Quantum mechanical study on plasmon resonances in small ring clusters

The collectivity of the electronic motion in small sodium clusters with ring structure is studied by time‐dependent density functional theory. The formation and development of collective resonances in the absorption spectra were obtained as a function of the ring radius. In small ring clusters, besides the lower‐energy mode and the higher‐energy mode, there is another plasmon resonance mode, that is, the reverse two‐dipole mode. For the reverse two‐dipole mode, the formations of these two dipoles are due to the external field inducement and the shielding effect, although the resonant excitation is mainly due to the coupling effect of the electrons of these two dipoles. © 2012 Wiley Periodicals, Inc.     

Density functional theory study of geometry and stability of small Zrn (n = 2–10) clusters

Geometric structures, electronic properties, and stabilities of small Zr_n and Zr (n = 2–10) clusters have been investigated using density functional theory with effective core potential LanL2DZ basis set. For both neutral and charged systems, several isomers and different multiplicities were studied to determine the lowest energy structures. Many most stable states with high symmetry were found for small Zr_n clusters. The most stable structures and symmetries of Zr clusters are the same as the neutral ones except n = 4 and 7. We found that the clusters with n > 3 possess highly compact structures. The clusters are inclined to form the caged‐liked geometry containing pentagonal structures for n > 8, which is in favor of energy. From the formation energy and second‐order energy difference, we obtained that 2‐, 5‐, 7‐atoms of neutral and 4‐, 7‐atoms cationic clusters are the magic numbers. Furthermore, the highest occupied molecular orbital‐lowest unoccupied molecular orbital gaps display that the Zr₃, Zr₆, Zr, and Zr are more stable in chemical stability. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Structural evolution of small gold clusters doped by one and two boron atoms

The potential energy surfaces (PES) of a series of gold–boron clusters with formula Au_nB (n = 1–8) and Au_mB₂ (m = 1–7) have been explored using a modified stochastic search algorithm. Despite the complexity of the PES of these clusters, there are well‐defined growth patterns. The bonding of these clusters is analyzed using the adaptive natural density partitioning and the natural bonding orbital analyses. Reactivity is studied in terms of the molecular electrostatic potential. © 2014 Wiley Periodicals, Inc.     

Theoretical study of aromaticity in inorganic tetramer clusters

Ground state geometry and electronic structure of M ₄ ^2- cluster (M = B, Al, Ga) have been investigated to evaluate their aromatic properties. The calculations are performed by employing the Density Functional Theory (DFT) method. It is found that all these three clusters adopt square planar configuration. Results reveal that square planar M ₄ ^2- dianion exhibits characteristics of multifold aromaticity with two delocalised π-electrons. In spite of the unstable nature of these dianionic clusters in the gas phase, their interaction with the sodium atoms forms very stable dipyramidal M₄Na₂ complexes while maintaining their square planar structure and aromaticity.     

Density functional study of AgnPd and AgnPdH clusters

Small Ag_nPd (n = 5) clusters and their hydrides Ag_nPdH (n = 5) have been studied by density functional theory calculations. For bare clusters, the structures in which the Pd atom has a maximum number of neighboring Ag atoms tend to be energetically favorable. Hydrogen prefers binding to Ag? Pd bridge site of Ag_nPd clusters except for Ag₅Pd. The binding energy has a strong odd–even oscillation. The electron transfers are from Ag atoms to Pd in bare clusters and are from metal clusters to H in cluster hydrides. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Electronic structure and stability of AlnPn (n = 2-4) clusters

The geometry, electronic configurations, harmonic vibrational frequencies, and stability of the structural isomers of aluminum phosphide clusters have been investigated using the density functional theory. For dimers and trimers, the lowest energy structures are cyclic (IIs, IIIs) with D(nh) symmetry. The caged structure with Td symmetry (Xs) lie lowest in energy among the tetramers. The Al--P bond dominates the structures for many isomers so that one preferred dissociation channel is loss of the AlP monomer. The hybridization and chemical bonding in the different structures are also discussed. Comparisons with silicon and boron nitride clusters, the ground state structures of Al(n)P(n) clusters are analogous to those of their corresponding Si(2n) counterparts. This similarity follows the isoelectronic principle.     

Electronic structures and thermochemical properties of the small silicon-doped boron clusters B(n)Si (n=1-7) and their anions

We perform a systematic investigation on small silicon-doped boron clusters B(n)Si (n=1-7) in both neutral and anionic states using density functional (DFT) and coupled-cluster (CCSD(T)) theories. The global minima of these B(n)Si(0/-) clusters are characterized together with their growth mechanisms. The planar structures are dominant for small B(n)Si clusters with n≤5. The B(6)Si molecule represents a geometrical transition with a quasi-planar geometry, and the first 3D global minimum is found for the B(7)Si cluster. The small neutral B(n)Si clusters can be formed by substituting the single boron atom of B(n+1) by silicon. The Si atom prefers the external position of the skeleton and tends to form bonds with its two neighboring B atoms. The larger B(7)Si cluster is constructed by doping Si-atoms on the symmetry axis of the B(n) host, which leads to the bonding of the silicon to the ring boron atoms through a number of hyper-coordination. Calculations of the thermochemical properties of B(n)Si(0/-) clusters, such as binding energies (BE), heats of formation at 0 K (ΔH(f)(0)) and 298 K (ΔH(f)([298])), adiabatic (ADE) and vertical (VDE) detachment energies, and dissociation energies (D(e)), are performed using the high accuracy G4 and complete basis-set extrapolation (CCSD(T)/CBS) approaches. The differences of heats of formation (at 0 K) between the G4 and CBS approaches for the B(n)Si clusters vary in the range of 0.0-4.6 kcal mol(-1). The largest difference between two approaches for ADE values is 0.15 eV. Our theoretical predictions also indicate that the species B(2)Si, B(4)Si, B(3)Si(-) and B(7)Si(-) are systems with enhanced stability, exhibiting each a double (σ and π) aromaticity. B(5)Si(-) and B(6)Si are doubly antiaromatic (σ and π) with lower stability.     

Reactivity of molecular oxygen with aluminum clusters: Density functional and Ab Initio molecular dynamics simulation study

Dissociative adsorption of molecular oxygen (O₂) on aluminum (Al) clusters has attracted much interest in the field of surface science and catalysis, but theoretical predictions of the reactivity of this reaction in terms of barrier height is still challenging. In this regard, we systematically investigate the reactivity of O₂ with Al clusters using density functional theory (DFT) and atom‐centered density matrix propagation (ADMP) simulations. We also calculate potential energy surfaces (PESs) of the reaction between O₂ and Al clusters to estimate the barrier energy of this reaction. The M06‐2X functional gives the barrier energy in agreement with the one calculated by coupled cluster singles and doubles with perturbed triples (CCSD(T)) while the TPSSh functional significantly underestimates the barrier height. The ADMP simulation using the M06‐2X functional predicts the reactivity of O₂ with the Al cluster in agreement with the experimental findings, that is, singlet O₂ readily reacts with Al clusters but triplet O₂ is less reactive. We found that the ability of a DFT functional to describe the charge transfer appropriately is critical for calculating the barrier energy and the reactivity of the reaction of O₂ with Al clusters. The M06‐2X functional is relevant for investigating chemical reactions involving Al and O₂. © 2016 Wiley Periodicals, Inc.     

Structural evolution of subnano platinum clusters

We present a theoretical study of the structural evolution of small minimum energy platinum clusters, using density functional theory (DFT). Three growth pathways were identified. At the subnanoscale, clusters with triangular packing are energetically most favorable. At a cluster size of approximately n = 19, a structural transition from triangular clusters to icosahedral clusters occurs. A less energetically favorable transition from triangular clusters to fcc‐like clusters takes place at around n = 38. Ionization potentials, electron affinities, and magnetic moments of the triangular clusters were also calculated. Understanding the structures and properties will facilitate studies of the chemical reactivity of Pt nanoclusters toward small molecules. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

Electronic factors determining the methane bond breaking process on small aluminum clusters

In order to understand the catalytic activity of small metal clusters as a function of their size, we have studied the interaction of CH₄ with Al₄ and Al₅ neutral and charged clusters, as well as neutral thermally expanded clusters in the two lowest lying spin states, using density functional theory. These calculations, via extended search, are used to determine the stable positions of H and CH₃ near the cluster, and the transition state to break the H─CH₃ bond. In order to understand the factors underlying the reactivity of the clusters, we have analyzed the electronic structure at the transition state. By an analysis of the change of the electronic density of states close to the transition state, we identify the orbitals involved in the bond breaking process. In conjunction with our previous studies of Al₂ and Al₃ clusters, we find that the small Al clusters, except for Al₅, lower the CH₃─H dissociation barrier with respect to the gas-phase value, although Al lacks occupied d-orbitals. Still, Al₅ does not catalyze methane bond breaking, which is attributed to the required interaction with low-lying Al sp-states. Furthermore, in all cases where stable methyl-aluminum-hydrides are possible, the recombinative desorption of methane is studied by vibrational analysis and application of transition state theory.     

Phase separation of off‐critical polymer blends of poly(styrene‐co‐maleic anhydride) and poly(methyl methacrylate). I. Kinetics of spinodal decomposition

The kinetics of phase separation via the spinodal decomposition of poly(styrene‐co‐maleic anhydride)/poly(methyl methacrylate) from a delay time period to late stages were investigated with a light scattering technique. The standard procedure for identifying four stages of spinodal decomposition, based on the characteristics of concentration fluctuations, was clearly introduced with the light scattering method. The spinodal limits were divided into four stages: the delay time, the early stage, the intermediate stage, and the late stage. The validity of the linearized theory was reviewed because it was used as an indicator of the limit of the early stage of spinodal decomposition, which divided the delay time period from the early stage and the early stage from the intermediate stage. The linearized theory fit the experimental results very well after the delay time. The scaled structure function of the melt‐mixed blend was analyzed. The universality of the scale structure function, F(x) = S(q,t)q_m³(t) (where S is the structure function, x is equal to q/q_m, q is the scattering wave vector, q_m is the maximum wave vector, and t is the time in seconds), indicated the late stage of phase separation and divided the late stage from the intermediate stage. The simple normalized scaling function profile for the cluster region proposed by Furukawa described the experimental data very well, whereas the profile for deep quenching, which was recently suggested, showed some discrepancies. As a result of the phase separation, the processing of this blend may be able to be developed to provide the most suitable morphology. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 871–885, 2004     

Theoretical investigations on geometrical and electronic structures of silver clusters

Geometrical structures and ground and excited states of silver clusters are theoretically investigated using long-range corrected (LC) density functional theory (DFT) calculations. The discrepancy between HOMO-LUMO gaps and the vertical ionization potential minus vertical electron affinity values, which should be the same values, is explored to reveal the significance of long-range exchange effects on the electronic states of metal clusters. The difference between HOMO-LUMO gaps and HOMO-LUMO excitation energies, which is called “exciton binding energy,” is also tested. As a result, it is found that the long-range exchange effects are requisite in DFT calculations to quantitatively investigate the ground and excited states of metal clusters. © 2018 Wiley Periodicals, Inc.     

Charge-transfer processes in the assembly of Si(n)O(m) neutral clusters

The chemical bond formation in oxygen-rich Si(n)O(m) clusters was investigated by sampling the potential energy surface of the model systems SiO + SiO(2) → Si(2)O(3) and (SiO)(2) + SiO(2) → Si(3)O(4) along a two-dimensional reaction coordinate, by density functional theory calculations. Evidence for crossing between the weakly bound neutral-neutral (SiO)(n) + SiO(2) and the highly attractive ion-pair (SiO)(n)(+) + SiO(2)(-) surfaces was found. Analysis of frontier molecular orbitals and charge distribution showed that surface crossing involves transfer of valence electron charge from (SiO)(2) to SiO(2). The sum of the natural atomic charges over the (SiO)(n) and (SiO(2)) groups of the Si(n)O(m) cluster products, gave a net positive charge on the (SiO)(n) "core" and a net negative charge on the (SiO(2)) groups. This is interpreted as the "ion-pair memory" left on the Si(n)O(m) products by the charge-transfer mechanism and may provide a way to assess the role of charge-transfer processes in the assembly of larger Si(n)O(m) neutral clusters.     

On the development of an effective model potential to describe water interaction in neutral and ionic clusters

Various effective components of the intermolecular interaction of water containing aggregates are examined and their modeling, in terms of the fundamental physical properties of the involved partners, is discussed. We focus, in particular, on the evolution of these components in going from the simplest neutral rare gas–water aggregates to bulk water and ionic water solutions. The analysis singled out that the model chosen to represent the van der Waals interaction as the composition of the action of three dispersion/induction–attraction centres and found to be appropriate to describe the lighter He–H₂O and Ne–H₂O systems, is not adequate to describe the heavier Ar–H₂O aggregate. It was found, instead, that by increasing the mass of the rare gas, other short range contributions to the interaction come into play. Moreover, it was also found that the water molecule tends to behave as a single centre as the strength of the interaction increases. This led to the development of an effective model potential suitable to describe water clusters in the range going from gaseous to condensed phase. The role of electrostatic contributions is also evaluated. The proposed potential model is tested by comparing molecular beam scattering and neutron diffraction experiments with results of molecular dynamics (MD) calculations.     

Structure and energetic of Bn (n = 2–12) clusters: Electronic structure calculations

The electronic and geometric structures, total and binding energies, first and second energy differences, harmonic frequencies, point symmetries, and highest occupied molecular orbital–lowest unoccupied molecular orbital (HOMO–LUMO) gaps of small and neutral B_n (n = 2–12) clusters have been investigated using density functional theory (DFT), B3LYP with 6‐311++G(d,p) basis set. Linear, planar, convex, quasi‐planar, three‐dimensional (3D) cage, and open‐cage structures have been found. None of the lowest energy structures and their isomers has an inner atom; i.e., all the atoms are positioned at the surface. Within this size range, the planar and quasi‐planar (convex) structures have the lowest energies. The first and the second energy differences are used to obtain the most stable sizes. A simple growth path is also discussed with the studied sizes and isomers. The results have been compared with previously available theoretical and experimental works. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

Structure of small TiCn clusters: A theoretical study

A theoretical study of the TiC_n (n = 1–8) clusters has been carried out at the B3LYP/6-311+G(d) level. Molecular properties for three different isomers, namely linear, cyclic, and fan species, have been determined. The fan isomers, where the titanium atom is essentially side-bonded to the entire C_n unit, are predicted to be more stable than both linear and cyclic isomers. Only for the largest studied species, TiC₈, the cyclic isomer is located lower in energy. An even–odd parity effect in the incremental binding energies is observed for the three isomers, n-even species being in general more stable for linear and fan isomers, whereas for the cyclic species n-odd clusters are favoured. A topological analysis of the electronic charge density shows that all cyclic isomers correspond to true monocyclic rings, whereas for the fan species a variety of different connectivities has been observed.     

Ab initio studies on the polarizability of lithium clusters: Some unusual results

The polarizability of lithium clusters was studied using ab initio as well as Density Functional Theory (DFT)‐based methods. The electron correlation was found not to play any major role in the evaluation of polarizability of the lithium clusters, contrary to the case of sodium and other types of clusters. The theoretical methods used in the present study are not able to reproduce the unusual features in the size evolution of the polarizability observed experimentally. An interesting feature is that the polarizability of lithium clusters calculated by various methods at 0K temperature is found to be higher than the experimental results measured at higher temperature, which is quite unusual. The significance of these issues is highlighted and the need of highly accurate DFT exchange‐correlation functionals and ab initio methods in the study of the electronic properties of lithium clusters is emphasized. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

Theoretical study of the decomposition mechanism of a series of group III triazides X(N3)3 (X = B,Al, Ga)

Density functional theory method is used to examine a series of group III triazides X(N₃)₃ (X = B, Al, Ga). These compounds, except for the C_3h planar B(N₃)₃ and Al(N₃)₃, are first reported here. C_3h planar structures are the most energetically favored for all singlet X(N₃)₃ systems. Potential‐energy surfaces for unimolecular decompositions of the C_3h and C_S planar X(N₃)₃ species have been investigated. Results show that decomposition of B(N₃)₃ obeys sequential fashion and follows a four‐step mechanism: (1) B(N₃)₃ → NB(N₃)₂ + N₂; (2) NB(N₃)₂ → cyc‐N₂BN₃ + N₂; (3) cyc‐N₂BN₃ → trigonal‐BN₃ + N₂; (4) trigonal‐BN₃ → linear‐NBNN. Decomposition of Al(N₃)₃ follows a two‐step mechanism: (1) Al(N₃)₃ → NAl(N₃)₂ + N₂; (2) NAl(N₃)₂ → linear‐AlN₃ + 2N₂. The dissociation of Ga(N₃)₃ follows only one‐step mechanism: Ga(N₃)₃ → angular‐GaN₃ + 3N₂. These findings may be helpful in understanding the decomposition mechanisms of group III triazides as well as the possible mechanism for XN film generation. © 2014 Wiley Periodicals, Inc.     

Mechanism for the gas‐phase hydrogen fluoride‐mediated decomposition of peroxyacetyl nitrate (PAN) studied by DFT method

Density functional theory has been used to study the mechanism of the decomposition of peroxyacetyl nitrate (CH₃C(O)OONO₂) in hydrogen fluoride clusters containing one to three hydrogen fluoride molecules at the B3LYP/6‐311++G(d,p) and B3LYP/6‐311+G(3df,3pd) levels. The calculations clarify some of the uncertainties in the mechanism of PAN decomposition in the gas phase. The energy barrier decreases from 30.5 kcal mol^?1 (single hydrogen fluoride) to essentially 18.5 kcal mol^?1 when catalyzed by three hydrogen fluoride molecules. As the size of the hydrogen fluoride cluster is increased, PAN shows increasing ionization along the O? N bond, consistent with the proposed predissociation in which the electrophilicity of the nitrogen atom is enhanced. This reaction is found to proceed through an attack of a fluorine to the PAN nitrogen in concert with a proton transfer to a PAN oxygen. On the basis of our calculations, an alternative reaction mechanism for the decomposition of PAN is proposed. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010