Architecture, electronic structure and stability of TM@Ge(n) (TM = Ti, Zr and Hf; n = 1-20) clusters: a density functional modeling

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.

Energy gap and aromatic molecular rings

The manuscript combines rational density functional theory simulations and experimental data to investigate the electrical properties of eight polycyclic aromatic hydrocarbons (PAHs). The optimized geometries reveal a preference for one-row, two-row and three-row ring distributions. Band structure plots demonstrate an inverse correlation between the number of aromatic rings and band gap size, with a specific order observed across the PAHs. Gas phase simulations support these findings, though differences in values are noted compared to the literature. Introducing a two-row ring distribution concept resolves discrepancies, particularly in azulene. The B3LYP function successfully bridges theoretical and experimental gaps, particularly in large PAHs. The manuscript highlights the potential for designing electronic devices based on different-sized PAHs, emphasizing a multi-ring distribution approach and opening new avenues for practical applications.

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.

Theoretical Insights into the Geometrical Evolution, Photoelectron Spectra, and Vibrational Properties of YGe n - (n = 6-20) Anions: From Y-Linked to Y-Encapsulated Structures

The structural evolution behavior of germanium anionic clusters doped with the rare-earth metal yttrium, YGe _n ^- (n = 6-20), has been investigated using a mPW2PLYP density functional scheme and an ABCluster structure searching technique. The results reveal that with increasing cluster size n, the structure evolution pattern is from the Y-linked framework (n = 10-14), where Y serves as a linker (the Y atom bridges two germanium subclusters), to the Y-encapsulated framework (n = 15-20), where the Y atom is located in the center of the Ge cage. The simulated PES spectra show satisfying agreement with the experimental PES spectra for n = 12-20, which reveals that the global minimum structures reported here are reliable. In particular, the anionic YGe₁₆ ^- nanocluster is found to be the most stable structure in the size range of n = 6-20 through analyzes of the relative stability, highest occupied molecular orbital (HOMO)-lowest unoccupied molecular orbital (LUMO) gap, spherical jellium model, and isochemical shielding surface. Moreover, spectral properties such as infrared and Raman spectra were reported. In addition, the UV-vis spectra of the YGe₁₆ ^- nanocluster are in good agreement with solar energy distribution, showing that such substances serve as multifunctional building blocks to be potentially used in optoelectronic devices or solar energy converters.

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 Ge₁₆M^0/− 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 Ge₁₆M^0/− 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 Ge₁₆M^0/− 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.

A theoretical study of geometric and electronic structures, stability and magnetic properties of both neutral and anionic Ge₁₆M^0/− clusters with M being a first-row 3d transition metal atom, is performed using quantum chemical approaches.

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, 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.

Computational Approach To Reveal the Structural Stability and Electronic Properties of Lithiated M/CNT (M = Si, Ge) Nanocomposites as Anodes for Lithium-Ion Batteries

This work is motivated to explore the structural stability and electronic and electrochemical properties of nanocomposites of M₄Li _n (M = Si and Ge)-carbon nanotube (CNT) by employing first-principles density functional theory calculations. By analyzing the structural stability of various M₄Li _n (n = 0-10) clusters, it is revealed that a tetrahedron-shaped M₄Li₄ Zintl cluster is found to be highly stable. Our study on the interaction between the lithiated clusters and CNT illustrates that the charge transfer from the former to latter plays a pivotal role in stabilizing these nanocomposites. The structural stability of those nanocomposites arises as a consequence of bonding between lithiated clusters and CNT, which is mediated through the cation-π interaction. The strength of the interaction between them is well reflected in electronic structure calculations by shifting the energy levels with respect to the Fermi energy. Further, the electrochemical properties of these nanocomposites are explored by forming an assembly of the cluster-inserted CNT. The calculated average intercalation voltage of the systems is found to be low (maximum ∼1.0 V for M = Si and 1.05 V for M = Ge), which demonstrates their anodic behavior.

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.

Titanium Digermanium: Theoretical Assignment of Electronic Transitions Underlying Its Anion Photoelectron Spectrum

Electronic structures of both the anionic and neutral triatomic species TiGe₂^-/0 were theoretically studied employing single-reference (DFT and RCCSD(T)) and multiconfigurational (CASSCF/CASPT2 and CASSCF/NEVPT2) methods with large basis sets. The ground state of TiGe₂^- (C_2v) was identified to be ⁴B₁, but the ²A₁ state is nearly degenerate, whereas the ³B₁ is clearly the ground state of the neutral TiGe₂ (C_2v). On the basis of the computed ground and excited states of both neutral and anionic structures, all electronic transitions giving rise to experimental anion photoelectron bands in the spectrum of TiGe₂^- can now be assigned. The X band of the anion photoelectron spectrum is attributed to a one-electron transition between two ground states ⁴B₁ → ³B₁. Three neutral excited states 2³A₂, 2⁵B₁, and 3⁵B₁ are energetically responsible for the B band upon one-electron photodetachement from the anionic ground state ⁴B₁. The C band is assigned to the transition ⁴B₁ → 2⁵A₁. A transition from the nearly degenerate ground state ²A₁ of the anion to the low-spin ¹A₁ of the final neutral state can be ascribed to the A band. Furthermore, the first two bands' progressions, whose normal vibrational modes were accessible from CASSCF/CASPT2 calculations, were also simulated by determination of multidimensional Franck-Condon factors.

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.

Study on structures and electronic properties of neutral and anionic TiSin(0,-1)(n = 1–8) clusters using G4 theory

The geometries, electronic structures and energies of small TiSi n species (n = 1–8) and their anions were systematically investigated by G4 theory. The ground-state structures of these clusters are presented herein. For neutral TiSi n (n = 1–8), the spin multiplicities of the ground-state structures are singlet, with the exception of n = 2, which exists in a triplet state. For anionic TiSi n-, the spin multiplicities of the ground-state structures are doublet, with the exception of n = 2, which is quartet. The adiabatic electron affinities for TiSi n are estimated to be 1.31 eV ( TiSi ), 1.46 eV ( TiSi 2), 1.53 eV ( TiSi 3), 1.71 eV ( TiSi 4), 2.06 eV ( TiSi 5), 2.16 eV ( TiSi 6), 2.20 eV ( TiSi 7) and 2.39 eV ( TiSi 8). In comparison with the available experimental data, the calculated adiabatic electron affinities differ from experimental values by an average absolute deviation of only 0.03 eV. Additionally, the dissociation energies of Ti atoms from TiSi n, and Si atoms from TiSi n and Si n clusters are estimated to examine relative stabilities.

Study of electronic properties, stabilities and magnetic quenching of molybdenum-doped germanium clusters: a density functional investigation

The evolution of electronic structures, properties and stabilities of neutral and cationic molybdenum encapsulated germanium clusters (Mo@Ge_n, n = 1 to 20) has been investigated.

Structural and bonding properties of small TiGen− (n = 2–6) clusters: photoelectron spectroscopy and density functional calculations

The structures of small TiGe_n⁻ clusters can be considered as Ti-substituted Ge_n+1 or Ti-capped Ge_n clusters.

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.