Electronic structure and thermochemical properties of silicon-doped lithium clusters Li(n)Si0/+, n = 1-8: new insights on their stability

A theoretical investigation on small silicon-doped lithium clusters Li(n)Si with n = 1-8, in both neutral and cationic states is performed using the high accuracy CCSD(T)/complete basis set (CBS) method. Location of the global minima is carried out using a stochastic search method and the growth pattern of the clusters emerges as follows: (i) the species Li(n)Si with n ≤ 6 are formed by directly binding one Li to a Si of the smaller cluster Li(n-1)Si, (ii) the structures tend to have an as high as possible symmetry and to maximize the coordination number of silicon. The first three-dimensional global minimum is found for Li(4)Si, and (iii) for Li(7)Si and Li(8)Si, the global minima are formed by capping Li atoms on triangular faces of Li(6)Si (O(h)). A maximum coordination number of silicon is found to be 6 for the global minima, and structures with higher coordination of silicon exist but are less stable. Heats of formation at 0 K (Δ(f)H(0)) and 298 K (Δ(f)H(298)), average binding energies (E(b)), adiabatic (AIE) and vertical (VIE) ionization energies, dissociation energies (D(e)), and second-order difference in total energy (Δ(2)E) of the clusters in both neutral and cationic states are calculated from the CCSD(T)/CBS energies and used to evaluate the relative stability of clusters. The species Li(4)Si, Li(6)Si, and Li(5)Si(+) are the more stable systems with large HOMO-LUMO gaps, E(b), and Δ(2)E. Their enhanced stability can be rationalized using a modified phenomenological shell model, which includes the effects of additional factors such as geometrical symmetry and coordination number of the dopant. The new model is subsequently applied with consistency to other impure clusters Li(n)X with X = B, Al, C, Si, Ge, and Sn.     

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.     

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     

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     

DFT calculations of static dipole polarizabilities and hyperpolarizabilities for the boron clusters Bn (n=3–8,10)

The static electric dipole polarizabilities and second‐order hyperpolarizabilities of several bare boron clusters have been calculated with density functional theory. The average second‐order hyperpolarizability γ_av reaches a saturation limit of about 50,000 a.u. already with B₅ for a given type of structure. The average polarizability per atom shows overall a decrease with increasing cluster size, while the average second hyperpolarizability per atom first increases from B₃ to B₆, and then starts to decrease. For the noncentrosymmetric clusters dipole moments and first‐order hyperpolarizabilities are reported. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 78: 131–135, 2000     

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     

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.     

羰基硼化合物B2n(CO)n (n＝1～6)的理论研究

运用密度泛函理论(DFT)的B3LYP/6-31G*方法, 对羰基硼化合物B_2n(CO)_n (n＝1～6)各种可能的结构进行了优化,对它们的几何构型、电子态、振动频率、核独立化学位移(NICS)和B₂CO的分子轨道进行了理论研究, 得到了B_2n(CO)_n (n＝1～6)结构的稳定性信息. 在它们的基态结构中, 羰基的配位方式是端配位(μ₁-CO), B_2n(CO)_n (n＝1～5)的基态构型是线形或平面结构, B₁₂(CO)₆的基态构型则较为复杂. B_2n(CO)_n (n＝1～3)的基态是三重态, B_2n(CO)_n (n＝4～6)的基态是单重态. 振动频率和轨道的研究为实验提供了重要的理论依据.     

B_n(BO)_n~(2-),CB_(n-1)(BO)_n~-,and C_2B_(n-2)(BO)_n (n=5-12):Cage-like boron oxide clusters analogous to closo-B_nH_n~(2-),CB_(n-1)H_n~-,and C_2B_(n-2)H_n

A density functional theory (DFT) investigation has been performed in this work on the cage-like boron-rich boron oxide clus-ters Bn(BO)2n-,CBn-1(BO)-n,and C2Bn-2(BO)n (n = 5-12) which are boronyl analogues of the closo-boranes BnHn2-,monocarbo-ranes CBn-1H-n,and dicarboranes C2Bn-2Hn. These boron oxide clusters possess similar geometrical and electronic structures with the corresponding boranes and carboranes and prove to be three-dimensional (3D) aromatic compounds,consistent with the previously proposed ...     

Electronic structures, vibrational and thermochemical properties of neutral and charged niobium clusters Nb(n), n = 7-12

Geometric and electronic structures, vibrational properties, and relative stabilities of niobium clusters Nb(n), n = 7-12, are studied using both DFT (BPW91 and M06 functionals) and CCSD(T) calculations with the cc-pVnZ-PP basis set. In each cluster, various lower-lying states are very close in energy in such a way that the ground state cannot be unambiguously established by DFT computations. Nb clusters tend to prefer the lowest possible spin state as the ground state, except for Nb(12) ((3)A(g)). The optimal structure of the cluster at a certain size does not simply grow from that of the smaller one by adding an atom randomly. Instead, the Nb clusters prefer a close-packed growth behavior. Nb(10) has a spherically aromatic character, high chemical hardness and large HOMO-LUMO gap. Electron affinities, ionization energies, binding energy per atom, and the stepwise dissociation energies are evaluated. Energetic properties exhibit odd-even oscillations. Comparison with experimental values shows that both BPW91 and M06 functionals are reliable in predicting the EA and IE values, but the BPW91 is deficient in predicting the binding and dissociation energies. We re-examine in particular the experimental far IR spectra previously recorded using the IR-MPD and free electron laser spectrometric techniques and propose novel assignments for Nb(7) and Nb(9) systems. The IR spectra of the anions are also predicted.     

The arsenic clusters Asn (n = 1-5) and their anions: structures, thermochemistry, and electron affinities

The molecular structures, electron affinities, and dissociation energies of the As(n)/As(-) (n) (n = 1-5) species have been examined using six density functional theory (DFT) methods. The basis set used in this work is of double-zeta plus polarization quality with additional diffuse s- and p-type functions, denoted DZP++. These methods have been carefully calibrated (Chem Rev 2002, 102, 231) for the prediction of electron affinities. The geometries are fully optimized with each DFT method independently. Three different types of the neutral-anion energy separations reported in this work are the adiabatic electron affinity (EA(ad)), the vertical electron affinity (EA(vert)), and the vertical detachment energy (VDE). The first dissociation energies D(e)(As(n-1)-As) for the neutral As(n) species, as well as those D(e)(As(-) (n-1)-As) and D(e) (As(n-1)-As(-)) for the anionic As(-) (n) species, have also been reported. The most reliable adiabatic electron affinities, obtained at the DZP++ BLYP level of theory, are 0.90 (As), 0.74 (As(2)), 1.30 (As(3)), 0.49 (As(4)), and 3.03 eV (As(5)), respectively. These EA(ad) values for As, As(2), and As(4) are in good agreement with experiment (average absolute error 0.09 eV), but that for As(3) is a bit smaller than the experimental value (1.45 +/- 0.03 eV). The first dissociation energies for the neutral arsenic clusters predicted by the B3LYP method are 3.93 eV (As(2)), 2.04 eV (As(3)), 3.88 eV (As(4)), and 1.49 eV (As(5)). Compared with the available experimental dissociation energies for the neutral clusters, the theoretical predictions are excellent. Two dissociation limits are possible for the arsenic cluster anions. The atomic arsenic results are 3.91 eV (As(-) (2) --> As(-) + As), 2.46 eV (As(-) (3) --> As(-) (2) + As), 3.14 eV (As(-) (4) --> As(-) (3) + As), and 4.01 eV (As(-) (5) --> As(-) (4) + As). For dissociation to neutral arsenic clusters, the predicted dissociation energies are 2.43 eV (As(-) (3) --> As(2) + As(-)), 3.53 eV (As(-) (4) --> As(3) + As(-)), and 3.67 eV (As(-) (5) --> As(4) + As(-)). For the vibrational frequencies of the As(n) series, the BP86 and B3LYP methods produce good results compared with the limited experiments, so the other predictions with these methods should be reliable.     

Ge_nEu(n=1-13)团簇的结构、电子及磁性质(英文)

利用密度泛函理论在广义梯度近似下研究了GenEu(n=1-13)团簇的生长模式和磁性.结果表明:对于GenEu(n=1-13)团簇的基态结构而言,没有Eu原子陷入笼中.这和SinEu以及其它过渡金属掺杂半导体团簇的生长模式不同.除GeEu团簇外,GenEu(n=2-13)团簇的磁矩均为7μB.团簇的总磁矩与Eu原子的4f轨道磁矩基本相等.Ge、Eu原子间的电荷转移以及Eu原子的5d、6p和6s间的轨道杂化可以增强Eu原子的局域磁矩,却不能增强团簇总磁矩.     

B2Cn+(n=1～9)团簇的结构及其稳定性

采用密度泛函理论(DFT)的B3LYP泛函, 在6-311G*水平上对B2Cn+(n=1～9)团簇的几何构型和电子结构进行了优化和振动频率计算. 结果表明, 在B2Cn+(n=1～9)团簇的基态构型中, B2C2+、B2C3+为具有D∞h对称性的线形结构, B2C7+为具有Cs对称性的立体环状结构, 其余均为平面构型; 其成键顺序为C—C成键优于B—C 成键, B—C成键优于B—B成键. 进一步得到了B2Cn+(n=1～9)团簇的总能量(ET)、零点能(EZ)、摩尔热容(Cp)、标准熵(S0)以及原子化能(ΔEn+). 其结果显示, 随着n的递增, ET、EZ、Cp、S0和ΔEn+数值均呈现增大趋势, 其中EZ数值呈现近似等梯度的增加趋势. 通过对B2Cn+(n=1～9)团簇基态结构的垂直电子亲合势的研究发现, n为奇数的B2Cn+团簇比n为偶数的稳定.     

Molecular structures and energetics of the (TiO2)n (n = 1-4) clusters and their anions

The (TiO2)n clusters and their anions for n = 1-4 have been studied with coupled cluster theory [CCSD(T)] and density functional theory (DFT). For n > 1, numerous conformations are located for both the neutral and anionic clusters, and their relative energies are calculated at both the DFT and CCSD(T) levels. The CCSD(T) energies are extrapolated to the complete basis set limit for the monomer and dimer and calculated up to the triple-zeta level for the trimer and tetramer. The adiabatic and vertical electron detachment energies of the anionic clusters to the ground and first excited states of the neutral clusters are calculated at both levels and compared with the experimental results. The comparison allows for the definitive assignment of the ground-state structures of the anionic clusters. Anions of the dimer and tetramer are found to have very closely lying conformations within 2 kcal/mol at the CCSD(T) level, whereas that of the trimer does not. In addition, accurate clustering energies and heats of formation are calculated for the neutral clusters and compared with the available experimental data. Estimates of the titanium-oxygen bond energies show that they are stronger than the group VIB transition metal-oxygen bonds except for tungsten. The atomization energies of these clusters display much stronger basis set dependence than the clustering energies. This allows the calculation of more accurate heats of formation for larger clusters on the basis of calculated clustering energies.     

CnBδ(δ=0, ±1; n =1～6)团簇的结构、稳定性和光谱

采用密度泛函理论(DFT)的B3LYP方法,在6-31G*和6-311＋G(3df)水平上对C_nB(n=1～6)团簇及其阴离子和阳离子的几何构型和电子结构进行了优化和振动频率计算.得到了C_nB(n=1～6)团簇的电离能,绝热电子亲合势以及C_nB^δ(δ=0,±1)团簇的能隙.结果表明C_nB^－(n=1～6)团簇的基态构型均为线形,这与等电子的C_n簇合物的结构是一致的; C_nB(n=1～6)团簇的基态构型中,除C₂B为不对称的三角形,C₆B为具有C_2v对称性的环状结构外,其余均为线形结构.阳离子团簇中n=2、3、6的基态结构具有C_2v对称性外,其它几个均为线形结构.从几何参数和振动频率上发现,采用密度泛函B3LYP方法在6-311＋G(3df)和6-31G*两种基组上计算得到的键长参数和振动频率非常接近,说明B3LYP方法在计算C_nB簇合物结构参数上对于基组的选择是不太敏感的.通过对C_nB(n=1～6)的光电子能谱性质的研究发现,C₄B容易获得一个电子形成阴离子团簇,但失去一个电子是很困难的,这与实验上观测到的结果非常吻合.     

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.     

Sin/Si-n(n=2-6)的结构和电子亲合能的密度泛函理论研究

选用四种不同的密度泛函理论方法(B3LYP,BLYP,BP86,B3P86),在全电子的双ζ加极化加弥散函数基组(DZP++)下,研究Sin/Si-n (n=2 -6 )体系的结构和电子亲合能.预测Si2 /Si-2 ,Si3 /Si-3 ,Si4 /Si-4 ,Si5 /Si-5 和Si6 /Si-6 的基态结构分别为C∞h(3Σ-g ) /C∞h(2Σ+g ),D3h(3A′2 ) /C2υ(2A1 ),D2h(1Ag) /D2h(2B2g),D3h(1A′1 ) /D3h(2A″2 )和C2υ(1A1 ) /D4h(2A2u).在电子亲合能方面,B3LYP方法预测的电子亲合能是最可靠的.预测Si2,Si3,Si4,Si5和Si6的电子亲合能分别为 2. 05, 2. 34, 2. 16, 2. 48和 2. 13eV.     

Electronic structure and thermochemical properties of small neutral and cationic lithium clusters and boron-doped lithium clusters: Li(n)(0/+) and Li(n)B(0/+) (n = 1-8)

The stability, electronic structure, and thermochemical properties of the pure Li(n) and boron-doped Li(n)B (n = 1-8) clusters in both neutral and cationic states are studied using electronic structure methods. The global equilibrium structures are established, and their heats of formation are evaluated using the G3B3 and CCSD(T)/CBS methods based on the density functional theory geometries. Theoretical adiabatic ionization energies (IE(a)) for the Li(n) clusters are in good agreement with experiment: Li(2) (G3B3, 5.21 eV; CCSD(T), 5.14 eV; expt, 5.1127 ± 0.0003 eV), Li(3) (4.16, 4.11, 4.08 ± 0.10), Li(4) (4.76, 4.68, 4.70 ± 0.05), Li(5) (4.11, 4.06, 4.02 ± 0.10), Li(6) (4.46, 4.32, 4.20 ± 0.10), Li(7) (4.07, 3.99, 3.94 ± 0.10), and Li(8) (4.49, 4.31, 4.16 ± 0.10). The Li(4) experimental IE(a) has been revised on the basis of the Franck-Condon simulations. Species Li(5)B, Li(6)B(+), Li(7)B, and Li(8)B(+) exhibit high stability as compared to their neighbors, which can be understood by considering the magic numbers of the phenomenological shell model (PSM).     

(BCO)+n(n=1-12)团簇的结构与稳定性

用密度泛函理论(DFT)的B3LYP方法, 在6-31G*水平上对(BCO)⁺_n(n=1-12)团簇的几何结构、电子结构、振动频率等性质进行了理论研究. 结果表明, (BCO)⁺_n团簇的基态结构均为羰基端配位(μ₁-CO)结构, 且含三元环和五元环数目越多或四元环和六元环的数目越少, 相应的结构越稳定. 能量分析得到, n 为奇数的(BCO)⁺_n团簇比n为偶数的稳定.