PuO分子X5Σ-态的势能函数及热力学函数的量子力学计算

在Pu的相对论有效原子实势近似和O原子6-311G^*全电子基函数下,用quadratic configuration interaction of singlely and doublely substitution(QCISD)方法计算了PuO分子基态X⁵Σ^-的Murrell-Sorbie解析势能函数和热力学函数,得到R_e,D_e,B_e,α_e,ω_关键词：     

榄香烯及其衍生物的计算化学研究I β-榄香烯13C NMR化学位移的理论计算

报道了抗癌新药β-榄香烯的¹³C NMR化学位移的量子化学计算.在分子力学MMX和量子化学RHF/6-31G^*或B3LYP/6-31G^*优化结构的基础上进行了两种规范变换方法GIAO和CSGT的Hartree-Fock和B3LYP (6-31G^*基组)的化学位移计算.并对计算结果进行了误差分析和线性相关分析.所有的这些结果中,采用GIAO规范变换方法都好于CSGT,而以GIAO-B3LYP/6-31G^*//B3LYP/6-31G^*计算的结果最好,RMS为4.3ppm,相关系数R²为0.998,SD为2.42 ppm.而GIAO-B3LYP/6-31G^*//MMX是一种能兼顾计算时间和计算精度的方法,其RMS、R²和SD分别为4.9、0.996和3.0 4 ppm.     

榄香烯及其衍生物的计算化学研究I β-榄香烯13C NMR化学位移的理论计算

报道了抗癌新药β-榄香烯的¹³C NMR化学位移的量子化学计算.在分子力学MMX和量子化学RHF/6-31G^*或B3LYP/6-31G^*优化结构的基础上进行了两种规范变换方法GIAO和CSGT的Hartree-Fock和B3LYP (6-31G^*基组)的化学位移计算.并对计算结果进行了误差分析和线性相关分析.所有的这些结果中,采用GIAO规范变换方法都好于CSGT,而以GIAO-B3LYP/6-31G^*//B3LYP/6-31G^*计算的结果最好,RMS为4.3ppm,相关系数R²为0.998,SD为2.42 ppm.而GIAO-B3LYP/6-31G^*//MMX是一种能兼顾计算时间和计算精度的方法,其RMS、R²和SD分别为4.9、0.996和3.0 4 ppm.     

氘代甲烷几何构型及物性的量子化学研究

用HF/6-31G^**、密度泛函方法B3LYP/31G^**、二级微扰MP2/6-31G^**、四级微扰MP4/6-31G^**方法对甲烷和氘代甲烷进行几何构型全优化,并将优化的结果与实验值进行比较.用上述4种方法对甲烷和氘代甲烷分子进行分子的振动基频计算.密度泛函、二级微扰、四级微扰优于HF/6-31G^**,尤其是密度泛函、四级微扰方法.密度泛函方法所用的机时远小于微扰方法.不同方法计算所得的氘代甲烷振动频率值与实验值的最大误差为10.4%,最小误差为2.0%.     

CrHn(n=0,+1,+2)分子及离子的势能函数

用原子分子反应静力学原理推导出CrHⁿ(n=0，+1，+2)的电子状态及其离解极限. 对H原子采用6-311++G^**基组，对Cr原子采用SVP(split valence polarization)全电子基组，用B3PW91方法计算了它们的平衡几何、电子状态，在此基础上分别计算CrH，CrH⁺的Murrell-Sorbie解析势能函数和CrH²⁺的解析势能函数及其对应的力常数、光谱参数，理论计算值与实验值和文献计算值符合较好. 从离解极限和通道解释了不同的势能函数形状. 计算表明：CrH⁺的势能曲线均具有对应于稳定平衡结构的极小点，说明CrH⁺可稳定存在. 而CrH²⁺离子的势能曲线对应于不稳定的排斥态，说明CrH²⁺是不稳定的. 关键词： n(n=0')" href="#">CrHⁿ(n=0 +2) 势能函数 光谱参数 稳定性     

电荷密度波超导体中的软声子和喇曼散射

基于Balseiro和Falicov的概念,我们用一个简单模型计算了电荷密度波(CDW)与超导共存系统中被电声子相互作用重整化的CDW振幅模式的谱函数A(ω),所得的A(ω)在ω≤2G(G为CDW带隙)区域有一个权重相当大的δ函数型的峰,而在ω>2(G²十△²)^1/2(△为超导能隙)区域是比较宽的连续谱,固定G,当△减少时峰的强度显著降低,但其位置仅有较小的变化;与此同时连续谱的权重增加,这些特点与Sooryakumar和Klein在电荷密度波超导体2H-Nbse₂中发现的喇曼出线的能隙模式的行为是一致的。 关键词：     

关于X射线衍射方程的Green函数解法

用傅氏积分解出在完整晶体下波动方程的Green函数,通过Green公式求出透射X射线波场D_h,D₀的表达式,并在入射波为平面波和球面波时,将得到的D_h,D₀值与其它作者的结果作了比较,也讨论了样品厚度与D_h,D₀的关系。 关键词：     

密度泛函方法对SiO分子基态（X 1Σ+）势能函数的研究

利用密度泛函B3P86方法,分别选用STO-3G,D95^**,6-311G,6-311++G,6-311++G^**,cc-PVTZ基组对SiO分子基态(X¹Σ⁺)进行结构优化计算.通过比较得出,cc-PVTZ基组为对SiO分子基态(X¹Σ⁺)进行结构优化最优基组的结论.使用密度泛函B3P86方法,选用cc-PVTZ基组进 关键词： B3P86 SiO 势能函数 光谱常数     

Si中D3d对称性态密度分布和缺陷对电子结构

本文考虑了晶体中总的电子态密度在低对称性下用点群不可约表示基函数分解的问题,并给出了Si中用D_3d群不可约表示基函数分解最近邻两原子总态密度的计算结果。结合在位势近似Koster-Slater格林函数方法,文中将计算结果用于Si中双空位和硫属元素杂质对(S₂⁰,Se₂⁰和Te₂⁰)缺陷态电子结构的讨论。讨论得到的结果是:与点缺陷和缺陷对的深缺陷态对称性相匹配的部分态密度的分布是相似的;在态密度对缺陷能级的驱赶作用下,S₂⁰等的A^s能级在A^s能级之上,双空位的E_g能级在E_u能级之上,这种情况与通常双原子分子成反键能级位置完全相反;所讨论的缺陷对的波函数在Bloch空间的分布情况与对应的点缺陷类似。 关键词：     

S2分子B″3Πu态的势能函数和光谱常数的理论研究

推导了S₂分子B″³Π_u态的合理离解极限.用Gaussian 94 QCISD(T)方法和6-311++G^**基组计算了S₂分子B″³Π_u以及X³Σ^-_g态的势能曲线.给出了S₂分子B″³Π_u态的Murrell-Sorbie势能函数和光谱常数.B″³Π_u与B³Σ^-_u态在排斥支重叠范围大；同时，B″³Π_u与X³Σ^-_g态有相同离解极限，因而，在吸引支有重叠.讨论了B″³Π_u与B³Σ^-_u和X³Σ^-_g态相互作用的特征. 关键词：     

Universal relation between Green functions in random matrix theory

We prove that in random matrix theory there exists a universal relation between the onepoint Green function G and the connected two-point Green function G_c given by N²G_c(z, w) = (∂²/∂z ∂w) log[(G(z) − G(w))/(z − w) + irrelevant factorized terms]. This relation is universal in the sense that it does not depend on the probability distribution of the random matrices for a broad class of distributions, even though G is known to depend on the probability distribution in detail. The universality discussed here represents a different statement than the universality we discovered some time ago, which states that a²G_c (az, aw) is independent of the probability distribution, where a denotes the width of the spectrum and depends sensitively on the probability distribution. It is shown that the universality proved here also holds for the more general problem of a hamiltonian consisting of the sum of a deterministic term and a random term analyzed perturbatively by Brézin, Hikami, and Zee.     

空间羣算符的矩阵元

本文首先通过对波失星直接乘积的分析指出,如果 ^*K″∈^*K?^*K′,则波矢峯G_k″可以有下面四种情况:A)G_k同G_k′,是G_k″的子峯,B)G_k=G_k′=G_k″,C)G_k″=G_s, D)G_s是G_k″的子峯。根据上述四种情况,分别考虑积分A=μ″^i″(k″)|f_μⁱ(k)|f_μ′^i′(k′)>的简约。并且证明,对所有四种情况,积分A的值均可由短阵U的矩阵元统一地表达出来。矩阵U是使可约表示Г′简约的转换矩阵,对四种情况,可约表示Г′分别是:A)(Г_kⁱ?Г_k′^i′)^(?),B)Гⁱ?Г_k′^i′,C)Г_k^i(s)?Г_k′^i′(s),D)(Г_k^i(s)?Г_k′^i′(s))^(?)。最后,利用准投影算符的方法,对矩阵U进行了计算,导出空间峯Wigner-Eckart定理的表式。     

管状和闭合磁畴壁的拓扑分类

本文从拓扑学角度,对管状磁畴壁和闭合磁畴壁静态结构的分类问题,做了统一处理。这两种磁畴壁的同伦类集合G_W⁽ⁿ⁾和G_W⁽ⁿ⁾,分别与S²→S²和S³→S²的n+1基点连续映射的相对同化类集合是一一对应的,因而构成同构于整数加群Z的群,分别称为n式管壁群和n式闭壁群。重新讨论了Slonczewski等人定义的“绕数”,找出了用它表征管壁 关键词：     

A general green function method for calculating electronic structure and vibrational modes at surfaces

We extend the (single-particle) Green function method for treating surface problems by (1) giving a simple analytical expression for the bulk Green function G₀⁺(ω) which is completely general, and (2) giving a new procedure for achieving self-consistency in electronic problems.     

Singular vectors of quantum group representations for straight Lie algebra roots

We give explicit formulae for singular vectors of Verma modules over U_q(G), where G is any complex simple Lie algebra. The vectors we present correspond exhaustively to a class of positive roots of G which we call straight roots. In some special cases, we give singular vectors corresponding to arbitrary positive roots. For our vectors we use a special basis of U_q(G ^-), where G ^- is the negative roots subalgebra of G, which was introducted in our earlier work in the case q=1. This basis seems more economical than the Poincaré-Birkhoff-Witt type of basis used by Malikov, Feigin, and Fuchs for the construction of singular vectors of Verma modules in the case q=1. Furthermore, this basis turns out to be part of a general basis recently introduced for other reasons by Lusztig for U_q(^-), where ^- is a Borel subalgebra of G.A. v. Humboldt-Stiftung fellow, permanent address and after 22 September 1991: Bulgarian Academy of Sciences, Institute of Nuclear Research and Nuclear Energy, 1784 Sofia, Bulgaria.     

Higher order field equations II; Limit properties of green's functions

In a previous paper wave propagation was studied according to a sixth-order partial differential equation involving a complex mass M. The corresponding Yang-Feldman integral equations (indicated as SM-YF-equations), were formulated using modified Green's functions G^M_R(x) and G^M_A(x), which then incorporate the partial differential equation together with certain boundary conditions. In this paper certain limit properties of these modified Green's functions are derived: (a) It is shown that for |M| → ∞ the Green's functions G^M_R(x) and G^M_A(x) approach the Green's functions Δ_R(x) and Δ_A(x) of the corresponding KG-equation (Klein-Gordon equation). (b) It is further shown that the asymptotic behaviour of G^M_A(x) and G^M_A(x) is the same as of Δ_R(x) and Δ_A(x) - and also the same as for D_R(x) and D_A(x) for t→ ± ∞, where D_R and D_A are the Green n's functions for the KG-equation with mass zero. It is essential to take limits in the sense of distribution theory in both cases (a) and (b). The property (b) indicates that the wave propagation properties of the SM-YF-equations, the KG-equation with finite mass and the KG-equation with mass zero are closely related in an asymptotic sense.     

Coupling effects in a photonic crystal microcavity with embedded semiconductor quantum dot

The present work investigates the effects of relevant parameters of InAs/GaAs quantum dot and photonic crystal slab-based microcavity on the QD–cavity coupling characteristics, in detail. We employ variational approach to find exciton state in QD and to find cavity modes we use the open source GME code. Calculations have performed in linear regime where excitons behave as bosons which correspond to the limit of low excitation. The dynamics of the system are studied using the first order correlation function (G⁽¹⁾(t,τ)). We will show how G⁽¹⁾ varies with time in both strong and weak coupling regimes. Our results indicate that the achieving of strong coupling regime is affected by the size of the quantum dot and how to engineer the photonic crystal microcavity to maximize the ratio of quality factor and mode volume.     

Einfaches Modell für monoatomare klassische Flüssigkeiten

A simple approximation for the conditional time-dependent pair distribution functionP(r′t ¦ rt) is proposed. With this approximation the van Hove-correlation-functionG _d (rt) is computed and compared with Ludwig's¹ computer results for liquid A1. Then we determine the velocity autocorrelationfunction ψ(t) under special assumptions for the particle motion. That function is compared with Rahman's² computer results for liquid Ar.     

原子的解析波函数——Ⅱ.第二周期元素的正常态原子与离子的解析波函数与能量积分的计算

我们在文献[1]中设计了一套五个参数的变分波函数用来计算了周期表中前面十个原子的能量,所得结果比过去一些作者用四参数波函数所算得的结果为好。我们在过去计算经验的基础上,另外找到了一套特别简单的解析波函数,其形式为1s电子:ψ₁(r)=N₁e^-μar,2s电子:ψ₂(r)=N₂[(μr)e^-μr-Ne^-μar],2p电子:ψ₃(r)=N₃(μr)cosθe^-μr,ψ₄(r)=N₄(μr)sinθe^iφ-μr,ψ₅(r)=N₅(μr)sinθe^-iφ-μr,式中的α与μ为变分参数;N₁,N₂,N₃,N₄,N₅为归一化因子;N为正交化系数。μ可用解析法来决定,因而只有一个参数α要由数值法来决定。我们用这样的波函数算出了第二周期元素的正常态原子和离子(共有八十几个原子态)的各电子的各种能量积分值及总能量值,并确定了波函数的最佳参数值。其结果与五参数波函数的计算结果相比,一般相差在万分之一至千分之一的范围内,并比最近有些作者用一种三参数波函数所算的结果还好。根据这些结果,我们还讨论了Slater近似计算法的可靠程度和适用范围。