Second-order Energy Difference Research Articles

Structural Evolution and Electronic Properties of TaSin-/0 (n = 2-15) Clusters: Size-Selected Anion Photoelectron Spectroscopy and Theoretical Calculations.

The structural evolution and electronic properties of TaSin-/0 (n = 2-15) clusters are explored using anion photoelectron spectroscopy accompanied by quantum chemical calculations. The Ta atom in TaSin-/0 is inclined to interact with more Si atoms and has high coordination numbers. The theoretical calculations show that TaSi2-/0 have trianglur structures and TaSi3-/0 adopt pyramid structures, while the geometries of TaSin-/0 (n = 4-7) are all exohedral structures dominated by bipyramid-based configurations with the Ta atom face-capping the Sin motifs. TaSi8-/0 and TaSi9-10- have boat-shaped geometries, whereas TaSi9-10 neutrals adopt bipyramid-based geometries instead of boat-shaped ones. TaSi11- and TaSi12 are confirmed as the critical size of transiting from exohedral to endohedral structures for anionic and neutral clusters, respectively. TaSi12-15-/0 have pentagonal or hexagonal prism-based geometries. Natural population analysis shows that the electron transfers from Sin skeletons to Ta atom. The second-order energy differences (Δ2E) and incremental binding energy (ΔEI) values exhibit strong odd-even alternations, suggesting that the TaSin-odd-/0 clusters are more stable than the adjacent TaSin-even-/0 ones, except that TaSi12-/0 are more stable than TaSi11-/0 and TaSi13-/0.

Li containing endohedral SWCNT: DFT study of the structural and electronic properties

We investigate the geometrical structures, relative stabilities, and electronic properties of lithium-doped endohedrally to the single-walled carbon nanotubes (5,0), (6,0), (7,0), (8,0), (7,7), and (8,8), through DFT calculations. The obtained optimized geometries reveal that Li atoms insertion dramatically modifies the nanotube structures. Averaged binding energies, fragmentation energies, second-order energy differences, and Mulliken population analysis are expressed as Li concentration functions. Results reveal Fermi level displacement towards the conduction band due to the Li atoms' charge transfer to the nanotube walls. Stability analysis identifies the complexes with superior relative stability. In particular, nanotubes (7.7) and (8.8) show storage capacities that exceed the graphite's intercalation limit.

The geometry, electronic and magnetic properties of VLi n (n = 2–13) clusters using the first-principles and PSO method

ABSTRACT In this paper, the growth pattern, magnetic and electronic structure of VLi n (n = 2–13) clusters are studied using density functional theory in generalised gradient approximation. The growth pattern showed that the VLi n (n = 2–13) clusters favoured the three-dimensional configuration and appeared cage-like structures with increasing size. The average binding energy, second-order energy difference and dissociation energy are discussed, and the VLi12 cluster is magnetic superatom. The spin magnetic moment of VLi12 cluster is 1 μ B and the molecular orbital arrangement is 1S21P61Dα 51Dβ 4. The chemical bonding patterns of the VLi12 cluster was obtained by using molecular orbital analysis and the adaptive natural density partitioning method.

Theoretical Investigation on Structure-Property Relationship of Asymmetric Clusters (CH3FBN3)n (n = 1– 6)

The structural, relative stability, electronic, IR vibrational, and thermodynamic properties of asymmetric clusters (CH3FBN3)n (n = 1–6) are systematically investigated using density functional theory (DFT) method. Results show that clusters (CH3FBN3)n (n = 2–6) form a cyclic structure with a B atom and a Nα atom binding together. Five main characteristic regions are observed and assigned for the calculated IR spectra. The size-dependent second-order energy difference shows that clusters (CH3FBN3)3 and (CH3FBN3)5 have relatively higher stability and enhanced chemical inertness compared with the neighboring clusters. These two clusters may serve as the cluster-assembled materials. The variations of thermodynamic properties with temperature T or cluster size n are analyzed, respectively. Based on enthalpies in the range of 200–800 K, the formations of the most stable clusters (CH3FBN3)n (n = 2–6) from monomer are thermodynamically favorable. These data are helpful to design and synthesize other asymmetric boron azides.

Theoretical study of the physicochemical characteristics for Boron-Germanium BGen (n = 1–20) clusters

We present a theoretical study on the equilibrium geometries, energetic, electronic, and magnetic characteristics of BGen (n = 1–20) clusters using the density functional theory (DFT) calculations. The most stable structures display a B atom located at the surface of BGen clusters, except for BGe9, 12, 16, 18, 19, 20. Larger clusters reveal higher binding energy, suggesting their greater stability compared to the corresponding Gen+1 clusters. The calculated fragmentation energy, second-order energy difference, and HOMO-LUMO energy gap reveal that the BGe9, 12 clusters are more stable than other cluster sizes. The calculated magnetic properties of the lowest-energy BGen clusters display a total spin magnetic moment equal to 1 μB, except for the BGe cluster, which takes the value 3 μB. These findings can be useful to the experimentalists in designing new Nano-catalytic systems.

Structures and properties of [Ag(Ag2S)n]+ clusters with n = 1–9: a density functional theory study

Silver sulfide clusters with size less than 2 nm are of much interest in photoelectric devices, such as photoconductive devices, infrared detectors and superconductors. The electronic structures of [Ag(Ag2S)n]+ (n = 1–9) clusters are investigated using the combined method of genetic algorithm (GA) and density functional theory (DFT). Results reveal that S atoms prefer to be at the tip of the structure, and Ag atoms tend to form S-Ag-S unit between two S atoms. With the increase of cluster size, the open structure evolves into closed centre-hollow structure. According to the stability analysis, [Ag(Ag2S)6]+ is a magic number cluster due to its high HOMO-LUMO gap, big average energy and high second-order energy difference. Ag-S bonds, S-Ag-S and triangular Ag3S3 units play key roles in stabilizing [Ag(Ag2S)n]+ clusters. According to the electron affinity energy analysis, the clusters are easier to get electrons when n = 1, 3, 5 and 9. Based on the charge analysis of the studied clusters, the charges on Ag and S atoms are positive and negative, respectively, which indicates that the charge transfer from Ag to S occurs in cluster. Infrared and Raman spectra are dependent on the symmetries of the clusters. The molecular orbitals of [Ag(Ag2S)6]+ and [Ag(Ag2S)8]+ present superatomic properties. We hope that the clusters studied here could provide valuable data for future experimental and theoretical study of cationic silver sulfide clusters.

A Density Functional Investigation on LinI (n = 1–8) Clusters

A density functional theory (DFT) investigation on isomeric structures of lithium-iodide clusters, and stabilities as well as electronic structure features of global equilibrium structures are reported. The relative energies and population values of structural isomers for LinI (n = 1–8) clusters are obtained at the B3LYP/Lanl2dz and B3LYP/6-311G(d,p) theory levels. The iodine atom prefers the apex position in the most stable structures within the coordination number two except Li6I and Li8I clusters. The binding energies, dissociation energies, second-order energy differences, HOMO–LUMO gaps, ionization and elimination energies of global minimum structures are calculated in order to get beneficial information about the stability and electronic properties of LinI (n = 1–8) clusters. The results of relative energies affirm an odd–even oscillation that LinI (n = 1, 3, 5, 7) clusters are more stable than neighboring clusters. The iodine atom also enhances the stability order of pure lithium clusters while the cluster size grows up this stability decreases, and lithium-iodide clusters become more reactive. The ionization and elimination energy results also show that LinI (n = 1–8) clusters can be classified as superalkalies due to owing lower ionization energies than Li atom and the interaction between pure lithium clusters and iodine atom can be realized as electrostatic bonding.

Structural evolution and magnetic properties of ScLin (n = 2–13) clusters: A PSO and DFT investigation**Project supported by the Natural Science Foundation of Xinjiang Uygur Autonomous Region, China (Grant Nos. 2018D01C079 and 2018D01C072).

The stable geometries, electronic structures, and magnetic behaviors of the ScLin (n = 2–13) clusters are investigated by using particle swarm optimization (PSO) and density functional theory (DFT). The results show that these clusters have three-dimensional (3D) structures except ScLi2, and ScLi12, and ScLi13 that possess the cage-like structures. In analyses of the average binding energy, second-order difference of energy, and fragmentation energy, ScLi12 cluster is identified as magnetic superatom. The magnetic moment for each of these clusters owns an oscillating curve of different cluster sizes, and their magnetic moments are further investigated using molecular orbitals and jellium model. Of ScLin (n = 2–13) clusters, ScLi12 has the largest spin magnetic moment (3 μB), and molecular orbitals of ScLi12 can be described as . Additionally, Mulliken population and AdNDP bonding analysis are discussed and the results reveal that the Sc atom and Lin atoms make equal contribution to the total magnetic moment, and atomic charges transfer between Sc atoms and Li atoms.

Structures, stabilities and electronic properties of Pt-Rh clusters based on DFT and Sutton-Chen potential

Using the density functional theory (DFT) at meta-generalized gradient approximation (meta-GGA) exchange-correlation TPSSTPSS functional with LANL2DZ pseudopotential, the variations of the geometric structures, stabilities and electronic properties with the changes of n and m of PtnRhm (n + m ≤ 6) clusters are systematically investigated. Clusters with higher nuclearity favor three dimensional structure while clusters with low nuclearity (n + m < 4) and Pt6 cluster favor planar two dimensional configuration. The results for various properties including average binding energies per atom, the second-order difference of energies, HOMO-LUMO gap, vertical ionization potentials, vertical electron affinities, and chemical hardness are evaluated as a function of size of the system. It is found that Pt3Rh2 and Pt5Rh clusters possess stronger stability. Furthermore, Sutton-Chen potential is applied to study the stable structures of 38- and 55-atom Pt-Rh clusters by using adaptive immune optimization algorithm. Structural characteristic and relative stability are discussed.

Solvation of lithium ion in helium clusters: Structural properties and relative stabilities

Structural study and relative stabilities of Li+-doped helium clusters Li+Hen (n = 1–18) has been reported in this work using two theoretical protocols. The first one is based on the basin-hopping optimization technique, where the total energy of each cluster is described by an additive model describing Li+-He and He–He interactions. The second one is the DFT calculations, in which the initial structures are generated by ABCluster algorithm and CALYPSO software. The CSA shape was found where the first solvation shell is completed at n = 10. The relative stabilities of Li+Hen (n = 1–18) clusters have been discussed based on the variation of the binding energy, second-order difference in energy, fragmentation energy and HOMO-LUMO energy gap as a function of the cluster size. The results showed that Li+He10 is the most stable cluster. The dipole moment is calculated and showed the polar character of the Li+Hen clusters. Finally, the interatomic interactions have been examined topologically by the means of AIM and non-covalent reduced density gradient (NC-RDG) analyses.

Electronic Structure and Properties of Silicon-Doped Boron Clusters BnSi withn= 15–24 and Their Anions

We investigated the structures and properties of medium size silicon-doped boron clusters in both neutral and anionic states BnSi0/– with n = 15–24. While geometries were optimized using DFT with both TPSSh and PBE functionals, energies were determined using the coupled-cluster theory (U)­CCSD­(T) with the 6-311+G­(d) basis set, with a calibration using the 6-311+G­(3df) basis set. Average binding energies, second-order energy differences, dissociation energies, and electron detachment energies were predicted by using the (U)­CCSD­(T) + ZPE energies for the entire series. The growth of the BnSi series considered does not follow a regular pattern, but a few trends can be established as follows: (i) most of the lowest-energy isomers of BnSi0/– clusters arise from a replacement of a B atom of the Bn+1 species by an Si atom or an addition of one Si atom into the neutral, anionic, or dianionic Bn species; (ii) the predominance of the planar structures for BnSi0/– clusters can be interpreted as a result of an effect of either the pure boron clusters or the Si dopant or also an effect of the negative charge; and (iii) the Si dopant prefers to be placed at an outer place of the Bn framework in order to exchange for, or to connect to, the peripheral B atoms in forming a low coordination number. The B19Si– anion whose planar motif, MOs shapes, electron distribution, and magnetic ring current are similar to those of the pure anions, B182–, B19–, and B202–, can be considered as a disk aromatic species involving 12 valence π-electrons. The MOs and electron distribution of the pseudotubes B20Si, B22Si, and B24Si can be interpreted by the hollow cylinder model. The first stable pseudotubular shape was found for the size B24Si whose thermodynamic stability is enhanced by both σ and π aromatic characters.

Density functional study of structures, stabilities and electronic properties of AgAunλ(λ=0,±1;n=1-12){\rm{AgAu}}_n^\lambda \left( {\lambda = 0, \pm 1;n = 1 - 12} \right) clusters: comparison with pure gold clusters

Abstract Geometrical structures, relative stabilities and electronic properties of neutral, cationic and anionic pure gold A u n + 1 λ {\rm{A}}u_{n + 1}^\lambda and Ag-doped bimetallic AgAu n λ ( λ = 0 , ± 1 ; n = 1 - 12 ) {\rm{AgAu}}_n^\lambda \left( {\lambda = 0, \pm 1;n = 1 - 12} \right) clusters have been systematically investigated by using density functional theory methodology. The optimized structures show that planar to three-dimensional structural transition occurs at n = 5 for cationic clusters. Due to strong relativistic effect of Au clusters, the ground state configurations of neutral and anionic bimetallic clusters favor planar geometry till n = 12. Silver atoms tend to occupy the most highly coordinated position and form the maximum number of bonds with Au atoms. The computed HOMO-LUMO energy gaps, fragmentation energies and second-order difference of energies show interesting odd-even oscillation behavior. The result indicates that AgAu5, AgAu 2 + {\rm{AgAu}}_2^ + and AgAu 2 - {\rm{AgAu}}_2^ - are the most stable clusters in this molecular system. The DFT based descriptors of bimetallic clusters are also discussed and compared with pure gold clusters. The high value of correlation coefficient between HOMO-LUMO energy gaps and DFT based descriptors supports our analysis. A good agreement between experimental and theoretical data has been obtained in this study.

Structural, electronic, electrical, and magnetic properties of Rhn (1 ≤ n ≤ 13) clusters

Douglas-Kroll-Hess calculations of bond lengths, binding energies, HOMO-LUMO energy gaps, vertical ionization potentials and electron affinities, dissociation energies, second-order difference of total energies, polarizabilities, and spin magnetic moments of small rhodium cluster are carried out using the BLYP functional along with the all-electron TZP+1d-DKH basis set. Our results agree well with the experimental values available in the literature. Overall, the spin magnetic moments computed in this work are the best published to date. These findings certainly add credibility to the ground state geometrical structures reported by us, which do not always coincide with the structures found earlier. Rh8 and Rh12 are the most stable clusters, while Rh5 and Rh7 are the most reactive. Mean dipole polarizabilities and polarizability anisotropies are also reported. It is the first time that these electrical properties are calculated and they are useful for understanding the electronic structures of the Rhn clusters.

Structure and stability of sodium-doped helium snowballs through DFT calculations

The lowest energy structures and relative stabilities of pure and sodium-doped helium clusters Na+Hen have been determined using DFT calculations. Firstly, a series of DFT functionals have been tested by the calculation of the potential energy curve of the Na+–He system in order to find the most suitable and reliable method for studying the Na+Hen clusters. The calculations showed that the M05-2X functional combined with the extended polarized and diffused Pople basis set 6-311++G(d,p) reproduce correctly the experimental Na+–He potential energy curve. Hence, the most stable geometries of Na+Hen clusters up to n = 20 have been optimized at M05-2X/6-311++G(d,p) level. An icosahedral geometry is obtained for the Na+He12 ensuring the closure of the first solvation shell and forming the so-called ‘Snowballs’ feature. The relative stabilities of the Na+Hen clusters are discussed on the basis of the dependence of the binding energy, fragmentation energy and second-order difference of energy as well as the HOMO–LUMO energy gap with the size of the clusters. The clusters Na+He8, Na+He9 and Na+He12 are found to be relatively more stable than their neighbors. The snowball formation was explained through natural population analysis. The non-covalent interaction NCI analysis was performed on the basis of the reduced density gradient RDG. Finally, binding enthalpy, entropy and Gibbs free energy are calculated and showed that the formation process of Na+Hen clusters is endothermic.

Cấu trúc và tính chất điện tử của cluster vàng AuN (N = 2-20)

Structures and electronic properties of gold cluster AuN (N = 2-20) are investigated by density functional theory (DFT) using LC-BLYP functional in conjunction with the consistent-correlation pseudo potential cc-pVDZ-PP basis set. The structural evolution and some basic thermodynamic parameters including the binding energy per atom, the second-order difference of energy, and the one-step fragmentation energy are determined and examined in details. Their electronic properties and stability trend are elucidated in terms of the PSM model. The optical spectra of Au6 cluster are also investigated by means of TD-DFT calculations.

Structural evolution from exohedral to endohedral geometries, dynamical fluxionality, and structural forms of medium-sized anionic and neutral Au2Sin (n = 8-20) clusters.

The structural evolution of medium-sized anionic and neutral Au2Sin (n = 8-20) clusters is investigated by using density functional theory (DFT) calculations and CCSD(T) methods in combination with the particle swarm optimization (CALYPSO) global search algorithm. The geometries of anionic and neutral Au2Sin clusters change from exohedral to endohedral ones with the increasing cluster sizes, and the critical size of forming Au2-endohedral structures for both anionic and neutral clusters is confirmed to be n = 20, in which a C2h symmetric Au2-endohedral cage-like structure is observed. Anionic and neutral Au2Sin clusters are primarily dominated by prism-based geometries with most of them adopting different structural features. It is found that the two Au atoms prefer to occupy low coordination sites and interact with fewer Si atoms. The Au atoms carry negative charges because of the electron-transfer from Sin frameworks. Meanwhile, the two Au atoms have very weak interactions. The second-order energy differences and incremental binding energies of anionic and neutral Au2Sin clusters exhibit an odd-even alternation and Au2Si20-/0 clusters are proven to have the highest chemical stability among these Au-Si clusters. Interestingly, Au2Si8-, Au2Si9-, Au2Si13-, Au2Si15-, and Au2Si17- anions, along with Au2Si13, Au2Si14, and Au2Si17 neutrals, have multiplicity of structural forms and their low-lying isomers show dynamical fluxionality due to the low barrier energies.

Investigation on Structural, Relative Stable, and Electronic Properties of Binary AlnLin (n = 2 – 12) Clusters through Density Functional Theory

In the present research, the structural, the relative stable, and the electronic properties of AlnLin (n = 2 – 12) clusters were investigated by density functional theory (DFT). By comparing the calculated values of Al2 and Li2 dimers with experimental ones, the reliability of the proposed method was proved. Furthermore, by considering the values of average binding energy (Eb), vertical ionization potential (VIP), vertical electron affinity (VEA), fragmentation energy (△E), second-order energy difference (△2E), HOMO-LUMO (HL) gap, and chemical hardness (η) were calculated. It was found Fragmentation energy, second-order energy difference, VIP, VEA, the chemical stability and HOMO-LUMO gap exhibit odd-even oscillatory behaviours along with cluster size and have extreme values at n = 5 revealed Al5Li5 cluster yielded excellent stability. Those can be well explained by the density of states (DOS) that Li and Al atoms with stronger covalent bonds. Therefore, Al5Li5 cluster can be used as an ideal candidate for calculating Wilson parameters of Al-Li alloys.

A comparative study of structure, stabilities and electronic properties of neutral and cationic [AuSin]λ and [Sin+1]λ (λ = 0, +1; n = 1–12) nanoalloy clusters

Structure, stabilities and electronic properties of [AuSin]λ and [Sin+1]λ (λ = 0, +1; n=1-12) nanoalloy clusters are studied invoking Density Functional Theory methodology. To understand the chemical stability of the lowest energy structure of cluster, chemical parameters like, Binding Energy, Fragmentation Energy, Second Order Difference in Energy and HOMO-LUMO energy gap are studied with the variation of cluster size. The binding energy of neutral and cationic Sin+1 and AuSin clusters is gradually increasing along with the cluster size n. The second order difference in energy for pure Sin+1 and doped cluster AuSin shows an interesting odd-even alternation behavior. It is found that Si7, AuSi5, [Si5]+ and [AuSi7]+ are the most stable clusters. The HOMO-LUMO energy gap of neutral and cationic AuSin cluster is high as compare to their corresponding neutral and cationic Sin+1 cluster. It indicates that doping of Au atom enhances the energy gap of silicon clusters. The computed HOMO-LUMO gap of neutral and cationic AuSin clusters are in the range of 1.35–2.94 eV, which is suitable for microelectronics, optoelectronic devices and photovoltaics applications. Density Functional Theory based descriptors viz. Electronegativity, Hardness, Softness and Electrophilicity Index are also reported. The HOMO-LUMO energy gap of pure Si and doped cluster AuSin displays odd-even oscillation behavior as a function of cluster size, n. The close agreement between theoretical and experimental results supports and validates our computational analysis.

Systematic Theoretical Study on Structural, Stability, Electronic, and Spectral Properties of Si2 (Q = 0, ±1; n = 1-11) Clusters of Silicon-Magnesium Sensor Material.

By using CALYPSO searching method and Density Functional Theory (DFT) method at the B3LYP/6-311G (d) level of cluster method, a systematic study of the structures, stabilities, electronic and spectral properties of Si2 (n = 1–11; Q = 0, ±1) clusters of silicon-magnesium sensor material, is performed. According to the calculations, it was found that when n > 4, most stable isomers in Si2 (n = 1–11; Q = 0, ±1) clusters of silicon-magnesium sensor material are three-dimensional structures. Interestingly, although large size Si2 clusters show cage-like structures, silicon atoms are not in the center of the cage, but tend to the edge. The Si2 and Si2 clusters obviously differ to their corresponding neutral structures, which are in good agreement with the calculated values of VIP, AIP, VEA, and AEA. |VIP-VEA| values reveal that the hardness of Si2Mgn clusters decreases with the increase of magnesium atoms. The relative stabilities of neutral and charged Si2 (n = 1–11; Q = 0, ±1) clusters of silicon-magnesium sensor material is analyzed by calculating the average binding energy, fragmentation energy, second-order energy difference and HOMO-LUMO gaps. The results reveal that the Si2, Si2, and Si2clusters have stronger stabilities than others. NCP and NEC analysis results show that the charges in Si2 (n = 1–11; Q = 0, ±1) clusters of silicon-magnesium sensor material transfer from Mg atoms to Si atoms except for Si2, and strong sp hybridizations are presented in Si atoms of Si2 clusters. Finally, the infrared (IR) and Raman spectra of all ground state of Si2 (n = 1–11; Q = 0, ±1) clusters of silicon magnesium sensor material are also discussed.

First principles study on small ZrAln and HfAln clusters: Structural, stability, electronic states and CO2 adsorption

We report a first principles study based on density functional theory on the structural and electronic properties of transition metal Zr and Hf doped small aluminum clusters with 1–7 aluminum atoms. We have adopted B3PW91/LANL2DZ basis set to minimize the geometries of ZrAln and HfAln clusters. The stability analysis reveals that the ZrAl4 and HfAl4 structures with C2v symmetry and square pyramid geometry are the lowest energy structures. The most stable structures in ZrAl5 and HfAl5 are distorted tetrahedron type structure with symmetry C1. The binding energy per atom for transition metal-doped Aln clusters increases with the cluster size, while the second-order difference in total energy shows oscillatory behavior with even and odd cluster size. The HOMO – LUMO gap for ZrAln clusters is larger than the HfAln clusters except for n = 6 and 7. The HfAl4 clusters have more tendencies to accept or give away electrons. The negative charge exists on Zr and Hf indicating the electron transfers from Al atom to transition metal, Zr and Hf. The thermodynamical analysis suggests that the HfAl6 clusters with spin multiplicity one have the highest exothermicity compared to not only all considered Al clusters but also other transition metal-doped Al clusters as reported in J. Phys. Chem. C, 120, 10027 (2016). This reveals that the HfAl6 clusters with a spin multiplicity of one have more tendency towards the adsorption of CO2 compared to other clusters. The calculated adsorption energy of CO2 on ZrAln and HfAln nano clusters reveals the potential application for CO2 reduction.