A Theoretical Study on Growth Patterns of Ni-Doped Germanium Clusters

Cr2 Gen - (n = 15-20) clusters with two Cr atoms exhibited antiferromagnetic coupling

In this work, we investigated the structural evolution, electronic and magnetic properties of Cr₂ Ge_n ^- clusters for n = 15-20 by using density functional theory (DFT) calculations. Low-energy structures for these clusters were fully searched through a self-developed genetic algorithm code combined with DFT calculations. The calculations show that all the two Cr atoms prefer to stay together to form a strong CrCr bond, which-except for size 20-is shorter than the nearest neighbor distance in Cr bulk. Sizes 15 and 16 adopt a wheel-like structure as the structural motif with the extra Ge atoms capped on the top, while larger sizes (n = 17-20) prefer fullerene-like Cr₂ @Ge₁₂ motifs. From the results of the average binding energies of Cr₂ Ge_n ^- , one can conclude that it is easier to form larger size clusters. In these lowest-lying isomers except for size 16, the two Cr atoms contribute opposite magnetic moments for the total magnetic moments of 1 μ_B , showing an antiferromagnetic state.

Geometries, electronic structures, and bonding properties of endohedral Group-14 Zintl clusters TM@E10 (TM = Fe, Co, Ni; E = Ge, Sn, Pb)

The geometries, electronic structures, and bonding properties of the title endohedral Zintl clusters have been studied by using ab initio calculations. [Fe@Ge₁₀ ]^4- and [Co@Ge₁₀ ]^3- have D_5h -symmetric pentagonal prismatic structure and [Fe@Sn₁₀ ]^4- adopts the C_2v -symmetric structure as their ground-state structures, whereas all the other clusters possess D_4d bicapped square antiprismatic structures, in consistent with the experimental values when available. Natural bonding orbital and electron localization function disclosed that the negative charges are localized on the central atoms rather than the cages while the TME ionic bonding interactions increase in the order of Ge < Sn < Pb. The energy decomposition analysis revealed that the total bonding energy ∆E_int between central TM and E₁₀ cage is above 150 kcal/mol. The ionic bonding interaction termed as electrostatic interaction ∆E_elstat increases in the order of Ge < Sn < Pb and becomes higher than the covalent bonding interactions termed as total orbital interactions ∆E_orb . Among the total orbital interactions, the π back donations from the TM-d orbitals to the empty cage orbitals consisting of E-p orbitals, the magnitude of which is importantly affected by the cage symmetry, are dominant contributions.

A joint experimental and theoretical study on structural, electronic, and magnetic properties of MnGen - (n = 3-14) clusters

A systematic structure and property investigation of MnGe_n ^- (n = 3-14) was conducted by means of density functional theory coupled with mass-selected anion photoelectron spectroscopy. This combined theoretical and experimental study allows global minimum and coexistence structures to be identified. It is found that the pentagonal bipyramid shape is the basic framework for the nascent growth process of MnGe_n ^- (n = 3-10), and from n = 10, the endohedral structures can be found. For n = 12, the anion MnGe₁₂ ^- cluster probably includes two isomers: a major isomer with a puckered hexagonal prism geometry and a minor isomer with a distorted icosahedron geometry. Specifically, the puckered hexagonal prism isomer follows the Wade-Mingos rules and can be suggested as a new kind of superatom with the magnetic property. Furthermore, the results of adaptive natural density partitioning and deformation density analyses suggest a polar covalent interaction between Ge and Mn for endohedral clusters of MnGe₁₂ ^-. The spin density and natural population analysis indicate that MnGe_n ^- clusters have high magnetic moments localized on Mn. The density of states diagram visually shows the significant spin polarization for endohedral structures and reveals the weak interaction between the Ge 4p orbital and the 4s, 3d orbitals of Mn.

A remarkable mixture of germanium with phosphorus and arsenic atoms making stable pentagonal hetero-prisms [M@Ge5E5]+, E = P, As and M = Fe, Ru, Os

A pentagonal hetero-prismatic structural motif was found for singly transition metal doped M@Ge₅E₅⁺ clusters, where the transition metal atom is located at the centre of a (5/5) Ge₅E₅ prism in which Ge is mixed with either P or As atoms. Structural characterization indicates that each (5/5) Ge₅E₅ prism is established by joining of two Ge₃E₂ and Ge₂E₃ strings in a prismatic fashion rather than two Ge₅ and E₅ strings. Each string results from a remarkable mixture of Ge and E atoms and contains only one E–E connection due to the fact that Ge–E bonds are much stronger than E–E connections. From the donor–acceptor perspective, the Ge₅E₅ tube donates electrons to the M center, which behaves as an acceptor. NBO atomic charge and ELI_D analyses demonstrate such electrostatic interactions of the M dopant with a Ge₅E₅⁺ tube which likely induce thermodynamic stability for the resulting M@Ge₅E₅⁺ cluster. CMO analysis illustrates that the conventional 18 electron count is recovered in the M@Ge₅E₅⁺ cations.

Geometric shape of the lowest-energy structure M@Ge₅E₅⁺.

Structure, stability, and electronic properties of niobium-germanium and tantalum-germanium clusters

The structural, electronic and magnetic properties of niobium- and tantalum-doped germanium clusters MGe_n (M = Nb, Ta and n = 1-19) were investigated by first principles calculations within the density functional theory (DFT) approach. Growth pattern behaviors, stabilities, and electronic properties are presented and discussed. Endohedral cage-like structures in which the metal atom is encapsulated are favored for n ≥ 10. The doping metal atom contributes largely to strengthening the stability of the germanium cage-like structures, with binding energy ordered as follows BE(Ge_n + 1) < BE (VGe_n) < BE(NbGe_n) < BE(TaGe_n). Our results highlight the relative high stability of NbGe₁₅, TaGe₁₅ and VGe₁₄. Graphical abstract Structure, stability, and electronic properties of niobium-germanium and tantalum-germanium clusters.

Spin State Energetics of VGe n -/0 (n = 5-7) Clusters and New Assignments of the Anion Photoelectron Spectra

The geometrical structures, electron leading configurations, and relative energies of the low-lying states of VGe _n ^-/0 (n = 5-7) clusters have been investigated with density functional theory and CASSCF/CASPT2 method. The pure GGA BP86 functional gave almost the same relative energy order for the low-lying states as the CASPT2 method. At the BP86 and CASPT2 levels, the ground states of VGe _n ^-/0 (n = 5-7) clusters were proposed to be the ¹ A₁ and ² A₁ of A-VGe₅ ^-/0 , ³ A″ and ² A″, ² A' (² E₂ ) of A-VGe₆ ^-/0 , and ¹ A' and ² A' of A-VGe₇ ^-/0 isomers. The adiabatic and vertical detachment energies (ADEs and VDEs) of the detachments of one electron from several orbitals of the anionic ground states were reported at the CASPT2 level. The calculated ADEs and VDEs corresponded well with the experimental values as observed in the 266 nm anion photoelectron spectra. © 2018 Wiley Periodicals, Inc.

Growth Behavior and Electronic Structure of Noble Metal-Doped Germanium Clusters

Structures, energetics, and electronic properties of noble metal-doped germanium (MGe_n with M = Cu, Ag, Au; n = 1-19) clusters are systematically investigated by using the density functional theory (DFT) approach. The endohedral structures in which the metal atom is encapsulated inside of a germanium cage appear at n = 10 when the dopant is Cu and n = 12 for M = Ag and Au. While Cu doping enhances the stability of the corresponding germanium frame, the binding energies of AgGe_n and AuGe_n are always lower than those of pure germanium clusters. Our results highlight the great stability of the CuGe₁₀ cluster in a D_4d structure and, to a lesser extent, that of AgGe₁₅ and AuGe₁₅, which exhibits a hollow cage-like geometry. The sphere-type geometries obtained for n = 10-15 present a peculiar electronic structure in which the valence electrons of the noble metal and Ge atoms are delocalized and exhibit a shell structure associated with the quasi-spherical geometry. It is found that the coinage metal is able to give both s- and d-type electrons to be reorganized together with the valence electrons of Ge atoms through a pooling of electrons. The cluster size dependence of the stability, the frontier orbital energy gap, the vertical ionization potentials, and electron affinities are given.

Structure, Stability, and Electronic and Magnetic Properties of VGen (n = 1-19) Clusters

We systematically study the equilibrium geometries and electronic and magnetic properties of Ge_n+1 and VGe_n (n = 1-19) clusters using the density functional theory approach within the generalized gradient approximation. Endohedral structures in which the vanadium atom is encapsulated inside a Ge_n cage are predicted to be favored for n ≥ 10. The dopant V atom in the Ge_n clusters has not an immediate effect on the stability of small germanium clusters (n < 6), but it largely contributes to strengthen the stability for n ≥ 7. Our study enhances the large stability of the VGe₁₄ cluster, which presents an O_h symmetry cagelike geometry and a peculiar electronic structure in which the valence electrons of V and Ge atoms are delocalized and exhibit a shell structure associated with the quasi-spherical geometry. Consequently, this cluster is proposed to be a good candidate to be used as the building blocks for developing new materials. The cluster size dependence of the stability, the vertical ionization potentials, and electron affinities of Ge_n+1 and VGe_n are presented. Magnetic properties and the partial density of states of the most stable VGe_n clusters are also discussed.

Transition from exohedral to endohedral structures of AuGen− (n = 2–12) clusters: photoelectron spectroscopy and ab initio calculations

AuGe₁₂⁻ has an I_h symmetric endohedral icosahedral structure. It also shows 3D aromaticity.

Structural and magnetic properties of CoGe(n)- (n=2-11) clusters: photoelectron spectroscopy and density functional calculations

A series of cobalt-doped germanium clusters, CoGe(n)(-/0) (n=2-11), are investigated by using anion photoelectron spectroscopy combined with density functional theory calculations. For both anionic and neutral CoGe(n) (n=2-11) clusters, the critical size of the transition from exo- to endohedral structures is n=9. Natural population analysis shows that there is electron transfer from the Ge(n) framework to the Co atom at n=7-11 for both anionic and neutral CoGe(n) clusters. The magnetic moments of the anionic and neutral CoGe(n) clusters decrease to the lowest values at n=10 and 11. The transfer of electrons from the Gen framework to the Co atom and the minimization of the magnetic moments are related to the evolution of CoGe(n) structures from exo- to endohedral.

STRUCTURAL, ELECTRONIC, MAGNETIC, AND OPTICAL PROPERTIES OF 3d TRANSITION METAL ENDOHEDRAL M@Ge12H12(M=Sc–Ni) CLUSTERS

The fulerine- Ni @ Ge 12 H 12 structure, which composes of four pentagons and four rhombi and is like a fullerene, has a closed-shell electronic structure, the largest HOMO–LUMO energy gap, the highest vertical ionization potential, and the lowest vertical electron affinity. All of these properties are characteristic of a magic cluster, therefore, we strongly suggest fulerine- Ni @ Ge 12 H 12 should be a magic cluster and promising as building blocks in developing cluster-assembled nanomaterials. This can be interpreted by the weak interaction between Ni and the cage together with the transference of two electrons from the 4s orbital to the 3d orbital of Ni . The magnetic moment of fulerine- M @ Ge 12 H 12( M = Sc – Ni ) varies from 0 to 3 μB, implying they have potential applications in developing new nanomaterials with tunable magnetic properties. The calculated TDDFT optical properties of fulerine- M @ Ge 12 H 12( M = Sc – Ni ) can be tuned broadly in the ultraviolet–visible region. This is very important for optoelectronic applications.

No quenching of magnetic moment for the GenCo (n=1-13) clusters: first-principles calculations

The authors predict that for the Ge(n)Co (n=1-13) clusters the magnetic moment does not quench, which is dark contrast to the previous results with transition-metal-doped Si(n) clusters. It may be due to the unpaired electrons of the Co atom in the clusters. For the ground state structures of the Ge(n)Co (n>or=9) clusters, the Co atom completely falls into the center of the Ge outer frame, forming metal-encapsulated Ge(n) cages. The doping of the Co atom enhances the stability of the host Ge(n) clusters. The Ge(10)Co cluster with the bicapped tetragonal antiprism structure is more stable than others, which agrees very well with the results of the experiment of the Co/Ge binary clusters by the laser vaporization.

Experimental and theoretical investigations of the thermodynamic stability of Ba-c(60) and K-C(60) compound clusters

A novel experimental set-up was used to study superstable (magic) Ba-C(60) and K-C(60) compound clusters. The most stable systems observed cannot be rationalized by simple electronic or by geometrical shell filling arguments. Annealing the clusters past the temperature necessary for the fragmentation of the initial metastable clusters formed at the source reveals information about their thermodynamic stability. Higher temperatures yield larger species, suggesting that similar experiments may be used to rationally produce nanoscale clusters with highly desirable properties. Density functional calculations reveal ionic (K, Ba) and covalent (Ba) bonding between C(60) and the metal atoms. The entropic contribution to the Gibbs free energy is shown to be essential in determining absolute and relative cluster stabilities. In particular, we demonstrate that at higher temperatures the entropy favors the formation of larger clusters. A simple criterion which may be used to determine the absolute and relative stabilities of general multicomponent clusters is proposed.

Chromium-doped germanium clusters CrGen (n = 1-5): geometry, electronic structure, and topology of chemical bonding

The structure and properties of small neutral and cationic CrGen(0,+) clusters, with n from 1 to 5, were investigated using quantum chemical calculations at the CASSCF/CASPT2 and DFT/B3LYP levels. Smaller clusters prefer planar geometries, whereas the lowest-lying electronic states of the neutral CrGe4, CrGe5, and cationic CrGe5+ forms exhibit nonplanar geometries. Most of the clusters considered prefer structures with high-spin ground state and large magnetic moments. Relative to the values obtained for the pure Gen clusters, fragmentation energies of doped CrGen clusters are smaller when n is 3 and 4 and larger when n = 5. The averaged binding energy tends to increase with the increasing number of Ge atoms. For n = 5, the binding energies for Ge5, CrGe5, and CrGe5+ are similar to each other, amounting to approximately 2.5 eV. The Cr atom acts as a general electron donor in neutral CrGen clusters. Electron localization function (ELF) analyses suggest that the chemical bonding in chromium-doped germanium clusters differs from that of their pure or Li-doped counterparts and allow the origin of the inherent high-spin ground state to be understood. The differential DeltaELF picture, obtained in separating both alpha and beta electron components, is consistent with that derived from spin density calculations. For CrGen, n = 2 and 3, a small amount of d-pi back-donation is anticipated within the framework of the proposed bonding model.

Geometries, Stabilities, and Growth Patterns of the Bimetal Mo2-doped Sin (n = 9−16) Clusters: A Density Functional Investigation

The behaviors of the bimetal Mo-Mo doped cagelike silicon clusters Mo2Sin at the size of n=9-16 have been investigated systematically with the density functional approach. The growth-pattern behaviors, relative stabilities, and charge-transfer of these clusters are presented and discussed. The optimized geometries reveal that the dominant growth patterns of the bimetal Mo-Mo doped on opened cagelike silicon clusters (n=9-13) are based on pentagon prism MoSi10 and hexagonal prism MoSi12 clusters, while the Mo2 encapsulated Sin(n=14-16) frames are dominant growth behaviors for the large-sized clusters. The doped Mo2 dimer in the Sin frames is dissociated under the interactions of the Mo2 and Sin frames which are examined in term of the calculated Mo-Mo distance. The calculated fragmentation energies manifest that the remarkable local maximums of stable clusters are Mo2-doped Sin with n=10 and 12; the obtained relative stabilities exhibit that the Mo2-doped Si10 cluster is the most stable species in all different sized clusters. Natural population analysis shows that the charge-transfer phenomena appearing in the Mo2-doped Sin clusters are analogous to the single transition metal Re or W doped silicon clusters. In addition, the properties of frontier orbitals of Mo2-doped Sin (n=10 and 12) clusters show that the Mo2Si10 and Mo2Si12 isomers have enhanced chemical stabilities because of their larger HOMO-LUMO gaps. Interestingly, the geometry of the most stable Mo2Si9 cluster has the framework which is analogous to that of Ni2Ge9 cluster confirmed by recent experimental observation (Goicoechea, J. M.; Sevov, S. C. J. Am Chem. Soc. 2006, 128, 4155).

Geometries and Electronic Properties of the Tungsten-Doped Germanium Clusters: WGen (n = 1−17)

Geometries associated with relative stabilities, energy gaps, and polarities of W-doped germanium clusters have been investigated systematically by using density functional theory. The threshold size for the endohedral coordination and the critical size of W-encapsulated Gen structures emerge as, respectively, n = 8 and n = 12, while the fullerene-like W@Ge(n) clusters appears at n = 14. The evaluated relative stabilities in term of the calculated fragmentation energies reveal that the fullerene-like W@Ge(14) and W@Ge(16) structures as well as the hexagonal prism WGe(12) have enhanced stabilities over their neighboring clusters. Furthermore, the calculated polarities of the W@Ge(n) reveal that the bicapped tetragonal antiprism WGe(10) is a polar molecule while the hexagonal prism WGe(12) is a nonpolar molecule. Moreover, the recorded natural populations show that the charges transfer from the germanium framework to the W atom. Additionally, the WGe(12) cluster with large highest occupied molecular orbital-lowest unoccupied molecular orbital (HOMO-LUMO) gap, large fragmentation energy, and large binding energy is supposed to be suitable as a building block of assembly cluster material. It should be pointed out that the remarkable features of W@Ge(n) clusters above are distinctly different from those of transition metal (TM) doped Ge(n) (TM = Cu and Ni) clusters, indicating that the growth pattern of the TMGe(n) depends on the kind of doped TM impurity.