Geometry,stability, and isomerization of BnN2 (n = 1−6) isomers

We perform a systematic study on the geometry, stability, nature of bonding, and potential energy surface of low‐lying isomers of planar and cyclic B_nN₂ (n = 1?6) at the CCSD(T)/6‐311+G(d)//B3LYP/6‐311+G(d) level. B_nN₂ (n = 2?4) clusters are structurally similar to pure boron clusters. The evolution of the binding energy per atom, incremental binding energy, and second‐order difference of total energy with the size of B_nN₂ reveals that the lowest energy isomer of B₃N₂ has high stability. B₅N₂ and B₆N₂ possess π‐aromaticity according to Hückel (4n + 2) rule. The aromaticity of some isomers of B₄N₂ and B₆N₂ is examined based on their valence molecular orbitals. At the CCSD(T)/6‐311+G(d)//B3LYP/6‐311+G(d) level, several B₂N₂, B₃N₂, B₄N₂, and B₅N₂ isomers are predicted to be stable both thermodynamically and kinetically, and detectable in future experiments. © 2013 Wiley Periodicals, Inc.     

硼碳团簇BnC2 (n＝1～6)的理论研究

应用密度泛函理论在B3LYP/6-311＋G(d)水平上研究了硼碳团簇B_nC₂ (n＝1～6)的几何结构、生长机制和相对稳定性. 计算结果表明, 对于n＝2～6的簇, 平面多环状构型为最稳定的结构, 其中C原子分布于环的顶点、有尽可能多的三配位硼原子和尽可能多的B—C键. 碳原子作为杂原子倾向掺杂于团簇的顶点位置, 它的掺杂不改变硼团簇的主体结构. 与平面多环状结构相比, 随着簇尺寸的增大, 三维结构和线性链结构更不稳定. 在低能线性结构中, C原子位于链两侧的第二个位置. 计算的碎片分裂能、递增键能以及HOMO-LUMO能隙表明, B₄C₂为幻数簇.     

VB2n-(n=8~12)团簇几何结构、电子及热力学特性的理论研究

基于卡里普索结构预测程序和密度泛函理论的第一性原理计算,搜索确定了VB_2n^-（n=8~12）团簇的基态和亚稳态结构。结果发现,V原子的掺杂完全改变了原硼团簇的结构并提高了原体系的稳定性。掺杂体系基态结构分别呈现高对称性的鼓状（VB₁₆^-：C_2v）、管状（VB₁₈^-：C_2v和VB₂₀^-：C_s）及笼状（VB₂₂^-：C₂和VB₂₄^-：D_3h）结构。基于基态结构,研究了体系的电荷转移和极化率,拟合出了光电子能谱、红外和拉曼谱图,分析了流变键和芳香特性。最后,研究了体系的热力学特性,讨论了温度对热力学参数的影响。     

Systematic LSD investigation on cationic boron clusters: B(n  2–14)

The geometrical structures and properties of small cationic boron clusters B(n = 2–14) have been investigated using the local spin density (LSD ) formalism. The nonlocal correction has also been calculated. The linear search for minima on the potential energy surface has been performed using analytical gradients of the LSD total energy. Most of the final structures of the cationic boron clusters prefer planar or quasi-planar nuclear arrangements and can be considered as fragments of a planar surface or as segments of a sphere. The calculated adiabatic ionization potentials of B_n exhibit features that are analogous to those of measured ionization potentials for boron clusters. Most of the calculated normal modes of the cationic clusters have frequencies that are around 1000 cm^?1 and have strong infrared intensities, and they correspond quite well with analogous properties of solid boron. © 1994 John Wiley & Sons, Inc.     

Far‐Infrared Spectra of Yttrium‐Doped Gold Clusters AunY (n=1–9)

The geometric, spectroscopic, and electronic properties of neutral yttrium‐doped gold clusters Au_nY (n=1–9) are studied by far‐infrared multiple photon dissociation (FIR‐MPD) spectroscopy and quantum chemical calculations. Comparison of the observed and calculated vibrational spectra allows the structures of the isomers present in the molecular beam to be determined. Most of the isomers for which the IR spectra agree best with experiment are calculated to be the energetically most stable ones. Attachment of xenon to the Au_nY cluster can cause changes in the IR spectra, which involve band shifts and band splittings. In some cases symmetry changes, as a result of the attachment of xenon atoms, were also observed. All the Au_nY clusters considered prefer a low spin state. In contrast to pure gold clusters, which exhibit exclusively planar lowest‐energy structures for small sizes, several of the studied species are three‐dimensional. This is particularly the case for Au₄Y and Au₉Y, while for some other sizes (n=5, 8) the 3D structures have an energy similar to that of their 2D counterparts. Several of the lowest‐energy structures are quasi‐2D, that is, slightly distorted from planar shapes. For all the studied species the Y atom prefers high coordination, which is different from other metal dopants in gold clusters.     

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.     

Theoretical study of structure and vibrational properties of MgnOn (n = 3–10) clusters

The structure and harmonic vibrations of Mg_nO_n (n = 3–10) clusters have been investigated using density functional theory. All structures are found to be cumulenic D_nh rings (equal bonds, alternating angles), with one intense out‐of‐plane mode and three infrared (IR)‐active degenerate modes, of which the highest one is extremely intense and increases asymptotically to 1000 cm^?1 for n = 10 at the B3LYP/6‐311++G(2d,2p) level. Comparisons with C_2n clusters show that B_nN_n and Be_nO_n clusters, the structure and bonding type for the Mg_nO_n clusters are consistent with those of the C_2n (n = 3, 5, 7,…) clusters B_nN_n(n = 3–10) and Be_nO_n(n = 3–10) clusters. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

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.     

Theoretical prediction for the structures of gas phase lithium oxide clusters: (Li2O)n (n = 1–8)

We apply genetic algorithm combining directly with density functional method to search the potential energy surface of lithium‐oxide clusters (Li₂O)_n up to n = 8. In (Li₂O)_n (n = 1–8) clusters, the planar structures are found to be global minimum up to n = 2, and the global minimum structures are all three‐dimensional at n ≥ 3. At n ≥ 4, the tetrahedral unit (TU) is found in most of the stable structures. In the TU, the central Li is bonded with four O atoms in sp³ interactions, which leads to unusual charge transformation, and the probability of the central Li participating in the bonding is higher by adaptive natural density partitioning analysis, so the central Li is in particularly low positive charge. At large cluster size, distortion of structures is viewed, which breaks the symmetry and may make energy higher. The global minimum structures of (Li₂O)₂, (Li₂O)₆, and (Li₂O)₇ clusters are the most stable magic numbers, where the first one is planar and the later both have stable structural units of tetrahedral and C_4v. © 2012 Wiley Periodicals, Inc.     

Structure and electronic properties of hollow‐caged C60 fullerene‐derived (MN4)nC6(10 − n) (M = Zn,Mg, Fe,n = 1−6) complexes

Unique hollow‐caged (MN₄)_nC_{6(10 ? n)} (M = Zn, Mg, Fe, n = 1?6) complexes designed by introduction of n porphyrinoid fragments in C₆₀ fullerene structure were proposed and the atomic and electronic structures were calculated using LC‐DFT MPWB95 and M06 potentials and 6‐311G(d)/6‐31G(d) basis sets. The complexes were optimized using various symmetric configurations from the highest O_h to the lowest C₁ point groups in different spin states from S = 0 (singlet) to S = 7 (quindectet) for M = Fe to define energetically preferable atomic and electronic structures. Several metastable complexes were determined and the key role of the metal ions in stabilization of the atomic structure of the complexes was revealed. For Fe₆N₂₄C₂₄, the minimum energy was reported for C_2h, D_2h, and D_4h symmetry of pentet state S = 2, so the complex can be regarded as unique molecular magnet. It was found that the metal partial density of states determine the nature of HOMO and LUMO levels making the clusters promising catalysts. © 2014 Wiley Periodicals, Inc.     

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     

The structure of small gallium nitride clusters

The geometry, vibrational frequencies and stability of the structural isomers of small gallium nitride clusters (n = 2–4) have been investigated using density functional theory. The lowest energy structures are cyclic. The ground electronic state of the cyclic forms for n > 2 is the singlet state. All of the cyclic structures have D_nh symmetry. The caged structures for Ga₄N₄ lie higher in energy than the planar cumulenic monocyclic ring. The Ga‐N bond dominates the structures for many isomers, so that one dissociation channel is loss of a GaN monomer. However, unlike the corresponding boron and aluminum clusters, dissociation into larger fragments is energetically favored. The structural properties of the gallium nitride clusters are similar to those of the analogous AIN (and BN) clusters. © 2000 John Wiley & Sons, Inc. Heteroatom Chem 11:281–286, 2000     

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     

Tetra- and hexaatomic cyclic clusters of main-group elements (XY)2 and (XY)3: an ab initio and density functional study

The electronic and molecular structure of planar (cyclic and linear) tetra- and hexaatomic clusters (XY) _n (XY = CC, BN, BeO, LiF; n = 2, 3) was studied using the ab initio CCD(full)/6-311+G** method and density functional approach (B3LYP/6-311+G**). The stability of cyclic clusters C₆, B₃N₃, and Be₃O₃ with D_3h symmetry is mainly determined by the aromaticity of their -electron systems.     

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.     

Stretching vibrations and structure of (HF) n (n=4–8) clusters

IR spectra of 24 structural isomers of (HF) _n (n=4–8) clusters were calculated in the framework of semiempirical theory of polyatomic molecule vibrations. Based on the results obtained and available experimental data it is proposed that (HF) _n associates comprising 3–5-membered cycles with attached monomeric HF units are present in molecular beams and gas phase.Ab initio calculations performed by the SCF method show the existence of local minima corresponding to such structures on the potential energy surface of (HF) _n clusters (n=4–6). Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 3, pp. 435–443, March, 1997.     

Theoretical Study of Structure and Stability of B n O and B n O2 Clusters

The structures and stabilities of B _n O and B _n O₂ clusters with n ≤ 6 are studied systematically by using density-functional theory. The lowest-energy structures of B _n O clusters favor two-dimensional, and can be obtained from B _n or B _n−1O. For B _n O₂, unexpectedly, all of the most stable B _n O₂ clusters but B₆O₂ are linear. Furthermore, in B _n O₂ clusters, the longer the distance between two O atoms, the more stable the structure. To investigate the relative stability of considered clusters, binding energies per atom, reaction energies, and fragmentation energies are also calculated and discussed.     

Exploring the Potential Energy Surface of E2P4 Clusters (E=Group 13 Element): The Quest for Inverse Carbon‐Free Sandwiches

Inverse carbon‐free sandwich structures with formula E₂P₄ (E=Al, Ga, In, Tl) have been proposed as a promising new target in main‐group chemistry. Our computational exploration of their corresponding potential‐energy surfaces at the S12h/TZ2P level shows that indeed stable carbon‐free inverse‐sandwiches can be obtained if one chooses an appropriate Group 13 element for E. The boron analogue B₂P₄ does not form the D_4h‐symmetric inverse‐sandwich structure, but instead prefers a D_2d structure of two perpendicular BP₂ units with the formation of a double B?B bond. For the other elements of Group 13, Al–Tl, the most favorable isomer is the D_4h inverse‐sandwich structure. The preference for the D_2d isomer for B₂P₄ and D_4h for their heavier analogues has been rationalized in terms of an isomerization‐energy decomposition analysis, and further corroborated by determination of aromaticity of these species.     

Theoretical study of several Fe(H2o)n2+ clusters at different temperatures

Several Fe(H₂O)_n²⁺ clusters, with n up to 20, have been studied, both by energy minimization in the pairwise approximation and by Monte Carlo simulation. In the last case the calculations have been carried out at three different temperatures in order to investigate the effect of thermal agitation. The most interesting result which can be deduced from this work is the existence of eight water molecules in the first hydration shell of the iron (II) ion. A microscopic analysis has shown that the minimum energy structure of the Fe(H₂O)₈²⁺ cluster presents a D_4d symmetry. This structure is slightly distorted as far as the temperature is increased. The validity of these theoretical predictions is discussed.     

(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.