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

Magnetic properties of CrMnGen (n = 3-20) clusters

Due to the potential applications in next-generation micro/nano electronic devices and functional materials, magnetic germanium (Ge)-based clusters are receiving increasing attention. In this work, we reported the structures, electronic and magnetic properties of CrMnGen with sizes n = 3-20. Transition metals (TMs) of Cr and Mn tend to stay together and be surrounded by Ge atoms. Small sized clusters with n ≤ 8 prefer to adopt bipyramid-based structures as the motifs with the excess Ge atoms absorbed on the surface. Starting from n = 9, the structure with one TM atom interior appears and persists until n = 16, and for larger sizes n = 17-20, the two TM atoms are full-encapsulated by Ge atoms to form endohedral structures. The Hirshfeld population analyses show that Cr atom always acts as the electron donor, while Mn atom is always the acceptor except for sizes 3 and 6. The average binding energies of these clusters increase with cluster size n, sharing a very similar trend as that of CrMnSin (n = 4-20) clusters, which indicates that it is favorable to form large-sized clusters. CrMnGen (n = 6, 13, 16, 19, and 20) clusters prefer to exhibit ferromagnetic Cr-Mn coupling, while the remaining clusters are ferrimagnetic.

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.

First-row transition metal doped germanium clusters Ge16M: some remarkable superhalogens

A theoretical study of geometric and electronic structures, stability and magnetic properties of both neutral and anionic Ge16M0/- clusters with M being a first-row 3d transition metal atom, is performed using quantum chemical approaches. Both the isoelectronic Ge16Sc- anion and neutral Ge16Ti that have a perfect Frank-Kasper tetrahedral T d shape and an electron shell filled with 68 valence electrons, emerge as magic clusters with an enhanced thermodynamic stability. The latter can be rationalized by the simple Jellium model. Geometric distortions from the Frank-Kasper tetrahedron of Ge16M having more or less than 68 valence electrons can be understood by a Jahn-Teller effect. Remarkably, DFT calculations reveal that both neutral Ge16Sc and Ge16Cu can be considered as superhalogens as their electron affinities (≥3.6 eV) exceed the value of the halogen atoms and even that of icosahedral Al13. A detailed view of the magnetic behavior of Ge16M0/- clusters shows that the magnetic moments of the atomic metals remain large even when they are quenched upon doping. When M goes from Sc to Zn, the total spin magnetic moment of Ge16M0/- increases steadily and reaches the maximum value of 3 μ B with M = Mn before decreasing towards the end of the first-row 3d block metals. Furthermore, the IR spectra of some tetrahedral Ge16M are also predicted.

Structural Evolution, Electronic Structures, and Vibrational Properties of Anionic LuGen (n = 5-17) Clusters: From Lu-Linked to Lu-Encapsulated Configurations

The structural evolution pattern and electronic properties of Lu-doped germanium anion clusters, LuGe_n^- (n = 5-17), have been investigated using a global search method combined with a double hybrid density functional theory and by comparing the theoretical PES spectra with the experimental ones. It is found that, for the structural growth patterns, a Lu-linked configuration is preferred for n = 10-14 in which the Lu atom as a linker connects two Ge subclusters and a Lu-encapsulated Ge cage-like motif is preferred for n = 15-17. The simulated PES spectra agree with experimental ones, revealing that the current global minimum structures are the true minima. The properties such as relative stability, charge transfer, highest-energy occupied molecular orbital-lowest-energy unoccupied molecular orbital (HOMO-LUMO) gap, IR, Raman, and ultraviolet-visible (UV-vis) spectra have been evaluated. The results of IR and Raman spectra could provide additional ways to experimentally identify the structure of these clusters. The results of stability, HOMO-LUMO gap, and UV-vis spectra could make the LuGe₁₆^- cluster the most suitable building block for further development as a potential optoelectronic material.

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.

Interpretation of photoelectron spectra of CoGen- (n = 4, 5) clusters by multiconfigurational RASPT2 calculations

The low-lying electronic states CoGe_n^-/0 (n = 4, 5) have been investigated with density functional theory and the state-of-the-art RASSCF/RASPT2 method to give assignments for the anion photoelectron spectra. The BP86 functional was employed to optimize the geometrical structures of the electronic states, while the RASSCF/RASPT2 was applied to calculate the single-point energies. With the RASSCF/RASPT2 approach, the active spaces are extended to a size of 21 orbitals for CoGe₄^-/0 and 24 orbitals for CoGe₅^-/0. The ground states of CoGe₄^-/0 are determined to be ³A″ and ²A″ of a trigonal bipyramidal structure in which the Co atom is situated at the equatorial corner of the bipyramid. The vertical detachment energies of the transitions from the anionic ground state to the neutral ²A″, 1⁴A″, ²A', 2⁴A″, 3⁴A″, 1⁴A', 2⁴A', and 6⁴A″ states are evaluated to be 2.29, 2.39, 2.60, 2.83, 3.17, 3.24, 3.47, and 4.00 eV. For the CoGe₅^-/0 clusters, the ground states are computed to be ¹A₁ and 1²A₂ of an octahedral structure. The vertical detachment energies of the removal of one electron from the anionic ground state to result in the 1²A₂, 1²A₁, 2²A₁, 1²B₁, 1²B₂, 4²B₁, 4²B₂, and 6²A₂ states are estimated to be 2.16, 2.79, 2.84, 3.06, 3.06, 3.59, 3.59, and 4.22 eV. All features in the photoelectron spectra of CoGe₄^- and CoGe₅^- are interpreted based on the computed electron detachment energies of the anionic ground states.

Thermochemical Properties and Growth Mechanism of the Ag-Doped Germanium Clusters, AgGe n λ with n = 1-13 and λ = -1, 0, and +1

A systematic investigation of the silver-doped germanium clusters AgGe n with n = 1-13 in the neutral, anionic, and cationic states is performed using the unbiased global search technique combined with a double-density functional scheme. The lowest-energy minima of the clusters are identified based on calculated energies and measured photoelectron spectra (PES). Total atomization energies and thermochemical properties such as electron affinity (EA), ionization potential (IP), binding energy, hardness, and highest occupied molecular orbital-lowest unoccupied molecular orbital (HOMO-LUMO) gap are obtained and compared with those of pure germanium clusters. For neutral and anionic clusters, although the most stable structures are inconsistent when n = 7-10, their structure patterns have an exohedral structure except for n = 12, which is a highly symmetrical endohedral configuration. For the cationic state, the most stable structures are attaching structures (in which an Ag atom is adsorbed on the Ge n cluster or a Ge atom is adsorbed on the AgGe n-1 cluster) at n = 1-12, and when n = 13, the cage configuration is formed. The analyses of binding energy indicate that doping of an Ag atom into the neutral and charged Ge n clusters decreases their stability. The theoretical EAs of AgGe n clusters agree with the experimental values. The IP of neutral Ge n clusters is decreasing when doped with an Ag atom. The chemical activity of AgGe n is analyzed through HOMO-LUMO gaps and hardness, and the variant trend of both versus cluster size is slightly different. The accuracy of the theoretical analyses in this paper is demonstrated successfully by the agreement between simulated and experimental results such as PES, IP, EA, and binding energy.

DFT-based investigation of different properties for transition metal-doped germanium TMGen (TM = Ru, Rh; n = 1-20) clusters

The geometries and energetic, electronic, and magnetic features of transition metal-doped germanium (TMGe_n with TM = Ru, Rh; n = 1-20) clusters are systematically studied by means of first principle computations on the basis of the density functional theory (DFT) approach. The doping TM atom largely participates to strengthen the Ge_n cluster stability by increasing the binding energies. A good stability is obtained for RuGe₁₂, RhGe₁₂, and RhGe₁₄ clusters. The various explored isomers of TMGe_n clusters possess a total spin magnetic moment going from 0 to 2μ_B, except for RhGe₂ with 3μ_B. These results open nice perspectives of these good candidate clusters for applications in nanoelectronics and nanotechnologies.

Structure and Stability of a Trefoil Leaf Motif of Metal-Doped Silicon and Germanium Clusters: M3@E20 with E = Si and Ge and M = Fe, Ru, and Os

The first trefoil leaf-shaped cluster, a novel structural motif, was discovered by quantum chemical computations using density functional theory methods for both binary M₃@E₂₀ silicon and germanium clusters in which a metallic M₃ cycle is encapsulated within a D_3h Si₂₀ or Ge₂₀ cage. The triatomic transition metal Fe₃, Ru₃, and Os₃ cycles exhibit a suitable size to be placed inside both Si and Ge cages and satisfy electronic conditions, which thermodynamically stabilize the mixed clusters. Stabilizing orbital interactions between the M₃ cycle and D_3h E₂₀ cage crucially contributes to the high stability of the resulting M₃@E₂₀ trefoil cluster. The novel trefoil leaf-shaped clusters can be used as building units to create different nanoassemblies.

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⁺.

Transformation between Hexagonal Prism and Antiprism of the Singly and Doubly Cr-Doped Ge12 Clusters

Structural transformation is a unique characteristic of atomic clusters, but it turns out very different from cluster to cluster. This theoretical study proves that the isomeric transformation between hexagonal prism and hexagonal antiprism is found for the doubly doped Cr₂Ge₁₂ cluster but not for singly doped CrGe₁₂ cluster. We confirm that the ground state of CrGe₁₂ is the distorted hexagonal prism C_2h at the ³B_g triplet state instead of various shapes predicted in the previous studies. Upon comparison between the estimation at the B3P86/6-311+G(d) level of theory and the detachment energies measured by photoelectron spectroscopy, hexagonal antiprismatic shape is identified as the most stable isomer of the Cr₂Ge₁₂ cluster and it is easy to transform to the hexagonal prism-a less stable isomer by the rotation of the hexagonal rings. That is the first evidence for the structural transformation between a hexagonal prism and an antiprism of the germanium clusters, referring to the ability of Ge-based clusters in the formation of tubular geometry by doping Cr atoms. All the low-energy isomers of both Cr-doped germanium clusters have high magnetic moments. Interestingly, there is a tuning in magnetic properties of Cr₂Ge₁₂ from the ferromagnetism of the lowest-lying hexagonal antiprism to the ferrimagnetism of the higher-energy hexagonal prism. The stronger Cr-Cr bond and stronger interaction between the Cr₂ moiety and the antiprism cage are accounted for by the higher stability of the hexagonal antiprismatic isomer.

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.

Predicting the structural evolution of Gen- (3 ≤ n ≤ 20) clusters: an anion photoelectron spectroscopy simulation

Spectroscopic evidence for the structural evolution of Gen- (3 ≤ n ≤ 20) clusters is provided by means of simulated anion photoelectron spectra (PES). Both adiabatic detachment energies and HOMO-LUMO gaps of the selected low-lying candidates match well with those measured in experiment. This work demonstrates that PES is a highly sensitive technique for probing both electronic and geometric structures of atomic clusters, whose structural evolution is an elemental signature with characteristic features.

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.

Structural and magnetic properties of FeGen-/0 (n = 3-12) clusters: Mass-selected anion photoelectron spectroscopy and density functional theory calculations

The structural, electronic, and magnetic properties of FeGe_n^-/0 (n = 3-12) clusters were investigated by using anion photoelectron spectroscopy in combination with density functional theory calculations. For both anionic and neutral FeGe_n (n = 3-12) clusters with n ≤ 7, the dominant structures are exohedral. The FeGe₈^-/0 clusters have half-encapsulated boat-shaped structures, and the opening of the boat-shaped structure is gradually covered by the additional Ge atoms to form Ge_n cage from n = 9 to 11. The structures of FeGe₁₀^-/0 can be viewed as two Ge atoms symmetrically capping the opening of the boat-shaped structure of FeGe₈, and those of FeGe₁₂^-/0 are distorted hexagonal prisms with the Fe atom at the center. Natural population analysis shows that there is an electron transfer from the Ge atoms to the Fe atom at n = 8-12. The total magnetic moment of FeGe_n^-/0 and local magnetic moment of the Fe atom have not been quenched.

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.

Computational Investigation of the Geometrical and Electronic Structures of VGen-/0 (n = 1-4) Clusters by Density Functional Theory and Multiconfigurational CASSCF/CASPT2 Method

Density functional theory and the multiconfigurational CASSCF/CASPT2 method have been employed to study the low-lying states of VGe_n^-/0 (n = 1-4) clusters. For VGe^-/0 and VGe₂^-/0 clusters, the relative energies and geometrical structures of the low-lying states are reported at the CASSCF/CASPT2 level. For the VGe₃^-/0 and VGe₄^-/0 clusters, the computational results show that due to the large contribution of the Hartree-Fock exact exchange, the hybrid B3LYP, B3PW91, and PBE0 functionals overestimate the energies of the high-spin states as compared to the pure GGA BP86 and PBE functionals and the CASPT2 method. On the basis of the pure GGA BP86 and PBE functionals and the CASSCF/CASPT2 results, the ground states of anionic and neutral clusters are defined, the relative energies of the excited states are computed, and the electron detachment energies of the anionic clusters are evaluated. The computational results are employed to give new assignments for all features in the photoelectron spectra of VGe₃^- and VGe₄^- clusters.