Augmentation of the Generalised n×n Eigenvalue Equation to a Generalised (n+1)×(n+1) Eigenvalue Equation

Generalised n×n eigenvalue equation B| _i = _i S ^b | _i (i=1,...,n) where B and S ^b are n×n Hermitian matrices while S ^b is in addition positive definite is considered. This equation is augmented to a generalised (n+1)(n+1) eigenvalue equation H| _k = _k S| _k (k=1,...,n+1) where Hermitian matrices H and S represent matrices B and S ^b , respectively, augmented by one additional row and one additional column. It is shown how the eigenvalues _k and the eigenvectors | _k of the augmented eigenvalue equation can be expressed in terms of the eigenvalues _i and the eigenvectors | _i of the original eigenvalue equation. Operation count to obtain by this method all augmented eigenvalues and eigenvectors is of the order O(n ²). Unless matrices involved are of some special kind such as sparse matrices or alike, this operation count is one order of magnitude smaller than operation count required by other presently known methods. In many practical cases operation count to obtain a single selected eigenvalue and/or eigenvector by this method is of the order O(n). In the case of the generalised eigenvalue equation, all other methods usually require again O(n ³) operations, even if only a single eigenvalue and/or eigenvector is required. Thus in many cases of interest operation count to obtain a selected eigenvalue and/or eigenvector by this method is two orders of magnitude smaller than operation count required by other methods.     

Gaussian binning of the vibrational distributions for the Cl + CH4(v(4/2) = 0, 1) → H + CH3Cl(n(1)n(2)n(3)n(4)n(5)n(6)) reactions

We test several binning techniques to obtain mode-specific final-state distributions for polyatomic reactions. Normal mode analysis is done after an exact transformation to the Eckart frame. Standard histogram binning (HB) and three different variants of the energy-based Gaussian binning (1GB) are employed to obtain the probabilities of the vibrational states. We consider the two major issues of the polyatomic quasiclassical product analysis, i.e., (1) rounding the classical action to the nearest integer can result in unphysical states and (2) the normal-mode analysis can break down for highly distorted geometries. We show that 1GB can handle issue 1 when the total vibrational energy is evaluated in the normal mode space using the harmonic approximation and both issues 1 and 2 can be solved when the total vibrational energy is calculated exactly in the Cartesian space. We found that anharmonicity in the quantized energy levels does not have a significant effect on the final-state distributions. Quasiclassical trajectory calculations are performed for the reactant ground-state and bending-excited Cl((2)P(3/2)) + CH(4)(v(4/2) = 0, 1) → H + CH(3)Cl reactions using an ab initio potential energy surface. The product analysis techniques are successfully applied to the CH(3)Cl product molecules and some qualitative features of the results are discussed.     

Heats of formation for Fe(CO)n(n=1–4)

The dissociation energies of Fe(CO)_n (n=2–4) are computed using correlation consistent basis sets and the CCSD(T) approach. The dissociation energies are extrapolated to the CBS limit and are corrected for core–valence (CV), scalar relativistic, spin–orbit, zero-point, and thermal effects. Our iron carbonyl bond strengths agree with experiment within the respective error bars. We use our dissociations energies at 298 K to obtain the heats of formation of Fe(CO)_n (n=1–4).     

羰基硼化合物(BCO)n(n==1～12)的理论研究

运用HF/3-21G方法和密度泛函理论(DFT)的B3LYP/6-31G*方法, 对羰基硼化合物(BCO)n(n=1~12)的各种可能结构进行了优化, 对在B3LYP/6-31G*水平上得到的几何构型、电子态、结合能、振动频率、核独立化学位移(NICS)、能量二次差分和热力学性质进行了理论研究, 得到了(BCO)n(n=1~12)结构的稳定性信息. 十二种基态结构都是端配位(μ1-CO), (BCO)n(n=1~3, 5, 6) 的基态是线型或平面结构, (BCO)n(n=4, 7~12)的基态是笼状结构; B—C平均键能呈现奇偶交替现象, 偶数的结构比奇数稳定; 能量二次差分得到同样的结论；羰基的振动频率与实验值非常吻合; 热力学性质的研究对实验具有重要的指导意义.     

Photoelectron imaging of tetrahydrofuran cluster anions (THF)(n) (-) (1≤n≤100)

Anionic tetrahydrofuran clusters (THF)(n) (-) (1≤n≤100) are studied with photoelectron imaging as gas-phase precursors for electrons solvated in THF. Photoelectron spectra of clusters up to n=5 show two peaks, one of which is attributed to a solvated open chain radical anion and the other to the closed THF ring. At n=6, the spectra change shape abruptly, which become more characteristic of (THF)(n) (-) clusters containing solvated electrons. From n=6-100, the vertical detachment energies (VDEs) of these solvated electron clusters increase from 1.96 to 2.71 eV, scaling linearly with n(-1/3). For fully deuterated (THF-d8)(n) (-) clusters, the apparent transition to a solvated electron cluster is delayed to n=11. Extrapolation of the VDEs to infinite cluster size yields a value of 3.10 eV for the bulk photoelectric threshold. The relatively large VDEs at onset and small stabilization with increasing cluster size compared to other solvated electron clusters may reflect the tendency of the bulk solvent to form preexisting voids that can readily solvate a free electron.     

(CoMn)n(n=1～5)合金团簇的结构和磁性

All geometry structures of (CoMn)n (n=1-5) clusters were optimized, and the energy, frequence and magnetism of (CoMn)n (n=1-5) clusters were calculated by using the local spin density approximation and generalized gradient approximation of density functional theory. The same ground state structures of CoMn alloy clusters were confirmed in two methods, and magnetism of CoMn alloy ground state clusters was studied systemically. In order to understand structure and magnetism of CoMn alloy clusters better, Co2n (n=1-5) and Mn2n (n=1-5) clusters were calculated by the same method as alloy clusters, whose ground state structure and magnetism were confirmed. Moreover, the ground state structure and magnetism of clusters with the corresponding CoMn alloy clusters was compared. Results indicated that for (CoMn)n (n=1-4) clusters, geometry structures of CoMn alloy clusters are the same as the corresponding pure clusters still, (CoMn)3 and (CoMn)4 exhibit magnetic bistability, show ferromagnetic and anti-ferromagnetic coupling, local magnetic moment of Co, Mn atoms in CoMn alloy clusters almost preserves magnetism of pure clusters still.     

(CoCr)n (n=1-5)合金团簇的结构和磁性

采用密度泛函理论中的广义梯度近似(GGA)对(CoCr)n (n=1-5)团簇的几何结构、电子结构和磁性进行了系统的研究, 确定了团簇的基态和亚稳态. 结果表明, CoCr二元合金团簇的基态几何构型呈对称有序排列, 其磁性均呈反铁磁性耦合; 团簇键长和配位数的大小对原子局域磁性有很明显的影响; 受Cr原子的影响, 在(CoCr)4团簇中, 非相邻的Co原子之间呈现反铁磁性耦合.     

(Cl2AlNH2)n和(H2AlNH2)n(n=1～5)簇结构及其热力学性质

用HF自洽场理论和密度泛函理论(DFT)的B3LYP方法,在6 31G水平上研究了低聚物(Cl2AlNH2)n和(H2AlNH2)n(n=1～5)簇的几何构型、电子结构和聚合反应热力学性质,比较了两个系列化合物中化学键的强度.结果表明,Cl2AlNH2和H2AlNH2分子为C2 (EC)平面型结构,其中Al－N为由一个σ键和一个键组成的双键.(Cl2AlNH2)n和(H2AlNH2)n(n=1～5)分子为Dnh对称,Al－N是典型的σ单键 .低聚物(Cl2AlNH2)n和(H2AlNH2)n的稳定性顺序分别为: 3 > 2 > 4> 5 > 1和8 > 7 > 9 > 11 > 6.     

Unitary group tensor operator algebras for many-electron systems. III. Matrix elements in U(n 1 +n 2) ⊃ U(n 1) × U(n 2) partitioned basis

Exploiting our earlier results [J. Math. Chem. 4 (1990) 295–353 and 13 (1993) 273–316] on the unitary group U(n) Racah-Wigner algebra, specifically designed for quantum chemical calculations of molecular electronic structure, and the related tensor operator formalism that enabled us to introduce spin-free orbital equivalents of the second quantization-like creation and annihilation operators as well as higher rank symmetric, antisymmetric and adjoint tensors, we consider the problem of U(n) basis partitioning that is required for group-function type approaches to the many-electron problem. Using the U(n) U(n ₁) × U(n ₂),n =n ₁ +n ₂ adapted basis, we evaluate all required matrix elements of U(n) generators and their products that arise in one- and two-body components of non-relativistic electronic Hamiltonians. The formalism employed naturally leads to a segmented form of these matrix elements, with many of the segments being identical to those of the standard unitary group approach. Relationship with similar approaches described earlier is briefly pointed out.     

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

 The possible geometrical structures and relative stability of (SiS₂) _n (n=1–6) silicon–sulfur clusters are explored by means of density functional theory quantum chemical calculations. The effects of polarization functions and electron correlation are included in these calculations. The electronic structures and vibrational spectra of the most stable geometrical structures of (SiS₂) _n are analyzed by the same method. As a result, the regularity of the (SiS₂) _n cluster growth is obtained, and the calculation may used for predicting the formation mechanism of the (SiS₂) _n cluster. Received: 17 November 1999 / Accepted: 3 November 2000 / Published online: 3 May 2001     

(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.     

(AlN)+n和(AlN)-n(n=1～15)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(AlN)+n和(AlN)-n(n=1～15)团簇的几何构型、红外光谱和热力学稳定性进行了研究,并对它们的电离能及电子亲和能进行了讨论.结果表明:(AlN)n团簇的电荷状态对簇合物的结构有较大影响,随着n的增大影响逐渐减小;所有平衡结构中不存在Al-Al和N-N键,Al-N键是惟一键型;(AlN)+n和(AlN)-n结构稳定性幻数与(AlN)n相同,即n=2,4,6,…等偶数结构较为稳定;(A1N)10团簇具有最大的电离能(IP=9.14 eV)和最小的电子亲和能(EA=0.19eV),较其他团簇更稳定.     

SiO2·(CO)n(n=1～2)结构和属性的理论研究

用密度泛函理论详细地研究了SiO2·(CO)n(n=1～2)的结构和属性.研究表明,SiO2·CO是一个T形的具有C2v对称性的分子,SiO2·(CO)2具有C2对称性的分子;频率计算结果与实验值一致,CO在与SiO2成键过程中,C-O伸缩振动频率有所增加,说明静电势在复合过程中起了重要作用;基组重叠误差(BSSE)修正在计算相互作用能时不可忽视,相互作用能和解离能的计算以及NBO分析表明,SiO2·(CO)2中的SiO2与CO之间的作用相对SiO2·CO来说较弱;SiO2和CO2与CO的成键特点不同,主要是缘于SiO2与CO2的能隙不同.     

簇合物(F2GaN3)n(n=1～4)的理论研究

采用密度泛函理论B3LYP/6-311+G*方法,计算研究了(F2GaN3)n(n=1～4)簇合物的结构和性质.研究表明,簇合物(F2GaN3)n(n=2～4)的优化构型均拥有Ga-Na-Ga连接的环状结构.讨论了几何参数随聚合度的变化关系.三聚体的船式构象较椅式构象的能量低16 kJ·mol-1,具有S4对称性的四聚...     

Density functional theory study on (F2AlN3) n (n = 1–4) clusters

Possible geometrical structures and relative stabilities of (F₂AlN₃) _n (n = 1–4) clusters were studied using density functional theory at the B3LYP/6-311+G* level. The optimized clusters (F₂AlN₃) _n (n = 2–4) possess cyclic structure containing Al–N_α–Al linkages, and azido in azides has linear structure. The IR spectra of the optimized (F₂AlN₃) _n (n = 1–4) clusters have three vibrational sections, the whole strongest vibrational peaks lie in 2218–2246 cm⁻¹, and the vibrational modes are N₃ asymmetric stretching vibrations. Trends in thermodynamic properties with temperature and oligomerization degree n are discussed, respectively. A study of their thermodynamic properties suggests that monomer 1A forms the most stable clusters (2A, 3A, and 4B) can occur spontaneously in the gas phase at temperatures up to 800 K.     

Density functional investigations on the (H2O)n·CCH and (H2O)n·HCC complexes (n=1–3)

The electronic structures and energies of (H₂O)_n·CCH and (H₂O)_n·HCC complexes (n=1–3) between CCH and water have been theoretically investigated at the UB3LYP/6-311++G(2df,p)//UB3LYP/6-311G(d,p) level. The complexes with n=2–3 are cyclic structures with homodromic hydrogen-bond chain. The (H₂O)_n·CCH (n=1–3) complexes show increasing stabilities towards CCH- or H₂O-eliminations of 2.3, 5.8 and 7.6 kcal/mol and are energetically more stable than the corresponding (H₂O)_n·HCC complexes by 0.8, 2.7 and 3.4 kcal/mol, respectively, due to the charge-separation-enhanced hydrogen bonds within (H₂O)_n·CCH (n=2,3). Strong interactions between CCH and (H₂O)₂ and (H₂O)₃ clusters suggest special solvent effects of water on the chemical behavior of unsaturated radicals.     

MonC4n(n＝1－4)原子簇的合成和表征

Ｍｏ_ｎＣ_（４ｎ）（ｎ＝１－４）原子簇的合成和表征美国奥克里季实验室的ＣｈａｒｇｍｉｎｇＪｉｎ等化学家最近对Ｍｏ（ＣＯ）６蒸气激光（ＸｅＣｌ激光，波长３０８ｎｍ）光解生成的超细粒子进行了结构鉴定和性质分析。这些粒子直径小于１μｍ，利用负离子质谱可确定...     

Stable Structure and Characteristic Spectroscopy of(CH3COCH3)n(n=1～7)Clusters

The stable acetone molecule clusters have been studied by using Beeke's threeparameter(B3LYP)density functional theory(DFT)with standard 6-31G(d)basis set.The calculated results show that the optimal structures of acetone clustets are cyclic and the cycles become larger and larger with the increase of cluster size.The strongest vibration peaks for neutral clusters are C=O stretching vibration.The C=O stretching peaks of cyclic acetone clusters split into double ones when n≥3,the frequencies are red-shifted and corresponding intensities increase with the increase of cluster size.     

(HAlNH)n(n=2～3)环状化合物的结构特征

用自洽场理论 (HF)和密度泛函理论 (DFT)的B3LYP方法 ,在 6 31G 的水平上对化合物(HAlNH) 2 和 (HAlNH) 3 的几何结构进行优化 ,并分别与环丁二烯C4 H4 和苯分子C6H6的结构和成键方式进行比较。以B3LYP STO 3G方法讨论其分子轨道波函数 (Ψ)。结果表明 :C4 H4 和 (HAlNH) 2 均为D2h对称 ,前者为长方形结构 ,形成两个孤立的π键 ;而后者为菱形结构 ,形成一个π44键。C6H6和 (HAlNH) 3分子点群分别为D6h和D3h,并均形成一个π66键。成键原子对分子轨道的贡献不同 ,其中C原子是完全等价的 ,而Al和N原子各不相同 ,N原子比Al的贡献要大得多