Geometries and electronic structures of Zr_(n)Cu(n=2–12) clusters: A joint machine-learning potential density functional theory investigation

Zr-based amorphous alloys have attracted extensive attention because of their large glassy formation ability, wide supercooled liquid region, high elasticity, and unique mechanical strength induced by their icosahedral local structures.To determine the microstructures of Zr–Cu clusters, the stable and metastable geometry of Zr_(n)Cu(n=2–12) clusters are screened out via the CALYPSO method using machine-learning potentials, and then the electronic structures are investigated using density functional theory. The results show that the Zr_(n)Cu(n ≥ 3) clusters possess three-dimensional geometries, Zr_(n)Cu(n≥9) possess cage-like geometries, and the Zr_(12)Cu cluster has icosahedral geometry. The binding energy per atom gradually gets enlarged with the increase in the size of the clusters, and Zr_(n)Cu(n=5,7,9,12) have relatively better stability than their neighbors. The magnetic moment of most Zr_(n)Cu clusters is just 1μB, and the main components of the highest occupied molecular orbitals(HOMOs) in the Zr_(12)Cu cluster come from the Zr-d state. There are hardly any localized two-center bonds, and there are about 20 σ-type delocalized three-center bonds.

LOCALIZED STUDIES ON ELECTRONIC STRUCTURE AND CHEMICAL BOND FOR [NCCuS_2MoS_2]^(2-) CLUSTER

The canonical and locatized molecutar orbiters of [NCCuS_2NoS_2]^(2-) cluster were calculated by means of CNDO quantum chemistry method. Then the energy and properties of corresponding chemicat bonds were discussed, especially, Cu-Sb-No three center conjugated π bonds and No-St-No conjugated π bonds were accounted for.

QUANTUM CHEMICAL CALCULATIONS ON THE ELECTRONIC STRUCTURE AND SPECTRA OF[Mo_3O_4-nSn]^(4+)(n=O-4)CLUSTER CATIONS

The electronic structure and spectra of [Mo3O4-nSn]^(4+)(n=0-4) cations were calculated by means of INDO/CI quantum chemistry method to account for the experimental data of their spectra in water solutions.

SEMI-EMPIRICAL CALCULATION FOR ELECTRONIC STRUCTURE OF C60 CLUSTER BY MOLECULAR DYNAMICS AND MNDO APPROACH

The electronic structure for C 60 was semi empirically investigated by using MD (molecular dynamics) and MNDO (modified neglect of diatomic overlap) approach of quantum chemistry.Especially,taking both σ and π orbitals into account,one electron energy levels,those symmetries and π orbital occupancies as well as electron excitation energies for different select rules,cohesive energy,ionization energies and electronic affinity forces were calculated.The obtained molecular orbital ratio shows a wide separation of σ and π types,and near HOMO and LUMO levels there are π orbitals mainly.The calculated semi empirical calculation results are in good agreement with experimental and ab initio calculation data.

Molecular Design and Electronic Structure of Polynuclear Rare Earth Complexes and Clusters

Studies on the electronic structure,molecular design,syntheses of some novel series of tetranuclear rare earth complexes in our laboratory have been reviewed.Spin-unrestricted localized INDO method was used to calculate the electronic structure and the chemical bonding in the typical rare earth cluster Sc[Sc_6Cl_(12)Co]was discussed.

A classification scheme for inorganic cluster compounds based on their electronic structures and bonding characteristics

A novel classification scheme for inorganic cluster compounds is presented based on the characteristics of their electronic structures.In the classification scheme,five distinct categories have been introduced,including Jellium clusters,Wadian clusters,electron-precise clusters,π-donor ligated metal-metal bonded clusters,and antiferro-magnetically coupled high-spin metal clusters.

Electronic structure and infrared spectrum of a W_n C^(0,±) (n = 1-6) cluster

WnC0＇± （n= 1-6） clusters are investigated by using the density functional theory （DFT） at the B3LYP/LANL2DZ level. We find that the neutral, anionic and cationic ground state structures are similar within the same size, and constituted by substituting a C atom for one W atom in the structures of Wn＋1 clusters. The natural bond orbital （NBO） charge analyses indicate that the direction of electron transfer is from the W atom to the 2p orbital of the C atom. In addition, the calculated infrared spectra of the WnC0＇± （n= 2-6） clusters manifest that the vibrational frequencies of neutral, anionic and cationic clusters are similar in a range of 80 cm-1-864 cm-1. The high frequency, strong peak modes are found to be an almost stretched deformation of the carbide atom. Finally, the polarizabilities of WnC0＇± （n= 1-6） clusters are also discussed.

A density-functional theory for (BAs) n clusters (n=1-14):structures,stabilities and electronic properties

This paper investigates the lowest-energy structures, stabilities and electronic properties of （BAs）n clusters （n=1- 14） by means of the density-functional theory. The results show that the lowest-energy structures undergo a structural change from two-dimensional to three-dimensional when n ： 4. With the increase of the cluster size （n=6）, the （BAs）n clusters tend to adopt cage-like structures, which can be considered as being built from B2As2 and six-membered rings with B-As bond alternative arrangement. The binding energy per atom, second-order energy differences, vertical electron affinity and vertical ionization potential are calculated and discussed. The caculated HOMO-LUMO gaps reveal that the clusters have typical semiconductor characteristics. The analysis of partial density of states suggests that there are strong covalence and molecular characteristics in the clusters.

Electronic Structure and Magnetic Properties of Rh_(13) Cluster with Three Possible Symmetries

Electronic and magnetic properties of 13-atom Rh clusters with three possible high symmetry geometries have been studied by using the first-principles DV-LSD method. An anomalous symmetry dependence of the cluster magnetism was found that the total magnetic moment of the icosahedral Rh13 cluster is smaller than that of the other two lower-symmetry clusters in a wide range of interatomic spacings. An energy difference is identified to explain this anomalous relationship, which has been found to be also useful for judging whether the broadening technique is correctly used and whether multiple input potentials must be used to reach the actual ground state in the LSD calculations. The calculated results are compared and discussed with those of previous theory and recent experiment. The actual geometry of the Rh13 cluster is suggested to be a distorted icosahedron.

The Electronic Structures and Catalytic Activities of Triruthenium Ketenylidene Clusters Supported on Oxides

he catalytic activities of [H_nRu_3(CO)_9(CCO)]￣(-(2-n)) (n=0, 1 , 2 , 3) support-ed on oxides have been estimated using INDO calculations and correlation betweencatalytic activity and electronic structure for these clusters have been established.The activity in ￣(13)CO isotopic exchange strongly relates to the bond orders of Ru-CO and C-CO, and the activity in alkylation with nucleophile or electrophile de-pends mainly on the net charges at Ca atoms. In addition, the possible species of[H_3Ru_3(CO)_9(CCO)]￣+ has been proposed although it has not been synthesized upto now.

The geometry structures and electronic properties of Li_mB_n(m+n=12) clusters

The geometric structures, electronic properties, total and binding energies, harmonic frequencies, the highest occupied molecular orbital to the lowest unoccupied molecular orbital energy gaps, and the vertical ionization potential energies of small LimBn （m＋ n = 12） clusters were investigated by the density functional theory B3LYP with a 6-31 I＋G （2d, 2p） basis set. All the calculations were performed using the Gaussian09 program. For the study of the LimBn clusters, the global minimum of the B 12 cluster was chosen as the starting point and the boron atoms were gradually replaced by Li atoms. The results showed that as the number of Li atoms increased, the stability of the LimBn cluster decreased and the physical and chemical properties became more active. In addition, on average there was a large charge transfer from the Li atoms to the B atoms.

Electronic Structure of the Clusters Containing Oxygen in Ni

The electronic structure of the clusters containing oxygen, the stacking fault and the complex in the transition metal Ni are calculated by the multiple-scattering Xa method. Energy levels,density of states and transfer of charge are obtained. Based on the calculation and analysis,the influences of impurity oxygen and structure defect on the electronic structure of the clusters are discussed, and it is found that the local Ni-o cluster with the interstitial oxygen is a stable atomic configuration.

Electronic Structure Effect on Model Cluster for L1_2 Structure of Al_3Ti Intermetallic Compound with an Addition of Alloying Elements Fe, Ni and Cu

By use of self-consistent field Xα scattered-wave (SCF-Xα-SW) method, the electronic structure was calculated for four models of Ti4Al14X (X=Al, Fe, Ni and Cu) clusters. The Ti4Al14X cluster was developed based on L12 Al3Ti-base intermetallic compound. The results are presented using the density of states (DOS) and one-electron properties, such as relative binding tendency between the atom and the model cluster, and hybrid bonding tendency between the alloying element and the host atoms. By comparing the four models of Ti4Al14X cluster, the effect of the Fe, Ni or Cu atom on the physical properties of Al3Ti-based L12 intermetallic compounds is analyzed. The results indicate that the addition of the Fe, Ni or Cu atom intensifies the relative binding tendency between Ti atom and Ti4Al14X cluster. It was found that the Fermi level (EF) lies in a maximum in the DOS for Ti4Al14Al cluster; on the contrary, the EF comes near a minimum tn the DOS for Ti4Al14X (X=Fe, Ni and Cu) cluster. Thus the L12 crystal structure for binary Al3Ti alloy is unstable, and the addition of the Fe, Ni or Cu atom to Al3Ti is benefical to stabilize L12 crystal structure. The calculation also shows that the Fe, Ni or Cu atom strengthens the hybrid bonding tendency between the central atom and the host atoms for Ti4Al14X cluster and thereby may lead to the constriction of the lattice of Al3Ti-base intermetallic compounds.

Structures, stabilities, and electronic properties of F-doped Sin （n=1～12） clusters：Density functional theory investigation

The geometries, stabilities, and electronic properties of FSin （n=1～12） clusters are systematically investigated by using first-principles calculations based on the hybrid density-functional theory at the B3LYP/6-311G level. The geometries are found to undergo a structural change from two-dimensional to three-dimensional structure when the cluster size n equals 3. On the basis of the obtained lowest-energy geometries, the size dependencies of cluster properties, such as averaged binding energy, fragmentation energy, second-order energy difference, HOMO–LUMO （highest occupied molecular orbital–lowest unoccupied molecular orbital） gap and chemical hardness, are discussed. In addition, natural population analysis indicates that the F atom in the most stable FSin cluster is recorded as being negative and the charges always transfer from Si atoms to the F atom in the FSin clusters.

Growth behavior and electronic properties of Ge_(n+1) and AsGe_n(n = 1–20) clusters: a DFT study

We present a systematic computational study based on the density functional theory(DFT) aiming to high light the possible effects of one As doping atom on the structural, energetic, and electronic properties of different isomers of Ge_(n+1) clusters with n = 1–20 atoms. By considering a large number of structures for each cluster size, the lowest-energy isomers are determined. The lowest-energy isomers reveal three-dimensional structures starting from n = 5. Their relative stability versus atomic size is examined based on the calculated binding energy, fragmentation energy, and second-order difference of energy. Doping Ge_(n+1) clusters with one As atom does not improve their stability. The electronic properties as a function of the atomic size are also discussed from the calculated HOMO–LUMO energy gap, vertical ionization potential, vertical electron affinity, and chemical hardness. The obtained results are significantly affected by the inclusion of one As atom into a Gen cluster.

Equilibrium geometries and electronic properties of Be_nLi (n=2-15) clusters from first principles

This paper studies the equilibrium geometries and electronic properties of Ben and BenLi clusters, up to n=15, by using density-functional theory（DFT） at B3LYP/6-31G（d） level. The lowest-energy structures of Ben and BenLi clusters were determined. The results indicate that a single lithium impurity enhances the stability and chemical reactivity of the beryllium clusters. It finds that the geometries of the host clusters change significantly after the addition of the lithium atom for n ≥8. The lithium impurity prefers to be on the periphery of beryllium clusters, and occupies vertex sites. Both Be4Li, Be9Li, and Be13Li were found to be particularly stable with higher average binding energy, local peaks of second-order energy difference and fragmentation energies. For all the BenLi clusters studied, we found charge transfers from the Li to Be site and co-existence of covalent and metallic bonding characteristics.

A First-principles Calculation of Structures and Stability of Al_(13)I Cluster

Using first-principles pseudo-potential plane wave method, the energetics, geometrical and electronic structures of three Al13I cluster isomers were calculated. The calculation results of the binding energy indicate Al13I cluster is more stable than Al13 cluster although its electrons are not a magic number as in Alia cluster, and among Al13I cluster isomers the ＂Bridge＂ structure is the most stable, the second is the ＂Ontop＂ structure, and the worst is the ＂Hollow＂ structure. By analyzing the geometrical structures of Al13I cluster isomers, it is found that after I atom and Al13 cluster combine the geometrical structures of Al13 moieties are changed besides Al13I Hollow cluster, in which the Alia moiety is still a regular icosahedron. For Al13I Ontop cluster, the Al13 moiety has a shrinking trend to I, whereas in Al13I Bridge cluster it is distorted. Mulliken population analysis shows for the interaction of electrons between Al-I atoms in Al13I cluster not only there exists an ionic bonding but there is a covalent bonding. Part of electrons in the Alia cluster transfer to I as Al13 cluster and I atom combine. The order of the strength of covalent bonding between Al13 moiety and I in Al13I cluster isomers is Al13IBridge〉Al13IHollow〉Al13I Ontop. Further analysis of electric structures of Al13 and Al13I clusters indicates a higher stability of Al13I cluster than Al13 cluster can be attributed to the s-p hybridization of 3s and 3p electrons of Al in Al13 moiety induced by 1 doped, which leads to fewer electrons N（EF） at EF in Al13I and a larger energy gap △EH-L between HOMO and LUMO levels in Al13I cluster. The distinguish of structural stability of Al13I cluster isomers mainly originates from their different magnitudes .in decrease of N（EF） and increase of △EH-L relative to Al13 cluster. The fewest N（EF） and the largest △EH-L are responsible for the high stability of Al13I Bridge cluster.

Probing Structure, Thermochemistry, Electron Affinity and Magnetic Moment of Dysprosium-doped Silicon Clusters DySi_n(n = 3～10) and Their Anions with Double-hybrid Density Functional Theory

The equilibrium geometries, electronic structures and electronic properties including adiabatic electron affinity（AEA）, vertical detachment energy（VDE）, simulated photoelectron spectroscopy, HOMO-LUMO gap, charge transfer, and magnetic moment for DySi_n（n = 3~10） clusters and their anions were systematically investigated by using the ABCluster global search technique combined with the B3 LYP and B2 PLYP density functional methods. The results showed that the lowest energy structure of neutral DySi_n（n = 3~10） can be regarded as substituting a Si atom of the ground state structure of Si_（n＋1） with a Dy atom. For anions, the extra electron effect on the structure is significant. Starting from n = 6, the lowest energy structures of DySi_n~？（n = 3~10） differ from those of neutral. The ground state is quintuplet electronic state for DySi_n（n = 3~10） excluding DySi_4 and DySi_9, which is a septet electronic state. For anions, the ground state is a sextuplet electronic state. The reliable AEA and VDE of DySi_n（n = 3~10） are reported. Analyses of HOMO-LUMO gaps indicated that doping Dy atom to silicon clusters can improve significantly their photochemical reactivity, especially for DySi_9. Analyses of NPA revealed that the 4 f electrons of Dy in DySi_4, DySi_9, and DySi_n~？ with n = 4 and 6~10 participate in bonding. That is, DySi_nbelongs to the AB type. The 4 f electrons of Dy atom provide substantially the total magnetic moments for DySi_n and their anions. The dissociation energies of Ln（Ln = Pr, Sm, Eu, Gd, Ho, and Dy） fromLn Sin and their anions were evaluated to examine the relative stabilities.

Simulation of water potential for the electronic structure of serine

First-principles, all-electron, ab initio calculations have been performed to construct an equivalent water potential for the electronic structure of serine （Ser） in solution. The calculation is composed of three steps. The first step is to search for the configuration of the Ser _ nH2O system with a minimum energy. The second step is to calculate the electronic structure of Ser with the water molecule potential via the self-consistent cluster-embedding method （SCCE）, based on the result obtained in the first step. The last step is to calculate the electronic structure of Set with the dipole potential after replacing the water molecules with dipoles. The results show that the occupied states of Ser are raised by about 0.017 Ry on average due to the effect of water. The water effect can be successfully simulated by using the dipole potential. The obtained equivalent potential can be applied directly to the electronic structure calculation of protein in solution by using the SCCE method.

Structural evolutions and electronic properties of Au_nGd(n=6–15)small clusters:A first principles study

Structural, electronic, and magnetic properties of AunGd （n = 6-15） small clusters are investigated by using first principles spin polarized calculations and combining with the ab-initio evolutionary structure simulations. The calculated binding energies indicate that after doping a Gd atom AunGd cluster is obviously more stable than a pure AUn＋l cluster. Au6Gd with the quasiplanar structure has a largest magnetic moment of 7.421 gB. The Gd-4f electrons play an important role in determining the high magnetic moments of AunGd clusters, but in Au6Gd and Aul2Gd clusters the unignorable spin polarized effects from the Au-6s and Au-5d electrons further enhance their magnetism. The HOMO-LUMO （here, HOMO and LUMO stand for the highest occupied molecular orbital, and the lowest unoccupied molecular orbital, respectively） energy gaps of munGd clusters are smaller than those of pure AUn＋l clusters, indicating that AunGd clusters have potential as new catalysts with enhanced reactivity.