Journal of Computational Methods in Sciences and Engineering

We search for the lowest-energy structure of XAu₄ (X=C, Si, Ge, Sn) clusters and calculate the photoelectron spectrum for the lowest-energy isomer of each species. The gradual destabilization of the tetrahedral geometry from C → Si → Ge → Sn, as well as the structural transition from the tetrahedral to the square planar geometry from SiAu₄ to GeAu₄, indicate that the change of electronic properties in the group IV elements also plays an important role in the structures of Group IV tetra-aurides in addition to the known H/Au analogy in these species.

Silicon is one of the most important semi conducting materials employed in microelectronic technologies. This chapter is dedicated to review the enormous effort made during the last years to develop confident methods to determinate the geometries and related properties of silicon clusters. Searching employing full global optimization of the energy surface, using techniques like Molecular Dynamics (MD), algorithms, and local optimization of structures built onto generic structural motifs are reported. Hybrid methodologies combining tight-binding (TB) with global optimization methods also contribute to the state of the art in the prediction of the structures, and calculation of properties of silicon clusters, based on all-electron DFT methods are also included.

The absorption and the emission spectra of undoped and doped silicon nanocrystals of different size and surface terminations have been calculated within a first-principles framework. The effects induced by the creation of an electron-hole pair on the atomic structure and on the optical spectra of hydrogenated silicon nanoclusters as a function of dimension are discussed showing the strong interplay between the structural and optical properties of the system. Starting from the hydrogenated clusters, (i) different Si/O bonding at the cluster surface and (ii) different doping configurations have been considered. We have found that the presence of a Si-O-Si bridge bond at the nanocrystal surface gives rise to significant excitonic luminescence features in the near-visible range that are in fair agreement with photoluminescence (PL) measurements on oxidized and SiO₂ embedded nanocrystals. The study of the structural, electronic and optical properties of simultaneously n- and p-type doped hydrogenated silicon nanocrystals with boron and phosphorous impurities have shown that B-P co-doping is energetically favorable with respect to single B- or P-doping and that the two impurities tend to occupy nearest neighbors sites. The co-doped nanocrystals present band edge states localized on the impurities that are responsible of a red-shifted absorption threshold with respect to that of pure un-doped nanocrystals in agreement with the experiment.

Optimum geometries of silicon clusters up to 71 atoms have been found by a recently developed Monte Carlo based global optimization method. Structural properties of these clusters have been investigated and the results have been compared with available results obtained by other methods. Radial distribution of atoms of Si₇₁ have been compared with the silicon crystal structure.

We report on first-principles quantum mechanical optimizations of the minimum energy equilibrium structure of neutral, Si n , and anionic, Si n − , pure silicon clusters, as well as the isoelectronic Si n M doped clusters ( M = Sc − , Ti , V + ) for n = 14 – 18 . We have published previously some of these results, but additional analysis is contributed here for the first time, particularly for the pure anionic silicon clusters and doped Si n Ti compounds. The lowest energy isomer of the anionic Si n − cluster shows different geometry than the neutral cluster, except for n = 15 , 17 . The geometries of a few low-lying energy isomers of doped Si n M does not relate to those of pure silicon clusters in the range of sizes considered in this work. For both pure and doped Si clusters, we analyze the trend of several electronic properties with the cluster size, like the binding energy, the addition energy of the impurity M to pure Si clusters, the second difference of total energy, the Homo-Lumo gap, the average Si-Si and Si-M distance, and the electron affinity. For Si 16 M doped clusters we found the largest binding energy, the highest second difference of energy, and the highest Homo-Lumo gap. These facts are manifestations of the special stability of Si 16 M clusters found in recent experimental mass spectra, which was rationalized in previous works as a combination of geometrical (near spherical cage-like structure) and electronic effects (l-selection rule of the spherical potential model). Here we present additional arguments, by comparing the partial orbital density of states of the near-spherical Frank-Kasper isomer of Si 16 Ti , with that of a non-spherical isomer of Si 16 Sc − anion. We have also computed the adiabatic electron affinity of pure and doped Si clusters. For doped clusters, the computed electron affinities are in very good agreement with available estimations from experimental photoelectrons spectra, but for pure neutral clusters the calculations underestimate by more than 18% the experimental values.

The structural, electronic, dynamical and spectral properties of Si₆ and its ions ( Si 6 1 − , Si 6 2 − , and Si 6 1 + ) have been examined using a variety of high level ab initio techniques, including quadratic configuration interaction, coupled cluster, and density functional theory (DFT) with the hybrid B3LYP functional. Various high quality correlation-consistent basis sets, ranging from 2Z up to 5Z quality, were employed for the DFT calculations. It is shown that not only the ground state structure, but also the structure of the excited states, as well as the structure of the anions and cations of Si₆ are controversial. Each one of the three competing structures for the ground state, with C_s/C_2v, D_4h, and C_2v symmetry, has been considered by different investigators as the lowest energy structure either of the neutral cluster, or of its anion or cation (or both). In a spirit of “structural democracy” it is demonstrated that the C_s/C_2v, D_4h, and _2v structures can be safely assigned as the ground states of the neutral, anion, and cation clusters respectively. The present results, which support the structural plasticity (fluxionality) of Si₆, are in excellent agreement with experiment, including Raman and IR spectra, ionization energies, electron affinities as well as vibrationally resolved photoelectron spectra. The paradigm of Si₆ could be very helpful for other silicon clusters as well.

The Si n K p ( + ) ( n ⩽ 6 , p ⩽ 2 ) clusters with different spin configurations have been systematically investigated by using the density functional theory with B3LYP. Equilibrium geometries, population analysis, binding energies, adiabatic and vertical ionization potentials as well as electric dipole moments and static dipolar polarizabilities, have been calculated and are discussed for each considered size. For the most stable isomers, the structure of the neutral Si n K p and cationic Si n K p + clusters are found to keep the frame of the corresponding Si n , potassium atoms being adsorbed at the surface. The localization of the potassium cation is not the same one as that of the neutral atom. K + ion is preferentially located on a Si atom while the K atom is preferentially attached at a bridge site. The population analysis show that the electronic structure of Si n K p can be described as Si n p − + p K + for the small sizes considered here. Binding energies and ionization potentials are compared to those of sodium and lithium-doped silicon clusters.

The dipole polarizabilities of the pure tetramers (C₄, Si₄) and mixed carbon silicon hetero-clusters (C_x Si 4 − x , 0 ⩽ x ⩽ 4 ) have been calculated within the framework of time independent and Time-Dependent (TD) Density Functional Theory (DFT) methods. The convergence of the two approaches is remarkably good revealing the absence of any systematic error. The Si- substitution leads to clusters with enhanced properties. The effect is more pronounced in the case of second hyperpolarizability (x 10³ e 4 a 0 4 E h − 3 ): 8.51(C₄) → 18.04(SiC₃) → 32.45(Si₂C₂) → 60.45(Si₃C) → 100.79(Si₄). To further extend our study, we have performed a spectral decomposition of dipole polarizabilities by employing the TD excitation energies and their corresponding oscillator strengths. Such a decomposition allows for a pictorial insight into some of the factors controlling the evolution of the property for these clusters.

First and second hyperpolarizabilities of small silicon clusters have been calculated using conventional ab initio methods systematically increasing the amount of electron correlation. Besides Si₅, upon successive addition of electron correlation in the MP2, MP3, MP4, CCSD, and CCSD(T) series, all clusters display the same behavior: i) the HF γ_// values are the smallest, ii) the MP2 γ_// values the largest, and iii) the latter values are good approximate to the reference CCSD(T) results because the overestimation is smaller than 10%. Contrary to the polarizability per Si atom, which decreases with the cluster size until reaching the bulk limit, the average second hyperpolarizability per Si atom presents a sawtooth behavior with maxima in γ_// associated with even numbers of Si and minima with odd numbers of Si atoms.

The present paper focuses on the application of semiempirical quantum molecular dynamics to explore: 1) the reaction dynamics of the elementary reaction Si + ( 2 P ) + H 2 , which is believed to play a significant role in the growth of thin silicon films, and 2) the dynamics of hydrogenated silicon nanoparticle growth (up to a size of about 1.1 nm) making use of predetermined parameters obtained from fluid model dynamics calculations to describe the experimentally employed silane plasma conditions. It has been shown that PM3 gives an adequate description of the silicon-hydrogen interactions that allows us to use it in conjunction with molecular dynamics simulation techniques to explore more in detail the dynamics of the Si + ( 2 P ) + H 2 reaction and even the growth and crystallization dynamics of small silicon nanoclusters. This success makes PM3 molecular dynamics a promising candidate for future in-depth explorations of chemical reactions involving silicon and hydrogen atoms.

The geometric and electronic structures of Si_n, Si n + , Si n − , Al Si n − 1 and P Si n − 1 clusters ( 2 ⩽ n ⩽ 13 ) has been investigated using the ab initio molecular orbital theory under the density functional theory formalism. Relative stabilities of these clusters have been analyzed based on their binding energies, second difference in energy ( Δ 2 E ) and fragmentation behavior. The equilibrium geometry of the neutral and charged Si_n clusters shows similar structural growth. The geometries of the Si n + and Al Si n − 1 are similar to those of the Si_n, but with small distortions. The ground state geometries of the Al Si n − 1 clusters shows that the impurity Al atom prefers to substitute for the Si atom, that has the highest coordination number in the host Si_n cluster. However for Si n − , n = 6 , 8, 11, and 13, significant changes have been observed in the ground state geometries of the negatively charged clusters as compared to their neutral counterparts. In general the geometries of the P substituted silicon clusters remain similar to that of negatively charged Si_n clusters with small local distortions. In general, the average binding energy of charged clusters is found to be higher than that of neutral Si_n clusters. However, significant differences have been observed in the electronic structure of neutral and charge cluster leading to their different stability pattern. While for neutral clusters, the Si₁₀ is magic, the extra stability of the Si 11 + cluster over the Si 10 + and Si 12 + bears evidence for the magic behavior of the Si 11 + cluster, which is in excellent agreement with the recent experimental observations (ref. [29]). Similarly for Al Si n − 1 clusters, which is iso-electronic with Si n + clusters show extra stability of the AlSi₁₀ cluster suggesting the influence of the electronic structures for different stabilities between neutral and charged clusters. For iso-electronic P Si n − 1 clusters, it is found that although for small clusters ( n < 4 ) substitution of P atom improves the binding energy of Si_n clusters but for larger clusters ( n > 4 ), the effect is opposite. The fragmentation behavior of all these clusters shows that while small clusters prefers to evaporate monomer, the larger ones dissociates into two stable clusters of smaller size. Finally, a good agreement between experimental and our theoretical results suggests good prediction of the lowest energy isomeric structures for all clusters calculated in the present study.