Theoretical investigation of geometry and stability of small lithium‐iodide LinI (n = 2–6) clusters

We present theoretical investigation of the structural characteristics and stabilities of neutral and positively charged Li_nI (n = 2‐6) species. The structural isomers were found by using a randomized algorithm to search for minima structures, followed by B3LYP optimizations; the single‐point RCCSD(T)/cc‐pwCVTZ(‐PP) calculations were performed in order to compute relative energies, binding energies per atom, adiabatic and vertical ionization energies, and dissociation energies. Stability was compared to the pure lithium clusters; there is a typical odd‐even alternation; iodine doped clusters are more stable than pure lithium clusters. Lithium “cage” transfers its valence electron to the iodine atom to form neutral and cationic clusters. An electron departures the lithium cage upon ionization. An important reason for the larger stability of closed‐shell species is the existence of the HOMO 3c/2e natural bond orbitals. © 2013 Wiley Periodicals, Inc.     

Comprehensive understanding of size‐, shape‐, and composition‐dependent polarizabilities of SimCn (m,n = 1–4) clusters

We performed a comprehensive study of the size‐, shape‐, and composition‐dependent polarizabilities of Si_mC_n (m, n = 1–4) clusters on the basis of the density‐functional‐based coupled perturbed Hartree–Fock calculations. We found better correlations between the polarizabilities and both the binding energies (E_b) and change in charge distribution (Δq) than the energy gaps. The α values exhibit overall decreasing and increasing trends with increases in the E_b and Δq values, respectively. For isomers with the same E_b values and different polarizabilities, Δq can well explain the difference in polarizabilities. The π‐electron delocalization effect is the best factor for understanding the shape‐dependence. For a given m/n value, the linear clusters have an obviously larger polarizability than both the prolate and compact clusters, irrespective of the cluster size. We fit a quantitative expression [α = A ? (A ? B) × exp(?k(m/n))] to describe the composition‐dependent polarizabilities. © 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     

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     

Density functional study of structural and electronic properties of AlnN (1 ≤ n ≤ 12) clusters

Low‐lying equilibrium geometric structures of Al_nN (n = 1–12) clusters obtained by an all‐electron linear combination of atomic orbital approach, within spin‐polarized density functional theory, are reported. The binding energy, dissociation energy, and stability of these clusters are studied within the local spin density approximation (LSDA) and the three‐parameter hybrid generalized gradient approximation (GGA) due to Becke–Lee–Yang–Parr (B3LYP). Ionization potentials, electron affinities, hardness, and static dipole polarizabilities are calculated for the ground‐state structures within the GGA. It is observed that symmetric structures with the nitrogen atom occupying the internal position are lowest‐energy geometries. Generalized gradient approximation extends bond lengths as compared with the LSDA lengths. The odd–even oscillations in the dissociation energy, the second differences in energy, the highest occupied molecular orbital–lowest unoccupied molecular orbital (HOMO–LUMO) gaps, the ionization potential, the electron affinity, and the hardness are more pronounced within the GGA. The stability analysis based on the energies clearly shows the Al₇N cluster to be endowed with special stability. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2006     

Structure and stability of coinage metal fluoride and chloride clusters (MnFn and MnCln,M = Cu,Ag, or Au; n = 1–6)

Calculations in the framework of the density functional theory are performed to study the lowest‐energy isomers of coinage metal fluoride and chloride clusters (M_nF_n, M_nCl_n, M = Cu, Ag, or Au, n = 1–6). For all calculated species starting from the trimers the most stable structures are found to be cyclic arrangements. However, planar rings are favored in the case of metal fluorides whereas metal chlorides prefer nonplanar cycles. Calculated bond lengths and infrared frequencies are compared with the available experimental data. The nature of the bonding, involving both covalent and ionic contributions, is characterized. The stability and the fragmentation are also investigated. Trimers are found to be particularly stable when considering the Gibbs free energies. © 2012 Wiley Periodicals, Inc.     

A density functional study on hydrated clusters of orthoboric acid, B(OH)3(H2O)n (n=1–5)

We have calculated the optimized structures and stabilization energies for hydrated clusters of orthoboric acid molecule, B(OH)₃(H₂O)_n (n=1–5), with a hybrid density functional approach. Although some ion-pair structures are revealed in the case of n=4 and 5 clusters, the most stable structure is found to be a non-proton-transferred form up to n=5 hydrated clusters. The calculated IR spectra of the stable B(OH)₃(H₂O)_n of n=3–5 clusters predict small red shifts of hydrogen-bonded OH frequencies. These geometry and IR results are related to the weak acidity nature of orthoboric acid.     

Electronic structure and stability of BP clusters: theoretical calculations for (BP)n (n = 2–4)

The geometry, electronic configurations, harmonic vibrational frequencies, and stability of the structural isomers of boron phosphide clusters have been investigated using density functional theory (DFT). CCSD(T) calculations show that the lowest‐energy structures are cyclic (IIt, IVs) with D_nh symmetry for dimers and trimers. The caged structure for B₄P₄ lie higher in energy than the monocyclic structure with D_2d symmetry (VIs). The B–P bond dominates the structures for many isomers, so that one preferred dissociation channel is loss of the BP monomer. The hybridization and chemical bonding in the different structures are also discussed. Comparisons with boron nitride clusters, the ground state structures of B_nP_n (n = 2, 3) clusters are analogous to those of their corresponding B_nN_n (n = 2, 3) counterparts. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2006     

Structure and stability of high‐spin Aun(n = 2–8) clusters

The structures and relative stability of the maximum‐spin ⁿ⁺¹Au_n and ⁿAu (n = 2–8) clusters have been determined by density‐functional theory. The structure optimizations and vibrational frequency analysis are performed with the gradient‐corrections of Perdew along with his 1981 local correlation functional, combined with SBKJC effective core potential, augmented in the valence basis set by a set of f functions. We predicted the existence of a number of previously unknown isomers. The energetic and electronic properties of the small high‐spin gold clusters are strongly dependent on sizes. The high‐spin clusters tend to holding three‐dimensional geometry rather than planar form preferred in low‐spin situations. In whole high‐spin Au_n (n = 2–8) neutral and cationic species, ⁵Au₄, ²Au, and ⁴Au are predicted to be of high stability, which can be explained by valence bond theory. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2009     

Theoretical study on the interaction of neutral and charged Tin (n = 1–7) clusters with one oxygen molecule

The interactions between the neutral and charged (?2, ?1, +1, and +2) Ti_n (n = 1–7) clusters and one O₂ molecule were investigated by density functional theory. The calculated results show that the oxygen molecule is dissociative on the neutral Ti_n clusters. Geometrically, the two O atoms are distributed at the two sides across the neutral Ti_n cluster for n = 1–4 and the oxygen atom favors the three‐fold hollow site for n = 5, 6, and 7. The binding energy per atom (E_b) and energy gap (E_gap) show higher stability and lower chemical activity of the neutral Ti_nO₂ (n = 1–7) systems compared with the corresponding Ti_n clusters. The adsorption energies (E_ad) exhibit a continuously ascending tendency except for n = 4. The results of the addition of different charges (?2, ?1, +1, and +2) on the most stable neutral Ti_nO₂ (n = 1–7) systems indicate that their geometries are usually perturbed. The stabilities of the neutral Ti_nO₂ systems are enhanced by adding one negative charge. The strongest interaction of the charged Ti_n clusters (?2, ?1, +1, and +2) with O₂ molecule is found at charge +2. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Ab initio investigation of water clusters (H2O)n (n = 2–34)

Various properties of typical structures of water clusters in the n = 2–34 size regime with the change of cluster size have been systematically explored. Full optimizations are carried out for the structures presented in this article at the Hartree–Fock (HF) level using the 6‐31G(d) basis set by taking into account the positions of all atoms within the cluster. The influence of the HF level on the results has been reflected by the comparison between the binding energies of (H₂O)_n (n = 2–6, 8, 11, 13, 20) calculated at the HF level and those obtained from high‐level ab initio calculations at the second‐order Møller–Plesset (MP2) perturbation theory and the coupled cluster method including singles and doubles with perturbative triples (CCSD(T)) levels. HF is inaccurate when compared with MP2 and CCSD(T), but it is more practical and allows us to study larger systems. The computed properties characterizing water clusters (H₂O)_n (n = 2–34) include optimal structures, structural parameters, binding energies, hydrogen bonds, charge distributions, dipole moments, and so on. When the cluster size increases, trends of the above various properties have been presented to provide important reference for understanding and describing the nature of the hydrogen bond. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010     

Theoretical investigation of gas phase ethanol–(water)n (n = 1–5) clusters and comparison with gas phase pure water clusters (water)n (n = 2–6)

Various properties (such as optimal structures, structural parameters, hydrogen bonds, natural bond orbital charge distributions, binding energies, electron densities at hydrogen bond critical points, cooperative effects, and so on) of gas phase ethanol–(water)_n (n = 1–5) clusters with the change in the number of water molecules have been systematically explored at the MP2/aug‐cc‐pVTZ//MP2/6‐311++G(d,p) computational level. The study of optimal structures shows that the most stable ethanol‐water heterodimer is the one where exists one primary hydrogen bond (O? H…O) and one secondary hydrogen bond (C? H …O) simultaneously. The cyclic geometric pattern formed by the primary hydrogen bonds, where all the molecules are proton acceptor and proton donor simultaneously, is the most stable configuration for ethanol–(water)_n (n = 2–4) clusters, and a transition from two‐dimensional cyclic to three‐dimensional structures occurs at n = 5. At the same time, the cluster stability seems to correlate with the number of primary hydrogen bonds, because the secondary hydrogen bond was extremely weaker than the primary hydrogen bond. Furthermore, the comparison of cooperative effects between ethanol–water clusters and gas phase pure water clusters has been analyzed from two aspects. First of all, for the cyclic structure, the cooperative effect in the former is slightly stronger than that of the latter with the increasing of water molecules. Second, for the ethanol–(water)₅ and (water)₆ structure, the cooperative effect in the former is also correspondingly stronger than that of the latter except for the ethanol–(water)₅ book structure. © 2012 Wiley Periodicals, Inc.     

Density functional study of HO(H2O)n (n = 1–3) clusters

The hydrogen bonding complexes HO(H₂O)_n (n = 1–3) were completely investigated in the present study using DFT and MP2 methods at varied basis set levels from 6‐31++G(d,p) to 6‐311++G(2d,2p). For n = 1 two, for n = 2 two, and for n = 3 five reasonable geometries are considered. The optimized geometric parameters and interaction energies for various complexes at different levels are estimated. The infrared spectrum frequencies and IR intensities of the most stable structures are reported. Finally, thermochemistry studies are also carried out. The results indicate that the formation and the number of hydrogen bonding have played an important role in the structures and relative stabilities of different complexes. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

A density functional study of the interaction of dihydrogen with MoN clusters (N = 2–8). Adsorption and dissociation of H2 and cluster reconstruction after desorption

The interaction of small Mo_N clusters (N = 2–8) with H₂ is investigated using a GGA version of the density functional theory as implemeted in the SIESTA code. Both the dissociation of H₂ and the charge transfer to the metallic clusters are studied in detail to gain insight into the reactive properties of the aggregates in the gas phase. The reconstruction of the clusters after H elimination is also investigated to learn about the possibility of reutilization of the aggregates in future process. Present results indicate that Mo₇ is particularly effective in dissociating H₂. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Electronic and magnetic properties of small RhnCa (n = 1–9) clusters: A DFT study

The equilibrium geometries, relative stabilities, electronic and magnetic properties of small Rh_nCa (n = 1–9) clusters have been investigated by DFT calculations. The obtained results show that the three‐dimensional geometries are adopted for the lowest‐energy Rh_nCa clusters, and the doped Ca atom prefers locating on the surface of the cluster. Based on the analysis of the second‐order difference of energies, fragmentation energies and the HOMO‐LUMO energy gaps, we identify that the Rh₄Ca, Rh₆Ca, and Rh₈Ca clusters are relatively more stable than their neighboring clusters, and the doping of Ca enhances the chemical reactivity of the pure Rh_n clusters, suggesting that the Rh_nCa clusters can be used as nanocatalysts in many catalytic reactions. The magnetic moment for these clusters is mostly localized on the Rh atoms, and the doping Ca atom has no effect on the total magnetic moment of Rh_nCa clusters. The partial density of states, VIP, VEA, and η of these clusters in their ground‐state structures were also calculated and discussed. © 2015 Wiley Periodicals, Inc.     

Interaction of NO molecules with Pd clusters: Ab initio density–functional study

The adsorption of NO molecules on small Pd_n (n = 1?6) clusters has been studied using first‐principles density‐functional theory. Three adsorption sites were considered: vertex (on–top), bridge, and hollow. Adsorption is strong, ranging from 2 to 3 eV. In all cases NO adsorbs in a bent configuration. Calculated shifts in N–O bond vibration frequencies (with anharmonic corrections) agree very well with available experimental data. In contrast to metallic Pd surfaces, adsorption of NO on palladium clusters causes considerable changes in geometry around adsorption site because palladium d‐orbitals rehybridize to maximize the overlap with NO orbitals (mainly the antibonding π*). Thus, the overall energetic effect of NO adsorption is the result of two competing processes: lowering of the total energy through tighter bonding with NO and rising the energy due to cluster deformation. The Pd_n–NO bond creation is governed by electron transfer from Pd–d orbitals into the NO π*. As a result, the Pd cluster becomes locally demagnetized (with total magnetic moment of 1 μ_B located at Pd atoms not connected to NO) and the NO molecule is activated: the N–O bond length is increased and the vibration frequency is redshifted. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2009     

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

The possible geometrical structures and relative stability of silicon–sulfur clusters (SiS₂) (n=1–6) are explored by means of density functional theory (DFT) quantum chemical calculations. We also compare DFT with second‐order Møller–Plesset (MP2) and Hartree–Fock (HF) methods. The effects of polarization functions, diffuse functions, and electron correlation are included in MP2 and B3LYP quantum chemical calculations, and B3LYP is effective in larger cluster structure optimization, so we can conclude that the DFT approach is useful in establishing trends. The electronic structures and vibrational spectra of the most stable geometrical structures of (SiS₂)_n⁻ are analyzed by B3LYP. As a result, the regularity of the (SiS₂)_n⁻ cluster growing is obtained, and the calculation may predict the formation mechanism of the (SiS₂)_n⁻ cluster. © 2001 John Wiley & Sons, Inc. Int J Quant Chem 81: 280–290, 2001     

Density functional study of structural, electronic, and optical properties of small bimetallic ruthenium-copper clusters

The structural, electronic, bonding, magnetic, and optical properties of bimetallic [Cu(n)Ru(m)](+/0/-) (n + m ≤ 3; n, m = 0-3) clusters were computed in the framework of the density functional theory (DFT) and time-dependent DFT (TD-DFT) using the full-range PBE0 nonlocal hybrid GGA functional combined with the Def2-QZVPP basis sets. Several low-lying states have been investigated and the stability of the ground state spinomers was estimated with respect to all possible fragmentation schemes. Molecular orbital and population analysis schemes along with computed electronic parameters illustrated the details of the bonding mechanisms in the [Cu(n Ru(m)](+/0/-) clusters. The TD-DFT computed UV-visible absorption spectra of the bimetallic clusters have been fully analyzed and assignments of all principal electronic transitions were made and interpreted in terms of contribution from specific molecular orbital excitations.     

Density Functional Theory Study on (Cl2GaN3)n(n=1–4) Clusters

The molecular geometries, vibrational properties, and thermodynamic properties of the clusters (Cl₂GaN₃)_n(n=1–4) have been predicted at the B3LYP/6‐311+G* level. The optimized clusters (Cl₂GaN₃)_n (n=2–4) all possess cyclic structures containing Ga N_α Ga linkages. The relationships between geometrical parameters and oligomerization degree n are discussed. The gas‐phase structures of the trimers prefer to exist in boat‐twisting conformation. As for the tetramer, the S₄ symmetry structure is the most stable. The infrared spectra are obtained and assigned by vibrational analysis. Thermodynamic properties derived from the infrared spectra on the basis of statistical thermodynamic principles are linearly correlated with the oligomerization degree n as well as the temperature. Meanwhile, thermodynamic analysis of the gas‐phase reaction suggests that the oligomerization is exothermic and favorable under high temperature.