Theoretical study on AlnO2 (n = 1–10) clusters and O2 adsorption on the Al(111) surface

The structural properties of neutral and ionic Al_nO₂ (n = 1–10) clusters have been systematically investigated using the density functional method B3LYP with a standard 6‐311+G(d) basis set. The calculated results show that in the Al_nO, Al_nO₂, and Al_nO (n ≥ 3) clusters, O atoms tend to penetrate into the aluminum clusters with some Al atoms moving outward. The binding energies and natural charges populations indicate that the oxygen‐etching is generally stronger in the order Al < Al_n < Al for n < 3, and Al > Al_n > Al for n ≥ 3. To further understand the mechanism of interaction between Al and O₂, the adsorption of O₂ on the Al(111) surface was studied using the density functional theory with plane wave pseudopotential method. The calculated results are consistent with the experimental observation that the O₂ molecule would dissociate on the Al(111) surface and be adsorbed in adjacent hollow sites, forming a local structure of Al₃O–Al₃O. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

Structures and properties of (H2GaN3)n (n = 1–4) clusters: A DFT study

Computations on the systems of (H₂GaN₃)_n (n = 1–4) are performed using the density functional theory (DFT)/B3LYP method with different basis sets. (H₂GaN₃)₂ possessing D_2h symmetry is found to exhibit the planar Ga₂N₂ ring structure. (H₂GaN₃)₃ involving a six‐membered Ga₃N₃ ring is found to exhibit two minima with very similar binding energies (ca. −235 ∼ −231 kJ · mol⁻¹). One minimum is the newly found boat‐like conformation possessing C_s symmetry. Another minimum possessing C_3v symmetry is the chair‐like conformation. (H₂GaN₃)₄ occurs in several structures with Ga₄N₄ eight‐membered ring structures that correspond to minima with slight energy differences among them. The structural changes of the clusters are large compared with the monomer. Frequency calculations are carried out on each optimized structure, and their infrared (IR) spectra are discussed. Thermodynamic properties demonstrate that the systems of H₂GaN₃ occur at dimer–trimer–tetramer equilibrium, and the trimer is the main component. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2004     

Theoretical study of endohedral metallofullerenes: Sc3−nLanN@C80 (n=0–3)

To provide theoretical insight into the structures and properties of Sc₃N@C₈₀, which has been isolated in high yield and purity as a new stable endohedral metallofullerene, density functional calculations are carried out for the Sc_3?nLa_nN@C₈₀ (n=0–3) series. Because of electron transfer from Sc₃N to C₈₀, the electronic structure of Sc₃N@C₈₀ is formally described as (Sc₃N)⁶⁺C$_{80}^{6-}$. The encapsulated Sc₃N cluster takes a planar structure with long Sc–Sc distances and is highly stabilized inside the I_h cage of C₈₀, which rotates rapidly. As the number of La atoms increases, the Sc_3?nLa_nN cluster is forced to maintain a pyramidal structure in Sc_3?nLa_nN@C₈₀. In addition, the C₈₀ cage takes an open‐shell electronic structure due to an increase in the number of electrons transferring from Sc_3?nLa_nN. These make the endohedral structure less stable and more reactive. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 1353–1358, 2001     

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.     

DFT studies on TinC2n (n=1–6) clusters

The geometric configurations and electronic structures of the Ti_nC_2n (n=1–6) clusters were studied by using the quantum chemical ab initio density functional theory (DFT) method. Our studies showed that these Ti_nC_2n (n=1–6) could grow gradually to form cyclic clusters through the subunits TiC₂ bonding to each other by C C or Ti C bond. The result could explain the existing experimental fact. The studies might also be helpful to the knowledge of the formation mechanism of the Met‐Cars. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 71: 313–318, 1999     

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     

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     

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     

叠氮二氢硼多聚体结构和性质的理论研究

本文采用DFT-B3LYP方法,以不同基组对叠氮二氢硼多聚体(H2BN3)n (n=1-4)进行计算研究.二聚体(H2BN3)2(C2h对称性)中含B2N2平面四元环结构.船式(Cs对称性)和椅式(C3v对称性)三聚体(H2BN3)3的结合能相近(-122 和 -126 kJ·mol-1),其中均含B3N3六元环结构.拥有B4N4八元环结构的四个四聚体的结合能只有稍微差别.与单体相比,簇合物的结构参数变化较大.由ΔG0T可知,298.2 K下单体形成二聚体在热力学上是不利的,而形成三聚体和四聚体是有利的.     

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.     

Quantum chemical study of IrFn (n = 1–7) clusters: An investigation of superhalogen properties

In present investigation, the interactions of iridium (Ir) atom with fluorine (F) atoms have been studied using the density functional theory. Up to seven F atoms were able to bind to a single Ir atom which resulted in increase of electron affinities successively, reaching a peak value of 7.85 eV for IrF₇. The stability and reactivity of these clusters were analyzed by calculating highest occupied molecular orbital (HOMO)–LUMO gaps, molecular orbitals and binding energies of these clusters. The unusual properties of these clusters are due to the involvement of inner shell 5d‐electrons, which not only allows IrF_n clusters to belong to the class of superhalogens but also shows that its valence can exceed the nominal value of 2. © 2012 Wiley Periodicals, Inc.     

Theoretical investigation of the structures and spectroscopic properties of (H2O4)n (n = 1–4) clusters

Density functional theory and ab initio calculations were performed to elucidate the hydrogen interactions in (H₂O₄)_n (n = 1–4) clusters. The optimized geometries, binding energies, and harmonic vibrational frequencies were predicted at various levels of theory. The trans conformer of the H₂O₄ monomer was predicted to be the most stable structure at the CCSD(T)/aug‐cc‐pVTZ level of theory. The binding energies per H₂O₄ monomer increased in absolute value by 9.0, 10.1, and 11.8 kcal/mol from n = 2 to n = 4 at the MP2/cc‐pVTZ level of theory (after the zero‐point vibrational energy and basis set superposition error corrections). This result implies that the intermolecular hydrogen bonds were stronger in the long‐chain clusters, that is, the formation of the longer chain in the (H₂O₄)_n clusters was more energetically favorable.     

Structure and stability of (AlN)n clusters

AIN and Al2N2 have been observed in the record of time-of-flight mass-spectra as positive ions. Associating with density functional theory(DFT) B3LYP method with 6-31G* basis set, we have carried out the optimizing calculations of the geometry, electronic state and vibrational frequency for (AIN)n (n = 1-15) clusters, moreover, discussed the character of the chemical bond and thermodynamical stability and explained the experimental mass spectra. The results show that there do not exist AI-AI and N-N bonds and only exists AI-N bond in the ground state structures of (AIN)n clusters; and the "magical number" regularity of (AIN)n is those whose atom number Is 4, 8, 12,16, 20, etc, all of which are times of four.     

Structure and stability for (AlN)_n~+ and (AlN)_n~- (n=1-15) clusters

Using density functional theory (DFT) method with 6-31G* basis set, we have carried out the optimizing calculation of geometry, vibrational frequency and thermodynamical stability for(AIN)n+ and (AIN)n- (n =1-15) clusters. Moreover, their ionic potential (IP) and electron affinity(EA) were discussed. The results show that the electrical charge condition of the cluster has a relatively great impact on the structure of the cluster and with the increase of n, this kind of impactis reduced gradually. There are no AI-AI and N-N bonds in the stable structure of (AIN)n+ or (AIN)n-, and the AI-N bond is the sole bond type. The magic number regularity of (AIN)n+, and (AIN)n- is consistent with that for (AIN)n, indicating that the structure with even n such as 2, 4,6, … is more stable. In addition, (AIN)10 has the maximal ionization power (9.14 eV) and the minimal electron affinity energy (0.19 eV), which manifests that (AIN)10 is more stable than other clusters.     

(GaP)n和(GaP)n－ (n＝10～16)团簇的结构与稳定性研究

采用密度泛函理论B3LYP/Lanl2dz方法对(GaP)_n和(GaP)_n^－ (n＝10～16)团簇的一系列异构体的结构和稳定性进行了研究. 讨论了中性团簇得到一个电子之后, 几何结构和电子性质的变化. 频率分析预测出最强吸收峰位于341～390 cm^－1区域. 从能隙、结合能和能量二次差分等方面综合考虑, 具有T_h对称性的(GaP)₁₂和(GaP)₁₂^－分别是中性(GaP)_n和阴离子(GaP)_n^－团簇中最稳定的, 而具有T_d点群结构的(GaP)₁₆也比较稳定, 究竟哪种结构易于合成还有待于实验的进一步证实. 在相同理论水平上计算了基态(GaP)_n (n＝10～16)的绝热电子亲合势(AEAs)及其基态阴离子的垂直电离能(VDEs), 这对以后的实验数据分析将有一定的参考价值.     

Theoretical investigation of LaC3n+ (n = 0, 1, 2) clusters by density functional theory

LaC₃ⁿ⁺ (n=0, 1, 2) clusters have been studied using B3LYP (Becke 3-parameter–Lee-Yang-Parr) density functional method. The basis set is Dunning/Huzinaga valence double zeta for carbon and [2s2p2d] for lanthanum, denoted LANL1DZ. Four isomers are presented for each cluster; two of them are edge binding isomers with C_2v symmetry, the other two are linear chains with C_∞v symmetry. Meanwhile, two spin states for each isomer, that is, singlet and triplet for LaC₃⁺, doublet and quartet for LaC₃ and LaC₃²⁺, respectively, are also considered. Geometries, vibrational frequencies, infrared intensities, and other quantities are reported and discussed. The results indicate that at some spin states; the C_2v symmetry isomers are the dominant structures, while for the other spin states, linear isomers are energetically favored. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 66 : 301–307, 1998     

Density functional calculations on CO attached to PtnRu(10−n) (n = 6–10) clusters

B3LYP and SCF‐Xα calculations have been performed on Pt_nRu_(10−n)CO (n = 6–10) clusters. The work aims to simulate the adsorption of CO on the (111) surface of platinum metal and to examine the electronic effects that arise when some Pt atoms are replaced with Ru. Adsorption energies and Pt C and C O stretching frequencies have been calculated for each cluster. Ru does affect the electronic structure of the clusters, the calculated adsorption energies, and frequencies, the Pt C frequency more than the C O. The donation‐backbonding mechanism that accompanies the shift in CO stretching frequency that occurs when CO adsorbs on platinum does not explain the differences in frequency shift observed in CO on various Pt/Ru surfaces. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 77: 589–598, 2000     

Hydrogen bonding structure and many‐body interactions in 1,3,5‐triazine–(water)3 and 1,2,4‐triazine–(water)3 complexes

The hydrogen bonding structure and many‐body interactions between 1,3,5‐triazine (1,2,4‐triazine) and three water molecules are studied using the density functional theory (DFT) B3LYP method and 6‐31++G** basis set. Various structures of 1,3,5‐triazine–(water)₃ and 1,2,4‐triazine–(water)₃ complexes are investigated, and the seven and eight stable structures are reported for 1,3,5‐triazine–(water)₃ and 1,2,4‐triazine–(water)₃, respectively. Many‐body analysis is also carried out to obtain relaxation energy and many‐body interaction energy (two‐, three‐, and four‐body), and the most stable conformer has the basis set superposition error corrected interaction energy of ?92.09 and ?99.53 kJ/mol. The two‐ and three‐body interactions have significant contribution to the total interaction energy, whereas the relaxation energy, four‐body interactions are very small for 1,3,5‐triazine–(water)₃ and 1,2,4‐triazine–(water)₃ complexes. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

Exploration on the structure,stability, and isomerization of planar CnB5 (n = 1−7) clusters

The structures, stabilities, nature of bonding, and potential energy surfaces of low‐energy isomers of planar C_nB₅ (n = 1?7) have been systematically explored at the CCSD(T)/6‐311+G(d)//B3LYP/6‐311+G(d) level. Incremental binding energy (IBE) and second order energy difference (Δ²E) analyses demonstrate that C_nB₅ clusters with even n have relatively higher stability. The nature of bonding in these clusters is discussed based on valence molecular orbital (VMO), and Mayer bond order (MBO). Hückel (4n + 2) rule and nucleus‐independent chemical shift (NICS) values suggest that the ground states of C₃B₅, C₄B₅, and C₇B₅ have π aromaticity. VMO, electron localization function (ELF), adaptive natural density partitioning (AdNDP), and NICS analyses reveal the double aromaticity of C₃B₅ cation. CB₅ and C₃B₅ are stable both thermodynamically and kinetically based on isomerization analysis. In addition, the simulated IR spectra are expected to be helpful for future experimental studies of these clusters.