氢同位素氚水T2O(X1A1)的解析势能函数

获得T₂O(X¹A₁)解析势能函数的主要困难在于Born-Oppenheimer近似下T₂O(X¹A₁)与H₂O(X¹A₁)势能函数的不可区分性.然而,在Born-Oppenheimer近似下,分子势能函数实际上是键长、键角这些 关键词： 2O(X¹A₁)')" href="#">T₂O(X¹A₁) 同位素效应 解析势能函数     

三角对称晶场下d8电子组态的EPR参量的普遍公式及其应用

本文考虑到d⁸电子组态中所有自旋三重态和自旋单态对基态的影响,用高阶微扰法导出了d⁸电子组态在三角对称晶场下光谱和基态EPR普遍公式。发现在三角对称晶场下,d⁸电子组态离子的g_⊥ > g_‖或g_⊥ < g_‖和D > 0或D < 0是以立方对称晶场为界,晶体中顺磁离子的配体沿C₃轴伸长或压缩所致。利用所得公式计算了NiCl₂和NiSiF₆·6H₂O晶体的EPR参量,其结果与实验吻合较好。     

N2O异构体结构与解析势能函数

在B3P86/cc-PVTZ水平上,对N₂O异构体进行优化计算,得出N₂O基态的单重态能量最低,其稳定构型为C_∞v构型,平衡核间距R₁=0.1121nm,R₂=0.1177nm,α＝180°,能量为-185.1188a.u.同时计算出基态的简正振动频率ω₁(Π)=601.5010 cm^{关键词： 异构体 多体项展式理论 解析势能函数}     

径向积分的解析计算

本文阐明的方法能方便地求出径向积分ⁿ₁^l₁F_Lⁿ₂^l₂(q)≡∫₀^∞> (R_n1^l₁(αr)jL(Kr)R_n2^l₂(αr)r²dr(q≡(K)/(α))的解析表达式。文中给出了L=0,1,2情况下各个径向积分的解析式,同时还以多重求和的形式络出了对各种量子数L,n₁,l₁,n₂,l₂适用的径向积分表达式。     

AlO2和Al2O分子的结构与解析势能函数

运用密度泛函理论的B3LYP方法在6-311++G^**水平上,对AlO₂,Al₂O分子的结构进行了优化计算,得到AlO₂,Al₂O分子的稳定结构都为D_∞h构型.　AlO₂电子态为X²Π_u,平衡核间距R_Al-O关键词： 2')" href="#">AlO₂ 2O')" href="#">Al₂O Murrell-Sorbie函数 多体项展式理论     

基态O和D原子的低能弹性碰撞及OD（X2Π）自由基的准确解析势与分子常数

利用CCSD（T）理论及相关一致五重基aug-cc-pV5Z构建了OD（X²Π）自由基的相互作用势, 计算了这个自由基的光谱常数D₀, D_e, R_e, ω_e, ω_eχe及B_e, 其值分别为44574,46225?eV,009702 nm, 2724923,453534和100096 cm^-1, 均与实验结果相符很好. 利用这一相互作用势, 在绝热近似下通过数值求解双原子分子核运动的径向薛定谔方程, 找到了J=0时OD（X²Π）自由基存在的全部23个振动态, 完整地求出了每一振动态的振动能级、振动经典转折点、惯性转动常数和离心畸变常数, 其值与实验结果相当一致. 在10×10^-11—10×10^-3a.u.的能量范围内研究了基态O和D原子沿OD（X²Π）势能曲线的弹性碰撞, 计算了这一碰撞的总截面和各分波截面, 分析了各分波截面对总截面的不同贡献. 结果表明: 总截面的形状主要由s分波截面决定, 尽管直到l = 12的其他分波截面均有形状共振存在, 但由于其强度较弱, 大都湮没在较强的s分波截面中. 关键词： 弹性碰撞 总截面 形状共振 光谱常数     

最短轨道凝聚模型的相变

应用重整化群计算最短轨道模型的生长几率分布{P_α,i}及其构型权重C_α(2×2原胞和3×3原胞),从而得出多分形热力学的配分函数Z(q,L),自由能F(q,L),能量E(q,L),比热c(q,L)和广义维数D_q,结果表明该模型在q=q_c≈0处发生相变,即当q < q_c时,生长几率分布{P_α,i}不具有多分形性质。     

确定等价电子杨盘基的等概率比对方法

给出了等价电子正则杨盘T^［λ］_ig的基本对称算子、完全对称算子概念,同时给出了这些对称算子作用于任一Slater函数_i所产生的根态、生成态概念.由正交归一化杨盘T^［λ］_ie的纵置换算子A^［λ］_ie的构造规则,给出了A^［λ］_ie中存在的对称算子和确定T^［λ］_ie的等概率比对方法,从而基本避免了牵涉到许多算子的极其复杂的代数,给出了求解N值较大的电子系统杨盘基问题的新方法. 关键词： 正则杨盘 对称算子 根态 等概率比对方法     

用耦合簇理论及相关一致五重基研究SiH$lt;sub$gt;2$lt;/sub$gt;($lt;i$gt;X$lt;/i$gt;$lt;sup$gt;1$lt;/sup$gt;$lt;i$gt;A$lt;/i$gt;$lt;sub$gt;1$lt;/sub$gt;)自由基的解析势能函数

运用单双迭代三重激发耦合簇理论和相关一致五重基对SiH₂的基态结构进行了优化, 并在优化结构的基础上进行了离解能和振动频率的计算. 结果表明: SiH₂的基态为C_2v结构, 平衡核间距R_Si—H= 0.15163 nm, H—Si—H键的键角α=92.363°, 离解能D_e（HSi—H）=3.2735 eV, 频率ν₁（a₁）=1020.0095 cm^-1, ν₂（a₁）=2074.8742 cm^-1, ν₃（a₁）=2076.4762 cm^-1. 这些结果与实验值均较为相符. 对H₂的基态使用优选出的cc-pV6Z基组、对SiH的基态使用优选出的aug-cc-pV5Z基组进行几何构型与谐振频率的计算并进行单点能扫描, 且将扫描结果拟合成了解析的Murrell-Sorbie函数. 与实验结果及其他理论计算结果的比较表明, 本文关于SiH自由基光谱常数（D_e,R_e, ω_e, B_e, α_e和ω_eχ_e）的计算结果达到了很高的精度. 采用多体项展式理论导出了SiH₂（C_2v, X¹A₁）自由基的解析势能函数, 其等值势能图准确再现了它的离解能和平衡结构特征. 同时还给出了SiH₂（C_2v, X¹A₁）自由基对称伸缩振动等值势能图中存在的两个对称鞍点, 对应于SiH+H→SiH₂反应, 势垒高度为0.5084 eV. 关键词： 2')" href="#">SiH₂ Murrell-Sorbie函数 多体项展式理论 解析势能函数     

MC与$lt;i$gt;M$lt;/i$gt;$lt;sub$gt;$lt;i$gt;n$lt;/i$gt;+1$lt;/sub$gt;$lt;i$gt;AC$lt;/i$gt;$lt;sub$gt;$lt;i$gt;n$lt;/i$gt;$lt;/sub$gt;稳定性与电子特征的第一性原理研究

研究MC与M_n+1AC_n(M=Sc, Ti, V, Cr, Mn; A=Al, Si, P, S; n=1, 2, 3)结构的稳定性与电子特征有利于探究三元层状结构M_n+1AC_n稳定性的内在原因和设计新型M_n+1AC_n结构. 第一性原理计算研究表明, M-3d与C-2p轨道间的电子转移对MC与M_n+1AC_n 的形成焓有较大影响. 供电子能力较强的前过渡金属可以形成稳定的MC结构. 计算结果显示, MC结构是缺电子体系, 其趋向于与具有一定供电子能力的MA结构结合形成M_n+1AC_n. 与M₂PC和M₂SC 相比, M₂AlC和M₂SiC可以更为容易地被分离成二维 M₂C结构. 关键词： MAX相结构 第一性原理 电子结构 过渡金属碳化物     

The ΔNγ electromagnetic transition form factors GM(q) and GE(q)

A parameter-free, nonperturbative calculation of the ΔNγ electromagnetic transition amplitudes GM*(q2), GE*(q2), and the resonant multipole ratio REM(q2)≡E1+3/2(q2)/M1+3/2(q2) is performed in terms of the well-known nucleon isovector Sachs form factor GMV. Our methods are fully relativistic with conservation of the electromagnetic current guaranteed. We find that GM*(q2) decreases more rapidly than the nucleon dipole form factor when −q21 GeV2/c2 and that REM(q2) remains small even for very high four-momentum transfer implying that the perturbative QCD prediction REM(q2)→1 is purely asymptotic and is valid only for extremely high |q2|.     

Measurement of the slope parameter for the neutral pion spectrum in KL → πππ decay

The π⁰ spectrum in the K_L⁰ → 3π decay was measured using a wire chambers magnetic spectrometer. In the usual approximation, the matrix element can be expressed as: M² ≈ 1 + 2a₀(M_K/M_π²)(2T_π⁰−T_π⁰max) + a₁(M_K²/M_π⁴)(2T_π⁰−T_π⁰max)². We obtained a₀ = −0.282 ± 0.011 and a₁ consistent with zero.     

A new two-mode thermo- and squeezing-mixed optical field

We propose a new two-mode thermo-and squeezing-mixed optical field, described by the new density operator ρ=1-e~f-|g|~2 e~(ga~+b~+)e~(fa~+a)|0〉 f_(bb) 〈0| e~(g*ab), where |0〉_(bb) 〈0| is the b-mode vacuum, e ~(fa~+a)represents the thermo-field, and e~(ga~+b~+) indicates squeezing. The photon statistics for ρ is studied by virtue of the method of integration within ordered product(IWOP) of operators. Such a field can be generated when a two-mode squeezed state passes through a one-mode dissipation channel.     

Dominant role of the 2D Van Hove singularity on the Fermi surface and generalized susceptibility of the quasi-2D superconductor La2−xMxCuO4 (M = Sr, Ba, …)

The dominant role of the 2D van Hove saddle point singularity on the Fermi surface (FS) and generalized susceptibility, χ(q), in the quasi-2D superconductor La_2-xM_xCuO₄ is shown for varying compositions x of divalent additions M=Sr, Ba …. Dramatic topological changes in the FS with x indicate that composition can play the role of pressure in the classic work of Lifshitz. Very close correlations of large peaks in χ(q) with Fermi surface nesting features are found, along the Γ-X and Γ-N directions in the Brillouin zone, for varying x. The peak at X and N for x=0 which apparently drives, via a soft phonon mode, the transition from the bct to the orthorhombic phase is shifted to smaller q values. These results are consistent with the semiconducting behavior of La₂CuO₄ and superconductivity when stabilized with x>0 additions. Finally, orbital frequencies (areas) and masses are given which show the range required for de Haas-van Alphen or other experiments.     

磁共振碳谱研究:应用分子子图指数估计与预测卤代烃化学位移

系统研究了核磁共振碳谱(¹³C NMR)与化学位移规律及其定量构谱关系(QSSR).本文提出了一组含多元素组成的分子子图指数矢量(VMSG),并发现它与卤代烃化学位移(CSRX)有很好线性相关性.采用多元线性回归(MVLR)进行准确估计与预测,结果良好.     

Entropy of planar random surfaces on the lattice

We study planar random surfaces on a hypercubic lattice in two and three dimensions by Monte Carlo techniques. Our data are consistent with the formula n₀(A;C) A^b₀A, where n₀(A;C) is the number of planar random surfaces with area A and boundary C. We find b₀ = −1.4 ± 0.2, = 5.31 ± 0.03 (for d = 2) and b₀ = −1.5 ± 0.2, = 7.13 ± 0.05 (for d = 3). The values of b₀ disagree with those obtained from the Polyakov string model.     

Magnetic properties and percolation threshold in diluted B-spinel ZnCr2xAl2−2xS4: a study through high-temperature expansions

By making use of high-temperature series expansions (HTSE) of the correlation functions, we study the thermal and disorder variation of the short-range order (SRO) in the particular B-spinel ZnCr_2xAl_2−2xS₄. We developed the HTSE for the q-dependent static structure factor S(q) to the order 6 in reciprocal temperature including both the nearest- and next-nearest-neighbour interactions J₁ and J₂, respectively. Respecting the experimental fact that the broad diffuse peak of the neutron is situated at the particular wave vector q₀=[0 0 0.79] and is insensitive to the temperature for a given ratio of dilution x, we have estimated the thermal variation of J₁ and J₂ in the case of the pure compound.

The bond percolation threshold x_p of the ZnCr_2xAl_2−2xS₄ is determined by studying the disorder variation of the correlation length ξ. The x_p is considered as the concentration at which ξ vanishes. The obtained values are x_p=0.27 when only J₁ is considered and 0.23 when both J₁ and J₂ are taken into account.     

Comparison of band structure and superconductivity in FeSe_(0.5)Te_(0.5) and FeS

The isovalent iron chalcogenides,FeSe_(0.5)Te_(0.5) and FeS,share similar lattice structures but behave very differently in superconducting properties.We study the underlying mechanism theoretically.By first principle calculations and tightbinding fitting,we find the spectral weight of the d_(X~2-Y~2) orbital changes remarkably in these compounds.While there are both electron and hole pockets in FeSe_(0.5)Te_(0.5) and Fe S,a small hole pocket with a mainly d_(X~2-Y~2) character is absent in FeS.We find the spectral weights of d_(X~2-Y~2) orbital change remarkably,which contribute to electron and hole pockets in FeSe_(0.5)Te_(0.5) but only to electron pockets in FeS.We then perform random-phase-approximation and unbiased singular-mode functional renormalization group calculations to investigate possible superconducting instabilities that may be triggered by electron-electron interactions on top of such bare band structures.For FeSe_(0.5)Te_(0.5) ,we find a fully gapped s~±-wave pairing that can be associated with spin fluctuations connecting electron and hole pockets.For Fe S,however,a nodal dxy(or d_(x~2-y~2) in an unfolded Broullin zone)is favorable and can be related to spin fluctuations connecting the electron pockets around the corner of the Brillouin zone.Apart from the difference in chacogenide elements,we propose the main source of the difference is from the d_(X~2-Y~2) orbital,which tunes the Fermi surface nesting vector and then influences the dominant pairing symmetry.     

核磁共振碳谱研究:烷烃化学位移和(CSS)与分子路径指数矢量(VPM)

系统研究了核磁共振碳谱和化学位移规律及其定量构谱关系(QSSR).本文研究了一组十元素分子路径指数矢量VPM,并发现它与烷烃化学位移和CCS有良好线性相关性.采用多元线性回归进行准确估计与预测,结果优良.     

Generalized Einstein manifolds

A Finslerian manifold is called a generalized Einstein manifold (GEM) if the Ricci directional curvature R(u,u) is independent of the direction. Let F⁰(M, g_t) be a deformation of a compact n-dimensional Finslerian manifold preserving the volume of the unitary fibre bundle W(M). We prove that the critical points g₀ F⁰(g_t) of the integral I(g_t) on W(M) of the Finslerian scalar curvature (and certain functions of the scalar curvature) define a GEM. We give an estimate of the eigenvalues of Laplacian Δ defined on W(M) operating on the functions coming from the base when (M, g) is of minima fibration with a constant scalar curvature H admitting a conformal infinitesimal deformation (CID). We obtain λ ≥ H/(n − 1) (Δf = λf). If M is simply connected and λ = H/(n − 1), then (M, g) is Riemannian and is isometric to an n-sphere. We first calculate, in the general case, the formula of the second variationals of the integral I (g_t) for G = g₀, then for a CID we show that for certain Finslerian manifolds, I″(g₀) > 0. Applications to the gravitation and electromagnetism in general relativity are given. We prove that the spaces characterizing Einstein-Maxwell equations are GEMs.