Function Of Coordination Number Research Articles

Structural Diversity of Sn(II) Phosphine Oxide Complexes with Weakly Coordinating Anions and Comparisons with Related Ge(II) and Pb(II) Species

AbstractA series of tin(II) triflate phosphine oxide complexes has been prepared from the reaction of Sn(OTf)2 (OTf− = [O3SCF3]−) with various ratios of OPPh3, OPMe3 or dppmO2 (dppmO2 = Ph2(O)PCH2P(O)Ph2). The complexes [Sn(OPPh3)n][OTf]2 (n = 2, 3 or 4), [Sn(OPMe3)n][OTf]2 (n = 2 or 3) and [Sn(dppmO2)n][OTf]2 (n = 1 or 2) have been isolated in moderate to good yields. Selected germanium(II) and lead(II) analogues have been made for comparison, namely [Ge(OPPh3)n][OTf]2 (n = 2 or 3) and [Pb(OPR3)4][OTf]2 (R = Me, Ph). The effect of changing the weakly coordinating OTf− anion for the non‐coordinating [BArF]− anion was investigated through anion metathesis, furnishing the complexes [Sn(OPPh3)n][BArF]2 (n = 3 or 4) and [Ge(OPPh3)3][BArF]2. The isolated solids were characterised by 1H, 19F{1H}, 31P{1H} and IR spectroscopy and microanalysis. Crystal structures were obtained for all complexes except [Ge(OPPh3)2][OTf]2 and [Sn(OPPh3)3][BArF]2, allowing comparisons of the structural features of these divalent group 14 complexes down the group and as a function of coordination number, ligand sterics and electronics.

Critical polynomials in the nonplanar and continuum percolation models.

Exact or precise thresholds have been intensively studied since the introduction of the percolation model. Recently, the critical polynomial P_{B}(p,L) was introduced for planar-lattice percolation models, where p is the occupation probability and L is the linear system size. The solution of P_{B}=0 can reproduce all known exact thresholds and leads to unprecedented estimates for thresholds of unsolved planar-lattice models. In two dimensions, assuming the universality of P_{B}, we use it to study a nonplanar lattice model, i.e., the equivalent-neighbor lattice bond percolation, and the continuum percolation of identical penetrable disks, by Monte Carlo simulations and finite-size scaling analysis. It is found that, in comparison with other quantities, P_{B} suffers much less from finite-size corrections. As a result, we obtain a series of high-precision thresholds p_{c}(z) as a function of coordination number z for equivalent-neighbor percolation with z up to O(10^{5}) and clearly confirm the asymptotic behavior zp_{c}-1∼1/sqrt[z] for z→∞. For the continuum percolation model, we surprisingly observe that the finite-size correction in P_{B} is unobservable within uncertainty O(10^{-5}) as long as L≥3. The estimated threshold number density of disks is ρ_{c}=1.43632505(10), slightly below the most recent result ρ_{c}=1.43632545(8) of Mertens and Moore obtained by other means. Our work suggests that the critical polynomial method can be a powerful tool for studying nonplanar and continuum systems in statistical mechanics.

Anisotropic stress state and small strain stiffness in granular materials: RC experiments and DEM simulations

The paper combines experimental and numerical analyses to study the relation between small strain stiffness and micro-structure of an idealized granular material under isotropic and anisotropic stress conditions. Results from the resonant column device on glass ballotini show that the relation between the maximum shear modulus and anisotropic stress components strongly depends on the applied stress path. Discrete element simulations (DEM) are performed to investigate the material behaviour along isotropic compression, triaxial compression and constant hbox {K}_0 deformation. The DEM analysis reveals that each stress path is associated with a characteristic evolution of the coordination number, i.e., the average number of contacts per particle. In turn, the maximum shear modulus is found to be a direct function of the coordination number. In order to include the micro-structure interpretation in the analytical description, a modified version of Hardin’s relation is proposed as a function of coordination number, void ratio and mean pressure.

Short-range order structure motifs learned from an atomistic model of a Zr50Cu45Al5 metallic glass

The structural motifs of a Zr50Cu45Al5 metallic glass were learned from atomistic models using a new structure analysis method called motif extraction that employs point-pattern matching and machine learning clustering techniques. The motifs are the nearest-neighbor building blocks of the glass and reveal a well-defined hierarchy of structures as a function of coordination number. Some of the motifs are icosahedral or quasi-icosahedral in structure, while others take on the structure of the most close-packed geometries for each coordination number. These results set the stage for developing clearer structure-property connections in metallic glasses. Motif extraction can be applied to any disordered material to identify its structural motifs without the need for human input.

Bond-length distributions for ions bonded to oxygen: results for the lanthanides and actinides and discussion of the f-block contraction

Bond-length distributions have been examined for 84 configurations of the lanthanide ions and 22 configurations of the actinide ions bonded to oxygen, for 1317 coordination polyhedra and 10 700 bond distances for the lanthanide ions, and 671 coordination polyhedra and 4754 bond distances for the actinide ions. A linear correlation between mean bond length and coordination number is observed for the trivalent lanthanides ions bonded to O2−. The lanthanide contraction for the trivalent lanthanide ions bonded to O2− is shown to vary as a function of coordination number, and to diminish in scale with an increasing coordination number. The decrease in mean bond length from La3+ to Lu3+ is 0.25 Å for coordination number (CN) 6 (9.8%), 0.22 Å for CN 7 (8.7%), 0.21 Å for CN 8 (8.0%), 0.21 Å for CN 9 (8.2%) and 0.18 Å for CN 10 (6.9%). The crystal chemistry of Np5+ and Np6+ is shown to be very similar to that of U6+ when bonded to O2−, but differs for Np7+.

A random matrix definition of the boson peak

The density of vibrational states for glasses and jammed solids exhibits universal features, including an excess of modes above the Debye prediction known as the boson peak located at a frequency . We show that the eigenvector statistics for boson peak modes are universal, and develop a new definition of the boson peak based on this universality that displays the previously observed characteristic scaling . We identify a large new class of random matrices that obey a generalized global tranlational invariance constraint and demonstrate that members of this class also have a boson peak with precisely the same universal eigenvector statistics. We denote this class as boson peak random matrices, and conjecture it comprises a new universality class. We characterize the eigenvector statistics as a function of coordination number, and find that one member of this new class reproduces the scaling of with coordination number that is observed near the jamming transition.

Comprehensive Fe-ligand vibration identification in {FeNO}6 hemes.

Oriented single-crystal nuclear resonance vibrational spectroscopy (NRVS) has been used to obtain all iron vibrations in two {FeNO}6 porphyrinate complexes, five-coordinate [Fe(OEP)(NO)]ClO4 and six-coordinate [Fe(OEP)(2-MeHIm)(NO)]ClO4. A new crystal structure was required for measurements of [Fe(OEP)(2-MeHIm)(NO)]ClO4, and the new structure is reported herein. Single crystals of both complexes were oriented to be either parallel or perpendicular to the porphyrin plane and/or axial imidazole ligand plane. Thus, the FeNO bending and stretching modes can now be unambiguously assigned; the pattern of shifts in frequency as a function of coordination number can also be determined. The pattern is quite distinct from those found for CO or {FeNO}7 heme species. This is the result of unchanging Fe–NNO bonding interactions in the {FeNO}6 species, in distinct contrast to the other diatomic ligand species. DFT calculations were also used to obtain detailed predictions of vibrational modes. Predictions were consistent with the intensity and character found in the experimental spectra. The NRVS data allow the assignment and observation of the challenging to obtain Fe–Im stretch in six-coordinate heme derivatives. NRVS data for this and related six-coordinate hemes with the diatomic ligands CO, NO, and O2 reveal a strong correlation between the Fe–Im stretch and Fe–NIm bond distance that is detailed for the first time.

Lattice density-functional theory of the attractive Hubbard model

The attractive Hubbard model is investigated in the framework of lattice density-functional theory (LDFT). The ground-state energy $E=T+W$ is regarded as a functional of the single-particle density matrix ${\ensuremath{\gamma}}_{ij}$ with respect to the lattice sites, where $T[\ensuremath{\gamma}]$ represents the kinetic and crystal-field energies and $W[\ensuremath{\gamma}]$ the interaction energy. Aside from the exactly known functional $T[\ensuremath{\gamma}]$, we propose a simple scaling approximation to $W[\ensuremath{\gamma}]$, which is based on exact analytic results for the attractive Hubbard dimer and on a scaling hypothesis within the domain of representability of $\ensuremath{\gamma}$. As applications, we consider one-, two-, and three-dimensional finite and extended bipartite lattices having homogeneous or alternating onsite energy levels. In addition, the Bethe lattice is investigated as a function of coordination number. Results are given for the kinetic, Coulomb, and total energies, as well as for the density distribution ${\ensuremath{\gamma}}_{ii}$, nearest-neighbor bond order ${\ensuremath{\gamma}}_{ij}$, and pairing energy $\ensuremath{\Delta}{E}_{p}$, as a function of the interaction strength $|U|/t$, onsite potential $\ensuremath{\varepsilon}/t$, and band filling $n={N}_{e}/{N}_{a}$. Remarkable even-odd and super-even oscillations of $\ensuremath{\Delta}{E}_{p}$ are observed in finite rings as a function of band filling. Comparison with exact Lanczos diagonalizations and density-matrix renormalization-group calculations shows that LDFT yields a very good quantitative description of the properties of the model in the complete parameter range, thus providing a significant improvement over the mean-field approaches. Goals and limitations of the method are discussed.

Hydration characteristics of Ca2+ and Mg2+: a density functional theory, polarized continuum model and molecular dynamics investigation

In this work, density functional theory, Møller–Plesset second-order perturbation theory, and ab initio molecular dynamics (AIMD) were used to investigate hydrated characteristics of Mg2+ and Ca2+ as a function of coordination number in the first hydration shell (CN) and cluster size. It is generally accepted that the CNs of Mg2+ and Ca2+ are both six. Calculations show that the hydration of Mg2+ generally prefers six-coordinated structures, whereas the CN value of Ca2+ varies from 6 to 8 as the hydration proceeds. Moreover, the first hydration of Ca2+ is found to be more flexible than that of Mg2+, as indicated by the results of transition state calculations and AIMD simulations. In addition, the constraint of Mg2+ on the first hydration shell is obviously stronger than that of Ca2+, while the constraint on the inner hydration shells fades slightly faster for Mg2+ than Ca2+. It is also found that the charge transfer from central cation to water molecules is affected only by the first hydration shell for Mg2+, whereas by the first and second hydration shells for Ca2+. Based on hydration characteristics, approximatively saturated ion hydration shells for the hydration of Mg2+ and Ca2+ were proposed.

Hydration of Copper(II): New Insights from Density Functional Theory and the COSMO Solvation Model

The hydrated structure of the Cu(II) ion has been a subject of ongoing debate in the literature. In this article, we use density functional theory (B3LYP) and the COSMO continuum solvent model to characterize the structure and stability of [Cu(H2O)n](2+) clusters as a function of coordination number (4, 5, and 6) and cluster size (n = 4-18). We find that the most thermodynamically favored Cu(II) complexes in the gas phase have a very open four-coordinate structure. They are formed from a stable square-planar [Cu(H2O)8](2+) core stabilized by an unpaired electron in the Cu(II) ion d(x(2)-y(2)) orbital. This is consistent with cluster geometries suggested by recent mass-spectrometric experiments. In the aqueous phase, we find that the more compact five-coordinate square-pyramidal geometry is more stable than either the four-coordinate or six-coordinate clusters in agreement with recent combined EXAFS and XANES studies of aqueous solutions of Cu(II). However, a small energetic difference (approximately 1.4 kcal/mol) between the five- and six-coordinate models with two full hydration shells around the metal ion suggests that both forms may coexist in solution.

Quenched molecular dynamics studies on the extraction energy of aluminum atoms

AbstractThe extraction energy of an aluminum atom is calculated at 0 K as a function of coordination number and defect depth for three surface orientations [(100), (110) and (111)]. For each orientation, atoms are selected and extracted one by one. A linear relationship is obtained between the extraction energy of surface atoms and their coordination numbers (with slight variations due to the geometrical configuration of the atoms). However, the study of the influence of the defect depth on the extraction energy highlights the role played by intrinsic stress on the extraction energy. Copyright © 2008 John Wiley & Sons, Ltd.

Size matters! Fragmentation chemistry of [Cu(L)n]2+ complexes of diacylglycerophosphocholines as a function of coordination number (n = 2–7)

[Cu(L)(n)](2+) complexes of 1,2-dihexanoyl-sn-glycero-3-phosphocholine (L = D6PC) are formed upon electrospray ionization mass spectrometry (ESI-MS) of an 8 mM solution of D6PC with 4 mM CuCl(2) in 10 mM ammonium acetate buffer, pH 6.1. The collision-induced dissociation (CID) reactions of the [Cu(L)(n)](2+) complexes were examined in a linear ion trap mass spectrometer. A rich fragmentation chemistry was observed, including: loss of a neutral ligand; intermolecular ligand-ligand S(N)2 methylation; metal ion induced ligand fragmentation via carboxylate abstraction; and phosphate abstraction. The dominant reaction channel depends on the size (n) of the complex. Thus loss of neutral ligand(s) is the sole reaction channel for n = 5-7. At n = 4, S(N)2 methylation and carboxylate abstraction start to compete with neutral ligand loss. At n = 2 the carboxylate abstraction and phosphate abstraction reactions dominate the CID spectrum. The carboxylate abstraction and phosphate abstraction reactions are likely to be driven via neighboring group pathways. PM3 calculations, carried out to compare competing neighboring pathways based on the relative stabilities of the product ions, suggest a preference for five-membered ring formation for ligand fragmentation involving both carboxylate and phosphate abstraction.

Bond valence sums and structural studies of antimony complexes containing Sb bonded only to O ligands

New R 0 values for Sb(III)–O of 1.955(13) Å and for Sb(V)–O of 1.912(12) Å were derived from a bond valence sum, or BVS, analysis of of 123 SbO n fragments with n = 3–7. These R 0 values can be used to calculate the oxidation state, or OS, of Sb in complexes where Sb is bonded only to O ligands. If the OS of the Sb ion is uncertain, the average R 0 value of 1.934 Å can be used to decide between the +3 or +5 OS from the observed Sb–O bond distances without any assumptions. The Sb–O distances used in deriving the R 0 values for the +3 and +5 complexes are tabulated as a function of coordination number and have a wide range of values, but the average Sb–O distance reflects the requirement that the BVS must equal the OS. To supplement the Sb–O data, 2 new antimony tartrates were synthesized, and their crystal structures were determined. A single crystal structure determination of NaSb(OH) 6, an unexpected reaction product, gave Sb–O distances that were also included in our BVS analysis.

Estimating the Number of Bound Waters in Gd(III) Complexes Revisited. Improved Methods for the Prediction of q-Values

Two literature computational methods for the prediction of the number of inner-sphere aqua ligands, q, have been applied to a test set of seven Gd(aminocarboxylate) complexes. The first method is based on the hypothesis that q should be proportional to the solvent-accessible surface area of the ligand-complexed Gd ion (Castonguay, L. A., Treasurywala, A. M., Caulfield, T. J., Jaeger, E. P., and Kellar, K. E. (1999) Prediction of q-Values and Conformations of Gadolinium Chelates for Magnetic Resonance Imaging. Bioconjugate Chem. 10, 958). The second method is based on the hypothesis that q-values can be deduced by examining series of steric energy versus ionic radii plots as a function of coordination number (Reichert, D. E., Hancock, R. D., and Welch, M. J. (1996) Molecular Mechanics Investigation of Gadolinium(III) Complexes. Inorg. Chem. 35, 7013). This study identifies deficiencies in these methods and, with respect to the first method, describes some apparent errors. Although neither method was reliable at predicting q, two alternate approaches based on either molecular mechanics strain thresholds or exposed Gd surface area thresholds are shown to predict observed q-values for all Gd aminocarboxylate complexes in the test set.

Ising model with dipole–quadrupole interaction on a Cayley tree: reentrant phase transitions

We formulate the Ising model with dipole–quadrupole interaction on a Cayley tree. As a function of coordination number, we discuss the reentrant character of phase boundaries. A critical line separates the disordered and antiferromagnetic phases. An interesting fact is that the model does not have any tricritical and multicritical points.

Bond Valence Sums in Coordination Chemistry. The Calculation of the Oxidation State of Cerium in Complexes Containing Cerium Bonded Only to Oxygen

A total of 119 CeO(n)fragments with n = 3-12 were analyzed by using the bond valence sum, or BVS, method to yield new R(0) values for Ce(III)-O of 2.121(13) A and for Ce(IV)-O of 2.068(12) A. These R(0) values can be used to calculate the oxidation state of Ce in complexes where Ce is bonded only to O ligands. Furthermore, the average R(0) value of 2.094 A gives a good indication of whether the oxidation state of the Ce ion is +3 or +4 from the observed distances without any assumptions. The fact that complexes with coordination numbers of 10-12 are in agreement is significant since this study is the first example which indicates that high coordination numbers also follow BVS rules. The Ce-O distances used in deriving the R(0) values for the +3 and +4 complexes are tabulated as a function of coordination number and have a wide range of values, but the average Ce-O distance reflects the requirement that the BVS must equal the oxidation state. Several examples are given where the oxidation state of the Ce ion is apparently incorrectly assigned, as well as cases where problems with the X-ray structure determinations are indicated by a disagreement between the postulated and calculated oxidation state.

Increased Coordination via Sulfur Donor Action in Cyclic Pentaoxyphosphoranes and the Parent Cyclic Phosphite. Influence of Pentafluorophenoxy Ligands1

The pentafluorophenoxy ligand was introduced into the new cyclic pentaoxyphosphoranes S[(t-Bu)MeC(6)H(2)O](2)P(OC(6)F(5))(O(2)C(6)Cl(4)) (1), S[(t-Bu)MeC(6)H(2)O](2)P(OC(6)F(5))(O(2)C(14)H(8)) (2), and S[(t-Bu)MeC(6)H(2)O](2)P(OC(6)F(5))(3) (3). X-ray analysis revealed hexacoordinate structures formed by sulfur donor action present as a bridging atom in flexible eight-membered rings for 1-3. X-ray analysis showed that sulfur coordination also occurred with the same type of ring system as part of the phosphite S[(t-Bu)MeC(6)H(2)O](2)P(OC(6)F(5)) (4) to give a pseudo-trigonal-bipyramidal geometry. The pentafluorophenoxy ligand present in the oxyphosphoranes 1-3 as well as in the phosphite 4 acts comparably to a chlorine atom in its ability to enhance phosphorus electrophilicity as measured by the degree of P-S coordination and geometrical displacement toward a more highly coordinated state. The phosphite 4 has a P-S donor distance of 2.876(2) Å, considerably longer than the range of P-S distances from 2.366(3) to 2.495(2) Å obtained for the pentaoxyphosphoranes 1-3. These data express quantitatively the relative electrophilicity of phosphorus as a function of coordination number and substituent composition.

Equilibrium Bond Lengths in Monoatomic Lattices of Metal Atoms as Function of Coordination Number

A recent work of Schmidt and Springborg on one-dimensional chains of metal atoms has prompted us to use a quantum-chemical model, posed in terms of dimer potential energy curves, to analyze equlibrium near-neighbour distances r0 as a function of local coordination number c. For five monoatomic metal atoms, H, K, Al, Pb and Bi, values of r0 are available for three or more different lattices. The increase of r0 from the dimer value correlates with c1/2 in the same general manner for four of the five atoms considered, Al being the exceptional case according to present theoretical calculations.

Equilibrium Bond Lengths in Monoatomic Lattices of Metal Atoms as Function of Coordination Number

A recent work of Schmidt and Springborg on one-dimensional chains of metal atoms has prompted us to use a quantum-chemical model, posed in terms of dimer potential energy curves, to analyze equlibrium near-neighbour distances r0 as a function of local coordination number c. For five monoatomic metal atoms, H, K, Al, Pb and Bi, values of r0 are available for three or more different lattices. The increase of r0 from the dimer value correlates with c1/2 in the same general manner for four of the five atoms considered, Al being the exceptional case according to present theoretical calculations.

Novel Aluminum and Gallium Atrane Structures and Reactivities

New monomeric azaaluminatranes and gallatranes of the type M(RNCH(2)CH(2))(3)N (M = Al, R = Me(3)Si (8) or tert-BuMe(2)Si (9); M = Ga, R = Me(3)Si (10) or tert-BuMe(2)Si (11)) have been prepared, with characterization including a molecular structure determination in the case of 8. Three dimeric azaalumatranes, namely, [Al(MeNCH(2)CH(2))(3)N](2) (12) and [Al(Me(3)SiNCH(2)CH(2))(2)(HNCH2CH2)N](2) (13) and [Ga(MeNCH(2)CH(2))(3)N](2) (14) have also been structurally characterized and all three compounds feature a central (M-N)(2) four-membered ring with a cis configuration of the nitrogen substituents. Some of the reaction chemistry of these systems is outlined and Al-27 NMR trends as a function of coordination number and geometry are discussed.