分子中的电子能谱

在轨道近似理论中,从原子体系的电子组态求相应所包含的各种谱项~(2s+1)L一般是利用Russell-Saunder偶合方法。对于非等价电子,总轨道角动量L和多重度S都可以通过矢量偶合的三角形规则得到,然后再互相组合成所有可能的谱项。对于等价电子,由于有Pauli原理的限制,某些谱项要消失掉,因此往往先由相应组态列出所有可能的简并态(指不存在电子相互作用时),从具有最大总轨道角动量的态开始分别一一     

碰撞能量对反应Sr＋HF转动取向的影响

在推广LEPS势能面上,用经典轨线方法,研究了反应碰撞能量对反应Sr＋HF的转动取向的影响.计算结果与产物轨道角动量模型进行比较.计算结果表明,随着碰撞能量的增加,产物转动取向越强烈.     

等价组态j-j偶合谱项的导出

在多电子原子中,将原子的状态与电子的状态相联系的方法通常有两种,一种是将原子的总轨道角动量L和总自旋角动量S偶合得到原子的总角动量J,这种偶合方式称为L-S偶合;另一种是将每个电子的轨道角动量与自旋角动量偶合先得到每个电子的总角动量j,然后再将各电子的总角动量偶合得到原子的总角动量J,这种偶合方式称为j-j偶合。实际上,L-S偶合或j-j偶合都是一种近似方法,而且是两种极端     

完全活性空间组态相互作用能量的拟合和外推

完全活性空间组态相互作用计算与完全活性空间中的活性电子数和活性轨道数有关,但完全活性空间组态相互作用的能量不是活性电子数和活性轨道数的单调递减函数,因此活性轨道数和活性电子数不能用来外推完全活性空间组态相互作用的能量。为此,我们定义了一个新的变量:活性空间中的最大未占满轨道数。我们对一系列单重态、双重态和三重态分子进行了完全活性空间组态相互作用的计算,并利用活性空间中的活性电子数和最大未占满轨道数这两个变量,对这些基态能量进行了拟合和外推,拟合的均方根误差都在10~(-6)数量级。外推能量的精度优于MP4,对小分子体系,其精度高于CCSD。外推的完全的组态相互作用(FCI)能量值和实际计算的FCI值也很接近。另外,我们还利用外推能量来优化双原子分子的平衡键长,并计算谐振频率,其精度优于CASSCF。     

轨道角动量本征值的解法

本文利用阶梯算符代替一般教科书中的角动量算符求解轨道角动量的本征值,方法简单,物理意义明确。     

Fe~＋（~6D）催化N_2O和CH_4制取甲醇循环反应的理论探究

本文采用密度泛函理论（DFT）B3LYP与耦合簇（CCSD）方法,研究了气相中四重态和六重态势能面上Fe＋催化N2O和CH4制取甲醇的微观机理.运用分子轨道理论和自然键轨道理论（NBO）对反应势能面进行分析,并通过自旋-轨道耦合（SOC）计算,讨论了势能面的交叉情况和自旋翻转的可能性.对Kozuch提出的能量跨度模型引入系间窜越几率加以修正,使其适用于非绝热两态反应.用修正后的能量跨度模型计算了催化剂的转化频率（TOF）,同时确定了整个反应的决速态.     

Mn掺杂TiO_2(101)提高锂空电池阴极催化活性的第一性原理研究

本文基于密度泛函理论对TiO_2(101)和Mn_xTi_(1-x)O_2(101)作为锂空电池阴极催化材料进行了研究,发现其表面能够生成两种不同结构的Li_2O_2,进一步地研究了其中最稳定的生成结构并通过计算锂空电池首次充放电过程中的过电势来评价催化性能.结果表明,Mn掺杂进入Ti O_2(101)对充放电的过电势均有降低作用,深入分析发现掺杂Mn对TiO_2促进阴极催化反应的本质因素源于掺杂原子Mn的d态轨道的分布以及其平均能量.掺杂原子的d态轨道在费米能级处的峰态诱导了附近O的p态轨道,二者共同作用在Mn_xTi_(1-x)O_2(101)的总态密度的费米能级处形成多个新峰,改变了催化剂的导电方式.此外,由于掺杂原子Mn的d态轨道的平均能量高于Ti原子,使得O的p态轨道受到更多的激发,促使在Mn掺杂原子附近的氧空位形成能降低,为放电过程阴极催化反应的氧还原提供了更多的活性位点并且有利于氧气的吸附与还原.     

铁原子与氮分子间的相互作用——单侧双配位构型

用密度泛函理论的B3LYP/6-311+G(d)方法对单侧双配位FeN2体系(简记为S-FeN2)不同自旋多重度的稳定态、范德华力作用态和过渡态的多个电子态的几何结构、电子结构、能量和振动频率进行了计算比较研究. 结果表明, S-FeN2体系三种自旋态间, Fe—N 距离R1和N—N 距离R2值均比较接近; 能量最低的是15B2态, 相近态有15B1、13B1和13B2, 彼此能差约25 kJ·mol-1. 三重态电子结构复杂, 单重态能量普遍偏高; 基组态Fe原子与N2间存在强的σ-π电子对排斥而无有效轨道重叠和电子转移, 其它组态4s13d7、4s13d64p1和3d74p1, Fe 和N2间发生σ(sd)-π和π-π*轨道重叠作用, 有少量电子转移, 体系呈现一定的离子性特征, 活化N2键长基本不超过120 pm. Fe 原子的电子单或双重被激发到由N2反键轨道为主要成分的分子轨道上时, 能使N2活化到单键程度甚至解离.     

含自旋轨道角动量耦合的耦合簇理论研究Zn2和Cd2二聚物的结构和光谱常数

在二分量相对论有效势和与之匹配的基组aug-cc-pvnz-pp (n=Q, 5)的基础上, 结合电子相关能的完备基组外推和四阶多项式拟合, 我们用含自旋轨道角动量耦合的耦合簇方法研究了Zn₂和Cd₂的结构和光谱常数. 尽管Zn₂和Cd₂的自旋轨道角动量耦合效应不及Hg₂的明显, 但还是把自旋轨道角动量耦合放在耦合簇迭代计算中, 以获得更加合理的理论结果. 通过比较, 理论结果与最新发表的实验结果或其他课题组的理论结果吻合得较好, 因此我们的理论计算将有助于丰富对Zn₂和Cd₂光谱性质的认识.     

FeO催化N_2与H_2反应生成NH_3的理论研究

本文采用密度泛函理论(DFT)UB3LYP方法对Fe O在基态五重态及第一激发态三重态势能面上催化N2与H2反应生成NH3的两态反应机理进行了研究,运用非共价作用预测反应位点,并运用分子中的原子(AIM)、电子定域化函数(ELF)及前线分子轨道理论对部分最低能量路径及最低能量交叉点(MECP)的机理进行了分析.计算了MECP处的自旋轨道耦合值(Hsoc)及系间窜越几率(PISC),通过应用能量跨度模型(energetic span model)确定了反应决速态,并从理论层面计算得到了反应中Fe O的催化转化频率(TOF).     

Stabilization of cluster dimers by centrifugal effects

The influence of finite angular momentum on the stabilization of an (Ar₁₃)₂ cluster dimer in Ar₁₃+Ar₁₃ collisions is investigated with simulations and simple models. Local optimizations on the effective rovibrational potentialenergy surface show that the centrifugal effects favor the mechanical stability of strongly prolate shapes. Molecular dynamics simulations are performed to study the collisions between two Ar₁₃ subclusters. At low collisional energy and large impact parameter, trapping of the product cluster in its dimer-like configuration is found. For larger values of the angular momentum, the “molecular” cluster is found to remain in this dimer-like structure during the time of the simulation. Intermediate values of the angular momentum allow isomerization into more compact structures, but still dimer-like. Again, the final product appears as dynamically stable. All of these dimer-like products have the thermodynamical properties of a rotating rigid-like body. At high energy, unimolecular evaporation rates from collisional heating are calculated and comparisons with the predictions of the Rice, Ramsperger, Kassel (RRK) and Weisskopf models are discussed. Qualitative agreement with the simulations, in particular concerning the evolution of the rates versus angular momentum is found. The rates decrease when angular momentum is increased, especially when the total energy is low. Thus, the enhancement of the stability of the product cluster by centrifugal effects has also a statistical character.     

Hamiltonian for rovibrational spectra of “hot” molecules

A variational method based on the determination of rotation as a state with a constant angular momentum has been proposed for calculating rovibrational energy levels of a polyatomic molecule. By using this method, energy level values can be determined for any vibrational state with arbitrary values of vibrational quantum numbers. This makes it possible to calculate the rovibrational energy levels of the “hot” molecules.     

Electron correlation and Hund's rule

It is suggested that simple electronic shielding effects induced by wave function antisymmetrization tend to govern the energy ordering of singlet and triplet terms within a two-electron atomic configuration. This approach gives rise to the following alternating rule: For the term of greatest orbital angular momentum within a configuration, the triplet lies below the singlet. The energy ordering reverses for the term of next highest angular momentum, and continues to alternate with each change of one unit in the orbital angular momentum until the term of lowest angular momentum is reached. In an examination of over 600 energy levels of the elements and their ions, the alternating rule reliably orders singlet–triplet energy levels in some 90% of the cases.     

A new method for the derivation of exact vibration-rotational kinetic energy operator in internal coordinates

An efficient angular momentum method is presented and used to derive analytic expressions for the vibration-rotational kinetic energy operator of polyatomic molecules.The vibration-rotational kinetic energy operator is expressed in terms of the total angular momentum operator J,the angular momentum operator J and the momentum operator p conjugate to Z in the molecule-fixed frame Not only the method of derivation is simpler than that in the previous work,but also the expressions ot the kinetic energy operators arc more compact.Particularly,the operator is easily applied to different vibrational or rovibrational problems of the polyatomic molecules by variations of matrix elements Gn of a mass-dependent constant symmetric matrix     

A time-dependent wave packet quantum scattering study of the reaction HD+ (v = 0 - 3;j0 = 1) + He --> HeH+(HeD+) + D(H)

Time-dependent wave packet quantum scattering (TWQS) calculations are presented for HD(+) (v = 0 - 3;j(0)=1) + He collisions in the center-of-mass collision energy (E(T)) range of 0.0-2.0 eV. The present TWQS approach accounts for Coriolis coupling and uses the ab initio potential energy surface of Palmieri et al. [Mol. Phys. 98, 1839 (2000)]. For a fixed total angular momentum J, the energy dependence of reaction probabilities exhibits quantum resonance structure. The resonances are more pronounced for low J values and for the HeH(+) + D channel than for the HeD(+) + H channel and are particularly prominent near threshold. The quantum effects are no longer discernable in the integral cross sections, which compare closely to quasiclassical trajectory calculations conducted on the same potential energy surface. The integral cross sections also compare well to recent state-selected experimental values over the same reactant and translational energy range. Classical impulsive dynamics and steric arguments can account for the significant isotope effect in favor of the deuteron transfer channel observed for HD(+)(v<3) and low translational energies. At higher reactant energies, angular momentum constraints favor the proton-transfer channel, and isotopic differences in the integral cross sections are no longer significant. The integral cross sections as well as the J dependence of partial cross sections exhibit a significant alignment effect in favor of collisions with the HD(+) rotational angular momentum vector perpendicular to the Jacobi R coordinate. This effect is most pronounced for the proton-transfer channel at low vibrational and translational energies.     

Internal energy and angular momentum effects on collision induced dissociation fragmentation patterns

Data are reported on the effects of internal energy and angular momentum on the collision induced dissociation CID fragmentation pattern. For the ions studied changes in the relative intensities of the fragment ions as internal energy varied were found to be larger than suggested by McLafferty and coworkers. Possible effects of angular momentum on the CID fragmentation pattern are discussed. The charge stripping spectra of the ions studied were found to be strongly dependent on initial energy and/or angular momentum. Hence care must be taken if charge stripping spectra are used to distinguish ion structures.     

A simple Hill-series approach to the linear potential

A simple Hill-series method is shown to yield accurate energy levels and expectation values for the linear potential for any angular momentum L and confinement radius R. The numerical results are verified by comparison with those from two hypervirial perturbation methods which are specially constructed to give accurate results at L = 0 for small R values and at L >?1 for R =?∞.     

Evaluation of the viscosity cross sections for elastic electron-atom collisions in krypton and xenon at low electron energies

The results of viscosity cross sections evaluations for elastic electron-atom scattering from rare gases krypton and xenon, carried out in the energy interval from 0.1 to 54.4 eV are presented and discussed. The evaluations are based on four independent sets of partialwave phaseshifts, one theoretical and three experimental, taken from literature. An analytical estimate for the contribution of all the terms not included in the summation, for truncation at any chosen value of the electron angular momentum, is derived. The validity of assumption of isotropic angular scattering is investigated in the energy range considered. The present results invariably show significant deviations from the values calculated with this assumption.     

Rotational distributions following van der Waals molecule dissociation: comparison between experiment and theory for benzene-Ar

The translational energy release distribution for dissociation of benzene-Ar has been measured and, in combination with the 6(1)(0) rotational contour of the benzene product observed in emission, used to determine the rotational J,K distribution of 0(0) benzene products formed during dissociation from 6(1). Significant angular momentum is transferred to benzene on dissociation. The 0(0) rotational distribution peaks at J=31 and is skewed to low K:Javerage=27, (K)average=10.3. The average angle between the total angular momentum vector and the unique rotational axis is determined to be 68 degrees. This indicates that benzene is formed tumbling about in-plane axes rather than in a frisbeelike motion, consistent with Ar "pushing off" benzene from an off-center position above or below the plane. The J distribution is very well reproduced by angular momentum model calculations based on an equivalent rotor approach [A. J. McCaffery, M. A. Osborne, R. J. Marsh, W. D. Lawrance, and E. R. Waclawik, J. Chem. Phys. 121, 1694 (2004)], indicating that angular momentum constraints control the partitioning of energy between translation and rotation. Calculations for p-difluorobenzene-Ar suggest that the equivalent rotor model can provide a reasonable prediction of both J and K distributions in prolate (or near prolate) tops when dissociation leads to excitation about the unique, in-plane axis. Calculations for s-tetrazine-Ar require a small maximum impact parameter to reproduce the comparatively low J values seen for the s-tetrazine product. The three sets of calculations show that the maximum impact parameter is not necessarily equal to the bond length of the equivalent rotor and must be treated as a variable parameter. The success of the equivalent rotor calculations argues that angular momentum constraints control the partitioning between rotation and translation of the products.     

Approximate Eigenvalue and Eigenfunction Solutions for the Generalized Hulthén Potential with any Angular Momentum

An approximate solution of the Schr?dinger equation for the generalized Hulthén potential with non-zero angular quantum number is solved. The bound state energy eigenvalues and eigenfunctions are obtained in terms of Jacobi polynomials. The Nikiforov–Uvarov method is used in the computations. We have considered the time-independent Schr?dinger equation with the associated form of Hulthén potential which simulate the effect of the centrifugal barrier for any l-state. The energy levels of the used Hulthén potential gives satisfactory values for the non-zero angular momentum as the generalized Hulthén effective potential.