Second-order Energy Difference Research Articles

Unveiling the effects of thallium and bismuth p-n doping on germanium-based clusters (n5 to n12) for applications in semiconductor materials

We report a computational investigation utilizing density functional theory (DFT) concerning the pure Gen, as well as their doped analogues (BiGen-1, TlGen-1) and p-n doped BiTlGen-2 clusters with n ranging from 5 to 12. To get a deeper insight in their properties, we focus on the size dependency of these Gen, BiGen-1, TlGen-1, and BiTlGen-2 clusters as well as their shape, relative stabilities, and thermochemical characteristics including binding energy, fragmentation energy, second-order energy difference, and HOMO-LUMO energy gaps. The systematic observations from the data of binding energies indicate that BiGen-1, TlGen-1 and BiTlGen-2 cluster have more structural and thermodynamic stability when compared with the pure Gen clusters. To validate the electronic characteristics of these clusters, additional energy gap-related parameters such as chemical hardness, vertical ionization potentials (VIP), and vertical electron affinities (VEA) are also computed. The doping seems to stabilize the Gen clusters and the highest stability has been achieved for BiGe7, TlGe9, and BiTlGe7 clusters as suggested by the combined effect of all these parameters.

Structural Evolution of Small-Sized Phosphorus-Doped Boron Clusters: A Half-Sandwich-Structured PB15 Cluster.

The present study is a theoretical investigation into the structural evolution, electronic properties, and photoelectron spectra of phosphorus-doped boron clusters PBn0/- (n = 3-17). The results of this study revealed that the lowest energy structures of PBn- (n = 3-17) clusters, except for PB17-, exhibit planar or quasi-planar structures. The lowest energy structures of PBn (n = 3-17), with the exceptions of PB7, PB9, and PB15, are planar or quasi-planar. The ground state of PB7 has an umbrella-shaped structure, with C6V symmetry. Interestingly, the neutral cluster PB15 has a half-sandwich-like structure, in which the P atom is attached to three B atoms at one end of the sandwich, exhibiting excellent relative and chemical stability due to its higher second-order energy difference and larger HOMO-LUMO energy gap of 4.31 eV. Subsequently, adaptive natural density partitioning (AdNDP) and electron localization function (ELF) analyses demonstrate the bonding characteristics of PB7 and PB15, providing support for the validity of their stability. The calculated photoelectron spectra show distinct characteristic peaks of PBn- (n = 3-17) clusters, thus providing theoretical evidence for the future identification of doped boron clusters. In summary, our work has significant implications for understanding the structural evolution of doped boron clusters PBn0/- (n = 3-17), motivating further experiments regarding doped boron clusters.

A computational investigation of XnK(X = Mn, Fe, co; n = 1–8) clusters by density functional theory

The properties of XnK(X = Mn, Fe, Co; n = 1–8) clusters have been systematically investigated using quantum calculations of LANL2DZ basis sets at the PBE1PBE level. By optimizing different structural isomers, we determined the ground state structure of XnK clusters, which tends to be compact as the cluster size increases. In order to study the stability of clusters, the average binding energies, dissociation energies and second-order difference of total energies of XnK clusters are calculated. The results show that the stability of FenK clusters is comparable to that of ConK clusters, and both are higher than that of MnnK clusters. Finally, the chemical activity and magnetic properties of the clusters are discussed. The dissociation energies, second-order difference of total energies, HOMO-LUMO energy gaps, and magnetic moments of the ground-state clusters show an irregular oscillatory behavior with atomic number. Fundamental insights obtained in this study can be useful in the design of Mn-K/Fe-K/Co-K catalysts.

The geometry, electronic and magnetic properties of Zr n Ni (n = 2-14) clusters: A first-principles jointed particle-swarm-optimization investigation

Zirconium-nickel binary alloys and metal glass have superior performance like ultrahigh fracture strength, good toughness. In this paper, the structures of small-sized Zr n Ni (n = 2–14) clusters have been searched using the particle swarm algorithm in combination with density-functional theory (DFT). The geometrical configuration tends to form a three-dimensional structure as the number of atoms in the cluster increases. By calculating the average binding energy per atom, second-order difference of energy, and dissociation energy of Zr n Ni (n = 2–14) clusters, it is demonstrated that Zr n Ni (n = 7, 12) clusters are more stable than their neighbors, and can be used as a candidate structure for magic number clusters. The electron localization function (ELF) calculations reveal those metallic bonds of Zr-Ni and Zr-Zr atoms. The Adaptive natural density partitioning results show that there are 20 three-center and 7 seven-center two-electron orbitals which make the quenching of magnetic moments of Zr12Ni atoms.

Structure and stability of Cu-doped Bn (n = 1–12) clusters: DFT calculations

The structural and stability properties of Cu-doped boron clusters (BnCu with n = 1–12) are investigated by the SCG (systematic growth algorithm) method in combination with density functional theory (DFT) calculations. The lowest-energy structures of BnCu clusters show similar arrangements with peripheral Cu-doping on preceding pure Bn clusters. Planar and quasi-planar structures are found for n = 3–6 and n = 10–12 while three-dimensional for n = 7–9. The relative stability of the clusters is further analyzed through the average binding energy, the first and second-order energy differences. The results show that B3Cu, B5Cu, B8Cu and B11Cu, are the most stable clusters. The electronic properties such as the ionization potential and electron affinity are calculated and compared with available experimental data. BnCu clusters with even number of boron atoms show higher electron affinities. The bonding character of the clusters is discussed.

Structure and stability of Mo-doped Cun (n = 1–12) clusters: DFT calculations

The thermodynamic and chemical stability of CunMo (n = 1–12) clusters are evaluated by density functional theory (DFT) calculations. The most stable structures are obtained by using the SCG (systematic growth algorithm) and corroborated by simulated annealing. The lowest-energy structures of CunMo clusters are planar and quasiplanar for n = 3–7, while icosahedral-like structures for n = 8–12. The relative stability of the clusters is further analyzed through the average binding energy, the fragmentation energy and second-order energy differences. The results of EB shows that doping with Mo slightly reduces the stability of small clusters with n = 1–7, however, for n = 8 onward, the doped clusters become more stable due to the formation of the icosahedral structure at Cu12Mo. The results show that Cu4Mo, Cu7Mo, Cu9Mo and Cu12Mo, are more stable than the neighbor clusters. In addition, the doped clusters show higher HOMO–LUMO gaps and total spin magnetic moments compared to pure Cun clusters. The IR spectra of the clusters are provided.

Investigation on the correlation of stability, reactivity, and structural properties of C/C2-doped neutral and charged Aln (n = 2–7) clusters

The equilibrium geometries, electronic structures, reactivity, and stability of C/C2-doped Aln0,± (n = 2–7) clusters were investigated computationally at B3LYP-D4/def2-TZVPP and CCSD(T)/def2-TZVPP levels of theory. The lowest energy structures of AlnC1,20,± clusters were the carbon atoms inserted inside the aluminium clusters. The stability of the neutral and charged clusters were investigated under various reaction conditions, such as dissociation of the clusters via Al0,+,C0,-,C20,--elimination and electron elimination from neutral (ionization) and anionic species (electron detachment). The dominant dissociation reaction channels are the Al-elimination from the neutral and anionic clusters, Al+-elimination from cationic clusters, rather than the C/C2-elimintion reaction. On the other hand, C-elimination are were more favorable compared to C2-elimination due to the stronger CC and Al-C bonds. In addition, binding energy, second-order difference of energy, chemical hardness, and electron affinity parameters were used to determine the stability and reactivity. The results show the singlet cluster (Al2,4,6C1,2 and Al3,5,7C0-20,±) have the greater stability than the doublet clusters (Al3,5,7C0-2 and Al2,4,6C1,20,±) and triplet clusters (Al2,4,6). It has been demonstrated that anionic clusters are more stable than the neutral species, and cationic species are less stable than that of neutral species. The current study could be useful in understanding the stability and reactivity of metal clusters after carbon doping, which is important in combustion, material science, and the astrochemical community.

Physicochemical Characteristics for Fen (n = 2–10) Cluster by Density Functional Theory

The In this work, we present a theoretical study on the equilibrium geometry and the energetic, electronic and magnetic properties of Fen (n = 2–10) based on the use of density functional theory (DFT). The results are obtained using Both Generalized Gradient Approximation according to the scheme described by Perdew-Burke-Ernzerhof (GGA-PBE). More stable structures obtained compared to other isomers have not been previously found. It is shown by the results calculated as the calculated fragmentation energy, and the second-order energy difference that Fen (n = 7,8,9) clusters are more stable than the other cluster sizes. The calculated magnetic properties of the most stable clusters display varying magnetic torque between values 3.00 μB and 3.35 μB, except for the Fe10 cluster, which takes the upper value 3.38 μB. These results are very important for experimental experts who are active in designing new nanocatalysis systems in the physical and chemical fields.

Structure and dynamics of 38-atom Ag-Pt nanoalloys using ANN based-interatomic potential

Silver–platinum nanoalloys are potential candidates as effective and less expensive catalysts than pure platinum-based catalysts. The reactivity of these nanoalloys depends crucially on their size, composition, and ordering of the constituent Ag and Pt atoms. Moreover, the presence of a second metal atom in these nanoalloys results in a variety of structural configurations in comparison to their pure counterparts. To explore the structural aspects further, in this paper, we developed an interatomic potential for Ag–Pt nanoalloys based on an artificial neural network model. We systematically carried out structural and energetic analysis of Ag38−nPtn (n = 1 −8) nanoalloys. Using neural network-based interatomic potential, we have also performed molecular dynamics simulations and global optimizations to search the global minimum structures as well as to investigate the effect of temperature on the structures of silver–platinum nanoalloys. We find the lowest energy isomers of Ag38−nPtn nanoalloys are a core–shell structure in which the Pt atoms occupy the core region while the Ag atoms are located in the surface region. The relative stability of nanoalloys has been investigated using excess energy and second-order energy difference calculations. The charge distribution over Pt and Ag atoms is determined for all the lowest energy isomers of Ag38−nPtn nanoalloys. Furthermore, the probability of the presence of a Pt atom on the surface sites in Ag38−nPtn nanoalloys has been calculated at finite temperatures. We find that at 360K, at least one Pt atom moves from the core to the surface region of the Ag38−nPtn nanoalloys.

SnAu clusters as detectors of CO and NO gases: A DFT study

Monitoring and control of CO and NO gases are now considered important for public health. These can be achieved by the research and development of novel sensors. Bimetallic Au–Me clusters such as Au-Pt, Au-Pd, and Au-Pb exhibit extremely high sensitivity, making them suitable for application in gas adsorption and sensing. Here, the ground-state structure, average binding energy, fragmentation energy, second-order energy difference, HOMO–LUMO gap, and average charge of SnnAun (n: 2–12) clusters were evaluated using density functional theory calculations. It was found that the SnnAun (n = 3, 8) clusters exhibited optimal performance in terms of chemical stability and charge transfer dynamics. Furthermore, the efficiency of CO and NO adsorption on the SnnAun (n = 3, 8) clusters was investigated in terms of the geometric, energetic, and electronic properties of the clusters. The results showed that CO and NO molecules chemisorb on the SnnAun (n = 3, 8) clusters, thereby allowing limited charge transfer, which significantly affects the physical properties and HOMO–LUMO gap of CO and NO molecules. These results suggest that the SnnAun (n = 3, 8) clusters can act as gas adsorbents for CO and NO molecules, and also can be used as effective sensors for NO detection.

An Open-Shell Superatom Cluster Ta10- with Enhanced Stability by United d-d π Bonds and d-Orbital Superatomic States.

We carried out a comprehensive study on the gas-phase reactions of Tan- (n = 5-27) with nitrogen using a customized reflection time-of-flight mass spectrometer coupled with a velocity map imaging apparatus (Re-TOFMS-VMI). Among the studied tantalum clusters, Ta10- exhibits prominent mass abundance indicative of its unique inertness. DFT calculation results revealed a D4d bipyramidal prolate structure of the most stable Ta10-, which was verified by photoelectron spectroscopy experiments. The calculations also unveiled that Ta10- has the largest HOMO-LUMO gap and second-order difference of binding energy among the studied clusters. This is associated with its well-organized superatomic orbitals, which consist of both 6s and 5d orbitals of tantalum atoms, allowing for splitting of superatomic 1D and 2P orbitals and an enlarged gap between the singly occupied molecular orbital (SOMO) and unoccupied β counterpart, which brings forth stabilization energy pertaining to Jahn-Teller distortion. Also, the SOMO exhibits a united d-d π orbital pattern that embraces the central Ta8- moiety.

Density Functional Study of Size-Dependent Hydrogen Adsorption on Ag n Cr (n = 1-12) Clusters.

Increasing interest has been paid for hydrogen adsorption on atomically controlled nanoalloys due to their potential applications in catalytic processes and energy storage. In this work, we investigate the interaction of H2 with small-sized AgnCr (n = 1–12) using density functional theory calculations. It is found that the cluster structures are preserved during the adsorption of H2 either molecularly or dissociatively. Ag3Cr–H2, Ag6Cr–H2, and Ag9Cr–H2 clusters are identified to be relatively more stable from computed binding energies and second-order energy difference. The dissociation of adsorbed H2 on Ag2Cr, Ag3Cr, Ag6Cr, and Ag7Cr clusters is favored both thermodynamically and kinetically. The dissociative adsorption is unlikely to occur because of a considerable energy barrier before reaching the final state for Ag4Cr or due to energetic preferences for n = 1, 5, and 8–12 species. Comprehensive analysis shows that the geometric structure of clusters, the relative electronegativity, and the coordination number of the Cr impurity play a decisive role in determining the preferred adsorption configuration.

Quantum Chemistry Study on the Structures and Electronic Properties of Bimetallic Ca2-Doped Magnesium Ca2Mgn (n = 1-15) Clusters.

Here, by utilizing crystal structure analysis through the particle swarm optimization (CALYPSO) structural searching method with density functional theory (DFT), we investigate the systemic structures and electronic properties of Ca2Mgn (n = 1–15) clusters. Structural searches found that two Ca atoms prefer to occupy the external position of magnesium-doped systems at n = 2–14. Afterward, one Ca atom begins to move from the surface into the internal of the caged skeleton at n = 15. Calculations of the average binding energy, second-order difference of energies, and HOMO–LUMO gaps indicated that the pagoda construction Ca2Mg8 (as the magic cluster) has higher stability. In addition, the simulated IR and Raman spectra can provide theoretical guidance for future experimental and theoretical investigation. Last, further electronic properties were determined, including the charge transfer, density of states (DOS) and bonding characteristics. We hope that our work will provide theoretical and experimental guidance for developing magnesium-based nanomaterials in the future.

Gorkov algebraic diagrammatic construction formalism at third order

Background: The Gorkov approach to self-consistent Green's function theory has been formulated by Som\`a, Duguet, and Barbieri in [Phys. Rev. C 84, 064317 (2011)]. Over the past decade, it has become a method of reference for first-principles computations of semimagic nuclear isotopes. The currently available implementation is limited to a second-order self-energy and neglects particle-number nonconserving terms arising from contracting three-particle forces with anomalous propagators. For nuclear physics applications, this is sufficient to address first-order energy differences (i.e., two neutron separation energies, excitation energies of states dominating the one-nucleon spectral function), ground-state radii and moments on an accurate enough basis. However, addressing absolute binding energies, fine spectroscopic details of $N\ifmmode\pm\else\textpm\fi{}1$ particle systems or delicate quantities such as second-order energy differences associated with pairing gaps, requires going to higher truncation orders.Purpose: The formalism is extended to third order in the algebraic diagrammatic construction (ADC) expansion with two-body Hamiltonians.Methods: The expansion of Gorkov propagators in Feynman diagrams is combined with the algebraic diagrammatic construction up to the third order as an organization scheme to generate the Gorkov self-energy.Results: Algebraic expressions for the static and dynamic contributions to the self-energy, along with equations for the matrix elements of the Gorkov eigenvalue problem, are derived. It is first done for a general basis before specifying the set of equations to the case of spherical systems displaying rotational symmetry. Workable approximations to the full self-consistency problem are also elaborated on. The formalism at third order it thus complete for a general two-body Hamiltonian.Conclusions: Working equations for the full Gorkov-ADC(3) are now available for numerical implementation.

Density functional theory study of BiRun (n = 3–20) clusters: Structural, electronic and adsorptive properties for hazardous gases

The geometric structures and electronic properties as well as adsorption of some harmful gas molecules for BiRun (n = 3–20) clusters are investigated using the generalized gradient approximation of density functional theory (DFT/GGA). The clusters largely show low symmetries (e.g., Cs) and generally exhibit the polyhedral structures with Bi atom at the vertices, while BiRu6, BiRu11, BiRu12 and BiRu17 clusters have the highest C5V symmetry and stability. Interestingly, the structure of BiRun (n = 3–20) clusters shows growth property, i.e., construction of BiRun (n = 3–20) by addition one Ru atom to BiRun−1, and Run and Run−1 clusters also have similar geometrical structures. BiRu5 and BiRu12 are found to exhibit relatively higher thermodynamic stability from the second-order energy difference. BiRu12 and BiRu6 can display the highest chemical stability and activity in view of the largest and smallest energy gap Eg, respectively. Vertical ionization potential (VIP) and vertical electron affinity (VEA) show the decreasing and increasing trends with n, respectively. As for the adsorption properties of these clusters for harmful gas molecules, excellent and good adsorption performances are found for CO and NH3 molecules adsorbed on BiRu14 and BiRu20, whereas NO and H2S molecules exhibit poor adsorption properties on these clusters. The study of this work would be helpful to construct and characterize the electronic properties of BiRun (n = 3–20) clusters and to explore their potential adsorption performances and the prospect to act as efficient sensors for the harmful gases.

A Comparison of Structure, Stability of Neutral and Cationic Vanadium-doped Germanium Clusters GenV0/+ (n = 2 - 8) by using Density Function Theorym clusters GenV0/+ (n = 2 - 8) by using density function theory

The geometries, stabilities and electronic properties of vanadium-doped germanium clusters GenV0/+ (n=2-8) were systematically investigated by using density functional theory (DFT) at the PBE level and the 6-311+G(d) basis set. The results show that the geometries of lowest-energy structures of the cationic clusters are only significant different from those of the neutral at n = 6 or 7. The ground state of neutral clusters is a doublet, except Ge2V which is a quartet while that of cationic clusters is a triplet, except Ge8V+, which is a singlet. The average binding energy values generally increase with increasing cluster size. The results from average binding energies showed that it is more stable for the cationic than neutral clusters at the same size. Furthermore, the calculated values of fragmentation energy, second-order energy difference, HOMO-LUMO gap and adiabatic ionization potential suggest that the neutral clusters possess higher stability when n = 2, 5, 8 and the cations are more stable when n = 2, 3, 5 and 6.

Growth mechanism, electronic properties and spectra of aluminum clusters

Density functional theory (DFT) and particle swarm optimization (PSO) have been applied to study the growth behavior, electronic properties and spectra of neutral, anionic and cationic aluminum clusters with 3–20 atoms. Many isomers have been obtained through a comprehensive structural search. The results indicate that the ground state structures of neutral and anionic aluminum clusters follow an identical periodic growth law. When the number of atoms is 6–11 and 13–18, Al atoms in these clusters grow around an octahedral cluster nucleus and an icosahedral cluster nucleus, respectively. For Aln+ (n ≤ 14 and n ≠ 7) clusters, the most stable structure is different from that of Aln or Aln−clusters. When n > 14, the ground state structure of Aln+ clusters is similar to that of Aln or Aln−clusters. The electronic properties of aluminum clusters have been analyzed by the averaged binding energy, second-order difference of energy, energy gap and dissociation energy. It is found that the Al7+ and Al13− clusters have very high stability and a large energy gap and can be regarded as two superatoms. The aluminum cluster with 18 or 40 valence electrons are the least likely to lose an electron. The dissociation behavior of Aln+ clusters caused by collision is reasonably explained by means of the dissociation energy. The optical absorption spectra of neutral aluminum clusters have been simulated by using the time-dependent density functional theory. The ground states of anionic aluminum clusters have been determined by comparing theoretical photoelectron spectra (PES) with experimental findings. Infrared and Raman spectra of cationic aluminum clusters have been forecasted and can assist in identifying the most stable structure in future experiments.

Probing structural and electronic properties of divalent metal Mg n+1 and SrMg n (n = 2–12) clusters and their anions

Divalent metal clusters have received great attention due to the interesting size-induced nonmetal-to-metal transition and fascinating properties dependent on cluster size, shape, and doping. In this work, the combination of the CALYPSO code and density functional theory (DFT) optimization is employed to explore the structural properties of neutral and anionic Mg n + 1 and SrMg n (n = 2–12) clusters. The results exhibit that as the atomic number of Mg increases, Sr atoms are more likely to replace Mg atoms located in the skeleton convex cap. By analyzing the binding energy, second-order energy difference and the charge transfer, it can be found the SrMg9 cluster with tower framework presents outstanding stability in a studied size range. Further, bonding characteristic analysis reveals that the stability of SrMg9 can be improved due to the strong s–p interaction among the atomic orbitals of Sr and Mg atoms.

Copper-carbon clusters CunCm (n, m = 1–6): Segregation, bonding and Raman spectra

Structural and electronic properties of the lowest-energy structures of CunCm (n, m = 1–6) clusters have been calculated using density functional theory. Among these thirty-six doped clusters, the segregation effect between carbon and copper atom is observed and C-clumping maintains the chain structure. The relative stabilities of CunCm have been examined by means of the averaged atomic binding energies, the second-order difference of energies and the fragmentation energies. The calculated electron localization function and Mayer bond order are in good agreement with adaptive natural density partitioning. The analysis of the structure and bonding properties of the weak Cu-C interaction contributes to understanding the growth mechanism of catalytic carbon fibers.

Geometric and electronic properties of AulPtm (l + m ≤ 10) clusters: a first-principles study.

The structural evolutions and electronic properties of AulPtm (l + m ≤ 10) clusters are investigated by using the first-principles methods. We use the inverse design of materials using the multi-objective differential evolution (IM2ODE) package to globally search the equilibrium structures and investigate the evolving trend from a two-dimensional structure to a three-dimensional structure on horizontal extension and vertical extension for AulPtm (l + m ≤ 10) clusters. The three-dimensional stable geometry of Au8Pt and Au8Pt2 is discovered for the first time in our work. We also notice that the equilibrium structures of AulPtm (l + m = 10 and l ≤ 8) tend to form a tetrahedral geometry and can be obtained by replacing the Au atom in the most stable structure of Aul+1Ptm-1 with the Pt atom, where Pt atoms assemble together and occupy the center of clusters and Au atoms prefer to lie on the vertex or edge position. The average binding energy (Eb) is mostly decided by Pt-Pt bond numbers, namely the numbers of Pt atoms, followed by Au-Pt bond numbers. The second-order energy difference (Δ2Ev and Δ2Eh) and the nearest-neighbor energy difference (Δ4Enn) show that Au6Pt, Au4Pt2, Au3Pt3, Au2Pt4 and AuPt7 clusters exhibit high relative physical stability, so we suggest that these clusters could be defined as the magic number clusters for AulPtm (l + m ≤ 10) clusters. The HOMO-LUMO energy gap (Eg), adiabatic ionization potential (AIP) and the adiabatic electron affinity (AEA) are also investigated to elaborate the relative electronic stability of all the clusters.