The Evolution of Bonding and Thermodynamic Properties of Boron‐Doped Small Carbon Clusters: An Ab Initio Study

Theoretical studies on BC_n (n=1–6) clusters are carried out using density functional theory, Møller–Plesset second‐order perturbation theory (MP2), coupled‐cluster calculations including up to triple excitations (CCSD(T)), and higher‐level approaches. All possible isomers depending on the positions of the boron atom are generated and the lowest‐energy isomers are determined for doublet and quartet electronic states. The three potential evolution paths of the clusters are determined as a function of their size. The energetic and electronic consequences for the increased size of structures differ significantly, which leads to representatives of the ground electronic state from different structural groups. The ab initio calculated thermal functions allow enhancements to the available atomization energies and improve the agreement between the calculated and experimental heat content.     

High Magnetic Moments in Manganese‐Doped Silicon Clusters

We report on the structural, electronic, and magnetic properties of manganese‐doped silicon clusters cations, Si_nMn⁺ with n=6–10, 12–14, and 16, using mass spectrometry and infrared spectroscopy in combination with density functional theory computations. This combined experimental and theoretical study allows several structures to be identified. All the exohedral Si_nMn⁺ (n=6–10) clusters are found to be substitutive derivatives of the bare Si_n+1⁺ cations, while the endohedral Si_nMn⁺ (n=12–14 and 16) clusters adopt fullerene‐like structures. The hybrid B3P86 functional is shown to be appropriate in predicting the ground electronic states of the clusters and in reproducing their infrared spectra. The clusters turn out to have high magnetic moments localized on Mn. In particular the Mn atoms in the exohedral Si_nMn⁺ (n=6–10) clusters have local magnetic moments of 4 μ_B or 6 μ_B and can be considered as magnetic copies of the silicon atoms. Opposed to other 3d transition‐metal dopants, the local magnetic moment of the Mn atom is not completely quenched when encapsulated in a silicon cage.     

Stability,Infrared Spectra and Electronic Structures of (ZrO2)n(n=3-6)Clusters:DFT Study

The stability, infrared spectra and electronic structures of (ZrO₂)_n (n=3–6) clusters have been investigated by using density‐functional theory (DFT) at B3LYP/6‐31G* level. The lowest‐energy structures have been recognized by considering a number of structural isomers for each cluster size. It is found that the lowest‐energy (ZrO₂)₅ cluster is the most stable among the (ZrO₂)_n (n=3–6) clusters. The vibration spectra of Zr? O stretching motion from terminal oxygen atom locate between 900 and 1000 cm^?1, and the vibrational band of Zr? O? Zr? O four member ring is obtained at 600–700 cm^?1, which are in good agreement with the experimental results. Mulliken populations and NBO charges of (ZrO₂)_n clusters indicate that the charge transfers occur between 4d orbital of Zr atoms and 2p orbital of O atoms. HOMO‐LUMO gaps illustrate that chemical stabilities of the lowest‐energy (ZrO₂)_n (n=3–6) clusters display an even‐odd alternating pattern with increasing cluster size.     

Structures and electronic properties of the small rubidium‐doped silicon RbSin (n = 1–12) clusters

The geometries, relative stabilities, and electronic properties of small rubidium‐doped silicon clusters RbSi_n (n = 1–12) have been systematically investigated using the density functional theory at the B3LYP/GENECP level. The optimized structures show that lowest‐energy isomers of RbSi_n are similar with the ground state isomers of pure Si_n clusters and prefer the three‐dimensional for n = 3–12. The relative stabilities of RbSi_n clusters have been analyzed on the averaged binding energy, fragmentation energy, second‐order energy difference, and highest occupied molecular orbital‐lowest unoccupied molecular orbital energy gap. The calculated results indicate that the doping of Rb atom enhances the chemical activity of Si_n frame and the magic number is RbSi₂. The Mulliken population analysis reveals that the charges in the corresponding RbSi_n clusters transfer from the Rb atom to Si atoms. The partial density of states and chemical hardness are also discussed. © 2014 Wiley Periodicals, Inc.     

Ground-state properties of CdxSn1–xTe: The role of d-electrons

Within the framework of density functional theory (DFT ), we calculate the ground-state electronic properties of Cd_xSn_1–x Te using norm-conserving pseudopotentials in connection with the local density (LDA ) and virtual crystal approximation (VCA ). Our particular interest is in the influence of the Cd-4d and the Sn-4d electrons by comparing results obtained with pseudopotentials, which either consider the d-electrons explicitly or in the frozen core. In the mixed crystal system Cd_xSn_1–x Te, the transition from a ten- (x = 0) to an eight-electron (x = 1) system is realized, which is accompanied by a change of the crystal structure from rock salt (SnTe) to zinc blende (CdTe). By calculating the ground-state energies, we find the equilibrium lattice constant as the function of x and the bulk modulus, as well as the crossover value of x for the transition from rock-salt to zinc blende. The calculated lattice constants and bulk moduli are in much closer agreement with experimental data if the d-electrons are taken into account explicitly, whereas the crossover is rather insensitive with respect to the d-electrons. In view of the electronic charge density, we demonstrate the decrease of ionicity for increasing x. © 1994 John Wiley & Sons, Inc.     

Structural,spectroscopic aspects,and electronic properties of (TiO2)n clusters: A study based on the use of natural algorithms in association with quantum chemical methods

In this article, we propose a stochastic search‐based method, namely genetic algorithm (GA) and simulated annealing (SA) in conjunction with density functional theory (DFT) to evaluate global and local minimum structures of (TiO₂)_n clusters with n = 1–12. Once the structures are established, we evaluate the infrared spectroscopic modes, cluster formation energy, vertical excitation energy, vertical ionization potential, vertical electron affinity, highest occupied molecular orbital (HOMO)‐lowest unoccupied molecular orbital (LUMO) gaps, and so forth. We show that an initial determination of structure using stochastic techniques (GA/SA), also popularly known as natural algorithms as their working principle mimics certain natural processes, and following it up with density functional calculations lead to high‐quality structures for these systems. We have shown that the clusters tend to form three‐dimensional networks. We compare our results with the available experimental and theoretical results. The results obtained from SA/GA‐DFT technique agree well with available theoretical and experimental data of literature. © 2013 Wiley Periodicals, Inc.     

Size effect on the structural and electronic properties of lead telluride clusters

Theoretical computations of (PbTe)_n (n = 21–45) clusters based on density functional theory have demonstrated that at cluster size of (PbTe)₂₂ there is a transition from the strong preference of fivefold coordination to sixfold coordination of lead and tellurium atoms. (PbTe)₂₄ cluster is the smallest tetragonal structure in which its central atoms have bulk‐like coordination. This quantum dot (QD) contains a single‐unit cell of lead telluride crystal, thus can be considered as an “infant crystal.” (PbTe)₃₂ cluster is a perfectly cubic cluster for which its inner (PbTe)₄ core enjoys bulk‐like coordination. This (PbTe)₄ core unit of (PbTe)₃₂ cubic cluster has exactly the same environment as a primitive cell of lead telluride crystal. The (PbTe)_8n, (n ≥ 3) clusters are the magic number species with bulk‐like structure such that (n = 3–5) the nanoblocks considered here (PbTe)₂₄, (PbTe)₃₂, and (PbTe)₄₀ clusters exhibiting bulk‐like structure that can be replicated to obtain the bulk crystal. The calculated dimensions of this special clusters provided a rubric for understanding the pattern of aggregation, that is, the creation of defined nanoblocks [(PbTe)_8n, (n ≥ 6)], when they were accumulated on an appropriate surface. It is evident that the QDs (PbTe)_8n, (n = 3–5) clusters show high stability compared to their neighboring clusters. This can also be seen from the second‐order energy difference, binding, and fragmentation energy graphs. © 2014 Wiley Periodicals, Inc.     

Structure and photoelectron spectral properties of I(-)·nCO2 clusters: an ab initio study

Structures and photoelectron spectral properties of I^??nCO₂ (n=1–7) clusters are presented at the level of second‐order Møller–Plesset perturbation theory with relativistic corrections. Triple split‐valence 6‐311++G(d,p) basis set functions are employed herein. It is observed that the CO₂ molecules approach the I^? anion from one side in all the clusters and that I^??nCO₂ clusters prefer the surface structure. The calculated vertical detachment energy of these clusters is in excellent agreement with the reported experimentally measured values (within 4 %). Efforts are also made to extract vertical detachment energy of large size of clusters, including the bulk. The extracted vertical detachment energy values for larger clusters (n=8–13) by employing the microscopic theory‐based expression are also close (within 4 %) to that of the experimentally measured values.     

Ab initio molecular orbital theory study of GaAs clusters: The geometry

We have studied the structure and geometry of neutral and charged atomic clusters consisting of Ga and As atoms via ab initio Hartree–Fock (HF) and second‐order Møller–Plesset methods. The Ga_mAs_n cluster with m≠n composition prefers a nontetrahedral geometry in the charge neutral (q=0) state. These clusters tend to be stable in tetrahedral geometry when appropriately charged. The Ga_mAs_n cluster with m=n composition (1:1 ratio of Ga to As atoms) tends to be stable in a tetrahedral geometry in the charge neutral (q=0) state. With increasing size of the cluster, the geometry of Ga_nAs_n cluster approaches the zinc‐belende‐type crystalline structure. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 77: 563–573, 2000     

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.     

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     

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     

Pyridine adsorption on small Nin‐cluster (n = 2,3,4): A study of geometry and electronic structure

Adsorption of pyridine on Ni_n‐clusters (with n = 2,3,4) is studied by quantum chemical calculations at B3LYP/LANL2DZ and B3LYP/6‐311G^** levels. First, Ni_n‐clusters are investigated for accessible structure and electronic states. The lowest electronic state with four unpaired electrons is predicted for Ni₄‐cluster based on geometry and electronic structure, showing that the cluster stability nicely depends on number of unpaired electrons. Correction for basis set superposition error of metal‐metal bond is appreciable and has increasing effect on cluster binding energy. Next, adsorption of pyridine in planar and vertical adsorption modes is investigated on rhombus Ni₄‐cluster. The vertical mode is found (at B3LYP/6‐311G^** level) as the most favorable adsorption mode. Adsorption energy (ΔE_ads) depends on cluster size; adsorption on Ni₄‐cluster is most favorable with ΔE_ads = ?207.33 kJ/mol. The natural bond orbital analysis reveals the charge transfer in adsorbate/metal‐cluster. Results of investigations for the Ni₂‐ and Ni₃‐cluster are also presented. © 2012 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.     

Emerging polymorphism in nanostructured TiO2: Quantum chemical comparison of anatase,rutile, and brookite clusters

Density functional theory (DFT) and time‐dependent DFT calculations have been performed on a set of 34 titanium dioxide clusters ((TiO2)_n with n ≤ 125) to investigate structural and electronic properties of nanostructured TiO₂ (nano‐TiO₂) materials. The investigated clusters include models of the three low‐energy polymorphic forms of TiO₂ anatase, rutile, and brookite. A systematic comparison of clusters of increasing size show clear trends for emerging bulk properties in the investigated systems as the surface‐to‐bulk ratio changes from small clusters dominated by undercoordinated surface atoms to more realistic model nanocrystals with significant bulk components. Differences and similarities in terms of atomic coordination, structural stability, and electronic properties for the three different polymorphic forms of nano‐TiO₂ are discussed. The calculations provide evidence for emerging polymorphism with increasing cluster sizes so that the different TiO₂ forms can be clearly distinguished based on structural characteristics associated with the local bonding environment of the constituent atoms. © 2013 Wiley Periodicals, Inc.     

Non-covalent Interactions and Charge Transfer between Propene and Neutral Yttrium-Doped and Pure Gold Clusters

The dopant and size-dependent propene adsorption on neutral gold (Au_n) and yttrium-doped gold (Au_n−1Y) clusters in the n=5–15 size range are investigated, combining mass spectrometry and gas phase reactions in a low-pressure collision cell and density functional theory calculations. The adsorption energies, extracted from the experimental data using an RRKM analysis, show a similar size dependence as the quantum chemical results and are in the range of ≈0.6–1.2 eV. Yttrium doping significantly alters the propene adsorption energies for n=5, 12 and 13. Chemical bonding and energy decomposition analysis showed that there is no covalent bond between the cluster and propene, and that charge transfer and other non-covalent interactions are dominant. The natural charges, Wiberg bond indices, and the importance of charge transfer all support an electron donation/back-donation mechanism for the adsorption. Yttrium plays a significant role not only in the propene binding energy, but also in the chemical bonding in the cluster-propene adduct. Propene preferentially binds to yttrium in small clusters (n<10), and to a gold atom at larger sizes. Besides charge transfer, relaxation also plays an important role, illustrating the non-local effect of the yttrium dopant. It is shown that the frontier molecular orbitals of the clusters determine the chemical bonding, in line with the molecular-like electronic structure of metal clusters.     

Global Minimum‐Energy Structure and Spectroscopic Properties of I2.−⋅n H2O Clusters: A Monte Carlo Simulated Annealing Study

The vibrational (IR and Raman) and photoelectron spectral properties of hydrated iodine‐dimer radical‐anion clusters, I₂^.? ? n H₂O (n=1–10), are presented. Several initial guess structures are considered for each size of cluster to locate the global minimum‐energy structure by applying a Monte Carlo simulated annealing procedure including spin–orbit interaction. In the Raman spectrum, hydration reduces the intensity of the I? I stretching band but enhances the intensity of the O? H stretching band of water. Raman spectra of more highly hydrated clusters appear to be simpler than the corresponding IR spectra. Vibrational bands due to simultaneous stretching vibrations of O? H bonds in a cyclic water network are observed for I₂^.? ? n H₂O clusters with n≥3. The vertical detachment energy (VDE) profile shows stepwise saturation that indicates closing of the geometrical shell in the hydrated clusters on addition of every four water molecules. The calculated VDE of finite‐size small hydrated clusters is extrapolated to evaluate the bulk VDE value of I₂^.? in aqueous solution as 7.6 eV at the CCSD(T) level of theory. Structure and spectroscopic properties of these hydrated clusters are compared with those of hydrated clusters of Cl₂^.? and Br₂^.?.