Published two‐body bond‐valence parameters for cation–oxygen bonds have been evaluated via the root mean‐square deviation (RMSD) from the valence‐sum rule for 128 cations, using 180 194 filtered bond ...lengths from 31 489 coordination polyhedra. Values of the RMSD range from 0.033–2.451 v.u. (1.1–40.9% per unit of charge) with a weighted mean of 0.174 v.u. (7.34% per unit of charge). The set of best published parameters has been determined for 128 ions and used as a benchmark for the determination of new bond‐valence parameters in this paper. Two common methods for the derivation of bond‐valence parameters have been evaluated: (1) fixing B and solving for Ro; (2) the graphical method. On a subset of 90 ions observed in more than one coordination, fixing B at 0.37 Å leads to a mean weighted‐RMSD of 0.139 v.u. (6.7% per unit of charge), while graphical derivation gives 0.161 v.u. (8.0% per unit of charge). The advantages and disadvantages of these (and other) methods of derivation have been considered, leading to the conclusion that current methods of derivation of bond‐valence parameters are not satisfactory. A new method of derivation is introduced, the GRG (generalized reduced gradient) method, which leads to a mean weighted‐RMSD of 0.128 v.u. (6.1% per unit of charge) over the same sample of 90 multiple‐coordination ions. The evaluation of 19 two‐parameter equations and 7 three‐parameter equations to model the bond‐valence–bond‐length relation indicates that: (1) many equations can adequately describe the relation; (2) a plateau has been reached in the fit for two‐parameter equations; (3) the equation of Brown & Altermatt (1985) is sufficiently good that use of any of the other equations tested is not warranted. Improved bond‐valence parameters have been derived for 135 ions for the equation of Brown & Altermatt (1985) in terms of both the cation and anion bond‐valence sums using the GRG method and our complete data set.
We show that the Fu–Kane–Mele invariant of the 2d time-reversal invariant crystalline insulators is equal to the properly normalized Wess–Zumino action of the so-called sewing-matrix field defined on ...the Brillouin torus. Applied to 3d, the result permits a direct proof of the known relation between the strong Fu–Kane–Mele invariant and the Chern–Simons action of the non-Abelian Berry connection on the bundle of valence states.
A computer program, 3DBVSMAPPER, was developed to generate bond‐valence sum maps and bond‐valence energy landscapes with minimal user intervention. The program is designed to calculate the spatial ...distributions of bond‐valence values on three‐dimensional grids, and to identify infinitely connected isosurfaces in these spatial distributions for a given bond‐valence mismatch or energy threshold and extract their volume and surface area characteristics. It is implemented in the Perl scripting language embedded in Accelrys Materials Studio and has the capacity to process automatically an unlimited number of materials using crystallographic information files as input.
Since their introduction in 1929, Pauling's five rules have been used by scientists from many disciplines to rationalize and predict stable arrangements of atoms and coordination polyhedra in ...crystalline solids; amorphous materials such as silicate glasses and melts; nanomaterials, poorly crystalline solids; aqueous cation and anion complexes; and sorption complexes at mineral-aqueous solution interfaces. The predictive power of these simple yet powerful rules was challenged recently by George et al. (2020), who performed a statistical analysis of the performance of Pauling's five rules for about 5000 oxide crystal structures. They concluded that only 13% of the oxides satisfy the last four rules simultaneously and that the second rule has the most exceptions. They also found that Pauling's first rule is satisfied for only 66% of the coordination environments tested and concluded that no simple rule linking ionic radius to coordination environment will be predictive due to the variable quality of univalent radii. We address these concerns and discuss quantum mechanical calculations that complement Pauling's rules, particularly his first (radius sum and radius ratio rule) and second (electrostatic valence rule) rules. We also present a more realistic view of the bonded radii of atoms, derived by determining the local minimum in the electron density distribution measured along trajectories between bonded atoms known as bond paths, i.e., the bond critical point (rc). Electron density at the bond critical point is a quantum mechanical observable that correlates well with Pauling bond strength. Moreover, a metal atom in a polyhedron has as many bonded radii as it has bonded interactions, resulting in metal and O atoms that may not be spherical. O atoms, for example, are not spherical in many oxide-based crystal structures. Instead, the electron density of a bonded oxygen is often highly distorted or polarized, with its bonded radius decreasing systematically from ∼1.38 Å when bonded to highly electropositive atoms like sodium to 0.64 Å when bonded to highly electronegative atoms like nitrogen. Bonded radii determined for metal atoms match the Shannon (1976) radii for more electropositive atoms, but the match decreases systematically as the electronegativities of the M atoms increase. As a result, significant departures from the radius ratio rule in the analysis by George et al. (2020) is not surprising. We offer a modified, more fundamental version of Pauling's first rule and demonstrate that the second rule has a one-to-one connection between the electron density accumulated between the bonded atoms at the bond critical point and the Pauling bond strength of the bonded interaction. Pauling's second rule implicitly assumes that bond strength is invariant with bond length for a given pair of bonded atoms. Many studies have since shown that this is not the case, and Brown and Shannon (1973) developed an equation and a set of parameters to describe the relation between bond length and bond strength, now redefined as bond valence to avoid confusion with Pauling bond-strength. Brown (1980) used the valence-sum rule, together with the path rule and the valence-matching principle, as the three axioms of bond-valence theory (BVT), a powerful method for understanding many otherwise elusive aspects of crystals and also their participation in dynamic processes. We show how a priori bond-valence calculations can predict unstrained bond-lengths and how bond-valence mapping can locate low-Z atoms in a crystal structure (e.g., Li) or examine possible diffusion pathways for atoms through crystal structures. In addition, we briefly discuss Pauling's third, fourth, and fifth rules, the first two of which concern the sharing of polyhedron elements (edges and faces) and the common instability associated with structures in which a polyhedron shares an edge or face with another polyhedron and contains high-valence cations. The olivine α-(MgxFe1-x)2SiO4 crystal structure is used to illustrate the distortions from hexagonal close-packing of O atoms caused by metal-metal repulsion across shared polyhedron edges. We conclude by discussing several applications of BVT to Earth materials, including the use of BVT to: (1) locate H+ ions in crystal structures, including the location of protons in the crystal structures of nominally anhydrous minerals in Earth's mantle; (2) determine how strongly bonded (usually anionic) structural units interact with weakly bonded (usually cationic) interstitial complexes in complex uranyl-oxide and uranyl-oxysalt minerals using the valence-matching principle; (3) calculate Lewis acid strengths of cations and Lewis base strengths of anions; (4) determine how (H2O) groups can function as bond-valence transformers by dividing one bond into two bonds of half the bond valence; (5) help characterize products of sorption reactions of aqueous cations (e.g., Co2+ and Pb2+) and oxyanions e.g., selenate (Se6+O4)2- and selenite (Se4+O3)2- at mineral-aqueous solution interfaces and the important role of protons in these reactions; and (6) help characterize the local coordination environments of highly charged cations (e.g., Zr4+, Ti4+, U4+, U5+, and U6+) in silicate glasses and melts.
This graduate level text presents the first comprehensive overview of modern chemical valency and bonding theory, written by internationally recognised experts in the field. The authors build on the ...foundation of Lewis- and Pauling-like localized structural and hybridization concepts to present a book that is directly based on current ab-initio computational technology. The presentation is highly visual and intuitive throughout, based on the recognizable and transferable graphical forms of natural bond orbitals (NBOs) and their spatial overlaps in the molecular environment. The book shows applications to a broad range of molecular and supramolecular species of organic, inorganic and bioorganic interest. Hundreds of orbital illustrations help to convey the essence of modern NBO concepts for those with no extensive background in the mathematical machinery of the Schrödinger equation. This book will appeal to those studying chemical bonding in relation to chemistry, chemical engineering, biochemistry and physics.
Abstract
Electrochemical water splitting is a common way to produce hydrogen gas, but the sluggish kinetics of the oxygen evolution reaction (OER) significantly limits the overall energy conversion ...efficiency of water splitting. In this work, a highly active and stable, meso–macro hierarchical porous Ni
3
S
4
architecture, enriched in Ni
3+
is designed as an advanced electrocatalyst for OER. The obtained Ni
3
S
4
architectures exhibit a relatively low overpotential of 257 mV at 10 mA cm
−2
and 300 mV at 50 mA cm
−2
. Additionally, this Ni
3
S
4
catalyst has excellent long‐term stability (no degradation after 300 h at 50 mA cm
−2
). The outstanding OER performance is due to the high concentration of Ni
3+
and the meso–macro hierarchical porous structure. The presence of Ni
3+
enhances the chemisorption of OH
−
, which facilitates electron transfer to the surface during OER. The hierarchical porosity increases the number of exposed active sites, and facilitates mass transport. A water‐splitting electrolyzer using the prepared Ni
3
S
4
as the anode catalyst and Pt/C as the cathode catalyst achieves a low cell voltage of 1.51 V at 10 mA cm
−2
. Therefore, this work provides a new strategy for the rational design of highly active OER electrocatalysts with high valence Ni
3+
and hierarchical porous architectures.
The reaction of MnCl
2
·4H
2
O, H
8
L (2,2′-bis-
p
-
t
Bu-calix4arene) and NEt
3
in a dmf/MeOH solvent mixture results in the formation of a mixed valent decametallic cluster of formula Mn
II
6
Mn
...III
4
(L)
2
(μ
3
-OH)
4
(μ-OH)
4
(MeOH)
4
(dmf)
4
(MeCN)
2
·MeCN (
3
). Complex
3
crystallises in the monoclinic space group
P
2
1
/
n
with the asymmetric unit comprising half of the compound. Structure solution reveals that the bis-calix4arene ligands are arranged such that one TBC4 moiety in each has undergone inversion in order to accommodate a Mn
III
4
Mn
II
6
metallic skeleton that describes three vertex-sharing Mn
III
2
Mn
II
2
butterflies. The structure is closely related to the species Mn
III
6
Mn
II
4
(L)
2
(μ
3
-O)
2
(μ
3
-OH)
2
(μ-OMe)
4
(H
2
O)
4
(dmf)
8
·4dmf (
4
), the major difference being the oxidation level of the Mn ions in the core of the compound. DFT calculations on the full structures reveal that replacing the Mn
III
ions in
4
for Mn
II
ions in
3
results in a significant decrease in the magnitude of some antiferromagnetic exchange contributions, a switch from ferromagnetic to antiferromagnetic in others, and the loss of significant spin frustration.
Isolation of structurally related Mn
III
4
Mn
II
6
and Mn
III
6
Mn
II
4
clusters using the 2,2′-bis-
p
-
t
Bu-calix4arene ligand framework reveals significant differences in magnetic exchange interactions and spin frustration effects.
Display omitted
•Nitrogenase-inspired MIL-53(FeII/FeIII) is first synthesized for N2 photo fixation.•Mixed-valence FeII/FeIII clusters mimic the active center in nitrogenase.•FeII are in-situ formed ...by ethylene glycol reductant in solvothermal process.•FeII/FeIII ratio is vital to coordinate catalytic activity and framework stability.•MIL-53(FeII/FeIII) stably yields 306 μmol h−1 g−1 NH3 under visible light.
Biological nitrogenases exhibit superior nitrogen fixation efficiency owing to their unique multi-iron metallocluster (Fe2+3Fe3+4M3+, M = Mo, V, Fe) coordinated by organic polypeptide. Herein, we design a kind of metal organic framework (MOF) photocatalyst, MIL-53(FeII/FeIII) (MIL = Material from Institute Lavoisier), in which the FeII and FeIII constitute the mixed-valence metalloclusters to mimic the Fe2+ active sites and high-valence metal ions in nitrogenases, respectively. Both the FeII and FeIII are coordinated by organic ligands (terephthalic acid), which afford the electron transfer chains as well as the support of monodispersed FeII active sites. The FeIII in MIL-53(FeII/FeIII) is partly in-situ reduced into FeII by ethylene glycol (EG) via one-step solvothermal method, and the FeII/FeIII ratio is regulated from 0.18:1 to 1.21:1 by varying the EG content. Our results show that the FeII/FeIII ratio can significantly affect the photocatalytic activity and structure stability, and MIL-53(FeII/FeIII)-1 with optimal FeII/FeIII ratio (1.06:1) achieves the highest ammonia evolution rate up to 306 μmol h−1 g−1, nearly 10-fold higher than that of other framework-based materials, while remaining stable after 24 h irradiation. Such nitrogenase-like design in MIL-53(FeII/FeIII) endows the efficient electron transfer, exposed active sites, and in particular rational synergy between the catalytic function and non-catalytic function. This work may open a new avenue to the rational design of nitrogen fixation photocatalysts based on framework materials.
High‐valence metal‐doped multimetal (oxy)hydroxides outperform noble metal electrocatalysts for the oxygen evolution reaction (OER) owing to the modified energetics between 3d metals and high‐valence ...dopants. However, the rational design of sufficient and subtle modulators is still challenging. With a multimetal layered double hydroxide (LDH) as the OER catalyst, this study introduces a series of operando high‐valence dopants (Cr, Ru, Ce, and V), which can restrict the 3+ valence states in the LDH template to prevent phase separation and operando transfer to the >3+ valence states for sufficient electronic interaction during the OER process. Through density functional theory simulations, ultrathin Cr‐doped NiFe (NiFeCr) LDH is synthesized with strong electronic interaction between Cr dopants and NiFe bimetallic sites, evidenced by X‐ray absorption spectroscopy. The resulting NiFeCr‐LDH catalyzes the OER with ultralow overpotentials of 189 and 284 mV, obtaining current densities of 10 and 1000 mA cm–2, respectively. Further, a NiFeCr‐LDH anode is coupled in the anion exchange membrane electrolyzers to promote alkaline water splitting and CO2‐to‐CO electrolysis, which achieves low full cell voltages at high current densities.
Guided by theoretical simulations, ultrathin Cr‐doped NiFe layered double hydroxide (LDH) is synthesized. The resulting NiFeCr‐LDH motivates the oxygen evolution reaction with ultralow overpotentials of 189 and 284 mV to obtain current densities of 10 and 1000 mA cm−2, respectively, and achieves low full‐cell voltages at high current densities for hydrogen production and CO2 electroreduction in anion exchange membrane electrolyzers.
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