Structural and electronic properties of TaSi(n) (n=1-13) clusters: a relativistic density functional investigation

Anion Photoelectron Spectroscopy and Quantum Chemistry Calculations of Gas-Phase TaSi17̅ and TaSi18̅ Clusters: Structural Determination, Bonding Characteristics, and Multiplicity of Structural Forms

This study explores the structures and chemical bonding properties of TaSi17̅ and TaSi18̅ clusters by employing anion photoelectron spectroscopy and theoretical computations. Utilizing CALYPSO and ABCluster programs for initial structure prediction, B3LYP hybrid functional for optimization, and CCSD(T)/def2-TZVPPD level for energy calculations, the research identifies the most stable isomers of these clusters. Key findings include the identification of two coexisting low-energy isomers for TaSi17̅, exhibiting Ta-endohedral fullerene-like cage structures, and the lowest-energy structures of TaSi17̅ and TaSi18̅ anions can be considered as derived from the TaSi16̅ superatom cluster. The study enhances the understanding of group 14 element chemistry and guides the design of novel inorganic metallic compounds, potentially impacting materials science.

Structural Determination and Bonding Characteristics of the Gas-Phase Ta2Si2̅ Anion and Its Neutral: Anion Photoelectron Spectroscopy and Theoretical Studies

The structures and bonding characteristics of Ta2Si2̅/0 clusters are investigated using anion photoelectron spectroscopy and quantum chemical calculations. The vertical detachment energy of the Ta2Si2̅ anion is measured to be 2.00 ± 0.08 eV using the 266 nm photon. It is found that the Ta2Si2̅ anion has three low-energy isomers with a C2v symmetric Ta-Ta dibridged structural framework, all of which contribute to the experimental photoelectron spectrum, while the Ta2Si2 neutral also has a C2v symmetric Ta-Ta dibridged structural framework. The charge-transfer from Ta atoms to Si atoms is discovered using atomic dipole moment corrected Hirshfeld analysis for the Ta2Si2̅ anion and Ta2Si2 neutral. Chemical bonding investigations show that both the Ta2Si2̅ anion and Ta2Si2 neutral have a strong covalent Ta-Ta bond, as well as σ and π double bonding patterns. Furthermore, the Ta atoms are linked together by a single 2c-2e Ta2 σ bond, whereas the Si atoms are linked together with the Ta atoms via four 2c-2e TaSi σ bonds, two 3c-2e TaSi2 σ bonds, one 4c-2e Ta2Si2 σ bond, and one 4c-2e Ta2Si2 π bond.

Anion photoelectron spectroscopy and density functional theory study of TM2Sin- (TM = V, Cr; n = 14-20) clusters

We investigated the structural evolution and electronic properties of medium-sized silicon cluster anions doped with two transition metal atoms, TM₂Si_n^- (TM = V, Cr; n = 14-20), by using mass-selective anion photoelectron spectroscopy combined with density functional theory (DFT) calculations. Putative ground state structures of these clusters were obtained by using a genetic algorithm coupled with the DFT calculations. It was found that the two TM atoms tend to form a TM-TM bond, which - except for V₂Si₁₉^- - is shorter than the nearest neighbour distance in the crystalline state of the respective metals. The V₂Si_n^- clusters with n = 14 to 17 exhibit structures based on a silicon hexagonal antiprism, while the larger ones exhibit more fullerene-like cage structures. Cr₂Si_n^- clusters follow the same trend, although with a silicon hexagonal prism structure for n = 14 and 15, and the transition to fullerene-like structures occurring at n = 17. Among these clusters, TM₂Si₁₈^- have the largest average binding energy and second order differences in energy, therefore the highest relative stability. All of the clusters possess total magnetic moment of 1 μB, but with very different contributions from the doped TM atoms. Especially in the Cr doped clusters there is a tendency towards an anitiferromagnetic arrangement of the magnetic moments of the two Cr atoms.

Structural and Electronic Properties of LaSin-/0 (n = 2-6) Clusters: Anion Photoelectron Spectroscopy and Density Functional Calculations

The structures and electronic properties of LaSi_n^- (n = 2-6) anions and their neutral counterparts were investigated by anion photoelectron spectroscopy and theoretical calculations. The vertical detachment energies of the most stable structures of LaSi_n^- (n = 2-6) were measured to be 1.28, 1.58, 2.30, 2.05, and 2.91 eV, respectively. The lowest-energy isomer of LaSi₂^- is an isosceles triangle with a C_2v symmetry. For LaSi_3-6^- clusters, the most stable isomers are polyhedrons with La atom face-capping the Si_n frameworks. The lowest-energy structures of neutral LaSi_2,4,5 clusters are similar to their anionic counterparts. The most stable isomer of neutral LaSi₃ is a planar structure with C_2v symmetry, which is different from the triangular pyramid structure of LaSi₃^- anion. The lowest-energy isomer of LaSi₆^- is a C_5v symmetric pentagonal bipyramid structure, while for neutral LaSi₆ cluster, the C_5v structure is not the most stable one. The natural population analysis showed that there is electron transfer from La atoms to Si atoms in LaSi_n^-/0 (n = 2-6). The ZZ tensor component in isochemical shielding surfaces and the anisotropy of the induced current density analyses indicate that the most stable isomer of LaSi₆^- has aromaticity.

Multiconfiguration Pair-Density Functional Theory for Transition Metal Silicide Bond Dissociation Energies, Bond Lengths, and State Orderings

Transition metal silicides are promising materials for improved electronic devices, and this motivates achieving a better understanding of transition metal bonds to silicon. Here we model the ground and excited state bond dissociations of VSi, NbSi, and TaSi using a complete active space (CAS) wave function and a separated-pair (SP) wave function combined with two post-self-consistent field techniques: complete active space with perturbation theory at second order and multiconfiguration pair-density functional theory. The SP approximation is a multiconfiguration self-consistent field method with a selection of configurations based on generalized valence bond theory without the perfect pairing approximation. For both CAS and SP, the active-space composition corresponds to the nominal correlated-participating-orbital scheme. The ground state and low-lying excited states are explored to predict the state ordering for each molecule, and potential energy curves are calculated for the ground state to compare to experiment. The experimental bond dissociation energies of the three diatomic molecules are predicted with eight on-top pair-density functionals with a typical error of 0.2 eV for a CAS wave function and a typical error of 0.3 eV for the SP approximation. We also provide a survey of the accuracy achieved by the SP and extended separated-pair approximations for a broader set of 25 transition metal–ligand bond dissociation energies.

Structural Evolution and Electronic Properties of TaSin-/0 (n = 2-15) Clusters: Size-Selected Anion Photoelectron Spectroscopy and Theoretical Calculations

The structural evolution and electronic properties of TaSi_n^-/0 (n = 2-15) clusters are explored using anion photoelectron spectroscopy accompanied by quantum chemical calculations. The Ta atom in TaSi_n^-/0 is inclined to interact with more Si atoms and has high coordination numbers. The theoretical calculations show that TaSi₂^-/0 have trianglur structures and TaSi₃^-/0 adopt pyramid structures, while the geometries of TaSi_n^-/0 (n = 4-7) are all exohedral structures dominated by bipyramid-based configurations with the Ta atom face-capping the Si_n motifs. TaSi₈^-/0 and TaSi_9-10^- have boat-shaped geometries, whereas TaSi_9-10 neutrals adopt bipyramid-based geometries instead of boat-shaped ones. TaSi₁₁^- and TaSi₁₂ are confirmed as the critical size of transiting from exohedral to endohedral structures for anionic and neutral clusters, respectively. TaSi_12-15^-/0 have pentagonal or hexagonal prism-based geometries. Natural population analysis shows that the electron transfers from Si_n skeletons to Ta atom. The second-order energy differences (Δ₂E) and incremental binding energy (ΔE^I) values exhibit strong odd-even alternations, suggesting that the TaSi_n-odd^-/0 clusters are more stable than the adjacent TaSi_n-even^-/0 ones, except that TaSi_12^-/0 are more stable than TaSi_11^-/0 and TaSi_13^-/0.

Relativistic quantum heat engine from uncertainty relation standpoint

Established heat engines in quantum regime can be modeled with various quantum systems as working substances. For example, in the non-relativistic case, we can model the heat engine using infinite potential well as a working substance to evaluate the efficiency and work done of the engine. Here, we propose quantum heat engine with a relativistic particle confined in the one-dimensional potential well as working substance. The cycle comprises of two isothermal processes and two potential well processes of equal width, which forms the quantum counterpart of the known isochoric process in classical nature. For a concrete interpretation about the relation between the quantum observables with the physically measurable parameters (like the efficiency and work done), we develop a link between the thermodynamic variables and the uncertainty relation. We have used this model to explore the work extraction and the efficiency of the heat engine for a relativistic case from the standpoint of uncertainty relation, where the incompatible observables are the position and the momentum operators. We are able to determine the bounds (the upper and the lower bounds) of the efficiency of the heat engine through the thermal uncertainty relation.

Bond dissociation energies of TiSi, ZrSi, HfSi, VSi, NbSi, and TaSi

Predissociation thresholds have been observed in the resonant two-photon ionization spectra of TiSi, ZrSi, HfSi, VSi, NbSi, and TaSi. It is argued that because of the high density of electronic states at the ground separated atom limit in these molecules, the predissociation threshold in each case corresponds to the thermochemical bond dissociation energy. The resulting bond dissociation energies are D₀(TiSi) = 2.201(3) eV, D₀(ZrSi) = 2.950(3) eV, D₀(HfSi) = 2.871(3) eV, D₀(VSi) = 2.234(3) eV, D₀(NbSi) = 3.080(3) eV, and D₀(TaSi) = 2.999(3) eV. The enthalpies of formation were also calculated as Δ_f,0KH°(TiSi(g)) = 705(19) kJ mol^-1, Δ_f,0KH°(ZrSi(g)) = 770(12) kJ mol^-1, Δ_f,0KH°(HfSi(g)) = 787(10) kJ mol^-1, Δ_f,0KH°(VSi(g)) = 743(11) kJ mol^-1, Δ_f,0KH°(NbSi(g)) = 879(11) kJ mol^-1, and Δ_f,0KH°(TaSi(g)) = 938(8) kJ mol^-1. Using thermochemical cycles, ionization energies of IE(TiSi) = 6.49(17) eV and IE(VSi) = 6.61(15) eV and bond dissociation energies of the ZrSi^- and NbSi^- anions, D₀(Zr-Si^-) ≤ 3.149(15) eV, D₀(Zr^--Si) ≤ 4.108(20) eV, D₀(Nb-Si^-) ≤ 3.525(31) eV, and D₀(Nb^--Si) ≤ 4.017(39) eV, have also been obtained. Calculations on the possible low-lying electronic states of each species are also reported.

Structural determination of niobium-doped silicon clusters by far-infrared spectroscopy and theory

The structures of niobium doped silicon cluster cations are determined by a combination of infrared multiple photon dissociation spectroscopy and density functional theory calculations.

Computational investigation of TiSin (n=2–15) clusters by the density-functional theory

The geometries, stabilities, and electronic properties of TiSin (n=2-15) clusters with different spin configurations have been systematically investigated by using density-functional theory approach at B3LYP/LanL2DZ level. According to the optimum TiSin clusters, the equilibrium site of Ti atom gradually moves from convex to surface, and to a concave site as the number of Si atom increases from 2 to 15. When n=12, the Ti atom in TiSi12 completely falls into the center of the Si outer frame, forming metal-encapsulated Si cages, which can be explained by using 16-electron rule. On the basis of the optimized geometries, various energetic properties are calculated for the most stable isomers of TiSin clusters, including the average binding energy, the highest occupied molecular orbital and lowest unoccupied molecular orbital (HOMO-LUMO) gap, fragmentation energy, and the second-order difference of energy. It is found that at size n=6,8,12 the clusters are more stable than neighboring ones. According to the Mulliken charge population analysis, charges always transfer from Si atoms to Ti atom. Furthermore, the HOMO-LUMO gaps of the most stable TiSin clusters are usually smaller than those of Sin clusters.

Electronic structures and chemical bonding in transition metal monosilicides MSi (M = 3d, 4d, 5d elements)

Bond distances, vibrational frequencies, electron affinities, ionization potentials, dissociation energies, and dipole moments of the title molecules in neutral, positively, and negatively charged ions were studied using the density functional method. Ground state was assigned for each species. The bonding patterns were analyzed and compared with both the available data and across the series. It was found that besides an ionic component, covalent bonds are formed between the metal s,d orbitals and the silicon 3p orbital. The covalent character increases from ScSi (YSi) to NiSi (PdSi) for 3d (4d) metal monosilicides, then decreases. For 5d metal monosilicides, the covalent character increases from LaSi to OsSi, then decreases. For the dissociation of cations, the dissociation channel depends on the magnitude of the ionization potential between metal and silicon. If the ionization potential of the metal is smaller than that of silicon, channel MSi+ --> M+ + Si is favored. Otherwise, MSi+ --> M + Si+ will be favored. A similar behavior was observed for anions, in which the dissociation channel depends on the magnitude of electron affinity.

Electronic and Geometric Stabilities of Clusters with Transition Metal Encapsulated by Silicon

Silicon clusters mixed with a transition metal atom, MSin, were generated by a double-laser vaporization method, and the electronic and geometric stabilities for the resulting clusters with transition metal encapsulated by silicon were examined experimentally. By means of a systematic doping with transition metal atoms of groups 3, 4, and 5 (M = Sc, Y, Lu, Ti, Zr, Hf, V, Nb, and Ta), followed by changes of charge states, we explored the use of an electronic closing of a silicon caged cluster and variations in its cavity size to facilitate metal-atom encapsulation. Results obtained by mass spectrometry, anion photoelectron spectroscopy, and adsorption reactivity toward H2O show that the neutral cluster doped with a group 4 atom features an electronic and a geometric closing at n = 16. The MSi(16) cluster with a group 4 atom undergoes an electronic change in (i) the number of valence electrons when the metal atom is substituted by the neighboring metals with a group 3 or 5 atom and in (ii) atomic radii with the substitution of the same group elements of Zr and Hf. The reactivity of a halogen atom with the MSi(16) clusters reveals that VSi(16)F forms a superatom complex with ionic bonding.

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.

Relativistic Computational Investigation: The Geometries and Electronic Properties of TaSin+ (n = 1−13, 16) Clusters

The equilibrium geometries, stabilities, and electronic properties of the TaSi(n)+ (n = 1-13, 16) clusters are investigated systematically by using the relativistic density functional method with generalized gradient approximation. The small-sized TaSi(n)+ clusters with slight geometrical adjustments basically keep the frameworks that are analogous to the neutrals while the medium-sized charged clusters significantly deform the neutral geometries, which are confirmed by the calculated AIP and VIP values. Furthermore, the optimized geometries of the charged clusters agree with the experimental results of Hiura and co-workers (Hiura, H.; Miyazaki, T.; Kanayama, T. Phys. Rev. Lett. 2001, 86, 1733). The highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) gaps of the charged clusters are generally increased as the cluster size goes from n = 1 to 13; and the large HOMO-LUMO gaps of charged clusters resulting from the positive charge indicate that their chemical stabilities are stronger than their neutral counterparts, especially for n = 4, 6, and 7 clusters. Additionally, the contributions of the d orbitals of the Ta atom to the HOMO and LUMO reveal that the chemical activity of the d orbitals of the Ta atom decreases gradually as the number of silicon atoms increases. This interesting finding is in good agreement with the recent experimental results on the reactive activities of the H2O and transition-metal silicon clusters (Koyasu, K.; Akutsu, M.; Mitsui, M.; Nakajima, A. J. Am. Chem. Soc. 2005, 127, 4998). Generally, the positive charge significantly influences the electronic and geometric structures of the charged clusters. Finally, the most stable neutral and charged TaSi16 clusters are found to be fullerene-like structures and the HOMO-LUMO gap in charged form is detectable experimentally.

Geometries and Electronic Properties of the Neutral and Charged Rare Earth Yb-Doped Sin (n = 1−6) Clusters: A Relativistic Density Functional Investigation

The neutral and charged YbSi(n) (n = 1-6) clusters considering different spin configurations have been systematically investigated by using the relativistic density functional theory with generalized gradient approximation. The total bonding energies, equilibrium geometries, Mulliken populations (MP), Hirshfeld charges (HC), fragmentation energies, and highest occupied molecular orbital-lowest unoccupied molecular orbital (HOMO-LUMO) gaps are calculated and discussed. The optimized geometries indicate that the most stable YbSi(n) (n = 1-6) clusters keep basically the analogous frameworks as the low-lying Si(n)(+1) clusters, while the charged species deviate from their neutral counterparts, and that the doped Yb tends to occupy the substitutional site of the neutral and charged YbSi(n) isomers. The relative stabilities are investigated in terms of the calculated fragmentation energies, exhibiting enhanced stabilities for the remarkably stable neutral and charged YbSi2 and YbSi5 clusters. Furthermore, the calculated MP and HC values show that the charges of the neutral and charged YbSi(n) clusters transfer from the Yb atom to Si(n) atoms and the Yb atom acts as an electron donor, and that the f orbitals of the Yb atom in the neutral and charged YbSi(n) clusters behave as core without involvement in chemical bonding. The calculated HOMO-LUMO gaps indicate that the YbSi2 and YbSi4+ clusters have stronger chemical stabilities. Comparisons of the Yb-doped Si(n) (n = 1-6) with available theoretical results of transition-metal-doped silicon clusters are made. The growth pattern is investigated also.

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.

Geometries, stabilities, and electronic properties of different-sized ZrSin (n=1–16) clusters: A density-functional investigation

The ZrSi(n) (n=1-16) clusters with different spin configurations have been systematically investigated by using the density-functional approach. The total energies, equilibrium geometries, growth-pattern mechanisms, natural population analysis, etc., are discussed. The equilibrium structures of different-sized ZrSi(n) clusters can be determined by two evolution patterns. Theoretical results indicate that the most stable ZrSi(n) (n=1-7) geometries, except ZrSi3, keep the analogous frameworks as the lowest-energy or the second lowest-energy Si(n+1) clusters. However, for large ZrSi(n) (n=8-16) clusters, Zr atom obviously disturbs the framework of silicon clusters, and the localized position of the transition-metal (TM) Zr atom gradually varies from the surface insertion site to the concave site of the open silicon cage and to the encapsulated site of the sealed silicon cage. It should be mentioned that the lowest-energy sandwich-like ZrSi12 geometry is not a sealed structure and appears irregular as compared with other TM@Si12 (TM = Re,Ni). The growth patterns of ZrSi(n) (n=1-16) clusters are concerned showing the Zr-encapsulated structures as the favorable geometries. In addition, the calculated fragmentation energies of the ZrSi(n) (n=1-16) clusters manifest that the magic numbers of stabilities are 6, 8, 10, 14, and 16, and that the fullerene-like ZrSi16 is the most stable structure, which is in good agreement with the calculated atomic binding energies of ZrSi(n) (n=8-16) and with available experimental and theoretical results. Natural population analysis shows that the natural charge population of Zr atom in the most stable ZrSi(n) (n=1-16) structures exactly varies from positive to negative at the critical-sized ZrSi8 cluster; furthermore, the charge distribution around the Zr atom appears clearly covalent in character for the small- or middle-sized clusters and metallic in character for the large-sized clusters. Finally, the properties of frontier orbitals and polarizabilities of ZrSi(n) are also discussed.