Theoretical study of silicon–sulfur clusters (SiS2)n (n = 1–6)

 The possible geometrical structures and relative stability of (SiS₂) _n (n=1–6) silicon–sulfur clusters are explored by means of density functional theory quantum chemical calculations. The effects of polarization functions and electron correlation are included in these calculations. The electronic structures and vibrational spectra of the most stable geometrical structures of (SiS₂) _n are analyzed by the same method. As a result, the regularity of the (SiS₂) _n cluster growth is obtained, and the calculation may used for predicting the formation mechanism of the (SiS₂) _n cluster. Received: 17 November 1999 / Accepted: 3 November 2000 / Published online: 3 May 2001     

A density functional theory investigation of CrSin (n=1–6) clusters

Clusters of the form CrSi_n (n=1–6) were investigated computationally using a density functional approach. In particular, geometry optimizations were carried out under the constraint of well-defined point group symmetries at the B3LYP level employing a pseudopotential method in conjunction with double zeta basis sets. In this article, the resulting total energies, Mulliken atomic net populations, overlap populations, fragmentation energies and geometries of CrSi_n (n=1–6) are presented and discussed, together with natural populations and natural electron configurations. In addition, we comment on the charge transfer within the clusters. From this analysis, the 3d orbital of the Cr atom in CrSi_n (n=1–6) cluster absorbs electrons. From this tendency, conclusions are drawn with respect to the electronic populations and the chemical bond between Si and Cr as well as Si and Si.     

Theoretical study on the structures and properties of (Br2AlN3) n (n = 1–4) clusters

To look for the single-source precursors, the structures and properties of (Br₂AlN₃) _n (n = 1–4) clusters are studied at the B3LYP/6-311+G* level. The optimized (Br₂AlN₃) _n (n = 2–4) clusters all possess cyclic structures containing Al-N_α-Al linkages. The relationships between the geometrical parameters and the oligomerization degree n are discussed. The gas-phase structures of the trimers prefer to exist in the boat-twisting conformation. As for the tetramer, the most stable isomers have the S ₄ symmetry structure. The IR spectra are obtained and assigned by the vibrational analysis. The thermodynamic properties are linearly related with the oligomerization degree n as well as with the temperature. Meanwhile, the thermodynamic analysis of the gas-phase reaction suggests that the oligomerization be exothermic and favorable under high temperature.     

Theoretical study of Aun clusters (n = 1–5) deposited on a rutile TiO2 (110) slab,concerning structure and stability

The initial nucleation of gold clusters Au_n (n = 1–5) on TiO₂ rutile (110) reduced surface is studied using density functional theory and a full-potential augmented-plane-wave method implemented in the WIEN2k code. The first two gold atoms remained tied to the surface with a bond length similar to those belonging to other well-known related materials, while the other gold atoms do not spread over the surface; they preferred to form a new layer. The occurrence of relativistic effects produced a preferential triangle geometry for Au₃ and a combination of triangular units for Au₄ and Au₅. The Au–Au average distance increased from n = 2 to n = 5, indicating an expansion with a tendency to the bond distance found in the bulk. We are reporting an early 2D→3D transition of small folding, from Au₃→Au₄, followed by an Au₄→Au₅ transition of evident 3D character.     

Structure, stability and electronic property of the gold-doped germanium clusters: AuGe n (n = 2–13)

The structure, stability and electronic property of the AuGe _n (n = 2–13) clusters with different spin configurations are systematically investigated with density-functional theory approach at UB3LYP/LanL2DZ level. In examining the lowest energy structures, it is found that the growth behaviors for the small-sized AuGe _n (n = 2–9) clusters and relatively large-sized AuGe _n (n = 10–13) clusters are different. As the number of Ge atom increases, the Au atom would gradually move from convex to surface and to interior sites. For the most stable structures of AuGe _n (n = 10–13) clusters, the Au atom would be completely surrounded by the Ge atoms to form Au-encapsulated Ge _n cages. Natural population analysis shows that the charges always transfer from the Au atom to the Ge _n framework except for the AuGe₂ cluster. This indicates that the Au atom acts as electron donor even the 5d orbitals of the Au atom are not significantly involved in chemical bonding. The analyses of the average atomic binding energies as well as the dissociation energies and the second-order differences of total energy show that the AuGe _n clusters with n = 5, 9 and 12 are more stable than their neighboring ones, in which the bicapped pentagonal prism AuGe₁₂ in D _2d symmetry is most stable. The highest occupied molecular orbital–lowest unoccupied molecular orbital gaps are explored to be in the region of semiconductors and the more stable clusters have slightly smaller gaps. It could be expected that the stable clusters might be considered as the novel building blocks in practical applications, e.g., the cluster-assembled semiconductors or optoelectronic material.     

Theoretical and experimental study of IR spectra of large phenol-acetylene clusters,Ph(Ac)n for 8 ≤ n ≤ 12

This work reports a combined theoretical and experimental study on large phenol-acetylene clusters, Ph(Ac)_n, 8 ​≤ ​n ​≤ ​12, extending our earlier work on the smaller clusters [Singh, G.; Nandi, A.; Gadre, S. R.; Chiba, T.; Fujii, A. J. Chem. Phys. 2017, 146, 154303]. Several trial cluster geometries are generated using the molecular electrostatic potential (MESP) for placing additional acetylene moieties, followed by geometry optimization at B97D/aug-cc-pVDZ level theory. The infrared spectra of energetically low-lying (within 0.5 ​mH window) isomers of the clusters are calculated and averaged. The O–H stretching band shows two peaks due to the presence of energetically close isomers differing in the arrangement of acetylenes around the O–H group. The acetylenic C–H stretching band appears around 3260 ​cm⁻¹. The C–H band shows a red shift of about 3 ​cm⁻¹ on going from n ​= ​8 to 12. Moderately size-selected IR spectra of Ph(Ac)_n (n ​= ​~10 and ~13) prepared by a supersonic jet expansion are measured for the acetylenic C–H region by infrared-ultraviolet double resonance spectroscopy combined with time-of-flight mass spectrometry. The observed spectral features are in agreement with the trends of the frequency shift and asymmetric line shape of the C–H stretch band predicted by the theoretical calculations.     

Theoretical study of the stability of small triply charged carbon clusters Cn3+ (n = 3–12)

Using density functional theory, coupled cluster and multireference methods, dissociation energies and 3rd ionization potentials for, respectively, triply charged and neutral carbon clusters have been evaluated. The results show that the smaller C_n³⁺ clusters are metastable, i.e., they present a fragmentation channel with negative dissociation energy. The lowest dissociation channel always corresponds to evaporation of a singly charged carbon atom. Good agreement with available experimental data is found for most two-fragment channels. The third ionization potential of the corresponding neutral species decreases with cluster size.     

Spatial structure and electronic spectrum of TiSi n − clusters (n = 6–18)

Results from optimizing the spatial structure and calculated electronic spectra of anion clusters TiSi _n ^? (n = 6–18) are presented. Calculations are performed within the density functional theory. Spatial structures of clusters detected experimentally are established by comparing the calculated and experimental data. It is shown that prismatic and fullerene-like structures are the ones most energetically favorable for clusters TiSi _n ^? . It is concluded that these structures are basic when building clusters with close numbers of silicon atoms.     

Theoretical study of negatively charged Fe(-)-(H2O)(n ≤ 6) clusters

Interactions of a singly negatively charged iron atom with water molecules, Fe(-)-(H(2)O)(n≤6), in the gas phase were studied by means of density functional theory. All-electron calculations were performed using the B3LYP functional and the 6-311++G(2d,2p) basis set for the Fe, O, and H atoms. In the lowest total energy states of Fe(-)-(H(2)O)(n), the metal-hydrogen bonding is stronger than the metal-oxygen one, producing low-symmetry structures because the water molecules are directly attached to the metal by basically one of their hydrogen atoms, whereas the other ones are involved in a network of hydrogen bonds, which together with the Fe(δ-)-H(δ+) bonding accounts for the nascent hydration of the Fe(-) anion. For Fe(-)-(H(2)O)(3≤n), three-, four-, five-, and six-membered rings of water molecules are bonded to the metal, which is located at the surface of the cluster in such a way as to reduce the repulsion with the oxygen atoms. Nevertheless, internal isomers appear also, lying less than 3 or 5 kcal/mol for n = 2-3 or n = 4-6. These results are in contrast with those of classical TM(+)-(H(2)O)(n) complexes, where the direct TM(+)-O bonding usually produces high symmetry structures with the metal defining the center of the complex. They show also that the Fe(-) anions, as the TM(+) ions, have great capability for the adsorption of water molecules, forming Fe(-)-(H(2)O)(n) structures stabilized by Fe(δ-)-H(δ+) and H-bond interactions.     

A first principle study of hydrogen storage in titanium-doped small carbon clusters (C2nTin,n = 2–6)

Structural Chemistry - Hydrogen storage in Ti-doped small carbon clusters, C2nTin (n = 2–6), has been studied using density functional theory. Using the principle of maximum hardness (η)...     

A theoretical study of the stability and electronic properties of GenRu (n = 2–10) clusters and their sensitivity toward SO2 adsorption

Structural Chemistry - In this work, the stability and electronic properties of the Ru-doped germanium clusters were investigated with DFT calculations at the TPSS/SDD level. The adsorption of the...     

Electronic structures of NbGen−/0/+ (n = 1–3) clusters from multiconfigurational CASPT2 and density matrix renormalization group-CASPT2 calculations

Density functional theory and multiconfigurational CASPT2 and density matrix renormalization group DMRG-CASPT2 have been employed to study the low-lying states of NbGe_n^−/0/+ (n = 1–3) clusters. With the DMRG-CASPT2 method, the active spaces are extended to a size of 20 orbitals. For most of the states, the CASPT2 relative energies are comparable with the DMRG-CASPT2 results. The leading configuration, bond distances, vibrational frequencies, and relative energies of the low-lying states of these clusters were calculated. The ground states of these clusters were computed to be ³Δ, ⁴Φ, and ⁵Φ of NbGe^−/0/+; ³A₂, ⁴B₁, and ³B₁ of cyclic-NbGe₂^−/0/+; and ¹A′, 1²A″ and 1²A′′ (²E), and ³A″ of tetrahedral-NbGe₃^−/0/+ isomers. For NbGe cluster, our calculations proposed that the ⁶∑ is almost degenerate with the ⁴Φ with the CASPT2 and DMRG-CASPT2 relative energies of 0.05 and 0.06 eV. The adiabatic detachment energies of NbGe_n⁻ (n = 1–3) clusters were estimated to be 1.46, 1.55, and 2.18 eV by the CASPT2 method. The relevant detachment energies of the anionic ground state and the ionization energies of the neutral ground states are evaluated at the CASPT2 level.     

A theoretical investigation on optimal structures of ethane clusters (C2H6)n with n ≤ 25 and their building-up principle

Geometry optimization of ethane clusters (C(2)H(6))(n) in the range of n ≤ 25 is carried out with a Morse potential. A heuristic method based on perturbations of geometries is used to locate global minima of the clusters. The following perturbations are carried out: (1) the molecule or group with the highest energy is moved to the interior of a cluster, (2) it is moved to stable positions on the surface of a cluster, and (3) orientations of one and two molecules are randomly modified. The geometry obtained after each perturbation is optimized by a quasi-Newton method. The global minimum of the dimer is consistent with that previously reported. The putative global minima of the clusters with 3 ≤ n ≤ 25 are first proposed and their building-up principle is discussed.     

Study on structures and electron affinities of small potassium–silicon clusters Si n K (n = 2–8) and their anions with Gaussian-3 theory

The neutral Si _n K (n = 2–8) clusters and their anions have been systematically studied by means of the higher level of Gaussian-3 schemes. Equilibrium geometries and electron affinities have been calculated and are discussed for each considered size. For neutral Si _n K clusters, the ground state structure is found to be “attaching structure”, in which the K atom is bound to Si _n clusters. The most stable isomer for their anions, however, is found to be “substitutional structures”, which is derived from Si_(n+1) by replacing the Si atom with a K. The dissociation energies of K atom from the lowest energy structures of Si _n K have also been estimated to examine relative stabilities.     

Gaussian density-functional study for small neutral (Al n ), positive (Al n + ) and negative (Al n − ) aluminium clusters (n=2–5)

The structures and properties of Al _n , Al _n ⁺ , Al _n ^– (n=1,5) clusters have been investigated by using the Linear Combination of Gaussian Type Orbitals (LCGTO) method, considering Local (LSD) and Non Local (NLSD) Spin Density Approximations and employing a Model Core Potential (MCP) that allows the explicit treatment of 3s ² 3p ¹ valence electrons. For each system different geometrical structures and electronic states have been considered. For Al₃, Al ₃ ⁺ , Al ₃ ^– the most stable geometry proved to be the equilateral triangle (D _3h ). Al₄ and Al ₄ ⁺ prefer the rhombus (D _2h ) structure, while the corresponding anion prefers the square (D _4h ) one. The trapezoidal form (C _2v ) is the most stable isomer for Al₅, Al ₅ ⁺ and Al ₅ ^– clusters. The analysis of vibrational frequencies shows that these structures are minima in the potential energy surface. The binding energies (D _e), the adiabatic ionization potentials (IP) and electron affinities (EA), the chemical potentials or absolute hardnesses () and electronegativities () have been computed. Results are in good agreement with the available experimental data and the previous high level theoretical computations.     

First principle study of CrF n (n = 1–7) nano clusters: An investigation of superhalogen properties

Quantum chemical calculations using gradient corrected density functional theory at B3LYP level reveals the unusual properties of a chromium (Cr) atom interacting with fluorine (F) atoms. Up to seven F atoms are bound to a single Cr atom, which results in increase of electron affinities as successive fluorine atoms are attached, reaching a peak value of 7.14 eV for CrF₆. The large HOMO–LUMO energy gap, both in neutral and anionic form, further provide evidence of their stability. These unusual properties brought about by involvement of inner shell 3d-electrons, which not only allow CrF _n (n = 1–7) clusters to belong to the class of superhalogens but also show that its valence can exceed the nominal value of 2.     

Electronic structure and stability of anionic AuGen (n = 1–20) clusters and assemblies: a density functional modeling

Structural Chemistry - In the present study electronic structure and stabilities of cationic gold-doped germanium clusters, AuGen (n?=?1 to 20), and their assemblies have been...     

Structure and stability of AuXe n Z (n = 1–3, Z = −1, 0, +1) clusters

We have explored the structures and stabilities of AuXe _n ^Z (n = 1–3, Z = ?1, 0, +1) cluster series at CCSD(T) theoretical level. The electron affinities and ionization potentials are correlated to the HOMO–LUMO gaps. The role of the interaction was investigated using the natural bond orbital analysis.     

Anticooperativity of FH···Cl− hydrogen bonds in [FH)nCl]− clusters (n = 1…6)

The change of cooperativity of FH···Cl⁻ hydrogen bonds upon sequential addition of up to six FH molecules to the Cl⁻ first coordination sphere is investigated. The geometry of clusters [(FH) _nCl]⁻ (n = 1…6) was calculated (CCSD/aug-cc-pVDZ) and compared with [(FH) _nF]⁻ clusters. The geometry is determined by the symmetry-driven electrostatic requirements and also by the fact that formation of each new FH···Cl⁻ bond creates a depression in the chlorine's electron cloud on the opposite side of Cl⁻ (σ-hole), which limits the range of directions available for subsequent H-bond formation. The mutual influence of FH···Cl⁻ hydrogen bonds is anticooperative—the addition of each FH molecule weakens H-bonds by 23–16% and decreases their covalent character (as seen by LMO-EDA decomposition and QTAIM analysis). Anticooperativity effects could be tracked by spectroscopic parameters (frequency of local HF mode ν_FH, chemical shift δ_H, spin–spin coupling constants ¹J_FH, ^1hJ_HCl, ^2hJ_FCl and nuclear quadrupolar constants χ_18F, χ_D, and χ_35Cl. © 2019 Wiley Periodicals, Inc.     

Searching new structures of beryllium-doped in small-sized magnesium clusters: Be2MgnQ (Q = 0, −1; n = 1–11) clusters DFT study

Using CALYPSO method to search new structures of neutral and anionic beryllium-doped magnesium clusters followed by density functional theory (DFT) calculations, an extensive study of the structures, electronic and spectral properties of Be₂Mg_n^Q (Q = 0, −1; n = 2–11) clusters is performed. Based on the structural optimization, it is found that the Be₂Mg_n^Q (Q = 0, −1) clusters are shown by tetrahedral-based geometries at n = 2–6 and tower-like-based geometries at n = 7–11. The calculations of stability indicate that Be₂Mg₅^Q=0, Be₂Mg₅^Q=−1, and Be₂Mg₈^Q=−1 clusters are “magic” clusters with high stability. The NCP shows that the charges are transferred from Mg atoms to Be atoms. The s- and p-orbitals interactions of Mg and Be atoms are main responsible for their NEC. In particular, chemical bond analysis including molecular orbitals (MOs) and chemical bonding composition for magic clusters to further study their stability. The results confirmed that the high stability of these clusters is due to the interactions between the Be atom and the Mg₅ or Mg₈ host. Finally, theoretical calculations of infrared and Raman spectra of the ground state of Be₂Mg_n^Q (Q = 0, −1; n = 1–11) clusters were performed, which will be absolutely useful for future experiments to identify these clusters.