Influence of applied pressure on bond distortions and electronic band structure of GeTe: First principle calculations

GeTe Thermoelectrics

Fundamental understanding and optimization of the emerging mixed organic-inorganic hybrid perovskites for solar cells require multiscale modeling starting from ab initio quantum mechanics methods. Particularly, it is important to correctly predict the structural and electronic properties such as phase stability, lattice parameters, band gaps, and band structures. Although density functional theory is the method of choice to address these properties and generate the input for subsequent multiscale, high-throughput, and data-driven approaches, standard exchange correlation functionals fail to reproduce the bandgap, particularly if spin-orbit coupling (SOC) is correctly taken into account. While many SOC-included hybrid functionals suffer from low transferability between different molecular ions and are computationally costly, we propose an efficient multistep simulation protocol based on the DFT-1/2 method. We apply this approach to APbI3 with A: FA, MA, Cs, and systems with mixed cations and show how the choice of the A-cation modifies the Pb-I scaffold and the hydrogen bonding and discuss their interplay with structural stability. Furthermore, band gaps, band structures, Rashba band splitting, Born effective charges as well as partial density of states (PDOS) are compared for different cases w/wo the SOC effect and the DFT-1/2 approach.

The high pressure behavior of nitrogen-rich energetic crystal 4-amino-3, 7-dinitrotriazolo-[5, 1, c] [1, 2, 4]triazine (DPX-26) in the hydrostatic pressure range of 0-130 GPa was investigated by employing the GGA/PBE-G06 method of periodic density functional theory (DFT). The changes of crystal structure, molecular structure and electronic structure of DPX-26 with pressure were analyzed by calculating lattice parameters (a, b, c), bond lengths, band gaps (ΔEg) and density of states (DOS). The results show that DPX-26 undergoes three significant structure transitions at 81, 82 and 92 GPa. The structural transformation occurs at 81 GPa with the destruction of intermolecular six membered rings. At 82 GPa, the triazole ring is severely distorted and dissociated with the elongation of C4-N7 bond. As the pressure reaches 92 GPa, the bond length of C4-N7 decreases from 0.2324 nm to 0.1333 nm, and the triazole ring is formed again. The increase of external pressure leads to the delocalization enhencement of the system.

Density functional theory (DFT) calculations on a tunable number of GaN (0001) planes give an invariant band structure, density of states (DOS) diagram, and band gap of the GaN unit cell. Dissimilar band structures and DOS diagrams are obtained for 1, 3, 5, 7, and 9 layers of GaN (101̄0) planes, but the same band structure as that of the (0001) plane returns for 2, 4, 6, and 8 (101̄0) planes. Furthermore, 1 to 4 layers of GaN (101̄1) planes exhibit dissimilar band structures, but the GaN unit cell band structure is obtained for 5 (101̄1) planes. While there are no changes to the Ga-N bond length and bond geometry for the (0001) planes, the (101̄0) planes present bond length variation and bond distortion with odd numbers of layers. Bond length and bond direction deviations are also obtained for 1 to 4 (101̄1) planes. These results suggest that slight structural deviations may be present near the GaN surface to produce facet-dependent properties, and such atomic position deviations in the surface layer can be observed in various semiconductors.

Montmorillonite is an important layered phyllosilicate material with many useful physicochemical and mechanical properties, which is widely used in medicine, environmental protection, construction industry, and other fields. In order to a get better understanding of the behavior of montmorillonite under high pressure, we studied its atomic structure, electronic and mechanical properties using density functional theory (DFT), including dispersion corrections, as function of the interlayer Na and Mg cations. At ideal condition, the calculations of lattice constants, bond length, band structure, and elastic modulus of Na- and Mg-montmorillonite are in good agreement with the experimental values. Under high pressure, the lattice constants and major bond lengths decreased with increasing pressure. The calculated electronic properties and band structure show only a slight change under 20 GPa, indicating that the effect of pressure on the electronic properties of Na- and Mg-montmorillonite is weak. The bulk modulus, shear modulus, Young’s modulus, shear wave velocity and compression wave velocity of Na- and Mg-montmorillonite are positively correlated with the external pressure, and the other mechanical parameters have a little change. The calculated studies will be useful to explore experiments in the future from a purely scientific point of view.

Introduction A zigzag boron nitride nanotube (ZBNNT) has a large intrinsic polarized dipole and a piezoelectric tunability with crystal chirality, nanotube diameter, and point defect. The piezoelectric coefficients (e33) of 8-ZBNNT with the VIA-group defects of SN and SeN are estimated to be 18.7×10-2 C/m2 and 14.9×10-2 C/m2, respectively. The coefficients of defect-mediated 8-ZBNNT are 97% and 57% bigger than that of pristine 8-ZBNNT. The elastic modulus of 8-ZBNNT is decreased due to the VIA-group defects, but is increased for the larger number of unit cells along zigzag rolling direction. The electronic band gap of 8-ZBNNT is reduced due to the VIA-group defects. The large piezoelectricity enhancement of 8-ZBNNT with VIA-group defect is attributable to the enhanced piezoelectricity from ionic contribution. Therefore, the unprecedented defect-mediated 8-ZBNNT provides a new material platform of mechanoelectronic devices for nanoscale sensors and energy conversions. Modeling and methodology Figure 1 shows the schematic of a single wall 8-ZBNNT with an atomic defect. The supercell is in a simple orthorhombic box with periodic boundary condition in 30 Å × 30 Å × Lc where Lc is the lattice parameter along the transport direction. The green atom “A” indicates the defect of a single substitution atom per a supercell. The average bond length is defined as the average length of atomic bond between the defect doping atom and the neighboring boron atoms. The first principle calculations were carried out by using the Virtual Nanolab Atomistix ToolKit (ATK) package with the density functional theory (DFT). The localized density approximation (LDA) exchange correlation with a double zeta polarized (DZP) basis was used with a mesh cut-off energy of 150 Ry. All atomic positions and lattice parameters were optimized by using the generalized gradient approximations (GGA) with the maximum Hellmann Feynman forces of 0.05 eV/Å, which was sufficient to obtain relaxed structures. The maximum number of fully self-consistent field (SCF) iteration steps was set to 100. Defect-mediated piezoelectricity The table I includes the piezoelectric coefficient (e33) and average bond length (a0) of 10- and 8-ZBNNT with different kinds of defects including SW deformation, IVA-group, and VIA-group defects within one supercell. Among the defects in ZBNNT, a single nitrogen vacancy or SW defect diminishes the piezoelectric coefficient (e33) of 10- and 8-ZBNNT. However, the atomic defects of IVA- and VIA-group elements in a nitrogen site enhance the piezoelectric coefficient. The piezoelectric coefficient of VIA-group defect is higher than that of IVA-group defect. The piezoelectric coefficient e33 of chalcogen defect SN and SeN in 8-ZBNNT is enhanced 97% and 57% from 9.49×10-2 C/m2 to 18.7×10-2 C/m2 and 14.9×10-2 C/m2, respectively, compared to that of pristine 8-ZBNNT. The table I includes the elastic modulus of pristine10-ZBNNT and 8-ZBNNT and the ZBNNT with defects. The elastic modulus of 10- and 8-ZBNNT with defects is smaller than that of pristine 10- and 8-ZBNNT. The elastic modulus of SW defects in ZBNNT is increased compared to that of pristine 10- and 8-ZBNNT. The structure with smaller elastic modulus has the larger strain response to the constant external stress. Therefore, the ZBNNT with IVA- and VIA-group atomic defects has an efficient response to the external stress for piezoelectric applications. 8-ZBNNT of SN and SeN with the smaller elastic modulus have the larger e33 compared to the structure with ON. Defect-mediated electronic band structure Figure 2 shows the electronic band structure of 8-ZBNNT with (a) pristine structure and (b) defects of ON, SN and SeN. The group VIA-group defects in 8-ZBNNT are n-type doping because the Fermi level is located in the conduction band while the VIA-group defects in 8-ZBNNT are p-type doping. The bandgap in 8-ZBNNT is also reduced from 3.37 eV to 3.16 eV, 3.12 eV and 3.20 eV for the VIA-group defect of ON, SN and SeN, respectively. However, the band gaps of 8-ZBNNT with the IVA-group defects of CN, SiN and GeN is slightly widened to 3.38 eV, 3.49 eV and 3.50 eV compared to the band gap 3.37 eV of pristine 8-ZBNNT, respectively. Conclusions The piezoelectricity of ZBNNT is significantly enhanced by atomic defects. The piezoelectric coefficients (e33) 8-ZBNNT with SN and SeN defects are increased up to 97% and 57%, respectively. The electronic band gap of 8-ZBNNT with defects is reduced. The large piezoelectricity enhancement of 8-ZBNNT with VIA-group defect is attributable to the enhanced piezoelectricity from ionic contribution. Therefore, the unprecedented defect-mediated 8-ZBNNT provides a new material platform of mechanoelectronic devices for nanoscale sensors and energy conversions. Acknowledges This work is supported by ARO W911NF-15-1-0535, NSF HRD-1137747, and NASA NNX15AQ03A. Figure 1

Band gap and partial density of states for ZnO: Under high pressure

Ab initio study of the effect of pressure on the structural and electronic properties of cubic LaAlO3 by density function theory using GGA, LDA and PBEsol exchange correlation potentials

A full potential all-electron calculation on electronic structure of NiO

Open AccessCCS ChemistryRESEARCH ARTICLE22 Apr 2022Computational Prediction of Graphdiyne-Supported Three-Atom Single-Cluster Catalysts Jin-Cheng Liu, Hai Xiao, Xiao-Kun Zhao, Nan-Nan Zhang, Yuan Liu, Deng-Hui Xing, Xiaohu Yu, Han-Shi Hu and Jun Li Jin-Cheng Liu Department of Chemistry, Key Laboratory of Organic Optoelectronics and Molecular Engineering of the Ministry of Education, Tsinghua University, Beijing , Hai Xiao Department of Chemistry, Key Laboratory of Organic Optoelectronics and Molecular Engineering of the Ministry of Education, Tsinghua University, Beijing , Xiao-Kun Zhao Department of Chemistry, Key Laboratory of Organic Optoelectronics and Molecular Engineering of the Ministry of Education, Tsinghua University, Beijing , Nan-Nan Zhang Department of Chemistry, Key Laboratory of Organic Optoelectronics and Molecular Engineering of the Ministry of Education, Tsinghua University, Beijing , Yuan Liu Department of Chemistry, Key Laboratory of Organic Optoelectronics and Molecular Engineering of the Ministry of Education, Tsinghua University, Beijing Department of Chemistry, Southern University of Science and Technology, Shenzhen, Guangdong , Deng-Hui Xing Department of Chemistry, Key Laboratory of Organic Optoelectronics and Molecular Engineering of the Ministry of Education, Tsinghua University, Beijing , Xiaohu Yu Shaanxi Key Laboratory of Catalysis, School of Chemical and Environment Sciences, Shaanxi University of Technology, Hanzhong, Shaanxi , Han-Shi Hu Department of Chemistry, Key Laboratory of Organic Optoelectronics and Molecular Engineering of the Ministry of Education, Tsinghua University, Beijing and Jun Li *Corresponding author: E-mail Address: [email protected] Department of Chemistry, Key Laboratory of Organic Optoelectronics and Molecular Engineering of the Ministry of Education, Tsinghua University, Beijing Department of Chemistry, Southern University of Science and Technology, Shenzhen, Guangdong https://doi.org/10.31635/ccschem.022.202201796 SectionsSupplemental MaterialAboutAbstractPDF ToolsAdd to favoritesDownload CitationsTrack Citations ShareFacebookTwitterLinked InEmail While heterogeneous single-atom catalysts (SACs) have achieved great success in the past decade, their application is potentially limited by their simplistic single-atom active centers, which make single-cluster catalysts (SCCs) a natural extension in the domain of heterogeneous catalysis. SCCs with precise numbers of atoms and structural configurations possess SAC merits, yet have greater potential for catalyzing complex reactions and/or bulky reactants. Through systematic quantum-chemical studies and computational screening, we report here the rational design of transition metal three-atom clusters anchored on graphdiyne (GDY) as a novel kind of stable SCC with great promise for efficient and atomically precise heterogenous catalysis. By investigating their structure and catalytic performance for the oxygen reduction reaction, the hydrogen evolution reaction, and the CO2 reduction reaction, we have provided theoretical guidelines for their potential applications as heterogeneous catalysts. These GDY-supported three-atom SCCs provide an ideal benchmark scaffold for rational design of atomically precise heterogeneous catalysts for industrially important chemical reactions. Download figure Download PowerPoint Introduction In the past decade, single-atom catalysts (SACs) have emerged as the new frontier of heterogeneous catalysis, owing to their high performance with regard to atomic efficiency, selectivity, stability, and activity, as well as precisely tunable quantum states through support manipulation.1–5 However, SACs are not always an optimal design for complex reactions, such as those that require multistep redox reactions (e.g., in photosynthesis and nitrogenase), interaction among two or more adsorbed bulky reactant molecules, or multiple functional sites (e.g., in order to break the cumbersome scaling relations).6 Atomic clusters that contain only a small number of atoms can exhibit unique and often unexpected properties for catalytic reactions such that SAC may not work well.7–9 The term "cluster" was coined by F.A. Cotton in the early 1960s to refer specifically to compounds containing metal–metal bonds. Up to now, there are many synthetic strategies of supported atomic clusters for heterogeneous catalysis, for instance, gas-phase mass filters or so-called "soft landing,"10 the precursor-preselected strategy from the confined effect of zeolitic or MOF frameworks,11–13 the host–guest strategy,14 the wet chemical reduction,15 the dendrimer-based strategy, and so on.16 Recently, single-cluster catalysts (SCCs) with atomically precise active centers composed of well-defined stable clusters with constant atomic constitutions and structures have been proposed as a natural extension of SACs for optimal design of complicated heterogeneous catalysts.6,10,11,14,17–21 However, the stability and thus the synthesis of SCCs pose a grand challenge because a delicate balance is required to prevent both further aggregation of the clusters to form large size clusters or nanoparticles and their dispersion to form supported single atoms. To form robust SCCs, a prototype material with natural pores or defect-anchoring sites is necessary. The synthesis of graphdiyne (GDY) by Li et al.22–26 presents an ideal substrate for hosting both SACs and SCCs since GDY has natural 6-membered rings (6MRs) and 18-membered rings (18MRs). There have been reports of metal/GDY complexes with various applications,27,28 and the 18MR-hole of GDY has been shown to provide a suitable site for anchoring a metal (M) single atom (SA) or single cluster (SC) as a heterogeneous catalyst.29 However, most previous work on Mx/GDY has focused on SAs. For example, nonnoble metal Fe and Ni SAs anchored on GDY (denoted as Fe1/GDY and Ni1/GDY) have been shown to perform better in the hydrogen evolution reaction (HER) than in the commercial Pt/C.29 By first-principles calculations, the stability and electronic structures of M1/GDY with 3d metals (M = Sc − Zn) were systematically investigated in our group.30 Additionally, Mo1/GDY,31 Ir1/GDY,32 W1/N-doped GY,33 Pt1/GDY,34 Fe1/GDY,35 AM1/GDY,36 and TM1/GDY37 (AM = alkali metal and TM = transition metal) were theoretically proposed as good catalysts for reactions including nitrogen fixation, CO oxidation, HER, oxygen reduction reaction (ORR), and water splitting. However, these studies on M1/GDY did not explore the possibility that the SA form of metal on GDY might be less stable than its SC form, particularly when compared with the highly stable triatomic cluster form.38,39 Ma et al.40 reported diatomic cluster catalysts on GDY for nitrogen reduction reaction. Zhang et al.41 speculated that the triangular 18MR-hole of GDY can accommodate three Li atoms at the three symmetric corners with a unique triangular configuration, and the resulting Li3/GDY can be used as anode material for lithium ion batteries. Qi et al.42 investigated the performance of Pd clusters on GDY for catalytic reduction but did not characterize the structure of Pd clusters. Very recently, we showed that the Os3/GDY and its analogs are a class of potential catalyst for selective semihydrogenation of acetylene.43 Moreover, we predicted that the M3 form is indeed the most stable for Pt and Ni supported on GDY and suggested an efficient strategy based on the electrochemical potential window (EcPW) to prepare them via an electrochemical route.39 The metal trimer SCCs have been reported to deliver excellent performance. Based on Ji et al.'s reported experimental work, the Ru3 cluster supported on N-doped carbon material was shown to be an efficient catalyst for selective oxidation of alcohols.11 The Ag3 cluster on alumina support was demonstrated with high activity and selectivity for direct propylene epoxidation.18 The [Cu3(μ-O)3]2+ cluster in mordenite was shown to exhibit high reactivity towards activation of inert C–H bonds in methane.21,44 By first-principles calculations, we predicted that the Fe3 cluster supported on Al2O3 leads to an associative mechanism for low-temperature ammonia synthesis with a high turnover frequency.20 However, in addition to the EcPW strategy, our group suggested efficient and specific ways to prepare stable metal trimer SCCs that are still lacking because of the delicate requirement for the interaction between metal and support. On the one hand, when the metal-support bonding is much stronger than the metal–metal bonding, the metal trimer SC will dissociate to form SAs. On the other hand, if the metal-support interaction is much weaker than the metal–metal bonding, the metal trimer SCs will aggregate into bigger clusters or nanoparticles. Thus, it is a prerequisite for a support for hosting the metal trimer SCC to balance the metal–metal and metal–support bonding strengths. In this work, we investigate the viability of GDY as a support for TM trimer SCCs from both thermodynamic and kinetic aspects by first-principles calculations. All in all, we have considered 13 late TM elements for M3/GDY. The geometries and electronic structures of M3/GDY have been further analyzed by taking Cu3/GDY and Pt3/GDY as two typical examples. Finally, we investigated the catalytic performance of these M3/GDY SCCs for three kinds of key reactions: ORR, HER, and CO2 reduction reaction (CO2RR). The computational results thus provide guidelines for their practical applications as heterogeneous catalysts. Computational Details All density functional theory (DFT) calculations were performed with the plane-wave basis sets of 400 eV cutoff kinetic energy to approximate the valence electron densities and projector-augmented wave method to account for the core–valence interaction,45 as implemented in the Vienna Ab initio Simulation Package (VASP) code.46,47 The spin-polarized Kohn–Sham formalism with gradient-corrected exchange and correlation functional of the Perdew–Burke–Ernzerhof (PBE) flavor was adopted.48 The Γ-point-only sampling was used for the Brillouin zone integration for the GDY(2 × 2)-based models, which were adopted for energy calculations. And a 3 × 3 × 1 Brillouin zone grid sampling was used for the GDY(1 × 1)-based models, which were adopted for electronic structure analysis. All atoms as well as the lattice parameters a and b were allowed to relax for geometry optimization. The optimized lattice constant for pristine GDY that we got is | a| = | b| = 9.46 Å, in good agreement with the previously reported value of 9.48 Å by Long et al.49 The convergence criteria were set to be 10−6 eV and 0.01 eV/Å for wavefunction and geometry optimization, respectively. Free energy correction for all species was performed for ORR, HER, and CO2RR reactions by VASPKIT.50 For free molecules, the ideal gas approximation was assumed. For adsorbates, the contributions from all degrees of freedom to the free energies were treated as vibrations under the harmonic approximation, with unphysically low frequencies reset to a threshold of 60 cm–1, which corresponds to the acoustic translational mode of the six-membered rings in water bulk.51,52 All electrochemical calculations were based on Computational Hydrogen Electrode (CHE) model.53 For ORR, we shifted the chemical potential of the electrons by the equilibrium potential of U = 1.23 eV [vs standard hydrogen electrode (SHE)], corresponding to the situation where the fuel cell has the maximum potential allowed by thermodynamics. Ab initial molecular dynamics (AIMD) simulations were carried out for all M3/GDY(2 × 2). The AIMD calculations were started with the optimized configurations with lattice parameters fixed and were performed for more than 15 ps with a time step of 1 fs. The canonical (NVT) ensemble and Nosé-Hoover thermostats were used with the temperature set to 300 K.54,55 AIMD annealing was performed for each Mx/GDY (M = Fe, Co, Ni, Cu, Ru, Rh, Pd, Ag, Os, Ir, Pt, Au; x = 1–20, 30) structure. Mx clusters were deposited onto the GDY surface by simulated annealing from 1000 to 100 K in 10 ps, followed by structure optimization. This modeling process was carried out to mimic any experimental deposition procedure that does not necessarily impose precise control on the chemical potential for the target metal element, such as the traditional impregnation and coprecipitation methods. Phonon dispersion was calculated using density-functional perturbation theory,56 as implemented in the VASP and analyzed by interfacing with the Phonopy code.57 Band structures of GDY, Cu3/GDY, and Pt3/GDY were computed along the special line of Γ (0, 0, 0) → M (0.5, 0.5, 0) → X (0, 0.5, 0) → Γ (0, 0, 0) at both PBE and Heyd–Scuseria–Ernzerhof (HSE06) levels.58 Band decomposed charge densities were calculated at the Γ point for both the conduction band minimum (CBM) and valence band maximum (VBM) with degenerate bands summed up. Real space wavefunctions of CBM and VBM at the Γ point were extracted by VASPKIT.50 The crystal orbital Hamilton population (COHP) analysis was performed with the LOBSTER 3.1.0 package, which reconstructs the orbital-resolved wavefunctions via projection of the delocalized plane waves to localized atomic-like basis sets.59,60 The fragment molecular orbital (MO) analysis was performed using spin-restricted DFT with PBE and Slater basis sets of triple-zeta with two polarization functions (TZ2P) as implemented in the Amsterdam Density Functional (ADF) program.61 The frozen core approximation was applied to C[1s2] and Cu[1s2–2p6]. Relativistic effects were introduced by the zero-order regular approximation method. The optimized Cu3/GDY molecular counterpart and its corresponding fragments (Cu3 and GDY) were constrained to the D3h symmetry. Results and Discussion Stability of M3/GDY Scheme 1a shows the structure of pristine GDY (the details are listed in Supporting Information Table S1), in which the length of the Cc≡Cd bond (and its symmetric equivalents) is 1.227 Å, close to that in acetylene (1.20 Å), indicating a typical triple-bond character. There are six C≡C bonds bordering the 18MR-hole of GDY, but only two of them are involved in coordination with metal SA in reported M1/GDY cases (Scheme 1b).30 Meanwhile the remaining space of an 18MR-hole may accommodate two additional metal atoms coordinated by the rest of the four triple bonds to form M3/GDY (Scheme 1c). Thus, we investigated the stability of M3/GDY by comparing the average binding energies Ebind (Ebind = [E(Mx/GDY) − x · E(M, bulk) − E(GDY)]/x, where x is the number of atoms composing the anchored cluster of metal clusters on GDY, with M covering groups VIII and IB TM elements since they are usually considered as good catalyst candidates. Scheme 1 | Schematic illustrations of (a) GDY, (b) M1/GDY, and (c) M3/GDY. Download figure Download PowerPoint M1/GDY can hardly be the most stable case. Instead, it is most unstable for Fe, Co, Cu, Ru, Rh, Os, Ir, Pt, and Au on GDY when compared with other-sized clusters (Figure 1 and Supporting Information Figures S6, S7, S14, and S15). As expected, M3/GDY is the most stable case for Mx/GDY (x = 1 − 10) cases except Ag, Os, and Au. Taking Cu as an example, the Ebind of Cu1 on GDY is 1.57 eV, but it decreases dramatically to the lowest value of 0.81 eV for Cu3. When adding one more Cu atom to Cu3/GDY, Ebind increases to 1.06 eV. Ebind peaks at Cu5 with a value of 1.18 eV and starts to decrease to 0.90 eV at Cu20, due to the formation of more metal–metal bonds. Thus, x = 3 becomes a magic number for the thermodynamic stability of these GDY-supported metal clusters. To determine the thermodynamical difference between each cluster from a metal particle, we add a dashed line as reference to M30/GDY, which represents a typical ∼1 nm nanoparticle, in each subpanel of Figure 1. The thermodynamically stable M3/GDY systems lie lower than the dashed line, whereas the metastable or unstable M3/GDY are above this dashed line. Indeed, Fe, Co, Ni, Cu, Rh, and Pt, are relatively stable, but Ru, Pd, Ag, Os, Ir, and Au are not as stable as supported large particles such as M30/GDY. The bulk limit of adding an atom of a large metal particle is 0 eV as shown in Figure 1 because the equation of Ebind refers to the average energy per atom in bulk metal, E(M, bulk). Figure 1 | The average binding energies (Ebind) relative to bulk limit, Ebind = [E(Mx/GDY) − x · E(M, bulk) − E(GDY)]/x, of metal clusters with 1–20 and 30 atoms on GDY. E(Mx/GDY) and E(GDY) is the energy of GDY-supported metal clusters and GDY respectively. x is the number of atoms composing the anchored cluster. E(M, bulk) is the average energy per atom in bulk metal. The black curve shows the Ebind changes from M1 to M30. The points for M3/GDY are marked in red circles, and their structures are shown in the insets. The dashed line is the reference Ebind of M30/GDY, which represents typical ∼1 nm nanoparticle. The results show that Fe, Co, Ni, Cu, Rh, and Pt are relatively stable whereas Ru, Pd, Ag, Os, Ir, and Au are not as stable as supported large particles such as M30/GDY. Download figure Download PowerPoint AIMD simulations and phonon dispersions of all M3/GDY cases further characterize their kinetic stability ( Supporting Information Figures S1–S5 and S14). In the 15 ps AIMD trajectories, all M3 clusters remain at the 18MR, except for Ag3/GDY and Au3/GDY. The root-mean-square deviations of M3 clusters are all at low levels with small fluctuations, indicating that no diffusion and decomposition occur within 15 ps. The phonon spectrum, showing no imaginary frequency, further confirms the kinetic stability of Cu3/GDY ( Supporting Information Figure S5). The outstanding stability of M3/GDY enables the possibility of synthesizing them with the reported EcPW strategy, due to the presence of chemical potential windows that distinguish the trimer cluster form from the other-sized forms anchored on the GDY support.39 The stability of M3/GDY originates from the specific interactions between the metal trimer clusters and the GDY support, which can be analyzed and elucidated from geometries and electronic structures discussed in the following sections. Geometries and electronic structures of M3/GDY Only with M3 in the plane of GDY may M3/GDY retain the D3h symmetry, but most M3 cannot fit into the 18MR-hole. The optimized M3/GDY structures show that only Cu3/GDY is of D3h symmetry, and the rest of the M3/GDY structures have distortions in both the GDY substrate and M3 cluster. We summarize the three types of distortions as shown in Figure 2. Type I distortion is with the rotation of both C≡C bonds and M3 within the GDY plane. Type II distortion is with the out-of-plane rotation of M3. Type III distortion is also with M3 moving out of plane but with one metal atom detached from GDY. The cases of Mn, Fe, Ni, Co, Pd, and Pt belong to Type I distortion, which is of C3h symmetry. All type I structures locate in the stable region as shown in Figure 1. This distortion is due to the between the 18MR-hole and M3 or the requirement for specific The cases of Ru, Rh, Os, and belong to type II distortion, which has no symmetry. The cases of and Au belong to type III distortion, in which M3 is out of the GDY plane with only two atoms coordinated to GDY and the remaining atom out and M3 to the GDY plane. The bond of and Ag3 are and Å, which are large to fit in the For type II and III except all of them are relatively with type I distortion, types II and III are more between the 18MR-hole and M3 and are more Figure | Type and III distortions of structures of M3/GDY. Type I is the rotation in the plane with C3h (M = Mn, Fe, Ni, Co, Pd, and Type II break the but also bond with 18MR-hole (M = Ru, Rh, Os, and Type III is out of the GDY plane (M = and Download figure Download PowerPoint We further investigate the electronic structures of GDY, Cu3/GDY, and Pt3/GDY as The electron and potential of GDY show that the six triple bonds of 18MR-hole provide localized electrons the GDY at the sites for TM atoms. In Cu3/GDY each Cu atom indeed forms two coordination bonds with the localized systems of C≡C bonds in the GDY the systems to the GDY plane And the three of form a bond with the bonding electrons localized above the of (Figure which the as a potential For in addition to the shows a localized red region between Pt and (Figure a typical the of changes from to ( decreases from to with from the cluster and Figure 3 | The of for and GDY, and Cu3/GDY, and and Pt3/GDY at the GDY plane and Å above respectively. The region represents electrons and The charge density at for (c) GDY, Cu3/GDY, and where the red region is by and the region is by Download figure Download PowerPoint The band structures and Supporting Information Figure show that the direct band of GDY is calculated to be and eV at PBE and in agreement with previous The VBM of GDY is composed of the by the C≡C bonds and with the corresponding composing the In Cu3/GDY, two new bands between the VBM and which are composed of the bond by Cu and the The rest of the 3d bands of are and localized between to eV the The CBM bands of GDY are due to the charge from to GDY, indicating the of The charge of is indicating that one electron of is to GDY. Thus, the cluster is of oxidation and the two bonding electrons the bond the which is a typical The analysis of interactions between GDY and is in Supporting Information Figure which leads to Figure | The band structures and corresponding densities of states at PBE for and GDY, and Cu3/GDY, and and The red are by and the are by The of charge density of (c) VBM and CBM of GDY, of Cu3/GDY, and VBM and CBM of Download figure Download PowerPoint For the direct band is and eV at PBE and respectively. from Cu3/GDY, there is no new band between the VBM and CBM of GDY. Instead, the of are into the GDY as shown in the band structure and density of leads to charge from to GDY and bonding between Pt and the C≡C bonds of GDY into bonds. The crystal orbital Hamilton population of C≡C bonds is from to eV, and the of single bonds increases from to eV ( Supporting Information Figure Thus, the bond along the which is with the bond length and analysis ( Supporting Information Figure performance of low oxidation states of the metal the metal clusters of M3/GDY are and thus are good catalysts for reduction reactions ( Supporting Information Figure In the GDY substrate can as an electron to the oxidation of the M3 cluster the catalytic we investigate the ORR, HER, and CO2RR to the catalytic of M3/GDY as a novel of There are two for is the associative where is to The other is the where The associative mechanism − → The mechanism → , followed by − → We that on all the of is thermodynamically the molecular and the species is thermodynamically unstable with to Thus, the mechanism on and the four electrochemical ( 1 − → ( − → ( 3 − → ( − → that the of which is a chemical is into step because we only the electrochemical based on the method by et Figure the between the energy for each electrochemical step and For step its increases as the for the rest of the their have with to Figure | (a) The free energy for at U = 1.23 on M3/GDY. (b) The between and for each electrochemical step on M3/GDY. is the energy of each electrochemical at U = 0 Download figure Download PowerPoint on all M3/GDY has the as shown in Figure and thus it is always the potential step that the Only the of Cu3/GDY, and are lower than 1 that and Ag3/GDY are not stable, only Cu3/GDY, and are most to be the potential catalysts for with an of and respectively. we the Cu3/GDY, and with and metal to further investigate the catalytic difference between M3/GDY and their metal ( Supporting Information Figure The of and are and respectively. is that the atomic is for but its performance is not as good as the metal The is that all M3 clusters on GDY are which will and be in the electrochemical oxygen results of on all M3/GDY is on the of the This is from the corresponding of metal among which the Au and are on the of the curve to the other metal with Pt and Pd close to the of the There are two for HER, the mechanism and the The reaction of both the key via the − → ( the step in which the can be the (e.g., the or the water The step can be the of two or the further of by the from the → ( the step − → ( the step On there is only one site to accommodate one Thus, only the

Electrons have not only charge and spin degrees of freedom, but also additional valley degrees of freedom. The search for valleytronic materials with large valley splits is important for the development of valleytronics. In this work, we applied first principles computations to calculate 1 L Hf3C2O2 at the level of HSE06. When the spin-orbit coupling (SOC) effect is considered, 1 L Hf3C2O2 is an indirect bandgap semiconductor with a bandgap of 0.952 eV. Meanwhile, valley splitting occurs between the conduction bands Γ and K, with a valley splitting value as high as 98.228 meV. Bader charge analysis was used to determine that Hf-O and Hf-C are ionic bonds. The computed elastic constants and phonon spectra proved that 1 L Hf3C2O2 is mechanically and dynamically stable. In addition, the Berry curvature of 1 L Hf3C2O2 is non-zero. In the work the effect of the electronic properties of 1 L Hf3C2O2 was also calculated with respect to the biaxial strain. The results show that the biaxial strain can well regulate the band gap and valley splitting. Finally, we calculated the effects of hole and electron doping on the band gap and valley splitting of 1 L Hf3C2O2. The results show that the band gap and valley splitting are linearly related to the doping concentration. Our study shows that 1 L Hf3C2O2 is a promising two-dimensional valleytronics material.

<p indent="0mm">Given the importance of two-dimensional (2D) materials in the development of microelectronic devices, condensed matter physics and chemistry concepts, the existence of electrodes with two-dimensional electronic structures has become a hot research direction. Two-dimensional calcium nitride (Ca₂N) with a layered structure is a new type of 2D electrode materials, the conduction electrons are confined between Ca layers, and the 2D confined electrons behave as anions, showing the unique topological characteristics of electrode materials, which has potential applications in high-performance electronic devices and chemical synthesis. The space group of Ca₂N belongs to <italic>R3m</italic>, and the layers are stacked along the direction of the <italic>c</italic> axis. The interaction between the layers is through the van der Waals force, and the weak molecular force between the layers makes the single layer Ca₂N easy to be stripped from the body phase like graphene. But the influence of its electrical properties and its changing rules are not sufficiently studied. Doping can effectively regulate the electronic band structure and improve the integration of thin-layer two-dimensional materials, so as to accurately control and optimize various properties of materials. What’s more, doping not only regulates the band structure of the system, but also affects the magnetic properties of the system. It provides a novel approach for designing and constructing high-performance microelectronic devices. Therefore, the electrical properties of pure Ca₂N and the regulation of doping on its electrical properties are studied by first principles calculation based on density functional theory. Calculations were conducted using the Vienna Ab-initio Simulation Package (VASP). The energy cutoff for the plane wave basis set was set to <sc>500 eV,</sc> and the interactions between ionic cores and valence electrons were described using the projector augmented wave (PAW) method. For the exchange-correlation functional, the generalized gradient approximation (GGA) with the Perdew-Burke-Ernzerhof (PBE) functional was employed. The effects of doping elements (B/C/O/F) on Ca₂N geometry and electronic structures, including atomic spacing, bond length and charge transfer, were investigated. The study reveals that the phonon spectrum of pristine two-dimensional Ca₂N shows no imaginary frequencies, indicating its thermodynamic stability. Similarly, after doping, the phonon spectra still exhibit no imaginary frequencies; however, bond distortions occur near the dopant atoms, altering the surface structure and significantly affecting the work function and electronic states. It is found that the Ca-N bond length of the nearest and second nearest neighbors is affected after all doping atoms replace N. Specifically, when B (boron) replaces N (nitrogen), the bond length between Ca and B is the longest, while the next-nearest Ca-N bond length significantly decreases. When B and C (carbon) are doped, there is a notable change in the charge distribution, which not only effectively alters the electronic states and magnetism of Ca₂N but also imparts semi-metallic characteristics. In contrast, F (fluorine) and O (oxygen) doping have a relatively minor impact on the electronic states of the system. Therefore, the appropriate selection of doping elements provides a guide for the functional chemically reactive monolayer Ca₂N electrode, so as to achieve a wide range of practical applications.

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