Coordination chemistry study of hydrated and solvated lead(II) ions in solution and solid state

The coordination chemistry of lead(II) in the oxygen donor solvents water, dimethylsulfoxide (dmso, Me(2)SO), N,N-dimethylformamide (dmf), N,N-dimethylacetamide (dma), N,N'-dimethylpropyleneurea (dmpu), and 1,1,3,3-tetramethylurea (tmu), as well as in the sulfur donor solvent N,N-dimethylthioformamide (dmtf), has been investigated by extended X-ray absorption fine structure (EXAFS) and/or large angle X-ray scattering (LAXS) in solution, and by single crystal X-ray diffraction and/or EXAFS of solid hydrates and solvates. Lead(II) may either form hemidirected complexes with large bond distance distribution and an apparent gap for excess electron density, or holodirected ones with a symmetric coordination sphere with normal bond distance distribution, depending on the strength of antibonding lead 6s/ligand np molecular orbital interactions and ligand-ligand interactions. The crystallographic data show that the solid lead(II) perchlorate and trifluoromethanesulfonate hydrate structures are hemidirected, while the solid lead(II) solvates of dma and dmpu have regular octahedral configuration with holodirected geometry and mean Pb-O bond distances in the range 2.50-2.52 ?. EXAFS data on the hydrated lead(II) ion in aqueous solution show broad bond distance distribution and a lack of inner-core multiple scattering contributions strongly indicating a hemidirected structure. The Pb-O bond distances found both by EXAFS and LAXS, 2.54(1) ?, point to a six-coordinate hydrated lead(II) ion in hemidirected fashion with an unevenly distributed electron density. The results obtained for the dmso solvated lead(II) ion in solution are ambiguous, but for the most part support a six-coordinate hemidirected complex. The mean Pb-O bond distances determined in dmf and dma solution by LAXS, 2.55(1) and 2.48(1) ?, respectively, indicate that in both solvate complexes lead(II) binds six solvent molecules with the former complex being hemidirected whereas the latter is holodirected. The dmpu and tmu solvated lead(II) ions have a regular holodirected octahedral configuration, as expected given their space-demanding characteristics and ligand-ligand intermolecular interactions. The dmtf solvated lead(II) ion in solution is most likely five-coordinate in a hemidirected configuration, with a mean Pb-S bond distance of 2.908(4) ?. New and improved ionic radii for the lead(II) ion in 4-8-coordination in hemi and holodirected configurations are proposed using crystallographic data.     

Crystal structure of lead(II) acetylacetonate and the structure of the acetylacetone solvated lead(II) ion in solution studied by large-angle X-ray scattering

The crystal structure of bis(acetylacetonato)lead(II) and the structure of the acetylacetone solvated lead(II) ion in solution have been determined by single-crystal X-ray diffraction and large-angle X-ray scattering (LAXS), respectively. The acetylacetone is deprotonated and acts as a bidentate anionic ligand (acac-) in the solid Pb(acac)2 compound. The lead(II) ion binds four oxygen atoms strongly in a nearly flat pyramidal configuration with Pb-O bond lengths in the range 2.32-2.37 A, and additionally three oxygens from neighboring complexes at 3.01-3.26 A. Acetylacetone acts as a solvent (Hacac) at dissolution of lead(II) trifluoromethanesulfonate forming a pentasolvate with a mean Pb-O bond distance of 2.724(5) A. The 6s2 lone electron pair on the lead(II) ion becomes stereochemically active in the crystalline acetylacetonate complex, while it is inactive in the solvate in solution. The solution was also analysed using IR and 1H NMR spectroscopy.     

A unique coordination environment for an ion: EXAFS studies and bond valence model approach of the encapsulated cation in the Preyssler anion

X-Ray absorption spectroscopy was used to probe the coordination of different encrypted cations in the Preyssler anions [M(n+)P5W(30)O(110)]((15-n)-)(M(n+)= Sr2+, Am3+, Eu3+, Sm3+, Y3+, Th4+, U4+ in decreasing order of ionic radius, IR), hereafter abbreviated [M(n+)PA](15-n)-. The increase of the M-W distance and the decrease of the M-P distance with increasing M ionic radius reveal that the M cation is displaced along the C5 axis within the Preyssler cavity. The slight change (0.07 A) of the M-O distance that does not correspond to the IR difference of 0.27 A confirms that the cavity retains its rigidity upon cation substitution. Geometric modeling of the encapsulated cation in the channel was performed for comparison to the EXAFS results. The position of the cation in the cavity was calculated as well as the M-O10, -W5 and -P5 distances. This modeling confirms the cation displacement toward the center of the Preyssler anion as the cation size increases, which is understood in terms of the non-homogenous electrostatic potential present within the cavity. The bond valence model approach was applied to obtain experimental bond valences. Only the bond valence sum (BVS) of Am3+ is close to its actual charge. Sums smaller than the actual valences of the +3 and +4 ions (2.39-2.63 for +3 cations, Y, Sm, Eu; 3.17 and 3.38 for +4 cations, U and Th, respectively) were obtained, and a larger sum (2.89) was obtained for Sr2+. The deviations from the formal M sums of the encapsulated ions are attributed to the rigidity of the Preyssler framework. The tendency toward coordinative unsaturation for electroactive cations, such as Eu3+, is thought to be the driving force for facile reduction. Unlike other inorganic chelating ligands, the Preyssler anion provides a unique redox system to stabilize an electroactive cation in a low oxidation state.     

Ab initio molecular dynamics simulation of a 1-ethyl-3-methylimidazolium fluoride-hydrogen fluoride mixture

The intermolecular structure and dynamics of an acidic 1-ethyl-3-methylimidazolium fluoride-hydrogen fluoride solution ([emim][F].2.3HF) have been studied through a Car-Parrinello molecular dynamics simulation. The calculated structure factor is found to be in good agreement with X-ray scattering data. The solution consists of [emim] cations and polyfluoride anions of the kind F(HF)n(-). With increasing n, the length of the H-F covalent bond in the polyfluoride species is found to decrease, with a concomitant blue shift in the frequency of its stretching mode. Evidence for the presence of a hydrogen bond between the acidic ring hydrogen of the cation and the fluoride ion is presented.     

Aspects of glycosidic bond formation in aqueous solution: chemical bonding and the role of water

A model of the specific acid-catalyzed glycosidic bond formation in liquid water at ambient conditions is studied based on constrained Car-Parrinello ab initio molecular dynamics. Specifically the reaction of alpha-D-glucopyranose and methanol is found to proceed by a D(N)A(N) mechanism. The D(N) step consists of a concerted protonation of the O(1) hydroxyl leaving group; this process results in the breaking of the C(1)-O(1) bond, and oxocarbenium ion formation involving C(1)=O(5). The second step, A(N), is the formation of the C(1)-O(m) glycosidic bond, deprotonation of the methanol hydroxyl group O(m)H(m), and re-formation of the C(1)-O(5) single bond. A focus of this study is the analysis of the electronic structure during this condensed phase reaction relying on both Boys/Wannier localized orbitals and the electron localization function ELF. This analysis allows the clear elucidation of the chemical bonding features of the intermediate bracketed by the D(N) and A(N) steps, which is a non-solvent equilibrated oxocarbenium cation. Most interestingly, it is found that the oxygen in the pyranose ring becomes "desolvated" upon double bond/oxocarbenium formation, whereas it is engaged in the hydrogen-bonded water network before and after this period. This demonstrates that hydrogen bonding and thus the aqueous solvent play an active role in this reaction implying that microsolvation studies in the gas phase, both theoretical and experimental, might lead to qualitatively different reaction mechanisms compared to solution.     

Speciation of the curium(III) ion in aqueous solution: a combined study by quantum chemistry and molecular dynamics simulation

The structures of aquo complexes of the curium(III) ion have been systematically studied using quantum chemical and molecular dynamics (MD) methods. The first hydration shell of the Cm3+ ion has been calculated using density functional theory (DFT), with and without inclusion of the conductor-like polarizable continuum medium (CPCM) model of solvation. The calculated results indicate that the primary hydration number of Cm3+ is nine, with a Cm-O bond distance of 2.47-2.48 A. The calculated bond distances and the hydration number are in excellent agreement with available experimental data. The inclusion of a complete second hydration shell of Cm3+ has been investigated using both DFT and MD methods. The presence of the second hydration shell has significant effects on the primary coordination sphere, suggesting that the explicit inclusion of second-shell effects is important for understanding the nature of the first shell. The calculated results indicate that 21 water molecules can be coordinated in the second hydration shell of the Cm3+ ion. MD simulations within the hydrated-ion model suggest that the second-shell water molecules exchange with the bulk solvent with a lifetime of 161 ps.     

Be(II) in aqueous solution--an extended ab initio QM/MM MD study

An ab initio quantum mechanical/molecular mechanical (QM/MM) molecular dynamics (MD) simulation at double-zeta restricted Hartree-Fock (RHF) level was performed at 293.15 K, including first and second hydration shell in the QM region to study the structural and dynamical properties of the Be(II)-hydrate in aqueous solution. The first tetrahedrally arranged hydration shell, with the four water molecules located at a mean Be-O distance of 1.61 A, is highly inert with respect to ligand exchange processes. The second shell, however, consisting in average of approximately 9.2 water ligands at a mean Be-O distance of 3.7 A and the third shell at a mean Be-O distance of 5.4 A with approximately 19 ligands rapidly exchange water molecules between them and with the bulk, respectively. Other structural parameters such as radial and angular distribution functions (RDF and ADF) and tilt- and theta-angle distributions were also evaluated. The dynamics of the hydrate were studied in terms of ligand mean residence times (MRTs) and librational and vibrational frequencies. The mean residence times for second shell and third shell ligands were determined as 4.8 and 3.2 ps, respectively. The Be-O stretching frequency of 658 cm(-1), associated with a force constant of 147 N m(-1) could be overestimated but it certainly reflects the exceptional stability of the ion-ligand bond in the first hydration shell.     

Interpreting ultrafast molecular fragmentation dynamics with ab initio electronic structure calculations

High-level ab initio electronic structure calculations are used to interpret the fragmentation dynamics of CHBr(2)COCF(3), following excitation with an intense ultrafast laser pulse. The potential energy surfaces of the ground and excited cationic states along the dissociative C-CF(3) bond have been calculated using multireference second order perturbation theory methods. The calculations confirm the existence of a charge transfer resonance during the evolution of a dissociative wave packet on the ground state potential energy surface of the molecular cation and yield a detailed picture of the dissociation dynamics observed in earlier work. Comparisons of the ionic spectrum for two similar molecules support a general picture in which molecules are influenced by dynamic resonances in the cation during dissociation.     

Topological/chemical distances and graph centers in molecular graphs with multiple bonds

A set of priority rules is defined for obtaining the graph center in multigraphs, i.e. in molecular graphs with multiple bonds. In order to obtain closer agreement between experimental bond distances in molecules and the relative magnitudes of entries in the distance matrix, a new type of distance is defined, called the “chemical distance”: CD = b^t-14, where b is the conventional bond multiplicity.     

Hydration of the calcium ion. An EXAFS, large-angle x-ray scattering, and molecular dynamics simulation study.

The structure of the hydrated calcium(II) ion in aqueous solution has been studied by means of extended X-ray absorption fine structure spectroscopy (EXAFS), large-angle X-ray scattering (LAXS), and molecular dynamics (MD) methods. The EXAFS data displayed a broad and asymmetric distribution of the Ca-O bond distances with the centroid at 2.46(2) A. LAXS studies on four aqueous calcium halide solutions (1.5-2 mol dm(-)(3)) gave a mean Ca-O bond distance of 2.46(1) A. This is consistent with a hydration number of 8 determined from correlations between mean distances and coordination numbers from crystal structures. The LAXS studies showed a second coordination sphere with a mean Ca.O(II) distance of 4.58(5) A, and for the hydrated halide ions the distances Cl.O 3.25(1) A, Br.O 3.36(1) A, and I.O 3.61(1) A were obtained. Molecular dynamics simulations of CaCl(2)(aq) were performed using three different Ca(2+)-OH(2) pair potentials. The potential from the GROMOS program gave results in agreement with experiments, i.e., a coordination number of 8 and an average Ca-O distance of 2.46 A, and was used for further comparisons. Theoretical EXAFS oscillations were computed for individual MD snapshots and showed very large variations, though the simulated average spectrum from 2000 snapshots gave satisfactory agreement with the experimental EXAFS spectra. The effect of thermal motions of the coordinated atoms is inherent in the MD simulation method. Thermal disorder parameters evaluated from simulated spatial atom distribution functions of the oxygen atoms coordinated to the calcium ion were in close agreement with those from the current LAXS and EXAFS analyses. The combined results are consistent with a root-mean-square displacement from the mean Ca-O distance of 0.09(2) A in aqueous solution at 300 K.     

Water molecule adsorption properties on the BiVO4 (100) surface

The water absorption properties at the surface of BiVO4 are attracting a great deal of attention because the system is a promising candidate as a photocatalyst operating in the visible light range. This has motivated the present investigation via first principles molecular dynamics, which has revealed that a H2O molecule is adsorbed molecularly, instead of dissociatively, at the fivefold Bi site with an adsorption energy of approximately 0.58 eV/molecule. The band gap of the system shrinks slightly (by approximately 0.2 eV) upon water adsorption and it is likely that oxygen atoms belonging to the adsorbed water molecules to the Bi sites are oxidized, as inferred by the small Bi-Owater equilibrium distance (approximately 2.6-2.8 A) very close to the Bi-O bond in the bulk crystal. In the case of water adsorption at a Bi site, the distance between Hwater and V, which is a reduction site, is larger than in the case of adsorption at a V site, indicating that the proton reduction processes may be suppressed.     

Glycosidic bond formation in aqueous solution: on the oxocarbenium intermediate

The mechanism of specific acid-catalyzed glycosidic bond formation between methanol and alpha-d-glucopyranoside in aqueous solution at 300 K was studied using Car-Parrinello molecular dynamics. The reaction was found to proceed through a non-solvent equilibrated oxocarbenium cation intermediate characterized by the loss of a hydrogen-bonding interaction between the ring oxygen and solvating water. The mechanism, which was found to be D(N)A(N) in nature, is discussed in detail.     

An unusual intramolecular transfer of the fluorobenzyl cation between two remote amidic nitrogen atoms induced by collision in the gas phase

A highly unusual rearrangement in collision-induced dissociation mass spectrometry is reported that involves intramolecular transfer of the fluorobenzyl cation between two remote amidic nitrogen atoms separated by five chemical bonds. The same intramolecular transfer was also observed for two related analogs. It is postulated that the ionic reactions are initiated by protonation of the first amidic nitrogen, resulting in formation of the fluorobenzyl cation and a neutral partner that are maintained together in the gas phase by electrostatic interactions as an intermediate ion-neutral complex. In the ion-neutral complex, the nascent fluorobenzyl cation approaches geometrically to the second amidic nitrogen atom on the neutral partner, and subsequently forms a new C-N bond and an isomeric precursor ion as the charge is retained on the amidic nitrogen. The newly formed isomeric precursor ion eventually undergoes the final fragmentation by amide bond cleavage. Alternatively, the ionic reactions proceed through a direct intramolecular transfer mechanism by which the molecular ion adopts to a ring-like configuration in the gas phase, so that both the donor and recipient nitrogens are geometrically close to each other within a bonding distance to permit a direct transfer between two sites even though they are separated by multiple chemical bonds.     

Arylthiazylamides: syntheses, structures, and bonding properties

Air-sensitive, thermally unstable tris(dimethylamino)sulfonium (TAS) salts (3) of the title anions [ArNSN]- have been prepared from corresponding sulfurdiimides Ar-N=S=N-SiMe3 (2) by Si-N bond cleavage with [(Me2N)3S]-[Me3SiF2]- (TASF). They are characterized by low-temperature X-ray crystallography as Z isomers. Because of the very short terminal S-N distance (144.2 (3h)-147.9 (3i)pm) and the relatively long internal S-N distance (158.3 (3i)-160.3 (3c) pm) the [ArNSN]- ions should be regarded as thiazylamides 1b, rare species containing a S triple bond N triple bond. A bonding model is developed and the experimental results are compared with those of restricted Hartree-Fock (RHF), density functional theory (DFT), and M?ller-Plesset second-order (MP2) calculations.     

Proton transport in triflic acid pentahydrate studied via ab initio path integral molecular dynamics

Trifluoromethanesulfonic acid hydrates provide a well-defined system to study proton dissociation and transport in perfluorosulfonic acid membranes, typically used as the electrolyte in hydrogen fuel cells, in the limit of minimal water. The triflic acid pentahydrate crystal (CF(3)SO(3)H·5H(2)O) is sufficiently aqueous that it contains an extended three-dimensional water network. Despite it being extended, however, long-range proton transport along the network is structurally unfavorable and would require considerable rearrangement. Nevertheless, the triflic acid pentahydrate crystal system can provide a clear picture of the preferred locations of local protonic defects in the water network, which provides insights about related structures in the disordered, low-hydration environment of perfluorosulfonic acid membranes. Ab initio molecular dynamics simulations reveal that the proton defect is most likely to transfer to the closest water that has the expected presolvation and only contains water in its first solvation shell. Unlike the tetrahydrate of triflic acid (CF(3)SO(3)H·4H(2)O), there is no evidence of the proton preferentially transferring to a water molecule bridging two of the sulfonate groups. However, this could be an artifact of the crystal structure since the only such water molecule is separated from the proton by long O-O distances. Hydrogen bonding criteria, using the two-dimensional potential of mean force, are extracted. Radial distribution functions, free energy profiles, radii of gyration, and the root-mean-square displacement computed from ab initio path integral molecular dynamics simulations reveal that quantum effects do significantly extend the size of the protonic defect and increase the frequency of proton transfer events by nearly 15%. The calculated IR spectra confirm that the dominant protonic defect mostly exists as an Eigen cation but contains some Zundel ion characteristics. Chain lengths and ring sizes determined from the hydrogen bond network, counted using graph theory techniques, are only moderately sensitive to quantum effects. Deliberately introducing a structural defect into the native crystal yields a protonic defect with one hydrogen bond to a sulfonate group that was found to be metastable for at least 10 ps.     

Solvation of radical cations in water--reactive or unreactive solvation?

The solvation and reaction of ethylene radical cation in aqueous solution has been studied with Car-Parrinello molecular dynamics simulations. All ab initio simulations were performed using a system of 56 water and one ethylene molecule. Using a favorable symmetrically solvated radical cation as the starting point of the simulation a fast addition of water (within 90 fs) to the radical cation is observed. The primary addition product is rapidly deprotonated (within 100 fs) to yield the ethanol-2-yl radical. A second simulation was initiated through vertical ionization of neutral hydrated ethylene, representing a significantly less favorable situation for the addition process. No addition of water can be observed in this second simulation over a time span of 1.7 ps. Taken together the two simulations are indicative of a rearrangement of the solvent shell which represents the major part of the overall reaction barrier. Under these circumstances, the reaction rate of an otherwise spontaneous reaction is limited by the intrinsic solvent relaxation time. This interpretation of the reactivity of hydrated radical cations reconciles previously conflicting experimental condensed phase and theoretical gas phase studies.     

Direct observation of the substitution effects on the hydrogen bridge dynamics in selected Schiff bases--a comparative molecular dynamics study

We have studied substituent effects on the properties of the intramolecular hydrogen bond of some ortho-hydroxy Schiff bases using density functional theory (DFT) based first-principle molecular dynamics (FPMD) and path integral molecular dynamics. The studied compounds possess a strong intramolecular hydrogen bond (r((O???N)) ≤ 2.6 A?), which can be tuned by substitution to either (i) enhance the basicity of the acceptor moiety by induction effects or (ii) decrease the hydrogen bond length through steric repulsion. DFT calculations and FPMD were employed to investigate structural and dynamical properties of the selected molecules, while quantum effects on the structural properties were assessed using path integral FPMD. The simulations were performed in vacuo and in the solid state to study the influence of the environment on the hydrogen bond and spectroscopic properties. We give computational support to the suggestion that induction effects are less effective to tune the intramolecular hydrogen bond properties of the discussed ortho-hydroxy Schiff bases than the steric or the environmental effects.     

Metal ion complexing properties of the highly preorganized ligand 2,9-bis(hydroxymethyl)-1,10-phenanthroline: a crystallographic and thermodynamic study

Metal ion complexing properties of the ligand 2,9-bis(hydroxymethyl)-1,10-phenanthroline (PDALC) are reported. For PDALC, the rigid 1,10-phenanthroline backbone leads to high levels of preorganization and enhanced selectivity for larger metal ions with an ionic radius of about 1.0 A that can fit well into the cleft of the ligand. Structures of PDALC complexes with two larger metal ions, Ca(II) and Pb(II), are reported. [Ca(PDALC) 2](ClO 4) 2 ( 1) is triclinic, Pi, a = 7.646(3), b = 13.927(4), c = 14.859(5) (A), alpha = 72.976(6), beta = 89.731(6), mu = 78.895(6) degrees , V = 1482.5(8) A (3), Z = 2, R = 0.0818. [Pb(PDALC)(ClO 4) 2] ( 2) is triclinic, Pi, a = 8.84380(10), b = 9.0751(15), c = 12.178(2) (A), alpha = 74.427(3), beta = 78.403(13), mu = 80.053(11) degrees , V = 915.0(2) A (3), Z = 2, R = 0.0665. In 1, the Ca(II) is eight-coordinate, with an average Ca-N of 2.501 A and Ca-O of 2.422 A. The structure of 1 suggests that Ca(II) is coordinated in a very low-strain manner in the two PDALC ligands. In 2, Pb(II) appears to be eight-coordinate, with coordination of PDALC and four O donors from perchlorates bridging between neighboring Pb atoms. The Pb has very short Pb-N bonds averaging 2.486 A and Pb-O bonds to the alcoholic groups of PDALC of 2.617 A. It is suggested that the Pb(II) has a stereochemically active lone pair situated on the Pb(II) opposite the two N donors of the PDALC, and in line with this, the Pb-L bonds become longer as one moves around the Pb from the sites of the two N donors to the proposed position of the lone pair. There are two oxygen donors from two perchlorates, nearer the N donors, with shorter Pb-O lengths averaging 2.623 A. Two oxygens from perchlorates nearer the proposed site of the lone pair form very long Pb-O bond lengths averaging 3.01 A. The Pb(II) also appears to coordinate in the cleft of PDALC in a low-strain manner. Formation constants are reported for PDALC in 0.1 M NaClO 4 at 25.0 degrees C. These show that, relative to 1,10-phenanthroline, the hydroxymethyl groups of PDALC produce a significant stabilization for large metal ions such as Cd(II) or Pb(II) that are able to fit in the cleft of PDALC but destabilize the complexes of metal ions such as Ni(II) or Cu(II) that are too small for the cleft.     

Equatorial and apical solvent shells of the UO2 2+ ion

First principles molecular dynamics simulations of the hydration shells surrounding UO(2)(2+) ions are reported for temperatures near 300 K. Most of the simulations were done with 64 solvating water molecules (22 ps). Simulations with 122 water molecules (9 ps) were also carried out. The hydration structure predicted from the simulations was found to agree with very well-known results from x-ray data. The average U=O bond length was found to be 1.77 A. The first hydration shell contained five trigonally coordinated water molecules that were equatorially oriented about the O-U-O axis with the hydrogen atoms oriented away from the uranium atom. The five waters in the first shell were located at an average distance of 2.44 A (2.46 A, 122 water simulation). The second hydration shell was composed of distinct equatorial and apical regions resulting in a peak in the U-O radial distribution function at 4.59 A. The equatorial second shell contained ten water molecules hydrogen bonded to the five first shell molecules. Above and below the UO(2)(2+) ion, the water molecules were found to be significantly less structured. In these apical regions, water molecules were found to sporadically hydrogen bond to the oxygen atoms of the UO(2)(2+), oriented in such a way as to have their protons pointed toward the cation. While the number of apical waters varied greatly, an average of five to six waters was found in this region. Many water transfers into and out of the equatorial and apical second solvation shells were observed to occur on a picosecond time scale via dissociative mechanisms. Beyond these shells, the bonding pattern substantially returned to the tetrahedral structure of bulk water.     

CRYSTAL STRUCTURE OF CATENA-BIS(NITRILOTRIACETATO) PENTAAQUATRILEAD(Ⅱ), [Pb_3{N(CH_2CO_2)_3}_2(H_2O)_5]_n

<正> The title complex crystallizes in the hexagonal space group P65 (No. 170) with a = 9. 020(1), c=48. 969(6) A , V = 3450. 3(9)A3, Z = 6, Dc= 3. 14 gcm-3 and μ(MoKa) = 21. 99 mm-1. The crystal structure (R = 0. 063 for 2173 observed data) consists of a three-dimehsional network featuring three independent lead(Ⅱ) atoms in 7-, 8-, and 9-coordination environments. The bond lengths of Pb-N are 2. 62(3) and 2. 63(3) A, and those of Pb-O range from 2. 49(4) to 3. 00(3) A.