Geometries, stabilities, and magnetic properties of MnGen (n=2–16) clusters: Density-functional theory investigations

Structural evolution and bonding properties of Nb1-2Gen-/0 (n = 3-7) clusters: Anion photoelectron spectroscopy and theoretical calculations

This study presents a collaborative experimental and theoretical investigation into the structures and electronic properties of niobium-doped germanium clusters. Anion photoelectron spectra for Nb1-2Gen- (n = 3-7) clusters were acquired using 266 nm photon energies, enabling the determination of adiabatic detachment energies and vertical detachment energies. In conjunction with these experimental measurements, density functional theory (DFT) calculations were conducted to validate the experimentally obtained electron detachment energies and elucidate the geometric and electronic structures of each anionic cluster. The agreement between DFT calculations and experimental data establishes a solid foundation for assessing the structural evolution and electronic properties of niobium-doped germanium clusters. It is noted that both neutral and anionic clusters exhibit predominantly similar overall structural characteristics, with the exception of Nb2Ge6- and Nb2Ge6. Furthermore, this investigation emphasizes the exceptional chemical stability of the D3d symmetric chair-shaped structure in Nb2Ge6-, providing insights into its bonding characteristics.

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.

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.

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.

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.

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.

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.

On the structural landscape in endohedral silicon and germanium clusters, M@Si12 and M@Ge12

Amongst the endohedral clusters of the tetrel elements, M@En, the 12-vertex species are unique in that three completely different geometries, the icosahedron (Ih, [Ni@Pb12](2-)), the hexagonal prism (HP, Cr@Si12) and the bicapped pentagonal prism (BPP, [Ru@Ge12](3-)) have been identified in stable molecules. We explore here the origins of this structural diversity by comparing stability patterns across isovalent and isoelectronic series, M@Si12, M@Ge12 and [M@Ge12](3-). The BPP structure dominates the structural landscape for high valence electron counts (57-60) while the HP has a rather narrower window of stability around the 54-56 count. Moreover the preference for an HP structure is unique to silicon: in no case is a rigorously D6h-symmetric structure the global minimum for M@Ge12. Distortions from the high-symmetry limits, where present, can be traced to degeneracies or near-degeneracies in the frontier orbital domains. In all cases the structure adopted is that which maximizes the delocalization of electron density between the metal and the cluster cage, such that both components attain stable electronic configurations.

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.