Photoionization studies of germanium and tin clusters in the energy region of 5.0–8.8 eV: Ionization potentials for Gen (n=2–57) and Snn (n=2–41)

Determination of Ground State Structures of Snx - (x=21-35) Clusters

In this work, an unbiased global search with a homemade genetic algorithm was performed to investigate the structural evolution and electronic properties of Snx - (x=21-35) clusters with density functional theory (DFT) calculations. All the ground-state structures for all these Snx - (x=21-35) clusters have been confirmed by the comparison of the experimental and simulated photoelectron spectra (PESs). It has been revealed that all Snx - (x=21-35) clusters are tricapped trigonal prism (TTP)-based structures consisting of two (for sizes x=21-28) or three (for x=29-35) TTP units, with the remaining atoms adsorbed on the surface or inserted between TTP units. The gradually decreasing HOMO-LUMO gaps indicate that these clusters are undergoing semiconductor-to-metal transformation. The average binding energies show that the structural stabilities of Snx - clusters are not as good as that of silicon and germanium clusters. It found that sizes x=23, 25, 29, 33 show high relative stability.

Delayed photodissociation of the tin cluster Sn22. Phys Chem Chem Phys 2024;26:1105-1112. [PMID: 38098439 DOI: 10.1039/d3cp04476a] [Citation(s) in RCA: 0] [Impact Index Per Article: 0]

Millisecond-delayed photodissociation of gas-phase Sn22- clusters stored in a Penning trap is investigated as a function of excitation energy. Sn15- is the only significant charged fragment, indicative of the break-off of neutral heptamers. Fits of the time-resolved fragmentation require a distribution of decay constants, caused by the finite width of the internal energy distribution of the cluster ensemble prior to photoexcitation. A lower limit for the dissociation energy for the loss of Sn7 is determined to be 2.1(1) eV, a factor of two above literature quantum chemical calculations.

Ionization potentials of metal clusters studied with a broad range, tunable vacuum ultraviolet light source

In this work, we present an alternative to complex laser setups or synchrotron light sources to accurately measure the ionization potentials of metal clusters. The setup is based on a commercial Xe flash lamp, combined with a vacuum monochromator, and has been applied to determine the ionization potentials of Snn clusters with n = 8-12 atoms. The uncertainty in the determination of the ionization potentials is mainly caused by the bandwidth of the monochromator. The adiabatic ionization potentials (AIPs) are extracted from experimental photoionization efficiency curves. Franck-Condon simulations are additionally used to interpret the shape and onset of the photo-ion yield. The obtained AIPs are (all energies are in eV) Sn8 (6.53 ± 0.05), Sn9 (6.69 ± 0.04), Sn10 (6.93 ± 0.03), Sn11 (6.34 ± 0.05), and Sn12 (IsoI 6.64 ± 0.04 and IsoIII 6.36 ± 0.05). Furthermore, the impact of multiple isomers present in the experiment on the photo-ion yield is addressed and compared with other experimental data in the literature.

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.

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.

Tin-carbon clusters and the onset of microscopic level immiscibility: Experimental and computational study

We report the experimental observation and computational analysis of the binary tin-carbon gas phase species. These novel ionic compounds are generated by impact of C60(-) anions on a clean tin target at some kiloelectronvolts kinetic energies. Positive Sn(m)C(n)(+) (m = 1-12, 1 ≤ n ≤ 8) ions were detected mass spectrometrically following ejection from the surface. Impact induced shattering of the C60(-) ion followed by sub-surface penetration of the resulting atomic carbon flux forces efficient mixing between target and projectile atoms even though the two elements (Sn/C) are completely immiscible in the bulk. This approach of C60(-) ion beam induced synthesis can be considered as an effective way for producing novel metal-carbon species of the so-called non-carbide forming elements, thus exploring the possible onset of molecular level miscibility in these systems. Sn2C2(+) was found to be the most abundant carbide cluster ion. Its instantaneous formation kinetics and its measured kinetic energy distribution while exiting the surface demonstrate a single impact formation/emission event (on the sub-ps time scale). Optimal geometries were calculated for both neutral and positively charged species using Born-Oppenheimer molecular dynamics for identifying global minima, followed by density functional theory (DFT) structure optimization and energy calculations at the coupled cluster singles, doubles and perturbative triples [CCSD(T)] level. The calculated structures reflect two distinct binding tendencies. The carbon rich species exhibit polyynic/cummulenic nature (tin end capped carbon chains) while the more stoichiometrically balanced species have larger contributions of metal-metal bonding, sometimes resulting in distinct tin and carbon moieties attached to each other (segregated structures). The Sn2C(n) (n = 3-8) and Sn2C(n)(+) (n = 2-8) are polyynic/cummulenic while all neutral Sn(m)C(n) structures (m = 3-4) could be described as small tin clusters (dimer, trimer, and tetramer, correspondingly) attached to a nearly linear carbon chain. For example, the 1:1 (Sn:C) Sn3C3 and Sn4C4 clusters are composed of all-tin triangle and rhombus, correspondingly, with a short carbon chain (C3, C4) attached on top. The cationic Sn3C(n)(+) (n = 1-5) and Sn4C(n)(+) (n = 1-4) species exhibit various intermediate geometries. Structure calculations at the CCSD(T) level are essential since the segregation effect is not as easily evident based on the most stable structures calculated by DFT alone. Dependences of bond energies (per atom) reflect the evolution of the segregation effect. The mass spectral abundances could be reasonably rationalized in terms of calculated stabilities of the cluster ions with respect to various dissociation channels.

Comparative study of small boron, silicon and germanium clusters: B(m)Si(n) and B(m)Ge(n) (m + n = 2-4)

Chemically speaking, atomic clusters are very rich, allowing their application in a broad range of technological areas such as developing functional materials, heterogeneous catalysis, and building optical devices. In this work, high level computational chemistry methods were used in a systematic manner to improve the characterization of small clusters formed by boron, silicon, germanium, mixed boron/silicon, and mixed boron/germanium. Calculations were carried out with both ab initio [MP2 and CCSD(T)] and density functional (B3LYP) methods with extended basis sets. The CCSD(T) results were then extrapolated to the complete basis set (CBS) limit. Finally, geometrical parameters, vibrational frequencies, and relative energies were then obtained and compared to data presented in the literature. Graphical Abstract Small boron, silicon and germanium clusters: BmSin and BmGen (m + n = 2-4).

Empty versus filled polyhedra: 11 vertex bare germanium clusters

The structures and energetics of centered 10-vertex Ge@Ge₁₀(z) (z = -4, -2, 0, +2, +4) clusters have been investigated by density functional theory (DFT) for comparison with the previously studied isomeric empty 11-vertex Ge₁₁(z) clusters. For the cationic species (z = +2, +4) such centered Ge@Ge₁₀(z) structures are shown to be energetically competitive (within ∼1 kcal mol⁻¹) to the lowest energy isomeric empty Ge₁₁(z) structures. These Ge@Ge₁₀(z) structures can be derived from the lowest energy empty 10-vertex Ge₁₀(z-4) structures by inserting a Ge⁴⁺ ion in the center. The outer 10-vertex polyhedron in the lowest energy Ge@Ge₁₀²⁺ dication structure is the most spherical D(4d) bicapped square antiprism, which is also the lowest energy structure of the empty Ge₁₀²⁻ dianion, as expected from the Wade-Mingos skeletal electron counting rules. For the tetracationic Ge₁₁⁴⁺ /Ge@Ge₁₀⁴⁺ system the lowest energy centered Ge@Ge₁₀⁴⁺ structure can be obtained by inserting a Ge⁴⁺ ion in the center of a C(3v) deltahedral empty Ge10 cluster. Centered 10-vertex polyhedral Ge@Ge₁₀(z) structures were also found for the neutral (z = 0) and dianionic (z = -2) systems but at significantly higher energies than the lowest energy isomeric empty Ge₁₁(z) structures.

A Stochastic Search for the Structures of Small Germanium Clusters and Their Anions: Enhanced Stability by Spherical Aromaticity of the Ge10 and Ge12(2-) Systems

Investigations on germanium clusters in the neutral, anionic, and dianion states Gen(x) (n = 2-12 and x = 0, -1, -2) are performed using quantum chemical calculations with the B3LYP functional and the coupled-cluster singles and doubles [CCSD(T)] methods, in conjunction with the 6-311+G(d) basis set. An improved stochastic method is implemented for searching the low-lying isomers of clusters. Comparison of our results with previous reports on germanium clusters shows the efficiency of the search method. The Ge8 system is presented in detail. The anionic clusters Gen(-/2-) are studied theoretically and systematically for the first time, and their energetics are in good agreement with available experiments. The clusters Ge10, Ge10(2-), and Ge12(2-) are, in their ground state, characterized by large highest occupied molecular orbital-lowest unoccupied molecular orbital gaps, high vertical and adiabatic detachment energies, and substantial average binding energies. The enhanced stability of these magic clusters can consistently be rationalized using the jellium electron shell model and the spherical aromatic character.

Orbitals in inorganic chemistry: metal rings and clusters, hydronitrogens, and heterocyles

A chemical orbital theory is useful in inorganic chemistry. Some applications are described for understanding and designing of inorganic molecules. Among the topics included are: (1) valence electron rules to predict stabilities of three- and four-membered ring metals and for those of regular octahedral M(6) metal clusters solely by counting the number of valence electrons; (2) pentagon stability (stability of five- relative to six-membered rings in some classes of molecules), predicted and applied for understanding and designing saturated molecules of group XV elements; (3) properties of unsaturated hydronitrogens N( m )H( n ) in contrast to those of hydrocarbons C( m )H( n ); (4) unusually short nonbonded distances between metal atoms in cyclic molecules.

Stabilities and fragmentation energies of Si(n) clusters (n = 2-33)

The structures of Si(n) (n = 2-33) were confirmed by genetic algorithm (GA)/tight binding (TB) search and ab initio calculations at the B3LYP/6- 311++G(2d) and PW91/6-311++G(2d) level, respectively. The fragmentation energies, binding energies, second differences in energy, and highest occupied molecular orbital (HOMO)-lowest unoccupied molecular orbital (LUMO) gaps in the size range 2≤n≤33 were calculated and analyzed systematically. We extended the cluster size involved in the fragmentation analyses up to Si(33), and studied the multi-step fragmentations of Si(n). The calculated result is similar to the fragmentation behavior of small silicon clusters studied previously, showing that Si(6), Si(7), and Si(10) have relatively larger stabilities and appear more frequently in the fragmentation products of large silicon clusters, which is in good agreement with the experimental observations.

The dissociation energy of the new diatomic molecules SiPb and GePb

The diatomic molecules SiPb and GePb were for the first time identified by producing high temperature vapors of the constituent pure elements in a "double-oven-like" molecular-effusion assembly. The partial pressures of the atomic, heteronuclear, and homonuclear gaseous species observed in the vapor, namely, Si, Ge, Pb, SiPb, GePb, Pb2, Gen, and Sin (n=2-3), were mass-spectrometrically measured in the overall temperature ranges 1753-1961 K (Ge-Pb) and 1992-2314 K (Si-Pb). The dissociation energies of the new species were determined by second- and third-law analyses of both the direct dissociation reactions and isomolecular exchange reactions involving homonuclear molecules. The selected values of the dissociation energies at 0 K (D0 degrees) are 165.1+/-7.3 and 141.6+/-6.9 kJ/mol, respectively, for SiPb and GePb, and the corresponding enthalpies of formation (DeltafH0 degrees) are 476.4+/-7.3 and 419.3+/-6.9 kJ/mol. The ionization efficiency curves of the two species were measured, giving the following values for the first ionization energies: 7.0+/-0.2 eV (SiPb) and 7.1+/-0.2 eV (GePb). A computational study of the species SiPb and GePb was also carried out at the CCSD(T) level of theory using the relativistic electron core potential approach. Molecular parameters, adiabatic ionization energies, adiabatic electron affinities, and dissociation energies of the title species were calculated, as well as the enthalpy changes of the exchange reactions involving the other Pb-containing diatomics of group 14. Finally, a comparison between the experimental and theoretical results is presented, and from a semiempirical correlation the unknown dissociation energies of the SiSn and PbC molecules are predicted as 234+/-7 and 185+/-11 kJ/mol, respectively.

Evolution of the electronic properties of Snn− clusters (n=4–45) and the semiconductor-to-metal transition

The electronic structure of Sn(n) (-) clusters (n=4-45) was examined using photoelectron spectroscopy at photon energies of 6.424 eV (193 nm) and 4.661 eV (266 nm) to probe the semiconductor-to-metal transition. Well resolved photoelectron spectra were obtained for small Sn(n) (-) clusters (n< or =25), whereas more congested spectra were observed with increasing cluster size. A distinct energy gap was observed in the photoelectron spectra of Sn(n) (-) clusters with n< or =41, suggesting the semiconductor nature of small neutral tin clusters. For Sn(n) (-) clusters with n> or =42, the photoelectron spectra became continuous and no well-defined energy gap was observed, indicating the onset of metallic behavior for the large Sn(n) clusters. The photoelectron spectra thus revealed a distinct semiconductor-to-metal transition for Sn(n) clusters at n=42. The spectra of small Sn(n) (-) clusters (n< or =13) were also compared with those of the corresponding Si(n) (-) and Ge(n) (-) clusters, and similarities were found between the spectra of Sn(n) (-) and those of Ge(n) (-) in this size range, except for Sn(12) (-), which led to the discovery of stannaspherene (the icosahedral Sn(12) (2-)) previously [L. F. Cui et al., J. Am. Chem. Soc. 128, 8391 (2006)].

Sn122-: Stannaspherene

Stannaspherene. The Sn122- cluster is discovered to be a highly stable and highly symmetric icosahedral cage bonded by four delocalized radial pi bonds and nine delocalized on-sphere sigma bonds from the 5p orbitals of the Sn atoms. It has a diameter of 6.1 A, with a large empty interior volume, and can host most transition metal atoms inside, giving rise to a large class of endohedral chemical building blocks for cluster-assembled nanomaterials.

Search for global-minimum geometries of medium-sized germanium clusters. II. Motif-based low-lying clusters Ge21–Ge29

We performed a constrained search for the geometries of low-lying neutral germanium clusters Ge(N) in the size range of 21 < or = N < or = 29. The basin-hopping global optimization method is employed for the search. The potential-energy surface is computed based on the plane-wave pseudopotential density functional theory. A new series of low-lying clusters is found on the basis of several generic structural motifs identified previously for silicon clusters [S. Yoo and X. C. Zeng, J. Chem. Phys. 124, 054304 (2006)] as well as for smaller-sized germanium clusters [S. Bulusu et al., J. Chem. Phys. 122, 164305 (2005)]. Among the generic motifs examined, we found that two motifs stand out in producing most low-lying clusters, namely, the six/nine motif, a puckered-hexagonal-ring Ge6 unit attached to a tricapped trigonal prism Ge9, and the six/ten motif, a puckered-hexagonal-ring Ge6 unit attached to a bicapped antiprism Ge10. The low-lying clusters obtained are all prolate in shape and their energies are appreciably lower than the near-spherical low-energy clusters. This result is consistent with the ion-mobility measurement in that medium-sized germanium clusters detected are all prolate in shape until the size N approximately 65.

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

Ni-doped germanium clusters have been systematically investigated by using the density functional approach. The growth-pattern behaviors, stabilities, charge transfer, and polarities of these clusters are discussed in detail. Obviously different growth patterns appear between small-sized Ni-doped germanium clusters and middle- or larger-sized Ni-doped germanium clusters. The Ni-convex or substituted Ge(n) frames for small-sized clusters as well as Ni-concaved or encapsulated Ge(n) frames for middle- or large-sized clusters are dominant growth patterns. The calculated fragmentation energies manifest that the magic numbers of stabilities are 5, 8, 10, and 13 for Ni-doped germanium clusters; the obtained relative stabilities exhibit that the Ni-encapsulated Ge(10) cluster is the most stable species of all different-sized clusters, which is in good agreement with available experimental observations of CoGe(10)(-). Natural population analysis shows that different charge-transfer phenomena depend on the sizes of the Ni-doped Ge(n) clusters. Additionally, the properties of frontier orbitals and the polarities of Ni-doped Ge(n) clusters are also discussed.

A computational investigation of copper-doped germanium and germanium clusters by the density-functional theory

The geometries, stabilities, and electronic properties of Ge(n) and CuGe(n) (n = 2-13) clusters have been systematically investigated by using density-functional approach. According to optimized CuGe(n) geometries, growth patterns of Cu-capped Ge(n) or Cu-substituted Ge(n+1) clusters for the small- or middle-sized CuGe(n) clusters as well as growth patterns of Cu-concaved Ge(n) or Ge-capped CuGe(n-1) clusters for the large-sized CuGe(n) clusters are apparently dominant. The average atomic binding energies and fragmentation energies are calculated and discussed; particularly, the relative stabilities of CuGe10 and Ge10 are the strongest among all different sized CuGe(n) and Ge(n) clusters, respectively. These findings are in good agreement with the available experimental results on CoGe10- and Ge10 clusters. Consequently, unlike some transition metal (TM)Si12, the hexagonal prism CuGe12 is only low-lying structure; however, the basket-like structure is located as the lowest-energy structure. Different from some TM-doped silicon clusters, charge always transfers from copper to germanium atoms in all different sized clusters. Furthermore, the calculated highest occupied molecular orbital and lowest unoccupied molecular orbital (HOMO-LUMO) gaps are obviously decreased when Cu is doped into the Ge(n) clusters, together with the decrease of HOMO-LUMO gaps, as the size of clusters increases. Additionally, the contribution of the doped Cu atom to bond properties and polarizabilities of the Ge(n) clusters is also discussed.

Search for global minimum geometries for medium sized germanium clusters: Ge12–Ge20

We have performed an unbiased search for the global minimum geometries of small-to-medium sized germanium clusters Gen(12< or =n< or =18) as well as a biased search (using seeding method) for Gen(17< or =n< or =20). We employed the basin-hopping algorithm coupled with the plane-wave pseudopotential density functional calculations. For each size, we started the unbiased search with using several structurally very different initial clusters, or we started the biased search with three different seeds. Irrespective of the initial structures of clusters we found that the obtained lowest-energy clusters of the size n=12-16 and 18 are the same. Among them, the predicted global minima of Gen(12< or =n< or =16) are identical to those reported previously [Shvartsburg et al., Phys. Rev. Lett. 83, 167 (1999)]. For n=17-20, we have identified two or three nearly isoenergetic low-lying isomers (for each size) that compete for the global minimum. Nearly all the low-lying clusters in the size range of 12< or =n< or =20 contain the tri-caped trigonal prism motif and are all prolate in geometry, in agreement with the experiment.