Zintl Phase Research Articles

First-principles calculations to investigate the bulk, electronic, optical and thermoelectric properties of BaGe[formula omitted]As[formula omitted] and BaGe[formula omitted]P[formula omitted] alloys

The structural, elastic, electronic, and optical properties of BaGe2As2 and BaGe2P2 have been theoretically investigated, but their thermoelectric properties have not been reported. The current work aimed at conducting an exhaustive study on the bulk, electronic, and optical properties as well as the thermoelectric property of BaGe2As2 and BaGe2P2 zintl phase compounds. Density functional theory implemented in Quantum ESPRESSO code combined with other processing codes such as Thermo−pw and BoltzTrap were employed in this study. The lattice constants computed were found to agree well with the other theoretical and experimental results, demonstrating validity of the study. Both compounds are brittle, elastically anisotropic and mechanically as well thermodynamically stable. The materials in this investigation were discovered to be semiconductors with indirect band gaps of 0.73 eV and 1.14 eV for BaGe2As2 and BaGe2P2 respectively. Therefore, both materials are appropriate for use in the electronics sector, notably in temperature control applications. The PDOS analysis suggests that P and As in BaGe2P2 and BaGe2As2, respectively, dominate the conduction band, whereas Ge dominates the valence band in both cases. The results also show that BaGe2P2 out-performs BaGe2As2 in terms of optical absorption coefficient. Both BaGe2As2 and BaGe2P2 are excellent p-type thermoelectric materials but BaGe2P2 has a greater figure of merit than BaGe2As2, making it a potential thermoelectric material. Lastly, the figure of merit values determined in this study are considered approximations since the lattice thermal conductivities of complex BaGe2As2 and BaGe2P2 compounds were not computed due to limited computational resources.

Direct Covalent Functionalization of H-Terminated 2D Germanane with Thiolated Molecules: Passivation and Tuning of Optoelectronic Properties.

Covalent molecular functionalization allows the physicochemical properties of 2D materials to be precisely tuned and modulated on-demand. Nonetheless, research on the molecular functionalization of 2D monoelemental graphene-like materials─known as Xenes─remains scarce, being mainly restricted to a specific type of solid-state chemical reaction based on the topotactic transformation of bulkier Zintl phases. Herein, a robust and general chemical approach is reported for the direct functionalization of commercially available H-terminated 2D germanene (2D-GeH) with thiolated molecules (R-SH) via Ge-S bond formation. While the material characterization data provide direct experimental evidence of the Ge-S chemical bonding, density functional theory (DFT) calculations also predict its existence. Remarkably, the anchored thiolated molecules also favor the passivation of the 2D Xene against air oxidation, enlarging its benefits for real implementation. As a proof-of-principle, a redox-responsive molecular moiety such as 6-(ferrocenyl)hexanethiol (Fc6-SH) has been exploited to induce changes in the optoelectronic properties of the resulting 2D-GeFc6 heterostructure by simply modulating the external bias potential, making it possible to optically and electrically read out a molecular switch on 2D Xene via implanting molecular responsiveness. Remarkably, the ON/OFF ratio has been shown to be dependent on the distance between the redox-responsive Fc moiety and the 2D Xene surface through the alkyl chain length. Overall, the reported a-la-carte molecular engineering approach provides the basis toward the rapid development of stable 2D-GeR derivatives exhibiting molecule-programmable properties.

Transforming carbon dioxide into a methanol surrogate using modular transition metal-free Zintl ions

Although not the only greenhouse gas, CO2 is the poster child. Unsurprisingly, therefore, there is global interest across industrial and academic research in its removal and subsequent valorisation, including to methanol and its surrogates. Although difficult to study, the heterogenous pnictogens represent one important category of catalytic materials for these conversions; their high crustal abundance and low cost offers advantages in terms of sustainability. Here, Zintl clusters based on these elements are studied as homogenous atom-precise models in CO2 reduction. A family of group 13 functionalized pnictogen clusters with the general formula [(R2E)Pn7]2– (E = B, Al, In; Pn = P, As) is synthesized and their catalytic competency in the reduction of CO2 probed. Trends in both turnover numbers and frequencies are compared across this series, and [(iBu2Al)P7]2– found to be very high-performing and recyclable. Electronic structures across the series are compared using density functional theory to provide mechanistic insights.

Open Sn Framework Structure Hosting Bi Guest atoms-Synthesis, Crystal and Electronic Structure of Na13Sn26Bi.

The large variety of structures of Zintl phases are generally well understood since their anionic substructures follow bonding rules according to the valence concept. But there are also exceptions, which make the semiconductors especially interesting in terms of structure-property relationships. Although several Na-Sn-Pnictides with a variety of structural motives are known, up to this point no ternary compound in the Na-Sn-Bi system has been described. In this paper we present the Zintl-phase Na13Sn25.73Bi1.27 comprising a complex, open-framework structure of Sn atoms, with one mixed Sn/Bi site, hosting Na atoms. An additional Bi atom is loosely connected with only weak contacts to the framework filling a larger cavity within the network. According to band structure calculations of the two ordered variants with either full occupation of the mixed site with Sn or Bi, resulting in Na13Sn26Bi and Na13Sn24Bi3, respectively, both compounds are semiconductors with band gaps of 0.5 eV. A comparison of the band structures with the structurally related binary compounds Na5Sn13 and Na7Sn12 shows that only the perfectly charge balanced Na7Sn12 is a semiconductor whereas Na5Sn13 is metallic. The rather specific electronic situation in the ternary compound is traced back to the loosely bound Bi atom, which acts as a guest atom according to Bix@Na13Sn26-yBiy, with x=1 and y=0.27, capable to change its oxidation state and thus to uptake additional electrons allowing the system to be a semiconductor. Therefore, Na13Sn25.73Bi1.27 can be understood as a rare example of an open framework structure of Sn atoms comprising Bi atoms in the cavities.

Synthesis, Structure and Catalytic Properties of Hyp3[Ge9Rh]PPh3

In single‐site homogeneous catalysts (SSHoCs) transition metal atoms are incorporated in the surface of a small homoatomic atom cluster. Within this concept the main group element cluster is considered as innocent support material, while the catalysis itself is realised at the transition metal atom. In the case of [Ge9] clusters, both transition metal atoms and the Ge atoms have low oxidation state. Thus improving the synthesis towards transition metal decorated Zintl cluster has become important in the last years, and the catalytic activity of these clusters is of high interest. An optimised one‐step synthetic protocol for Hyp3[Ge9Rh]PPh3 is presented. The product is characterised by NMR spectroscopy, LIFDI/MS and single crystal structure determination. The Rh atom is incorporated in the clusters surface and bridges a deltahedral cluster face, whereby one of the triangular edge opens forming an almost planar face of three Ge and one Rh atom. PPh3 ligand dissociation as well as the catalytic activity in the isomerisation of 1‐hexene and allylbenzene as well as the hydrogenation of those substrates with hydrogen is investigated.

First principle study of electronic, optoelectronic, and thermoelectric properties of zintl phase alloys BaAg2X2 (X = S, Se, Te) for renewable energy

Novel Zintl phases exhibiting promising thermoelectric properties have garnered considerable traction, largely attributed to the accuracy of computational estimates. In the present investigation, the density functional theory-based WIEN2k code is employed to analyze the structural, optoelectronic, and transport behavior of the BaAg2X2 (X = S, Se, Te) Zintl phase. All these compositions belong to the stable trigonal phase with nominal expansion in the unit cell with the replacement of S with Se and Te. A negative value of enthalpy of formation of −2.30, −2.0, and −1.80 for BaAg2S2, BaAg2Se2, and BaAg2Te2, respectively, assures their thermodynamic stability. These compositions demonstrate dynamic stability, as evidenced by the nonexistence of negative (-ve) frequency values in their phonon spectra. Increasing the size of chalcogens enhances the spin-orbit coupling and reduces the bandgap value from 2.10 to 1.55 eV. The examination of optical response suggests that studied compositions display high absorption and low energy loss in the visible range, rendering them suitable for optoelectronic devices. The temperature-dependent transport behavior is computed using BoltzTrap code, and the RT value of power factor is recorded as 0.89 × 1011, 0.65 × 1011, and 0.54 × 1011 Wm− 1K− 2 for BaAg2X2 (X = S, Se, Te). A high power factor value at elevated temperatures indicates the promising efficacy of studied compositions in thermoelectric device applications.

β-Yb2CdSb2—A Complex Non-Centrosymmetric Zintl Polymorph

The ternary Zintl phase, Yb2CdSb2, was discovered to exist in two different polymorphic forms. In addition to the orthorhombic α-Yb2CdSb2 (space group Cmc21) known for its excellent thermoelectric properties, we present the synthesis and characterization of the crystal and electronic structure of its monoclinic variant, β-Yb2CdSb2. Structural characterization was performed with the single-crystal X-ray diffraction method. β-Yb2CdSb2 crystallizes in a monoclinic crystal system with the non-centrosymmetric space group Cm (Z = 33, a = 81.801(5) Å, b = 4.6186(3) Å, c = 12.6742(7) Å, β = 93.0610(10)°) and constitutes a new structure type. The complex crystal structure of β-Yb2CdSb2 contrasts with the previously studied β-Ca2CdPn2 (Pn = P, As, Sb) polymorphs, although it shares similar structural features. It consists of three different layers, made of corner-sharing [CdSb4] tetrahedra and stacked in the ABC sequence. The layers are interconnected via [CdSb3] trigonal planar units. Multiple Yb and Cd atomic sites exhibit partial occupancy, resulting in extensive structural disorder. Valence electron partitioning within the Zintl–Klemm formalism yields the formulation (Yb2+)1.98(Cd2+)1.01(Sb3−)2(h+)0.02, highlighting the nearly charge-balanced composition. Detailed electronic structure calculations reveal the closed band gap and presumably semimetallic nature of β-Yb2CdSb2 with the band structure features hinting at potential topological properties.

Structure prediction of stable sodium germanides at 0 and 10 GPa

In this paper we used random structure searching (AIRSS) to carry out a systematic search for crystalline Na-Ge materials at both 0 and 10 GPa. The high-throughput structural relaxations were accelerated using a machine-learned interatomic potential (MLIP) fit to density-functional theory (DFT) reference data, allowing ∼1.5 million structures to be relaxed. At ambient conditions we predict three new Zintl phases, Na3Ge2,Na2Ge, and Na9Ge4, to be stable and a number of Ge-rich layered structures to lie in close proximity to the convex hull. The known NaδGe34 clathrate and Na4Ge13 host-guest structures are found to be relatively stabilized at higher temperature by vibrational contributions to the free energy. Overall, the low-energy phases exhibit exceptional structural diversity, with the expected mixture of covalent and ionic bonding confirmed using the electron-localization function (ELF). The local Ge structural motifs present at each composition were determined using smooth overlap of atomic positions (SOAP) descriptors and the Ge-K edge was simulated for representatives of each motif, providing a direct link to experimental x-ray absorption spectroscopy (XAS). Two Ge-rich phases are predicted to be stable at 10 GPa; NaGe3 and NaGe2 have simple kagome and simple hexagonal Ge lattices respectively with Na contained in the pores. NaGe3 is isostructural with the MgB3 and MgSi3 family of kagome superconductors and remains dynamically stable at 0 GPa. Removing the Na from NaGe2 results in the hexagonal lonsdalite Ge allotrope, which has a direct band gap. Published by the American Physical Society 2024

Faster and Safer "In situ" Synthesis of Germanane and Silicane.

Germanane (GeH) and silicane (SiH), members of the Xanes family, have garnered significant attention as 2D materials due to their diverse properties, which hold promise for applications in electronics, optoelectronics, energy storage, and sensing. Typically, highly concentrated hydrochloric acid (HCl) or hydrofluoric acid (HF) is employed in the synthesis of these Xanes, but both routes are problematic due to slow kinetics and safety concerns, respectively. Here for the first time, a faster and safer method is demonstrated for Xanes synthesis that harnesses the generation of HF "in situ" using a solution of HCl and lithium fluoride (LiF) salt, overcoming the key challenges of the conventional methods. A variety of characterization techniques to establish a baseline is utilized for both Xanes and to provide a holistic knowledge regarding this method, the possible consequences of this approach, and the possibility of applying it to other layered Zintl phases. The novel synthesis protocol results in high-quality GeH and SiH with bandgaps (Eg) of 1.75 and 2.47eV respectively, highlighting their potential suitability for integration into semiconductor applications.

Low lattice thermal conductivity induced by rattling-like vibration in Zintl phase Na2CaCdSb2 compound with high ZT from two-channel model

Zintl phase compounds, characterized by the traits of a phonon-glass and electron-crystal, stand out as promising candidates for thermoelectric applications. This study delves into the thermoelectric properties of Zintl phase Na2CaCdSb2 compound through a synergy of first-principles calculations, machine learning interatomic potential approach based on the two-channel model, and high-throughput screening calculations. With an indirect bandgap of 1.02 eV, Na2CaCdSb2 compoundpossesses an high carrier mobility. The high valence band degeneracy and anisotropic band (light-heavy band) lead to a high power factor for the p-type Na2CaCdSb2 compound. The strong fourth-order anharmonicity of the rattling-like Na atom manifests the low lattice thermal conductivity on the basis of two-channel model. The loosely bonding Na atom displays random rotations and dynamically disordered orientations, leading to the weakly disordered nature of Na2CaCdSb2 compound. The unique crystal structure of Na2CaCdSb2 compound coupled with the abundance of diffusion-like phonons play a pivotal role in the phonon transport. Considering the low lattice thermal conductivity and high power factor with the framework of two-channel model, the n-type and p-type Na2CaCdSb2 compounds exhibit optimal figure-of-merits (ZT) of 1.0 and 2.0 at 600 K, showcasing excellent thermoelectric performance. Meanwhile, an optimal ZT of 2.3 is achieved for p-type Na2CaCdSb2 compound at the same temperature along the x-direction. Our present study not only provides fundamental insights into the thermal and electronic transport properties of Na2CaCdSb2 compound under the two-channel model in combination with the four-phonon scattering and multiple carrier scattering rates, but also rationalizes the high-order phonon interactions and thermal transport properties under two-channel model.

Effect of cations on the structural, optoelectronic, and thermoelectric properties of AMg2N2 (A = Yb, Sm, Eu) Zintl compounds; An ab-initio study

Zintl phases are prominent for their attribution to optical and thermoelectric meeds. AMg2N2 (A = Yb, Sm, Eu) compounds of the zintl family were investigated through first-principles studies for structural, electronic, optical, and thermoelectric properties. Potential functionals; PBE-GGA, TB-mBJ, and Hybrid (YS-PBE0) were used to study these compounds. The behavior of all compounds YbMg2N2, SmMg2N2, and EuMg2N2 was semiconducting with band gaps 3.75 eV, 2.22 eV, and 2.67 eV respectively through YS-PBE0. The density of states (DOS) study reveals that the leading role was offered by A-d orbitals to construct conduction bands and by A-f orbitals to form valence bands. The optical nature of these materials was studied from the optical parameters like; dielectric function ε(ω), refractive index n(ω), energy loss function L(ω), absorption coefficient α(ω), extension coefficient k(ω), reflectivity R(ω), and optical conductivity σ(ω). From this study, it is revealed that these samples are active in the visible and ultra-violet (UV) regions, due to which these materials are supposed to be suitable candidates for optoelectronic applications. Furthermore, the thermoelectric character of the titled compounds was scrutinized through the BoltzTraP2 code. The thermoelectric efficiency in the form of thermoelectric figure of merit(ZT) of AMg2N2 (A = Yb, Sm, Eu) compounds are achieved 1.17, 0.64, and 0.43 respectively at somehow high temperature 950 K. From ZT and optimized level of carriers’ concentrations, these materials are considered to be efficient thermoelectric.

Study of the fundamental physical characteristics of the Zintl phase K2BaCdSb2

The structural, elastic, thermodynamic, electronic, and thermoelectric characteristics of K2BaCdSb2 were investigated utilizing ab initio methods. The structural, elastic, and thermodynamic properties were calculated using the pseudopotential plane wave approach with the GGA-PBEsol exchange-correlation functional. The computed equilibrium structural characteristics closely match the available data. The anticipated elastic constants reveal that K2BaCdSb2 is mechanically stable, brittle, and exhibits significant elastic anisotropy. The full potential linearized augmented plane wave approach with the Tran-Blaha modified Becke-Johnson potential was used to determine the electronic structure of K2BaCdSb2.It is found that K2BaCdSb2 is a semiconductor with a Γ-Γ type direct bandgap of 0.85 eV. Bonding analysis shows the bond between Cd and Sb atoms within the [CdSb2]4− polyanion is of covalent nature and that between the K/Ba atom and the [CdSb2]4− polyanion is of ionic character. The thermoelectric characteristics of K2BaCdSb2 were analyzed at a temperature of 500 K for of charge-carrier concentrations from 1 × 1018 to 3 × 1020 cm−3.When the concentration of holes is 1.0 × 1020 cm−3, The power factor reaches a value of 17 × 1010 W m−1 K−2.s−1 for a hole concentration of 1.0 × 1020 cm−3. For the p-doped K2BaCdSb2 with a concentration of 1.0 × 1018cm−3, the electronic figure of merit is 0.95.

Ultralow Lattice Thermal Conductivity of Zintl‐Phase CaAgSb Induced by Interface and Superlattice Scattering

Zintl phases attract extensive attention due to the characteristic of “electron‐crystal, phonon glass”. In this work, an ultralow lattice thermal conductivity ≈0.59 W m−1 K−1 at 300 K and ≈0.3 W m−1 K−1 at 623 K is obtained in CaAgSb Zintl phase, which is much lower than that of other well‐known Zintl compounds. The origin of this ultralow lattice thermal conductivity is explored through first‐principles calculations and Cs‐corrected scanning transmission electron microscopy. Theoretical phonon calculations provide evidence for complex phonon characteristics such as avoided‐crossing effect and low‐frequency flat band that favor the low lattice thermal conductivity. Moreover, subsequent microstructure results reveal abundant structural defects created in the CaAgSb sample, including superlattice structure and interface structure, which further contribute to the ultralow lattice thermal conductivity.

First-principles study of optoelectronic and thermoelectric aspects of novel zintl phase SrAg2X2 (X = S, Se, Te) alloys for green energy applications

This work comprehensively investigates the solar energy harvesting and thermoelectric capabilities of innovative Zintl phase SrAg2X2 (X = S, Se, Te) alloys. Herein, the analysis of the structural, optoelectronic, and thermoelectric characteristics of Zintl SrAg2X2 (X = S, Se, Te) compounds has been conducted utilizing the WIEN2k code. The formation energy has been evaluated to elaborate the thermodynamic stability of Zintl compounds. The materials demonstrate characteristics of semiconductors, with anticipated band gap values of 1.78 eV for SrAg2S2, 1.63 eV for SrAg2Se2, and 1.50 eV for SrAg2Te2. The optical characteristics have been examined to assess the potential use of these phases in optoelectronic and photovoltaic systems. The standard Boltzmann transport theory has been used to analyze thermoelectric parameters concerning temperature and chemical potential. Thermoelectric features have also verified the p-type characteristics of these semiconductors. Considerably higher predicted values of the power factor and higher figure of merit demonstrate the capability of thermal energy conversion. Consequently, these outstanding optoelectronic and thermoelectric aspects values indicate that this class of materials may be highly suitable for use in solar and thermoelectric systems.

Investigation on the hydrogen storage properties, electronic, elastic, and thermodynamic of Zintl Phase Hydrides XGaSiH (X = sr, ca, ba)

This study presents a comprehensive investigation of the electronic, mechanical, and thermodynamic properties of Zintl phase hydrides XGaSiH (X = Sr, Ca, Ba) using Density Functional Theory (DFT) and the FP-LAPW method within the WIEN2k package. Our analysis covers the structural stability, electronic properties, and hydrogen interaction mechanisms in these compounds. The hydrides exhibit narrow band gaps, with values ranging from 0.1 to 0.5 eV using GGA and LDA functionals, and 0.6–1.0 eV with mBJ-GGA and mBJ-LDA. The hydrogen storage capacities are determined to be 0.34 wt %, 0.47 wt %, and 0.40 wt % for SrGaSiH, CaGaSiH, and BaGaSiH, respectively, highlighting their potential for energy storage applications. Thermodynamic properties, evaluated through the quasi-harmonic Debye model, provide insights into the Grüneisen parameter, heat capacity, and thermal expansion coefficient over a range of pressures (0–50 GPa) and temperatures (up to 1000 K). Elastic constants reveal that these compounds are mechanically stable, with a notable anisotropy in the {100} plane and varying degrees of compressibility among the different hydrides. Our study further highlights the slightly ordered hexagonal Ga and Si layers, which contribute to the enhanced hydrogen storage capabilities of these materials. The compounds demonstrate high structural stability, facilitating effective hydrogen retention and release at practical temperatures, making them promising candidates for hydrogen storage applications. Additionally, the analysis of electronic band structures and density of states suggests significant conductivity potential, with band gaps ranging from 0.1 to 1.0 eV, depending on the computational method used. The unique combination of structural, electronic, thermodynamic, and mechanical properties in XGaSiH compounds positions them as valuable materials for renewable energy applications. These findings lay the groundwork for future research focused on optimizing these materials through structural modifications or doping to enhance performance metrics such as hydrogen storage capacity and electrical conductivity.

Influence of Eu-doping on transport properties of synthesized zintl phase compounds EuxYb1−xZn2Sb2 under microwave-assisted solid-state

Influence of Eu-doping on transport properties of synthesized zintl phase compounds EuxYb1−xZn2Sb2 under microwave-assisted solid-state

Silicon Clathrate-Supported Catalysts with Low Work Functions for Ammonia Synthesis.

Diamond-type silicon has a work function of ≈4.8eV, and conventional n- or p-type doping modifies the value only between 4.6 and 5.05eV. Here, it is shown that the alkali clathrates AxSi46 have substantially lower work functions approaching 2.6eV, with clear trends between alkali electropositivity and clathrate cage size. The low work function enables alkali clathrates such as K8Si46 to be effective Haber-Bosch catalyst supports for NH3 synthesis. The catalytic properties of Si, Ge, and Sn-based clathrates are investigated while supporting Fe and Ru on the surface. The activity largely scales with the work function, and low activation energies below 60kJ mol-1 are observed due to strong electron donation effects from the support. Ru metal and Sn clathrates seem to be unsuitable for stability issues. Compared to other similar hydride/electride catalysts, the simple structure and composition combined with stability in air/water make a systematic study of these clathrates possible and open the door to other electron-rich Zintl phases and related intermetallics as low-work function materials suitable for catalysis. The observed low work function may also have implications for other existing electronic applications.

Unveiling the Potential of Redox Chemistry to Form Size-Tunable, High-Index Silicon Particles.

Silicon particles of intermediate sizes (75-200 nm) scatter visible wavelengths, making them promising candidates for optical devices. The solution synthesis of silicon particles in this size range, however, has proved challenging for chemists over the past few decades. Here, a solution-phase synthesis provides a pathway toward reaching size tunability between 45 and 230 nm via changing the reactant ratio in the reaction between a silicon Zintl phase (Na4Si4) with an amidinate-stabilized Si(IV) coordination complex. Coherent domain sizes, determined from powder X-ray diffraction, show that the crystallite sizes are uniform across all particle sizes, perhaps indicating an aggregation mechanism for particle growth. The amidinate ligands act to stabilize the particle surface. Combined surface techniques (ToF-SIMS, FTIR, and X-ray photoelectron spectroscopy) confirm the presence of amidinate ligands, as well as primary amine and a passive oxidation layer on the surface of the particles. The refractive index is measured for an individual particle using holographic optical microscopy, displaying a refractive index of nearly 4.1 at a wavelength of 532 nm. Thus, these particles should scatter light intensely at visible wavelengths, making them promising candidates for optical manipulation.

Enhanced thermoelectric performance of a p-type Mg3Sb2-based Zintl phase compound via Ge doping

Mg3Sb2-based thermoelectric materials are considered promising due to their non-toxic and cost-effective characteristics. Despite the low intrinsic thermal conductivity of these materials, their thermoelectric performance is significantly limited by a low carrier concentration. First principle calculations on p-type Mg3Sb2-based materials suggest that doping Ge at the Sb sites can notably enhance carrier concentration. Consequently, through vacuum melting combined with spark plasma sintering (SPS), samples of p-type Mg3Sb2-xGex (0≤x ≤ 0.05) were prepared. All Ge-doped samples display an increased carrier concentration, leading to a significant increase in the electrical conductivity and power factor (PF). Interestingly, the effect of Ge doping on thermal conductivity is minimal, making the Mg3Sb1.97Ge0.03 sample reaches the maximum thermoelectric figure of merit of 0.39 at 723 K, a fivefold increase compared to the undoped sample. This substantiates the efficacy of Ge as an efficient p-type dopant.

Topological Octet-Rule Implementation for Deltahedral Boron Hydrides and Related Zintl Clusters of the Main-Group Elements: Flexible Octet-Rule Fulfillment by Mixed 2- and 3-Center Fractional Bonding Scenarios.

In the large class of main-group Zintl phases, the octet rule plays a key role for the polyanions following the pseudoatom concept and the 8-N rule, such that a unique correspondence between atomic partial structure and its electron count results. In the conceptual framework of the Wade's type of clusters the relations to the octet rule are less obvious, and its structural implications are not clear. For this purpose, a topological implementation of the octet rule (TORI) within a delocalized bonding scenario is introduced. It is based on the average topology of the deltahedral cluster skeletons and the octet rule applied to delocalized fractional 2- and 3-center bond distributions. For a given skeletal electron pair count SEP, TORI yields values (ttoc, ytoc) similar to the styx approach. Two hierarchically different types of octet-rule fulfillment are identified, the cluster-wise and the local one. The local octet-rule fulfillment always implies the cluster-wise one, while the converse is not true. Deltahedral clusters with different skeletal shapes but the same Wade's SEP count can be distinguished with respect to different octet-rule fulfillment. The TORI approach opens a perspective to compare Zintl phases containing Wade-type clusters with those containing 8-N type of partial structures on the basis of octet-rule implications. The main difference to the 8-N type of partial structures identified is the more flexible way of octet-rule fulfillment in the Wade's type clusters, which does not prevent them from realizing the same cluster topology with different SEP counts. The TORI approach works with delocalized fractional bonds and is consistent with the concept of PSEPT; it just adds an additional facet.