PnN基态分子势能函数与热力学函数的理论计算

在Pu的相对论有效原子实势近似和N原子6—311G*全电子基函数下，用密度泛函B3LYP方法计算得到PuN分子基态X^6∑^+的结构与势能函数、力常数与光谱数据．同时计算得到PuN(g)分子在298K时的标准生成热力学函数ΔfH^0、ΔS^0和ΔfG^0，分别为—487．239kJ／mol、95．345J／mo1 K和—515、6661 kJ／mol．     

气固氢化反应热力学函数计算的近似方法

在有效原子实势近似下, 采用Gaussian 98程序及B3LYP/SDD密度泛函方法计算得到了ZrCo和ZrCoH分子的结构及能量E、熵S. 在此基础上, 近似以气态分子总能量中的振动能Ev代替该分子处于固态时的振动能量, 以电子运动和振动运动熵Sev代替分子处于固态的熵, 计算了不同温度下固态ZrCo与H2, D2, T2反应的热力学函数ΔH, ΔG, ΔS及氢化反应平衡压力, 导出了氢化反应温度与平衡压力的依赖关系. 计算得出ZrCoH, ZrCoD, ZrCoT的生成焓(398-598 K)分别为82.81 , 81.54和80.49kJ/mol, 与实验结果很好符合.     

AuZn和AuAl分子基态与低激发态的势能函数与热力学性质

用密度泛函理论B3LYP方法计算研究AuZn和AuAl分子基态与低激发态的结构与势能函数,导出分子的光谱数据.结果表明,AuZn和AuAl分子基态分别为X²Σ和X¹Σ,基态与低激发态的势能函数均可用Murrell-Sorbie函数来表达.AuZn分子低激发态a⁴Σ的绝热激发能为43529kJ/mol,AuAl分子低激发态a³Σ的绝热激发能为19991kJ/mol.计算固体AuZn和AuAl的内能和熵时,近似以气体分子的电子能和振动能代替固体分子的内能,用电子熵和振动熵代替固体分子的熵.在此近似下,计算得到AuZn和AuAl基态与低激发态固态分子生成反应热力学性质与温度的关系. 关键词： AuZn和AuAl B3LYP 热力学性质 势能函数     

PuNO分子结构与势能函数

本文运用密度泛函理论的B3LYP方法, 对钚原子应用LANL2DZ收缩价基函数, 氮、氧原子采用AUG-cc-pVTZ基函数, 分别对PuN, PuO, NO和PuNO体系进行了结构优化, 得到PuNO分子最稳构型为C_∞v (Pu-N-O), 电子态为⁶Σ^- (基态), 平衡核间距R_ON=0.12257 nm, R_NPu=0.22951 nm, 离解能D_e=8.10537 eV. 同时优化得到PuNO 分子存在两种亚稳态平衡构型分别为C_∞v (Pu-O-N), ⁶Σ^- (电子态)和C_s (O-Pu-N), A" (电子态), 以及分子体系相应的力学常数等. 拟合出PuN, PuO 和NO 分子的Murrell-Sorbie势能函数, 并使用多体项展式理论得到了PuNO分子的分析势能函数, 其等值势能图准确再现了PuNO分子最稳态构型及两个亚稳态构型的离解能和结构特性, 由此讨论了该分子体系的势能面静态特征.     

CoH生成热力学函数的量子力学计算

用B3LYP/SDD密度泛函方法计算了CoH的微观性质、CoH(g)、CoD(g)和CoT(g)的能量 (E)和熵(S) ,进而计算Co与H2 、D2 、T2 反应的ΔH 、ΔG 、ΔS .CoH分子的基电子状态为三重态 ,Re、D 0 、ωe 分别为 1.5 2nm、2 77.84kJ/mol和 132 1cm-1,与实验值基本一致 .在固态分子的E和S的计算中 ,以气态分子计算得到的总能量中的振动能Ev 代替固态能量 ,以总熵中的电子振动熵SEv代替固态熵 .导出了Co与氢同位素气体反应的ΔH 、ΔG 、ΔS 及平衡氢压力与温度的关系 .CoH的室温下平衡离解压力很低 ,表明CoH是一种稳定的氢化物 ,这与CoH分子的D 0 很大的实验事实一致 .     

Na2H的基态结构与势能函数

采用二次组态相关(QCISD)方法对NaH分子进行理论计算,得到它的几何结构、光谱性质,并拟合出它的Murrell-Sorbie势能函数.应用密度泛函(B3LYP)方法,在6-311G(3df,3pd)基组水平上对Na2H分子的基态结构进行优化,并用同样的基组对该分子进行了进一步的频率计算.结果发现Na2H分子的基态稳态结构为C2v构型,采用多体项展式理论导出了它的解析势能函数,其等值势能图准确再现了Na2H分子的结构特征和离解能.并报导了该分子对称伸缩振动等值势能图中存在的两个对称鞍点,对应于反应NaH Na→Na2H,活化能大约为14.56 kJ/mol.     

N2HF体系的结构与势能函数

用QCISD/6-311++G方法对N2HF体系进行优化得到其基态的平衡几何结构,属于C∞v构型,(1∑)态.计算表明N2HF分子是一特殊的van der Waals分子.应用多体项展式方法,导出了N2HF分子的解析势能函数,该函数正确的复现了N2HF体系的平衡结构及能量变化.势能面的静态特征表明:N2+HF→N2-HF反应是一个有阈能的反应,即是需活化能的反应,反应过程需克服144.21 kJ/mol的势垒.然后,就N2HF→N2+HF反应机理进行了讨论.     

PuH分子的X~8Σ~ 态的势能函数及热力学函数的从头计算

在考虑相对论有效原子实势(RECP)近似下,用QCISD方法计算了PuH分子基态X8Σ 的MurrellSorbie解析势能函数和热力学函数。Re,De,Be,αe,ωe,ωeχe的理论计算值,分别为2.28,1.2227eV,3.2334,0.07742,1146.2632,24.7514(cm-1)。还给出了PuH(g)在298.15-911K之间的生成热力学函数ΔH0,ΔS0,ΔG0和Cp的计算值     

PuH分子的X~8Σ~+ 态的势能函数及热力学函数的从头计算

在考虑相对论有效原子实势(RECP)近似下,用QCISD方法计算了PuH分子基态X8Σ+的MurrellSorbie解析势能函数和热力学函数。Re,De,Be,αe,ωe,ωeχe的理论计算值,分别为2.28,1.2227eV,3.2334,0.07742,1146.2632,24.7514(cm-1)。还给出了PuH(g)在298.15-911K之间的生成热力学函数ΔH0,ΔS0,ΔG0和Cp的计算值     

TiO基态 (X 3 Δr) 的势能函数与光谱常数

应用群论及原子分子反应静力学方法推导了TiO分子基态(X³Δ_r)的离解极限.采用不同的计算方法,包括密度泛函B3LYP,B3P86,BP86,B3PW91和MP2,MP4方法,结合不同基组计算了TiO分子基态的平衡核间距、能量和振动频率.研究表明,使用B3LYP方法,对O原子使用6-311+G基组,Ti原子使用6-311+ +G^**基组时计算得到的平衡几何结构、分子离解能和谐振频率与实验值符合得最好.使用优选出的方法和基组对T 关键词： TiO 势能函数 光谱常数 密度泛函理论     

Analytic Functions and Integrable Hierarchies–Characterization of Tau Functions

We prove the dispersionless Hirota equations for the dispersionless Toda, dispersionless coupled modified KP and dispersionless KP hierarchies using an idea from classical complex analysis. We also prove that the Hirota equations characterize the tau functions for each of these hierarchies. As a result, we establish the links between the hierarchies.     

GG Functions and their Relations to General Hypergeometric Functions

In this Letter, we present a new approach to the notion of hypergeometric functions.     

奇偶对相干态的维格纳函数和层析图函数

利用纠缠态η〉表象下的维格纳算符,重构了奇偶对相干态的维格纳函数.根据维格纳函数在相空间中随变量ρ和γ的变化规律,讨论了奇偶对相干态的非经典性质和量子干涉效应.研究发现,奇偶对相干态总呈现非经典性质,并且当q取奇数时,奇偶对相干态更容易出现非经典性质.奇偶对相干态的量子干涉效应的显著程度与q取值有关,但对于q的同一取值,奇对相干态的量子干涉效应更为显著.利用纠缠态η〉表象下的维格纳算符Δ1,2(ρ,γ)和纠缠态η,τ1,τ2〉的投影算符之间满足的拉东变换,获得了奇偶对相干态的量子层析图函数.     

Incomplete Delta Functions

By applying projection operators to state vectors of coordinates, we obtain subspaces in which these states are no longer normalized according to Dirac's delta function but normalized according to what we call incomplete delta functions. We show that this class of functions satisfy identities similar to those satisfied by the Dirac delta function. The incomplete delta functions may be employed advantageously in projected subspaces and in the link between functions defined on the whole space and the projected subspace. We apply a similar procedure to finite-dimensional vector spaces for which we define incomplete Kronecker deltas. Dispersion relations for the momenta are obtained and sums over poles are defined and obtained with the aid of differences of incomplete delta functions.     

Asymptotic Behaviour of Spectral Functions and Singularities of Wightman Functions and Field Commutators

Singularties of Wightman functions and field commutators are studied in localizable and nonlocalizable cases including the spectral behaviour σ(q²) = exp (αq²), α > 0.     

Slippery Wave Functions

Superfluids and superconductors show a very surprising behavior at low temperatures. As their temperature is reduced, materials of both kinds can abruptly fall into a state in which they will support a persistent, essentially immortal, flow of particles. Unlike anything in classical physics, these flows produce neither friction nor resistance. A major accomplishment of Twentieth Century physics was the development of an understanding of this very surprising behavior via the construction of partially microscopic and partially macroscopic quantum theories of superfluid helium and superconducting metals. Such theories come in two parts: a theory of the motion of particle-like excitations, called quasiparticles, and of the persistent flows itself via a huge coherent excitation, called a condensate. Two people, above all others, were responsible for the construction of the quasiparticle side of the theories of these very special low-temperature behaviors: Lev Landau and John Bardeen. Curiously enough they both partially ignored and partially downplayed the importance of the condensate. In both cases, this neglect of the actual superfluid or superconducting flow interfered with their ability to understand the implications of the theory they had created. They then had difficulty assessing the important advances that occurred immediately after their own great work. Some speculations are offered about the source of this unevenness in the judgments of these two leading scientists.     

Plasma Transfer Functions

The concept of transfer function which is so valuable for lumped dynamical systems is developed for plasma problems. Methods of construction of transfer functions for problems with boundary excitation as well as internal excitation are discussed.     

矢量的表意功能

矢量的方向性特征很容易在教学实践中被忽视，甚至在矢量的表述中也常会有学生不能完整地体会其表意功能，而造成此种尴尬的根本缘由是教师对矢量的表意功能缺乏应有的教学关注。本文截取教学实践中的片段而作理性剖析，意在引发应有的关注。     

Correlation Functions, Cluster Functions, and Spacing Distributions for Random Matrices

The usual formulas for the correlation functions in orthogonal and symplectic matrix models express them as quaternion determinants. From this representation one can deduce formulas for spacing probabilities in terms of Fredholm determinants of matrix-valued kernels. The derivations of the various formulas are somewhat involved. In this article we present a direct approach which leads immediately to scalar kernels for the unitary ensembles and matrix kernels for the orthogonal and symplectic ensembles, and the representations of the correlation functions, cluster functions, and spacing distributions in terms of them.     

Generalized q-Modified Laguerre Functions

In this paper we define a new q-special function A _n (x, b, c; q). The new function is a generalization of the q-Laguerre function and the Stieltjes–Wigert function. We deduced all the properties of the function A _n (x, b, c; q). Finally, lim _q1 A _n ((1 – q)x, –, 1;q) gives L _n ^(,)(x,q), which is a -modification of the ordinary Laguerre function.