, O}, where N(im) is the imino nitrogen of His50, N(-) a deprotonated amido backbone nitrogen that we attribute to His50, H(2)O an exchangeable water molecule, and O an unidentified oxygen ligand. Moreover, we propose that the free amino terminus (Met1) participates in the complex as an axial ligand. The MXAN analysis of the XAS k-edge absorption data allowed us to independently validate the structural features proposed on the basis of the magnetic parameters of the Cu(II)-aS99 complex and then to further refine the quality of the proposed structural model.

Full-potential multiple scattering theory with space-filling cells for bound and continuum states.

We present a rigorous derivation of a real-space full-potential multiple scattering theory (FP-MST) that is free from the drawbacks that up to now have impaired its development (in particular the need to expand cell shape functions in spherical harmonics and rectangular matrices), valid both for continuum and bound states, under conditions for space partitioning that are not excessively restrictive and easily implemented. In this connection we give a new scheme to generate local basis functions for the truncated potential cells that is simple, fast, efficient, valid for any shape of the cell and reduces to the minimum the number of spherical harmonics in the expansion of the scattering wavefunction. The method also avoids the need for saturating 'internal sums' due to the re-expansion of the spherical Hankel functions around another point in space (usually another cell center). Thus this approach provides a straightforward extension of MST in the muffin-tin (MT) approximation, with only one truncation parameter given by the classical relation l(max) = kR(b), where k is the electron wavevector (either in the excited or ground state of the system under consideration) and R(b) is the radius of the bounding sphere of the scattering cell. Moreover, the scattering path operator of the theory can be found in terms of an absolutely convergent procedure in the l(max) --> ∞ limit. Consequently, this feature provides a firm ground for the use of FP-MST as a viable method for electronic structure calculations and makes possible the computation of x-ray spectroscopies, notably photo-electron diffraction, absorption and anomalous scattering among others, with the ease and versatility of the corresponding MT theory. Some numerical applications of the theory are presented, both for continuum and bound states.

Structural characterization of a zinc high-affinity binding site in rhodopsin.

For the first time to our knowledge, X-ray absorption spectroscopy (XAS) has been used to investigate the environment of putative Zn(2+) binding sites in rhodopsin. We studied native purified nondeionized rhodopsin without any further addition of Zn(2+), as well as with 1.5 mol of Zn(2+)-as zinc chloride-per mole of protein. Three different binding sites in rhodopsin were considered based on computational chemistry studies, and a quantitative analysis of the XAS signal was performed by fitting the experimental data to their simulated XAS spectra. Our results demonstrate that Zn(2+) is intrinsically bound to rhodopsin and are compatible with the existence of an octahedral coordination involving six oxygen atoms in the first shell (average Zn-O distance of 2.08 A), and with a second coordination shell containing one or two phosphorus or sulfur atoms at an average distance of 2.81 A.

Full-potential multiple scattering for core electron spectroscopies.

We present a rigorous derivation of a real space full-potential multiple-scattering theory (FP-MST), valid both for continuum and bound states, that is free from the drawbacks that up to now have impaired its development, in particular the need to use cell shape functions and rectangular matrices. In this connection we give a new scheme to generate local basis functions for the truncated potential cells that is simple, fast, efficient, valid for any shape of the cell and reduces to the minimum the number of spherical harmonics in the expansion of the scattering wavefunction. This approach provides a straightforward extension of MST in the muffin-tin (MT) approximation, with only one truncation parameter given by the classical relation l(max) = kR(b), where k is the photo-electron wavevector and R(b) the radius of the bounding sphere of the scattering cell. Some numerical applications of the theory are presented, both for continuum and bound states.

X-ray absorption spectroscopy of hemes and hemeproteins in solution: multiple scattering analysis.

A full quantitative analysis of Fe K-edge X-ray absorption spectra has been performed for hemes in two porphynato complexes, that is, iron(III) tetraphenylporphyrin chloride (Fe(III)TPPCl) and iron(III) tetraphenylporphyrin bis(imidazole) (Fe(III)TPP(Imid)2), in two protein complexes whose X-ray structure is known at atomic resolution (1.0 A), that is, ferrous deoxy-myoglobin (Fe(II)Mb) and ferric aquo-myoglobin (Fe(III)MbH2O), and in ferric cyano-myoglobin (Fe(III)MbCN), whose X-ray structure is known at lower resolution (1.4 A). The analysis has been performed via the multiple scattering approach, starting from a muffin tin approximation of the molecular potential. The Fe-heme structure has been obtained by analyzing independently the Extended X-ray Absorption Fine Structure (EXAFS) region and the X-ray Absorption Near Edge Structure (XANES) region. The EXAFS structural results are in full agreement with the crystallographic values of the models, with an accuracy of +/- 0.02 A for Fe-ligand distances, and +/-6 degrees for angular parameters. All the XANES features above the theoretical zero energy (in the lower rising edge) are well accounted for by single-channel calculations, for both Fe(II) and Fe(III) hemes, and the Fe-N p distance is determined with the same accuracy as EXAFS. XANES evaluations of Fe-5th and Fe-6th ligand distances are determined with 0.04-0.07 A accuracy; a small discrepancy with EXAFS (0.01 to 0.05 A beyond the statistical error), is found for protein compounds. Concerns from statistical correlation among parameters and multiple minima in the parameter space are discussed. As expected, the XANES accuracy is slightly lower than what was found for polarized XANES on Fe(III)MbCN single crystal (0.03-0.04 A), and states the actual state-of-the-art of XANES analysis when used to extract heme-normal parameters in a solution spectrum dominated by heme-plane scattering.