Electron Counting Rule Research Articles

Intermediate Yb valence in the Zintl phases Yb14MSb11(M=Zn,Mn,Mg) : XANES, magnetism, and heat capacity

${\mathrm{Yb}}_{14}\mathrm{Mn}{\mathrm{Sb}}_{11}$ is a magnetic Zintl compound as well as being one of the best high temperature $p$-type thermoelectric materials. According to the Zintl formalism, which defines intermetallic phases where cations and anions are valence satisfied, this structure type is nominally made up of 14 ${\mathrm{Yb}}^{2+}$, 1 ${\mathrm{MnSb}}_{4}^{9\ensuremath{-}}$, 1 ${\mathrm{Sb}}_{3}^{7\ensuremath{-}}$, and 4 ${\mathrm{Sb}}^{3\ensuremath{-}}$ atoms. When Mn is replaced by Mg or Zn, the Zintl defined motifs become 13 ${\mathrm{Yb}}^{2+}$, 1 ${\mathrm{Yb}}^{3+}$, 1 (Mg, Zn)${\mathrm{Sb}}_{4}^{10\ensuremath{-}}$, 1 ${\mathrm{Sb}}_{3}^{7\ensuremath{-}}$, and 4 ${\mathrm{Sb}}^{3\ensuremath{-}}$. The predicted existence of ${\mathrm{Yb}}^{3+}$ based on simple electron counting rules of the Zintl formalism calls the Yb valence of these compounds into question. X-ray absorption near-edge structure, magnetic susceptibility, and specific heat measurements on single crystals of the three analogs show signatures of intermediate valence Yb behavior and in particular, reveal the heavy fermion nature of ${\mathrm{Yb}}_{14}{\mathrm{MgSb}}_{11}$. In these isostructural compounds, Yb can exhibit a variety of electronic configurations from intermediate ($M=\mathrm{Zn}$), mostly 2+ ($M=\mathrm{Mn}$), to 3+ ($M=\mathrm{Mg}$). In all cases, there is a small amount of intermediate valency at the lowest temperatures. The amount of intermediate valency is constant for $M=\mathrm{Mn}$, Mg and temperature dependent for $M=\mathrm{Zn}$. The evolution of the Yb valence correlated to the transport properties of these phases is highlighted. The presence of Yb in this structure type allows for fine tuning of the carrier concentration and thereby the possibility of optimized thermoelectric properties along with unique magnetic phenomena.

Observable but Not Isolable: The RhAu24 (PET)181+ Nanocluster.

The synthesis and characterization of RhAu24 (PET)18 (PET = 2-phenylethanethiol) is described. The cluster is cosynthesized with Au25 (PET)18 and rhodium thiolates in a coreduction of RhCl3 , HAuCl4 , and PET. Rapid decomposition of RhAu24 (PET)18 occurs when purified from the other reaction products, precluding the study of isolated cluster. Mixtures containing RhAu24 (PET)18 , Au25 (PET)18 , and rhodium thiolates are therefore characterized. Mass spectrometry, X-ray photoelectron spectroscopy, and chromatography methods suggest a combination of charge-charge and metallophilic interactions among Au25 (PET)181- , rhodium thiolates and RhAu24 (PET)18 resulting in stabilization of RhAu24 (PET)18 . The charge of RhAu24 (PET)18 is assigned as 1+ on the basis of its stoichiometric 1:1 presence with anionic Au25 (PET)18 , and its stability is contextualized within the superatom electron counting rules. This analysis concludes that the Rh atom absorbs one superatomic electron to close its d-shell, giving RhAu24 (PET)181+ a superatomic electron configuration of 1S2 1P4 . Overall, an updated framework for rationalizing open d-shell heterometal dopant electronics in thiolated gold nanoclusters emerges.

Multiple robust Dirac states in hexagonal lattice induced by p−d electron-counting rule and bilayer stacking

In this paper, we predict two-dimensional transition metal boride $\mathrm{Ti}{\mathrm{B}}_{2}{\mathrm{C}}_{2}$ and $\mathrm{Hf}{\mathrm{B}}_{2}{\mathrm{C}}_{2}$ nanosheets, which exhibit favorable mechanical and thermal properties. Young's moduli of $\mathrm{Ti}{\mathrm{B}}_{2}{\mathrm{C}}_{2}$ and $\mathrm{Hf}{\mathrm{B}}_{2}{\mathrm{C}}_{2}$ are 137.8 and 128.9 N/m, respectively. Both nanosheets could sustain up to 500 K based on our ab initio molecular dynamics results. In addition, both nanosheets are semimetallic, exhibiting 12 Dirac cones in the first Brillouin zone, six pairs of which form compensated electron-hole pockets. Under different types of external strains, both $\mathrm{Ti}{\mathrm{B}}_{2}{\mathrm{C}}_{2}$ and $\mathrm{Hf}{\mathrm{B}}_{2}{\mathrm{C}}_{2}$ are robust, and the Dirac cones could be tuned to be anisotropic. We propose that the multiple Dirac cones are induced by a combination of the $p\ensuremath{-}d$ electron-counting rule and bilayer stacking; to verify our opinion, we also predicted and proved that $T{\mathrm{B}}_{2}{\mathrm{Si}}_{2}$ ($T$ = Ti, Zr, Hf) are mechanical stable two-dimensional nanosheets with multiple Dirac cones based on phonon and electronic band structure calculations.

Band alignment at β -Ga2O3/III-N (III = Al, Ga) interfaces through hybrid functional calculations

The band alignment and the chemical bonding at the β-Ga2O3/AlN and β-Ga2O3/GaN interfaces are studied through hybrid functional calculations. We construct realistic slab models with III–O (III = Al, Ga) bonds dominating the chemical bonding at both interfaces. The epitaxial relationships between β-Ga2O3 and wurtzite AlN and GaN determined from experiments are adopted in our slab models. These models satisfy electron counting rules, and all the dangling bonds are saturated at the interfaces. β-Ga2O3 is found to form type II heterojunctions with both wurtzite AlN and GaN. For the interfaces with AlN and GaN substrates, the calculated valence band offsets are 0.74 and 0.90 eV, respectively. These are in good agreement with the experimental values. The obtained band alignments are useful for designing optical and electronic devices based on β-Ga2O3 and group III nitrides.

On the 13C‐NMR chemical shift anisotropy patterns and aromatic character in strained fullerenes: Computational analysis of D6h/D2d‐C36 fullerene

AbstractThe NMR characterization of small C36 hollow fullerene exposes a stable cage with structural features based on its strained curved π‐surface in a D6h‐symmetry. Our results indicate that planar‐like aromatic properties of the D6h‐C36 isomer decrease to a nonaromatic cage for D2d‐C36 after Stone‐Wales transformation of an equatorial [6.6] bond. This is given by the decrease of conjugation in the strained π‐surface after Stone‐Wales transformation. Calculated nuclear shielding shows that the main shielding component is always oriented perpendicularly to the cage π‐surface despite the larger curvature degree, as a result of the sp2 character of carbon atoms, resembling C60. Moreover, the D6h‐ and D2d‐C36 cages differ in their charge distribution properties, leading to charge accumulation in the strained cap of the former that leads to a polymerization‐prone cage, which contrasts with that expected for the D2d structure. Hence, structural rearrangements of these non‐Hirsch aromatic fullerenes show that their inherent global behavior requires considering the structural features besides electron counting rules.

Endohedrally Doped Cage Clusters.

The discovery of carbon fullerene cages and their solids opened a new avenue to build materials from stable cage clusters as "artificial atoms" or "superatoms" instead of atoms. However, cage clusters of other elements are generally not stable. In 2001, ab initio calculations showed that endohedral doping of Zr and Ti atoms leads to highly stable Zr@Si16 fullerene and Ti@Si16 Frank-Kasper polyhedral clusters with large HOMO-LUMO gaps. In 2002, Zr@Ge16 was shown to form a Frank-Kasper polyhedron, suggesting the possibility of designing novel clusters by tuning endohedral and cage atoms. These results were subsequently confirmed from experiments. In the past nearly two decades, many experimental and theoretical studies have been carried out on different clusters, and many very stable cage clusters with possibly high abundance have been found by endohedral doping. Indeed in 2017, Ta@Si16 and Ti@Si16 cage clusters have been synthesized in bulk quantity of about 100 mg using a dry-chemistry method, giving rise to a new hope of developing cluster-based materials in macroscopic quantity besides the well-known C60 fullerene solid. Also, wet-chemistry methods have been used to synthesize endohedrally doped clusters as well as ligated clusters and their solids, which auger well for the development of novel nanostructured materials using atomically precise clusters with unique properties. In this comprehensive review, we present results of many such developments in this fast-growing field including (i) endohedrally doped Al, Ga, and In clusters, (ii) small endohedral carbon fullerene cages with ≤ 28 carbon atoms, (iii) metal doped boron cages, (iv) endohedrally doped cages of group 14 elements (Si, Ge, Sn, and Pb), (v) coinage metal (Cu, Ag, Au) cages doped with a transition metal atom as well as their ligated clusters and crystals, (vi) endohedrally doped cages of compound semiconductors, and (vii) multilayer Matryoshka cages and core-shell structures. In a large number of cases, we have performed ab initio calculations to present updated results of the most stable atomic structures and fundamental electronic properties of the endohedrally doped cage clusters. We discuss electronic, magnetic, optical, and catalytic properties in order to shed light on their potential applications. The stability of the doped cage clusters has been correlated to the concept of filling the electronic shells for superatoms such as within a spherical potential model and also using various electron counting rules including Wade-Mingos rules, systems with 18 and 32 electrons, and the spherical aromaticity rule. We also discuss cluster-cluster interaction in cluster dimers and assemblies of some of the promising doped cage clusters in different dimensions. Finally, we give a perspective of this field with a bright future.

An electron-counting rule to determine the interlayer magnetic coupling of the van der Waals materials

In layered magnetic materials, the magnetic coupling between neighboring van der Waals layers is challenging to understand and anticipate, although the exchange interaction inside a layer can be well rationalized for example by the superexchange mechanism. In this work, we elucidate the interlayer exchange mechanism and propose an electron-counting rule to determine the interlayer magnetic order between van der Waals layers, based on counting the d-orbital occupation (dn, where n is the number of d-electrons at the magnetic cation). With this rule, we classify magnetic monolayers into two groups, type-I () and type-II (n ≥ 5), and derive three types of interlayer magnetic coupling for both insulators and metals. The coupling between two type-II layers prefers the antiferromagnetic (AFM) order, while type-I and type-II interface favors the ferromagnetic (FM) way. However, for two type-I layers, they display a competition between FM and AFM orders and even lead to the stacking dependent magnetism. Additionally, metallic layers can also be incorporated into this rule with a minor correction from the free carrier hopping. Therefore, this rule provides a simple guidance to understand the interlayer exchange and further design van der Waals junctions with desired magnetic orders.

Polyhedral [M2B5] Metallaborane Clusters and Derivatives: An Overview of Their Structural Features and Chemical Bonding.

A large number of metallaborane clusters and their derivatives with various structural arrangements are known. Among them, M2B5 clusters and derivatives constitute a significant class. Transition metals present in these species span from group 4 to group 7. Their structure can vary from oblatonido, oblatoarachno, to arachno type open structures. Many of these clusters appear to be hypoelectronic and are often considered as ‘rule breakers’ with respect to the classical Wade–Mingos electron counting rules. This is due to their unique highly oblate (flattened) deltahedral structures featuring a cross-cluster M−M interaction. Many theoretical calculations were performed to elucidate their electronic structure and chemical bonding properties. In this review, the synthesis, structure, and electronic aspects of the transition metal M2B5 clusters known in the literature are discussed. The chosen examples illustrate how, in synergy with experiments, computational results can provide additional valuable information to better understand the electronic properties and electronic requirements which govern their architecture and thermodynamic stability.

Family of Mo4Ga21-Based Superconductors

Endohedral cluster superconductors are an emerging field, where simple electron counting rules govern the phase stability and transition temperature. Nontrivial microscopic properties of the superc...

Superatomic Ligand-Field Splitting in Ligated Gold Nanoclusters.

Gold nanoclusters are attractive because of their electronic and optical properties. Many theoretical models have been proposed to explain their electronic structures through an electron-counting approach. However, subtle features may not be well explained by electron-counting rules. In this work, we have discovered a unique example of ligand-controlled skeletal bonding in two recently reported gold nanoclusters with very similar compositions and geometries. We have shown that the superatomic orbitals of the common kernel of the two clusters undergo different ligand-field splitting because of the different ligand-field strengths in the two clusters. Such a difference is clearly revealed by constructing the Jellium orbitals via an orbital alignment process, and a subsequent localization of the Jellium orbitals allows us to obtain localized bonding models. Finally, on the basis of localized bonding models, we predict the existence of a ligated gold cluster with a [Au32]4+ kernel.

Tuning the high-κ oxide (HfO2, ZrO2)/4H-SiC interface properties with a SiO2 interlayer for power device applications

SiC based power devices are promising for the next generation energy-efficient power converters. But its device performance is always largely limited by the tradition thermal SiO2 gate dielectric. The high-κ dielectric gate oxides have been widely used in Si and III-V devices. However, high quality dielectric layer using high-κ oxide for SiC power device is still lacking sufficient theoretical investigation. In this paper, the properties of XO2/4H-SiC (X = Hf or Zr) interfaces with a SiO2 interlayer are systematically studied by density-functional supercell calculations. Reliable interface atomic structures without any gap states have been built according to the electron counting rule. Based on the models, the electronic structure of each interface is obtained by hybrid functional. The interfacial characteristics including the averaged potential and charge transfer analysis are calculated in detail. The calculated band edge line-ups are comparable with the experimental reports. In term of the band alignment, HfO2 and ZrO2 directly bonding to SiC are not suitable dielectric materials for SiC based power device, due to the relatively smaller conduction band offsets (CBO). While introducing the SiO2 interlayer can effectively tune the interface properties, especially the band alignment. With HfO2(ZrO2)/SiO2 stack as the dielectric layer for 4H-SiC, the interface has the large CBO (>1 eV) to efficaciously confine the channel carriers, indicating that the HfO2(ZrO2)/SiO2/4H-SiC stack is the promising strategy for SiC based power device applications.

Structural stability and electronic properties of Sr induced (5×4) reconstruction on Si(111) surface

Honeycomb-chain-channel (HCC) and π-bond Seiwatz chain (SC) are the well-known reconstructions induced by alkaline earth metal on Si(111) surface. Here we identify by ab initio calculations a stable intermediate phase of Sr/Si(111)-(5×4) HCC+SC. This new reconstruction satisfies the electron counting rule with the Sr coverage of 3/10 monolayer. In each (5×4) surface unit cell, six Sr atoms are distributed as evenly as possible in the two channels. One of the channels contains two Sr atoms on the top site T4 and one Sr atom on the hollow site H3, while another channel contains two Sr atoms on site H3 and one on site T4. Electronic band structures and band-decomposed charge density distributions show that there are seven occupied surface states (S1–S5, Σ1 and Σ2) and two unoccupied surface states (S6 and S7) near the Fermi level. Moreover, we find that this new (5×4) surface structure is a semiconductor with a surface band gap of 0.62 eV, determined by the S2 and S6 surface states in honeycomb Si chains.

Observation of Möbius Aromatic Planar Metallaborocycles.

Möbius aromaticity was developed for twisted annulenes with electron counting rules opposite to those of Hückel aromaticity. The introduction of transition metals makes it possible for planar cyclic systems to exhibit Möbius aromaticity. Here we report the first planar monocyclic metallaboron systems with Möbius aromaticity. The structures and bonding of two rhenium-boride clusters are studied by high-resolution photoelectron imaging and ab initio calculations. The ReB3- cluster is shown to have a near-pyramidal structure, while ReB4- is found to be a planar pentagonal ring. Chemical bonding analyses show that both ReB4- and ReB4 possess four delocalized π-electrons, including two π-electrons in an orbital of Möbius topology. NICS calculations reveal strong aromatic characters in ReB4- and ReB4, consistent with the 4n electron counting rule for Möbius aromaticity.

Strengthening boron carbide through lithium dopant

AbstractThe high strength of boron carbide (B4C) is essential in its engineering applications such as wear‐resistance and body armors. Here, by employing density functional theory simulations, we demonstrated that the strength of B4C can be enhanced by doping lithium to boron‐rich boron carbide (B13C2) to form r‐LiB13C2. The bonding analysis on r‐LiB13C2 indicates that the electron counting rule (or Wade's rule) is satisfied in r‐LiB13C2 whose formula can be written as r‐Li+(B12)2‐(CB+C). The shear deformation on r‐LiB13C2 indicates that its ideal shear strength is larger than that of B4C because of the existing of Li dopant. The failure process of r‐LiB13C2 under ideal shear deformation initiates from breaking the icosahedral‐icosahedral B‐B bonds. Then these B atoms react with the middle B in the C‐B‐C chain, resulting in the disintegration of icosahedral clusters and brittle failure. More interesting, the nanotwinned r‐LiB13C2 is even stronger than r‐LiB13C2 because of the directional nature of covalent bonding at the twin boundaries. This suggests that the nanotwinned r‐LiB13C2 has a significant enhanced strength compared to B4C. Our simulation results illustrate the deformation mechanism of Li‐doped boron carbide and its nanotwinned microstructure. We proposed to improve the strength of boron carbide by doping Li into B13C2 and increasing its twin densities.

Water adsorption behaviors of high index polar surfaces in ZnO

The density functional theory method study is performed to investigate the adsorption structures and mechanisms of water adsorption on ZnO high index polar surfaces. It is found that compared to the nonpolar 101¯0 and (0001) surfaces, high index polar surfaces present higher ability to adsorb water molecules. The dissociative adsorption configurations are energetically more favorable than the molecular adsorption ones, i.e., the adsorbed water molecule would like to decompose into a hydroxyl group and a H atom on high index polar surfaces. The structural calculations and electronic properties suggest that the electron counting rule plays an important role in determining the energetically favorable configurations. This detailed and systematic work not only improves our understanding of the water adsorption on high index polar surfaces, but also it may ultimately aid the applications of nanostructures coated by high index polar surfaces.

Rational Design of Stable Dianions and the Concept of Super-Chalcogens.

Super-atoms are homo/heteroatomic clusters that mimic the chemistry of atoms in the periodic table. While a considerable amount of research over the past three decades has revealed many super-atoms that mimic group I (alkali metals) and group 17 (halogens) elements, little effort has been made to identify super-atoms that mimic the chemistry of chalcogens, i.e., those belonging to group 16 elements. This is particularly important as super-chalcogens can form the building blocks of new materials, just as super-alkalis and super-halogens form a variety of super-salts with unique properties. Using first-principles calculations and various electron counting rules, some of which have been prevalent in chemistry for a century, we provide a route to the rational design of dianions that are stable in the gas phase. And unlike the group 16 atoms, these super-chalcogens can retain the second electron without spontaneous electron emission or fragmentation. A new class of super-chalcogenides with unique properties could be formed with these super-chalcogens as building blocks.

Atomic structure and band alignment at Al2O3/GaN, Sc2O3/GaN and La2O3/GaN interfaces: A first-principles study

The atomic structures, chemical bonding and band alignment at trivalent oxides X2O3 (where X = Al, Sc and La) and GaN interface are studied based on the density functional supercell calculations. The insulating interfaces with small roughness and a clean bandgap are built based on the electron counting rule. The results prove that GaO bonds dominate the interfacial chemical bonding for all the interfaces, and the calculated oxide/GaN band alignment consistent with the experimental values. All the oxides are proved to have the type-I band alignment with GaN with hybrid functional calculation. For the Al2O3 interface, the calculated valence band offset is 1.17 eV, while that for the Sc2O3 and La2O3 interface are 0.81 eV and 0.95 eV, respectively. The calculated conduction band offsets are all larger than 1 eV, and as large as 1.8 eV for the Al2O3 interface. The theoretically calculated band alignments indicate that the studied trivalent oxides Al2O3, Sc2O3 and La2O3 are all suitable gate insulators for GaN-based MOSFET applications.

Chemical bonding and band alignment at X2O3/GaN (X = Al, Sc) interfaces

The chemical bonding and the band alignment at Al2O3/GaN and Sc2O3/GaN interfaces are studied using density functional supercell calculations. Using bonding models based on the electron counting rule, we have created the insulating interfaces with a small roughness and a clean bandgap. Ga-O bonds dominate the interfacial chemical bonding at both interfaces. The calculated band alignment agrees with the experimental values. For the Al2O3 interface, the calculated valence band offset is 1.17 eV using hybrid functionals, while that for the Sc2O3 interface is 0.81 eV. The conduction band offsets for both are larger than 1 eV, and is as large as ∼2 eV for the Al2O3 interface. The calculated band alignments indicate that Al2O3 and Sc2O3 are both suitable insulators for GaN-based MOSFET applications.

First-principles modeling of GaN(0001)/water interface: Effect of surface charging.

The accumulation properties of photogenerated carriers at the semiconductor surface determine the performance of photoelectrodes. However, to the best of our knowledge, there are no computational studies that methodically examine the effect of "surface charging" on photocatalytic activities. In this work, the effect of excess carriers at the semiconductor surface on the geometric and electronic structures of the semiconductor/electrolyte interface is studied systematically with the aid of first-principles calculations. We found that the number of water molecules that can be dissociated follows the "extended" electron counting rule; the dissociation limit is smaller than that predicted by the standard electron counting rule (0.375 ML) by the number of excess holes at the interface. When the geometric structure of the GaN/water interface obeys the extended electron counting rule, the Ga-originated surface states are removed from the bandgap due to the excess holes and adsorbates, and correspondingly, the Fermi level becomes free from pinning. Clearly, the excess charge has a great impact on the interface structure and most likely on the chemical reactions. This study serves as a basis for further studies on the semiconductor/electrolyte interface under working conditions.

Templating Structural Progessions in Intermetallics: How Chemical Pressure Directs Helix Formation in the Nowotny Chimney Ladders.

In the structural diversity of intermetallic phases, hierarchies can be perceived relating complex structures to relatively simple parent structures. One example is the Nowotny Chimney Ladder (NCL) series, a family of transition metal-main group (T-E) compounds in which the T sublattices trace out helical channels populated by E-atom helices. A sequence of structures emerges from this arrangement because the spacing along the channels of the E atoms smoothly varies relative to that of the T framework, dictated largely by optimization of the valence-electron concentration. In this Communication, we show how this behavior is anticipated and explained by the Density Functional Theory-Chemical Pressure (DFT-CP) schemes of the NCLs. A CP analysis of the RuGa2 parent structure reveals CP quadrupoles on the Ga atoms (telltale signs of soft atomic motion) that arise from overly short Ru-Ga contacts along one axis and underutilized spaces in the perpendicular directions. In their placement and orientation, the CP quadrupoles highlight a helical path of facile movement for the Ga atoms that avoids further compression of the already strained Ru-Ga contacts. The E atoms of a series of NCLs (in their DFT-optimized geometries) are all found to lie along this helix, with the CP quadrupole character being a persistent feature. In this way, the T sublattice common to the NCLs encodes helical paths by which the E-atom spacing can be varied, creating a mechanism to accommodate electronically driven compositional changes. These results illustrate how CP schemes can be combined with electron-counting rules to create well-defined structural sequences, potentially guiding the discovery of new intermetallic phases.