⇦Chinese Physics Letters, 2021, Vol. 38, No. 1, Article code 017302 Layered Transition Metal Electride Hf$_{2}$Se with Coexisting Two-Dimensional Anionic $d$-Electrons and Hf–Hf Metallic Bonds Xihui Wang (王西惠)1†, Xiaole Qiu (邱潇乐)2†, Chang Sun (孙畅)1, Xinyu Cao (曹新宇)1, Yujie Yuan (袁宇杰)1, Kai Liu (刘凯)2*, and Xiao Zhang (张晓)1* Affiliations 1State Key Laboratory of Information Photonics and Optical Communications & School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, China 2Department of Physics and Beijing Key Laboratory of Opto-electronic Functional Materials & Micro-nano Devices, Renmin University of China, Beijing 100872, China Received 20 October 2020; accepted 18 November 2020; published online 6 January 2021 Supported by the National Natural Science Foundation of China (Grant No. 11774424), the Fundamental Research Funds for the Central Universities (Grant No. 2017RC20), the Research Funds of Renmin University of China (Grant No. 20XNH064), the CAS Interdisciplinary Innovation Team, the Beijing Natural Science Foundation (Grant No. Z200005), and the Research Innovation Fund for College Students of Beijing University of Posts and Telecommunications.
†Xihui Wang and Xiaole Qiu contributed equally to this work.
*Corresponding authors. Email: kliu@ruc.edu.cn; zhangxiaobupt@bupt.edu.cn Citation Text: Wang X H, Qiu X L, Sun C, Cao X Y, and Yuan Y J et al. 2021 Chin. Phys. Lett. 38 017302    Abstract Electrides are unique materials, whose anionic electrons are confined to interstitial voids, and they have broad potential applications in various areas. In contrast to the majority of inorganic electrides, in which the anionic electrons primarily consist of $s$-electrons of metals, electrides with anionic $d$-electrons are very rare. Based on first-principles electronic structure calculations, we predict that the layered transition metal chalcogenide Hf$_{2}$Se is a novel electride candidate with anionic $d$-electrons. Our results indicate that the anionic electrons confined in the Hf$_{6}$ octahedra vacancy between [Hf$_{2}$Se] layers mainly come from the Hf-5$d$ orbitals. In addition, the anionic electrons coexist with the Hf–Hf multiple-center metallic bonds located in the center of neighboring Hf$_{4}$ tetrahedra. The calculated work function (3.33 eV) for the (110) surface of Hf$_{2}$Se is slightly smaller than that of Hf$_{2}$S, which has recently been reported to exhibit good electrocatalytic performance. Our study of Hf$_{2}$Se will enrich the electride family, and promote further research into the physical properties and applications of electrides. DOI:10.1088/0256-307X/38/1/017302 © 2021 Chinese Physics Society Article Text Electrides are peculiar materials, where electrons play the role of anions. Anionic electrons in electrides mostly tend to occupy the crystallographic interstitial sites, not belonging to any particular atoms or covalent bonds. The anionic electrons in electrides are also distinct from the itinerant electrons in metals because their wave functions are usually confined in the cavities between cations. Since the discovery of organic electrides,[1,2] various inorganic electrides with improved thermal stability have also been synthesized. In particular, the first inorganic electride [Ca$_{24}$Al$_{28}$O$_{64}$]$^{4+}\cdot$4$e^{-}$ ($C_{12}$A$_{7}$) with low work function has an important application in terms of promoting the catalytic efficiency of ammonia synthesis at ambient pressure and low temperature.[3,4] In addition, some inorganic materials behave like electrides under extreme conditions. For example, anionic electrons in Na and Na$_{2}$He under high pressure are localized at the interstitial sites.[5,6] Due to their unique structural, physical, and chemical properties, inorganic electrides have attracted intense attention, both in terms of fundamental science and potential areas of application. According to the dimensionality of anionic electron distributions, inorganic electrides can be classified as zero-dimensional (0D),[7] one-dimensional (1D),[8] two-dimensional (2D),[9–11] and three-dimensional (3D) electrides.[12] Of these, 2D electrides exhibit some distinctive properties. For example, in 2D electride Ca$_{2}$N,[9] the anionic electrons are partially delocalized and confined between neighboring Ca–N layers, becoming a 2D electron gas with rather high carrier mobility and concentrations in comparison with 0D electrides. More interestingly, Ca$_{2}$N can be exfoliated into thermally and mechanically stable thin flakes, where the electron gas is present on the surface.[13,14] This type of 2D electron gas can be used as a solid-state dopant to tune the physical properties of van der Waals 2D materials, e.g., the structural transition of few-layer MoTe$_{2}$ or graphene.[15,16] The anionic electrons in most of the electrides discovered to date originate mainly from the $s$-orbital electrons of metals, while $d$-orbital electrides are very scarce. In 2D electride Y$_{2}$C and YCl, the $d$ electrons of Y form polar covalent bonds with C and Y–Y metallic bonds, respectively, rather than anionic electrons.[10,17] Recently, 1D electride Sr$_{3}$CrN$_{3}$ is reported to have exhibited a partially filled $d$ shell of Cr$^{4+}$, but whether the anionic electrons come from the Cr$^{4+}$ or Sr$^{2+}$ is subject to debate, since the Sr atoms are in the 1D electron channel.[18] Research to discover new electrides with anionic $d$-electrons is therefore very much required. In addition to the experimental exploration of electrides, high-throughput computational screening, based on first-principles calculations and certain material design principles, provides another critical approach to the discovery of novel electrides.[19–23] Many potential electrides have been predicted, some of which have been verified by experiments, such as Y$_{2}$C, Sr$_{3}$CrN$_{3}$, Sr$_{8}$P$_{5}$, and Sr$_{5}$P$_{3}$.[10,18,23] Recently, the predicted layered electride Hf$_{2}$S with 2D anionic electrons has been successfully synthesized.[24] Analysis shows that a self-passivation behavior leads to a strong oxidation resistance in water and acid solutions, facilitating a persistent reaction for electrocatalytic hydrogen evolution.[24] Based on the above considerations, in this work, we theoretically explore the electronic structures and physical properties of an isostructural material, Hf$_{2}$Se. It is found that Hf$_{2}$Se is a 2D electride with anionic $d$-orbitals and Hf–Hf metallic bonds. The electronic structure calculations of Hf$_{2}$Se in this work were performed based on the density functional theory (DFT), as implemented via the Vienna ab initio simulation package (VASP).[25] The electron–ion interactions were described using the projector-augmented wave (PAW) method.[25] A generalized gradient approximation in the Perdew–Burke–Ernzerhof form (GGA-PBE) was adopted for the exchange-correlation functional.[26] The plane-wave basis-set cutoff was set to 450 eV. A $22\times 22\times 6$ $k$-point grid for Brillouin zone sampling was used to optimize the structure and obtain a self-consistent solution of the Kohn–Sham equation. Optimized atomic positions were obtained via the total energy and force minimization method, where the minimum force criterion was 0.001 eV/Å. To determine the work function ($\varPhi_{\rm WF}$) of Hf$_{2}$Se, two slab models for the (001) (18 atoms) and (110) (90 atoms) surfaces were constructed, perpendicular to or parallel to the edge-sharing metal octahedral layer, respectively. For these slab models, the vacuum was set to 20 Å. The respective $k$-point grids were $15\times15\times1$ and $7\times7\times1$ for the (001) and (110) surfaces. The values of $\varPhi_{\rm WF}$ were calculated by means of the equation $\varPhi_{\rm WF} = e\varPhi_{\rm vac}-E_{\rm F}$, where $\varPhi_{\rm vac}$ is the electrostatic potential of the vacuum region, and $e$ is the electron charge.[27] Figure 1(a) shows the structure of Hf$_{2}$Se with the space group $P$63/$mmc$ (No. 194).[28] The basic unit is the [Hf$_{2}$Se] layer, where Se atoms are sandwiched between Hf atoms, forming an edge-shared [Hf$_{6}$Se] trigonal prismatic coordination slab. These Hf–Se layers stack along the $c$-axis with an ABAB sequence, restoring the inversion symmetry. The $a$- and $c$-axial lattice constants of Hf$_{2}$Se are 3.44 Å and 12.32 Å, respectively, which are larger than those of the isostructural compound Hf$_{2}$S ($a = 3.37$ Å and $c = 11.79$ Å)[28] owing to the larger ionic radius of Se$^{2-}$ ions. It should be noted that Hf$_{2}$Se has an anti-2H-NbS$_{2}$ structure, where the sites of Nb and S atoms are occupied inversely by Se and Hf atoms in Hf$_{2}$Se. The Hf–Se distance ($d_{\rm Hf-Se}$) in the [Hf$_{2}$Se] layer is 2.51 Å, comparable with that of 1T-HfSe$_{2}$ ($d_{\rm Hf-Se} = 2.65$ Å),[29] suggesting that the bonding between Hf and Se atoms in the [Hf$_{2}$Se] layer is primarily ionic. For most reported electrides, the formation of the interstitial void in the metal polyhedron is the key structural ingredient in the hosting of anionic electrons, such as the interlayer Ca$_{6}$ octahedra in Ca$_{2}$N and Y$_{6}$ octahedra in Y$_{2}$C.[9,10] Similarly, for Hf$_{2}$Se, two kinds of interstitial voids, comprising Hf$_{4}$ tetrahedra and Hf$_{6}$ octahedra, exist in the interlayer space. The interlayer distance $d_{\rm inter}$ in Hf$_{2}$Se is about 3.08 Å, similar to the thickness of the [Hf$_{2}$Se] layer. Compared with Ca$_{2}$N ($d_{\rm inter} = 3.86$ Å) and Y$_{2}$C ($d_{\rm inter} = 3.29$ Å),[9,10] the smaller interlayer distance in Hf$_{2}$Se implies that there may be more electrons between the [Hf$_{2}$Se] layers, leading to interlayer electrostatic interaction. Moreover, since the most stable valence state of Se ions is $-2$, and the valence state of Hf ion is usually $+$4, the [Hf$_{2}$Se] layer should be positively charged. Based on the requirements of charge neutrality, there are 6 excess electrons per Hf$_{2}$Se formula, indicating the intrinsic electron-rich character of Hf$_{2}$Se. These electrons locate at the interstitial sites between the [Hf$_{2}$Se] layers, which is consistent with the above analysis.
cpl-38-1-017302-fig1.png
Fig. 1. (a) Crystalline structure of Hf$_{2}$Se with a hexagonal unit cell. (b) Calculated electron localization function (ELF) of Hf$_{2}$Se with an isosurface value of 0.65. The ELF attractors at the centers of the Hf$_{4}$ tetrahedron (site A) and Hf$_{6}$ octahedron (site B) are indicated by dashed red and blue circles, respectively. Enlarged views of the ELF attractors located at (c) site A and (d) site B. (e) The 2D ELF contour in the (110) plane.
In order to unveil the electride features of Hf$_{2}$Se, we have calculated the electron localization function (ELF) of Hf$_{2}$Se, which is widely used as an indicator of confined interstitial electrons in the electrides.[30,31] Figures 1(b)–1(e) depict the ELF results for Hf$_{2}$Se. The virtually spherically distributed ELF attractors around the cores of the Se atoms clearly indicate the ionic bonding between Hf and Se atoms.[32] More importantly, there are two ELF attractors, located at the centers of the Hf$_{4}$ tetrahedron (site A, highlighted by the red circle) and the Hf$_{6}$ octahedron (site B, highlighted by the blue circle), between adjacent [Hf$_{2}$Se] layers. As shown in Figs. 1(c) and 1(d), the former is larger than the latter, and has a higher ELF value [Figs. 1(e)] when approaching the center of the tetrahedron [Fig. 1(c)]. In addition, the ELF attractor in the Hf$_{4}$ tetrahedron penetrates to the Hf$_{6}$ octahedron, with a finite value of ELF between two polyhedrons [Figs. 1(c) and 1(d)], suggesting the strong interaction between them, possibly due to the short distance ($\sim $2.13 Å).
cpl-38-1-017302-fig2.png
Fig. 2. (a) Total and (b) projected band structures of Hf$_{2}$Se. (c) Total and projected density of states (DOS) of Hf$_{2}$Se. The inset shows the enlarged part of the DOS in the energy range $-3$ eV to 0 eV. The Fermi level $E_{\rm F}$ is set to zero. (d), (e), and (f) The partial charge densities with an isosurface value of $1.3\times 10^{-2} e$/Å$^{3}$ for band pairs 1, 2, and 3, respectively.
To further evaluate the electride characteristics of Hf$_{2}$Se, we investigated the band structure and the partial charge densities for bands near the Fermi level. Figure 2(a) shows the band structure of Hf$_{2}$Se, with six bands between $-3.5$ and 0 eV ($E_{\rm F}$), denoted as band pairs 1, 2, and 3. It should be noted that there are two Hf$_{2}$Se formulae for one unit cell ($Z = 2$). In order to identify the contributions of interstitial electrons, the charge density was decomposed over the atom-centered spherical harmonics with a Wigner–Seitz radius of 1.56 Å, and the interstitial region was set as an empty sphere, placed at the center of the Hf$_{6}$ octahedral site.[9,33] The projected band structures and density of states (pDOS) in Figs. 2(b) and 2(c) show the contribution of Hf and Se elements to the bands in the vicinity of the Fermi surface. The existence of bands crossing the Fermi energy level $E_{\rm F}$ indicates that Hf$_{2}$Se may exhibit metallic behavior. The band structure and DOS of Hf$_{2}$Se are similar to those of Hf$_{2}$S.[24] From the pDOS, we learn that between $-8$ and $-3.5$ eV, the Se-2$p$ states are dominant, with a minor contribution from Hf-3$d$ states. This confirms the strong ionic bonding between Hf and Se atoms, which is consistent with the ELF analysis. The three band pairs near the Fermi surface are mainly derived from Hf-5$d$ states and interstitial electrons [inset of Fig. 2(c)]. We observe that in the energy range of band pair 3, the contribution from the interstitial sites is comparable to the pDOS of Hf atoms. The significant pDOS contributed by the interstitial sites is a typical characteristic of electrides, similar to that observed with respect to Ca$_{2}$N and Y$_{2}$C.[9,10] The partial charge density (PCD) results further confirm the origin of the three band-pairs, as shown in Figs. 2(d)–2(f). The PCD of band-pair 3 distributes dominantly in the Hf$_{6}$ octahedron, corresponding to the ELF attractor at site B [Fig. 1(d)]. Due to the full occupancy of band pair 3, there should be two anionic electrons per Hf$_{2}$Se formula, located at the Hf$_{6}$ octahedron. In contrast, in the energy ranges of band pairs 1 and 2, the pDOS of the Hf-5$d$ state is larger than that of the interstitial electrons. The PCDs in Figs. 2(d) and 2(e) clearly indicate that these band pairs are mainly formed by the electrons in the Hf$_{4}$ tetrahedral sites. Moreover, these strongly localized electrons lead to the strong ELF attractor at site A [Fig. 1(c)]. Due to the (nearly) fully occupied band pair 2(1), there are approximate four electrons per Hf$_{2}$Se formula, situated at the Hf$_{4}$ tetrahedral sites. In addition, the energy overlap of these three band pairs indicates the strong interaction between the electrons in the Hf$_{4}$ tetrahedra and Hf$_{6}$ octahedra, which is in accord with the results of the ELF. Although the electrons in the voids of both Hf polyhedrons exhibit similar features, such as obvious ELF attractors, as well as large PCDs, it is likely that those electrons in site A may not be the anionic electrons, but may instead form Hf–Hf multiple-center metallic bonding states, since the Hf$_{4}$ tetrahedron has a relatively small volume $V$ ($\sim $5.26 Å$^{3}$) with a much shorter distance, $d_{\rm cv}$, between the center and the vertex of the tetrahedron ($\sim $2.13 Å) as compared to those of the Hf$_{6}$ octahedron ($V = 21.12$ Å$^{3}$, $d_{\rm cv} = 2.51$ Å). A similar situation has been observed for YCl and Y$_{2}$Cl$_{3}$.[17] Based on the above analysis, the compound of Hf$_{2}$Se may be expressed as [Hf$_{2}$Se]$^{2+}\cdot 2e^{-}$. Taking into account that the anionic electrons in Hf$_{6}$ octahedra come primarily from the Hf-5$d$ orbitals, the interstitial electrons in Hf$_{2}$Se thus originate from Hf-5$d$ electrons, and coexist with the localized Hf–Hf metallic bonds, a process which differs from that of the well-known 2D electrides such as Ca$_{2}$N and Y$_{2}$C, whose anionic electrons come from the $s$-orbital electrons of Ca or Y atoms. Given that interstitial electrons in electrides play the role of anions, in general, true anions could be inserted into the interstitial sites to host anionic electrons without introducing a large lattice strain.[8,17,34] More importantly, the inserted anions will significantly alter the band structure, particularly with respect to bands originating from the anionic electrons, and their related physical properties. For example, the substitution of chlorine atoms for anionic electrons leads to a transition from ferromagnetic [Gd$_{2}$C]$^{2+}\cdot 2e^{-}$ to antiferromagnetic Gd$_{2}$CCl by attenuating the interatomic exchange interactions.[34] Since the interstitial void of the Hf$_{6}$ octahedron in Hf$_{2}$Se should host two anionic electrons, here oxygen atoms are inserted into the centers of Hf$_{6}$ octahedra [denoted by small green balls in Fig. 3(a)] where the Wyckoff position of O atoms is (0, 0, 0). Figure 3(b) illustrates the ELF of Hf$_{2}$SeO with an isosurface value of 0.65. We observe nearly spherically distributed ELF attractors at the centers of the Hf$_{6}$ octahedra, indicating the ionic bonding between Hf and O atoms. This is similar to the case of Y$_{5}$Si$_{3}$H.[34] At the same time, it can be seen that the ELF attractors in the Hf$_{4}$ tetrahedra of Hf$_{2}$SeO shrink when compared to those of Hf$_{2}$Se [see Fig. 1(b)]. This suggests that the inserted O atoms have a significant influence on the electrons in the Hf$_{4}$ tetrahedra, due to strong Coulomb interaction between them at so short a distance. The band structure, total DOS, and pDOS of Hf$_{2}$SeO are shown in Fig. 3(c). Band pairs 1 and 2, mainly composed mainly of Hf-5$d$ orbitals, are still between $-3$ and 0 eV ($E_{\rm F}$), similar to Hf$_{2}$Se, but the dispersions of these bands change to some extent due to the presence of O atoms, which is consistent with the results of the ELF. In contrast, band pair 3, originating from the anionic electrons in Hf$_{2}$Se, disappears; instead, bands of oxygen 2$p$ orbitals emerge in the range of $-9$ to $-7$ eV below the $E_{\rm F}$. In this way, the anionic electrons in the Hf$_{6}$ octahedra have been completely transferred to O ions, and the formal valence state of Hf$_{2}$SeO should be [Hf$_{2}$Se]$^{2+}$O$^{2-}$. Such evolution of the band structure has also been observed in Y$_{5}$Si$_{3}$H and NaBa$_{2}$OH.[34,35] Briefly, the above results further suggest that the interstitial electrons at the Hf$_{6}$ octahedra of Hf$_{2}$Se are anionic.
cpl-38-1-017302-fig3.png
Fig. 3. (a) Crystalline structure of Hf$_2$SeO. The small green balls represent the O atoms located at the center of the Hf$_{6}$ octahedra. (b) ELF with an isosurface value of 0.65 for Hf$_{2}$SeO. (c) Band structure, total DOS and pDOS of Hf$_{2}$SeO. The Fermi level $E_{\rm F}$ is set to zero. Those bands consisting primarily of O-2$p$ states are highlighted by red lines.
A low work function, possibly owing to the relatively loose anionic electrons, is another unique feature of electrides.[9,10,27] We therefore investigated the work function, $\varPhi_{\rm WF}$, of Hf$_{2}$Se, using the slab models presented in Fig. 4. The calculated $\varPhi_{\rm WF}$ of the (110) and (001) surfaces of Hf$_{2}$Se are about 3.33 and 4.18 eV, respectively. The different work functions of these two surfaces indicate the obvious anisotropic characteristics of Hf$_{2}$Se. Both these values are rather low for an ionic compound,[36–40] and are comparable to those of Y$_{2}$C (3.08 eV),[10] revealing the electride nature of Hf$_{2}$Se with loosely bound electrons. The $\varPhi_{\rm WF}$ of the (110) surfaces is slightly smaller than that found in Hf$_{2}$S ($\varPhi_{\rm WF} \sim 3.6$ eV).[24] Since Hf$_{2}$S exhibits a self-passivated behavior with a strong oxidation resistance in water and acid solutions, resulting in an electrocatalytic reaction with excellent long-term sustainability,[24] it would be very interesting to verify whether Hf$_{2}$Se will also show comparable or even better electrocatalytic performance in the future.
cpl-38-1-017302-fig4.png
Fig. 4. Calculated work function of Hf$_{2}$Se for the (a) (110) and (b) (001) surfaces. Insets of (a) and (b) show the side views of the slab models for the (110) and (001) surfaces, respectively. The $E_{\rm F}$ is taken as zero (dashed line).
In summary, we have studied the electronic structures and the interesting features of the novel 2D electride candidate, Hf$_{2}$Se, based on first-principles calculations. Our results indicate that metallic Hf$_{2}$Se can host anionic electrons between [Hf$_{2}$Se] layers, originating mainly from Hf-5$d$ orbitals. These interstitial electrons coexist with Hf–Hf metallic bonds, such that the chemical formula of Hf$_{2}$Se could be written approximately as [Hf$_{2}$Se]$^{2+}\cdot 2e^{-}$. Moreover, Hf$_{2}$Se exhibits relatively low work functions. This study should shed light on discovering and designing novel electrides with multiple functions for practical applications. References Electrides: Early Examples of Quantum ConfinementCHEMISTRY: Electrons as AnionsAmmonia synthesis using a stable electride as an electron donor and reversible hydrogen storeWork Function of a Room-Temperature, Stable Electride [Ca24Al28O64]4+(e–)4Transparent dense sodiumA stable compound of helium and sodium at high pressureHigh-Density Electron Anions in a Nanoporous Single Crystal: [Ca24Al28O64]4+(4e-)Electron Confinement in Channel Spaces for One-Dimensional ElectrideDicalcium nitride as a two-dimensional electride with an anionic electron layerTwo-Dimensional Transition-Metal Electride Y 2 CExploration for Two-Dimensional Electrides via Database Screening and Ab Initio CalculationStructural Diversity and Electron Confinement in Li 4 N: Potential for 0-D, 2-D, and 3-D ElectridesExperimental Demonstration of an Electride as a 2D MaterialObtaining Two-Dimensional Electron Gas in Free Space without Resorting to Electron Doping: An Electride Based DesignProbing a divergent van Hove singularity of graphene with a Ca 2 N support: A layered electride as a solid-state dopantLong-Range Lattice Engineering of MoTe 2 by a 2D ElectrideIdentifying quasi-2D and 1D electrides in yttrium and scandium chlorides via geometrical identificationSr 3 CrN 3 : A New Electride with a Partially Filled d -Shell Transition MetalHigh-Throughput Identification of Electrides from All Known Inorganic MaterialsHigh-Throughput ab Initio Screening for Two-Dimensional Electride MaterialsFirst-Principles Prediction of Thermodynamically Stable Two-Dimensional ElectridesComputer-Assisted Inverse Design of Inorganic ElectridesExploration of Stable Strontium Phosphide-Based Electrides: Theoretical Structure Prediction and Experimental ValidationWater- and acid-stable self-passivated dihafnium sulfide electride and its persistent electrocatalytic reactionEfficient iterative schemes for ab initio total-energy calculations using a plane-wave basis setGeneralized Gradient Approximation Made SimpleLow work function of the (1000) Ca2N surfaceThe group IV di-transition metal sulfides and selenidesThe lithium intercalates of the transition metal dichalcogenidesA simple measure of electron localization in atomic and molecular systemsIs Mayenite without Clathrated Oxygen an Inorganic Electride?ELF: The Electron Localization FunctionHigh-Pressure Electrides: The Chemical Nature of Interstitial QuasiatomsWater Durable Electride Y 5 Si 3 : Electronic Structure and Catalytic Activity for Ammonia SynthesisTernary inorganic electrides with mixed bondingTunable Schottky barrier in graphene/graphene-like germanium carbide van der Waals heterostructureA novel physical parameter extraction approach for Schottky diodesA simulation study of field plate termination in Ga 2 O 3 Schottky barrier diodesSchottky barrier MOSFET structure with silicide source/drain on buried metalSchottky Barrier Formation at a Carbon Nanotube–Scandium Junction
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