Structures and stability of medium silicon clusters. II. Ab initio molecular orbital calculations of Si12–Si20

Structures and electronic properties of VSin- (n = 14-20) clusters: a combined experimental and density functional theory study

We present a systematic study of the structures and electronic properties of vanadium-doped silicon cluster anions, VSi_n^- (n = 14-20), by combining photoelectron spectroscopy (PES) measurements and density functional theory (DFT) based theoretical calculations. High resolution PES of low temperature (10 K) clusters are acquired at a photon wavelength of 248 nm. Low-lying structures of VSi_14-20^- are obtained by a genetic algorithm based global minimum search code combined with DFT calculations. Excellent agreement is found between the measured PES and the simulated electron density of states of the putative ground-state structures. We conclude that clusters with sizes n = 14 and n = 15 prefer cage-like structures, with the encapsulated vanadium atom bonding with all silicon atoms, while a fullerene-like motif is more favorable for n ≥ 16. For the sizes n = 16 to 19, the structures consist of a V@Si₁₄ with two, three, four, and five Si atoms on the surface of the cage. For n = 20 the structure consists of a V@Si₁₅ with five Si atoms on the surface of the cage. VSi₁₄^- has the highest stability and stands out as a simultaneous closing of electronic and geometrical shells.

Study on the growth behavior and photoelectron spectroscopy of neodymium-doped silicon nanoclusters NdSin0/- (n = 8-20) with a double-hybrid density functional theory

Structural evolution, magnetic moment, and thermochemical and spectral properties of NdSi_n^0/- (n = 8-20) nanoclusters were studied. Optimized structures for NdSi_n demonstrated that the configuration with quintet ground state prefers Nd-substituted for a Si of the most stable Si_n + 1 (n = 8-11) structure to Nd-linked configuration with Si₉ tricapped trigonal prism subcluster (n = 12-19). Finally, the configuration prefers to Nd-encapsulated into Si cage framework (n = 20). For anion, the evolution at the quartet state prefers Nd-linked structure for n = 8-19 (excluded 9), and prefers Nd-encapsulated structure of n = 20. The spectral information including electron affinity, vertical detachment energy, and simulated photoelectron spectroscopy were also observed. The 4f electrons of Nd atom in NdSi_n with n = 8-10 hardly participate in bonding, but take part in remaining neutral clusters and all anionic NdSi_n^- clusters. The calculations of average bond energy, HOMO-LUMO gap, and chemical bonding analyses reveal that NdSi₂₀^- possesses perfect thermodynamic and ideal chemical stability, making it as the most appropriate constitutional units for novel multi-functional semiconductors.

The stability, electronic, and magnetic properties of rare-earth doped silicon-based clusters

The rare-earth doped silicon-based clusters exhibit remarkable structural, physical, and chemical properties, which make them attractive candidates as building units in designing of cluster-based materials with special optical, electronic, and magnetic properties. The structural, stability, electronic, and magnetic properties of pure silicon Si_n + 1 (n = 1-9) and rare-earth doped clusters Si_nEu (n = 1-9) are investigated using the "stochastic kicking" (SK) global search technique combined with density functional theory (DFT) calculations. It was found that: 1) the ground state structures of pure silicon clusters tend to form compact structures rather than cages with the increase of cluster size; 2) the ground state structures for doped species were found to be additional or substitutional sites, and the rare-earth atoms tend to locate on the surface of the silicon clusters; 3) the average binding energy of the doped clusters increased gradually and exhibited the final phenomenon of saturation with the increase of clusters size. The average binding energy of doped clusters was slightly higher than that of pure silicon clusters of the same size, which indicated that the rare-earth atom encapsulated by silicon enhanced the stability of the silicon clusters to some degree; 4) the doped clusters have strong total magnetic moments, which mainly originated from the contribution of rare-earth atoms, whereas the contribution of silicon atoms were almost negligible. As the cluster size increased, the total magnetic moments of binary mixed clusters tended to be stable.

Structural growth pattern of neutral and negatively charged yttrium-doped silicon clusters YSi n 0/- (n=6-20): from linked to encapsulated structures

A global search for the low energy of neutral and anionic doped Si clusters YSi n 0/- (n = 6-20) was performed using the ABCluster global search technique coupled with a hybrid density functional method (mPW2PLYP). In light of the calculated energies and the measured photoelectron spectroscopy values, the true minima of the most stable structures were confirmed. It is shown that the structural growth pattern of YSi n - (n = 6-20) is from Y-linked two subcluster structure to a Y-encapsulated structure in Si cages, while that of YSi n (n = 6-20) is from substitutional to linked structures, and as the number of Si atoms increases, it evolves toward the encapsulated structure. Superatom YSi20 - with a high-symmetry endohedral I h structure has an ideal thermodynamic stability and chemical reactivity, making it the most suitable building block for novel optical, optoelectronic photosensitive or catalytic nanomaterials.

Medium-sized [Formula: see text] (n = 14-20) clusters: a combined study of photoelectron spectroscopy and DFT calculations

Size-selected anionic silicon clusters, [Formula: see text] (n  =  14-20), have been investigated by photoelectron spectroscopy and density functional theory (DFT) calculations. Low-energy structures of the clusters are globally searched for by using a genetic algorithm based on DFT calculations. The electronic density of states and vertical detachment energies have been simulated by using ten DFT functionals and compared to the experimental results. We systematically evaluated the DFT functionals for the calculation of the energetics of silicon clusters. CCSD(T) single-point energies based on MP2 optimized geometries for selected isomers of [Formula: see text] are also used as benchmark for the energy sequence. The HSE06 functional with aug-cc-pVDZ basis set is found to show the best performance. Our global minimum search corroborates that most of the lowest-energy structures of [Formula: see text] (n  =  14-20) clusters can be derived from assembling tricapped trigonal prisms in various ways. For most sizes previous structures are confirmed, whereas for [Formula: see text] a new structure has been found.

Ab initio study of medium sized boron-doped silicon clusters SinBm, n = 11-13, m = 1-3

The ground state and energetically low structures of neutral SinBm clusters, of medium size with n = 11-13, m = 1-3, are identified, presented and rationalized. Structures of the nanoclusters are predicted using density functional theory (DFT) and employing the HSE06 range-separated hybrid exchange-correlation functional. For these systems the functional is shown to offer systematic performance when benchmarked against high accuracy coupled-cluster CCSD(T) and compared to well known functionals used in the literature. Discrepancies for small size systems present in the literature are addressed and resolved. The structural evolution patterns of the clusters are discussed and common structural features (substructures) are identified. Cluster geometries are extensively searched via a particle swarm optimization algorithm alongside more traditional methodologies. In addition to the binding energies (that include zero-point energy corrections) of the structures, the optical gaps and UV/visible absorption spectra are reported, employing the CAM-B3LYP functional that was benchmarked against the high level EOM-CCSD level of theory. The computed infrared spectra are provided and discussed in length with respect to structural details. Their effectiveness as charge transfer units is examined. Optical gaps range between 1.4-2.5 eV, and are adjustable through the boron and silicon content of the clusters, which, along with the increased structural stability, offers promise for applications in optoelectronics.

Parametrization of a Reactive Force Field (ReaxFF) for Molecular Dynamics Simulations of Si Nanoparticles

A novel computational approach, based on classical reactive molecular dynamics simulations (RMD) and quantum chemistry (QC) global energy optimizations, is proposed for modeling large Si nanoparticles. The force field parameters, which can describe bond breaking and formation, are derived by reproducing energetic and structural properties of a set of Si clusters increasing in size. These reference models are obtained through a new protocol based on a joint high temperature RMD/low temperature Basin Hopping QC search. The different procedures of estimating optimal force field parameters and their performance are discussed in detail.

Understanding the structural transformation, stability of medium-sized neutral and charged silicon clusters

The structural and electronic properties for the global minimum structures of medium-sized neutral, anionic and cationic Si_n^μ (n = 20–30, μ = 0, −1 and +1) clusters have been studied using an unbiased CALYPSO structure searching method in conjunction with first-principles calculations. A large number of low-lying isomers are optimized at the B3PW91/6-311 + G* level of theory. Harmonic vibrational analysis has been performed to assure that the optimized geometries are stable. The growth behaviors clearly indicate that a structural transition from the prolate to spherical-like geometries occurs at n = 26 for neutral silicon clusters, n = 27 for anions and n = 25 for cations. These results are in good agreement with the available experimental and theoretical predicted findings. In addition, no significant structural differences are observed between the neutral and cation charged silicon clusters with n = 20–24, both of them favor prolate structures. The HOMO-LUMO gaps and vertical ionization potential patterns indicate that Si₂₂ is the most chemical stable cluster, and its dynamical stability is deeply discussed by the vibrational spectra calculations.

Theoretical study on the structures and optical absorption of Si₁₇₂ nanoclusters

The structures and optical properties of silicon nanoclusters (Si NCs) have attracted continuous interest in the last few decades. However, it is a great challenge to determine the structures of Si NCs for accurate property calculation due to the complication and competition of various structural motifs. In this work, a Si172 NC with a size of about 1.8 nm was investigated using a genetic algorithm combined with tight-binding and DFT calculations. We found that a diamond crystalline core with 50 atoms (1.2 nm) was formed in the Si172 NC. It can be expected that at a size of about 172 atoms, a diamond crystalline structure can nucleate from the center of the Si NCs. The optical properties of the pure and hydrogenated Si172 NC structures also have been studied using the TDDFT method. Compared with the pure Si172 NC, the absorption peaks of the hydrogenated Si172 NC are obviously blue-shifted.

Structures, Stabilities, and Electronic Properties of Small-Sized Zr2Si n (n=1–11) Clusters: A Density Functional Study

Ab initio methods based on density functional theory at B3LYP level have been applied in investigating the equilibrium geometries, growth patterns, relative stabilities, and electronic properties of Zr2-doped Si n clusters. The optimisation results shown that the lowest-energy configurations for Zr2Si n clusters do not keep the corresponding silicon framework unchanged, which reflects that the doped Zr atoms dramatically affect the most stable structures of the Si n clusters. By analysing the relative stabilities, it is found that the doping of zirconium atoms reduces the chemical stabilities of silicon host. The Zr2Si4 and Zr2Si7 clusters are the magic numbers. The natural population and natural electronic configuration analyses indicated that the Zr atoms possess positive charge for n=1–6 and negative charge for n=7–11. In addition, the chemical hardness, chemical potential, infrared, and Raman spectra are also discussed.

Discovery of a silicon-based ferrimagnetic wheel structure in V(x)Si(12)(-) (x = 1-3) clusters: photoelectron spectroscopy and density functional theory investigation

Our studies show that VSi(12)(-) adopts a V-centered hexagonal prism with a singlet spin state. The addition of the second V atom leads to a capped hexagonal antiprism for V(2)Si(12)(-) in a doublet spin state. Most interestingly, V(3)Si(12)(-) exhibits a ferrimagnetic, bicapped hexagonal antiprism wheel-like structure with a total spin of 4 μ(B).

An insight into the structures, stabilities, and bond character of B(n)Pt (n=1∼6) clusters

We perform a systematical investigation on the geometry, thermodynamic/kinetic stability, and bonding nature of low-lying isomers of BnPt (n=1-6) at the CCSD(T)/[6-311+G(d)/LanL2DZ]//B3LYP/[6-311+G(d)/LanL2DZ] level. The most stable isomers of BnPt (n=1-6) adopt planar or quasi-planar structure. BnPt (n=2-5) clusters can be generated by capping a Pt atom on the B-B edge of pure boron clusters. However, For B6Pt with non-planar structure, a single doped Pt atom significantly affects the shape of the host boron cluster. The dopant of the Pt atom can improve the stability of pure boron clusters. The valence molecular orbital (VMO), electron localization function (ELF), and Mayer bond order (MBO) are applied to gain insight into the bonding nature of BnPt (n=2-6) isomers. The aromaticity for some isomers of BnPt (n=2-6) is analyzed and discussed in terms of VMO, ELF, adaptive natural density partitioning (AdNDP), and nucleus-independent chemical shift (NICS) analyses. Results obtained from the energy and cluster decomposition analyses demonstrate that B2Pt and B4Pt exhibits as highly stable. Importantly, some isomers of BnPt (n=2-5) are stable both thermodynamically and kinetically, which are observable in future experiment.

Evaluation of optical and electronic properties of silicon nano-agglomerates embedded in SRO: applying density functional theory

In systems in atomic scale and nanoscale such as clusters or agglomerates constituted by particles from a few to less than 100 atoms, quantum confinement effects are very important. Their optical and electronic properties are often dependent on the size of the systems and the way in which the atoms in these clusters are bonded. Generally, these nanostructures display optical and electronic properties significantly different to those found in corresponding bulk materials. Silicon agglomerates embedded in silicon rich oxide (SRO) films have optical properties, which have been reported to be directly dependent on silicon nanocrystal size. Furthermore, the room temperature photoluminescence (PL) of SRO has repeatedly generated a huge interest due to its possible applications in optoelectronic devices. However, a plausible emission mechanism has not been widely accepted in the scientific community. In this work, we present a short review about the experimental results on silicon nanoclusters in SRO considering different techniques of growth. We focus mainly on their size, Raman spectra, and photoluminescence spectra. With this as background, we employed the density functional theory with a functional B3LYP and a basis set 6-31G* to calculate the optical and electronic properties of clusters of silicon (constituted by 15 to 20 silicon atoms). With the theoretical calculation of the structural and optical properties of silicon clusters, it is possible to evaluate the contribution of silicon agglomerates in the luminescent emission mechanism, experimentally found in thin SRO films.

Initial geometries, interaction mechanism and high stability of silicene on Ag(111) surface

Using ab initio methods, we have investigated the structures and stabilities of Si_N clusters (N ≤ 24) on Ag(111) surface as the initial stage of silicene growth. Unlike the dome-shaped graphene clusters, Si clusters prefer nearly flat structures with low buckling, more stable than directly deposition of the 3D freestanding Si clusters on Ag surface. The p-d hybridization between Ag and Si is revealed as well as sp² characteristics in Si_N@Ag(111). Three types of silicene superstructures on Ag(111) surface have been considered and the simulated STM images are compared with experimental observations. Molecular dynamic simulations show high thermal stability of silicene on Ag(111) surfaces, contrast to that on Rh(111). The present theoretical results constitute a comprehensive picture about the interaction mechanism of silicene on Ag(111) surface and explain the superiority of Ag substrate for silicene growth, which would be helpful for improving the experimentally epitaxial growth of silicene.

DENSITY FUNCTIONAL THEORY STUDIES OF CHARGED, COPPER-DOPED, SMALL SILICON CLUSTERS, ${\rm CuSi}_{n}^{+}/{\rm CuSi}_{n}^{-}$ (n = 1–7)

The structures and stabilities of charged, copper-doped, small silicon clusters [Formula: see text] (n = 1–7) have been systematically investigated using the density functional theory method at the B3LYP/6-311+G* level. For comparison, the geometries of neutral CuSi n clusters were also optimized at the same level, although most of them have been reported previously [see Xiao CY, Abraham A, Quinn R, Hagelberg F, Comparative study on the interaction of scandium and copper atoms with small silicon clusters, J Phys Chem A106:11380, 2002; Liu X, Zhao GF, Guo LJ, Wang XW, Zhang J, Jing Q, Luo YH, First-principle studies of the geometries and electronic properties of Cu m Si n (2 ≤ m + n ≤ 7) clusters, Chin Phys16:3359, 2007]. Our results for the ground state structures of neutral CuSi n clusters agree well with those of Liu et al. and Xiao et al. except for CuSi3 and CuSi7 . Removing or adding an electron greatly changes some ground state structures, i.e. for [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], and [Formula: see text]; others are almost unchanged, e.g. [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text]. The ground states of ionic [Formula: see text] are all singlet, except for the smaller CuSi- and [Formula: see text]. Based on the optimized geometries, various energetic properties, including binding energies, second-order difference energies, the highest occupied molecular orbit and the lowest unoccupied molecular orbital (HOMO–LUMO) energy gaps, ionization potential and electron affinities, were calculated for the most stable isomers of [Formula: see text]. All the results indicate that anionic [Formula: see text] and cationic [Formula: see text] clusters are relatively stable. The higher stability of the latter has been confirmed by Beck's observations.

GLOBAL GEOMETRY OPTIMIZATION OF SILICON CLUSTERS EMPLOYING EMPIRICAL POTENTIALS, DENSITY FUNCTIONALS, AND AB INITIO CALCULATIONS

Si n clusters in the size range n = 4–30 have been investigated using a combination of global structure optimization methods with DFT and ab initio calculations. One of the central aims is to provide explanations for the structural transition from prolate to spherical outer shapes at about n = 25, as observed in ion mobility measurements. Firstly, several existing empirical potentials for silicon and a newly generated variant of one of them were better adapted to small silicon clusters, by global optimization of their parameters. The best resulting empirical potentials were then employed in global cluster structure optimizations. The most promising structures from this stage were relaxed further at the DFT level with the hybrid B3LYP functional. For the resulting structures, single point energies have been calculated at the LMP2 level with a reasonable medium-sized basis set, cc-pVTZ. These DFT and LMP2 calculations were also carried out for the best structures proposed in the literature, including the most recent ones, to obtain the currently best and most complete overall picture of the structural preferences of silicon clusters. In agreement with recent findings, results obtained at the DFT level do support the shape transition from prolate to spherical structures, beginning with Si 26 (albeit not completely without problems). In stark contrast, at the LMP2 level, the dominance of spherical structures after the transition region could not be confirmed. Instead, just as below the transition region, prolate isomers are obtained as the lowest-energy structures for n ≤ 29. We conclude that higher (probably multireference) levels of theoretical treatments are needed before the puzzle of the silicon cluster shape transition at n = 25 can safely be considered as explained.

Graph theory meets ab initio molecular dynamics: atomic structures and transformations at the nanoscale

Social permutation invariant coordinates are introduced describing the bond network around a given atom. They originate from the largest eigenvalue and the corresponding eigenvector of the contact matrix, are invariant under permutation of identical atoms, and bear a clear signature of an order-disorder transition. Once combined with ab initio metadynamics, these coordinates are shown to be a powerful tool for the discovery of low-energy isomers of molecules and nanoclusters as well as for a blind exploration of isomerization, association, and dissociation reactions.

An ab initio calculation study of silicon and carbon binary clusters C7Si(n) (n = 1-7)

Binary C(7)Si(n) (n = 1-7) clusters are studied using density functional calculations at the level of B3LYP/6-311G(d). Lowest-energy structures have been determined theoretically and their properties such as binding energies, second differences in energy and highest-occupied and lowest-unoccupied molecular orbital gaps have been analyzed. It is found that the lowest-energy structures of the C(7)Si(n) (n = 1-7) clusters change from linear to planar when n ≥ 3, and in the planar structures C atoms prefer to form five- and six-membered rings surrounded by extra Si atoms in the form of the C(2)Si units.

Search for structures, potential energy surfaces, and stabilities of planar BnP(n = 1 ∼ 7)

We have systematically explored and investigated the geometrical structures, stability, growth pattern, bonding character, and potential energy surface (PES) of the possible isomers of each cluster for planar B(n)P (n = 1 ∼ 7) at the CCSD(T)/6-311+;G(d)//B3LYP/6-311+G(d) level. A large number of planar structures for the possible isomers of B(n)P (n = 1 ∼ 7) and transition states are located. Isomers 1a ∼ 7a of B(n)P are the lowest-energy structures and 2a, 4a, as well as 6a are more stable than their neighbors. For the lowest-energy structures (1a ∼ 7a) of B(n)P, P atom lies at the apex and tends to form two B-P bonds with boron atoms. They exhibit planar zigzag growth feature or approximately spherical-like growth pattern. Results from molecular orbital analysis demonstrate that the formation of the delocalized π MOs and the σ-radial and σ-tangential MOs plays a critical role in stabilizing the structures of lowest-energy isomers (2a ∼ 7a) of B(n)P. Importantly, isomers 3a, 3c, 3d, 4a, 4b, 5b, and 5c of B(n)P are stable both thermodynamically and kinetically at the CCSD(T)/6-311+G(d)// B3LYP/6-311+G(d) level and detectable in laboratory, which is valuable for further experimental studies of B(n)P.

Structures of Pb(n) (n = 21-30) clusters from first-principles calculations

Neutral lead clusters Pb(n) (n = 21-30) were studied using a genetic algorithm (GA)/tight-binding (TB) search combined with density functional theory (DFT)-Perdew-Burke-Ernzerhof (PBE) calculations. The calculated results show that the Pb(n) (22 ≤ n ≤ 30) clusters favor endohedral cage structures with two (Pb(22 - 26)) or three (Pb(27 - 30)) endohedral atoms. The binding energies, stabilities, and highest occupied molecular orbital-lowest unoccupied molecular orbital (HOMO-LUMO) gaps of the Pb(n) clusters were also discussed. The results from our calculations also indicate that Pb(24) and Pb(28) are especially stable clusters compared with their neighbors.