Application of the Lie algebraic approach to diffractionally and rotationally inelastic molecule–surface scattering

The Lie algebraic approach of Alhassid and Levine [Phys. Rev. A 18 , 89 (1978)] is applied to the molecule–surface scattering. Specially, the diffractionally and rotationally inelastic scattering of a diatomic molecule from a solid surface is dealt with. Within the framework of the close-coupling method, we construct a Hamiltonian for the scattering system and use it to generate a dynamical algebra h₆. By solving equations of motion for the group parameters, the scattering wave functions near the surface are obtained. Computed transition probabilities of diffractively and rotationally inelastic scattering of H₂ from LiF(001) surface with the use of Lie algebraic method are seen to agree well with the coupled-channel calculations. The Lie algebraic method thus appears to have a wide range of validity for describing the dynamics of gas–surface scattering. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 63: 981–989, 1997     

Statistical mechanics of energy transfer in gas–surface scattering: A dynamical Lie algebraic approach

The dynamical Lie algebraic (DLA) method is used to describe statistical mechanics of energy transfer in rotationally inelastic molecule–surface scattering. Statistical average values of an observable for the scattering system are calculated in terms of density operator formalism in statistical mechanics. Employing a cubic expansion procedure of molecule–surface interaction potential leads to generation of a dynamical Lie algebra. Thus these statistical average values as a function of the group parameters can be obtained analytically in this formulation. The group parameters can be found from solving a set of coupled nonlinear differential equations. The DLA method, which has no need for determination of transition probabilities in advance as made routinely in the calculation, offers an efficient alternative to the method for computing the statistical average values. This method is much less computationally intensive because most of calculations can be analytically carried out. The average final rotational energies and their dependence on the main dynamic variables and the average interaction potential are presented for the rotationally inelastic scattering of NO molecules from a flat, static Ag(111) surface. Direct comparison is made between the predictions of this model calculation and experiment. The model reproduces well the degree of rotational excitation and correlation between the average final translational and the average rotational energies. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001     

Statistical mechanics in rotationally inelastic scattering of molecules from surface within the dynamical Lie algebraic method

The dynamical Lie algebraic (DLA) method of Alhassid and Levine [Phys. Rev. A 18 (1978) 89] is applied to statistical mechanics in rotationally inelastic scattering of molecules from surfaces. Specifically, the method is generalized to include the motion of surface atoms, i.e., phonons. For given Hamiltonian and initial state, the set of constraints required to obtain the solution of the motion equations is determined by an algebraic procedure. It is furthermore found possible to derive the motion equations for the mean values of the constraints. Application of the method to the scattering of NO molecules from a Pt(1 1 1) surface is made. The mean values of the final energies of NO molecules scattered from the surface obtained using the DLA method are in good agreement with experimental results in qualitative trends. The DLA method thus appears to have a wide range of validity for describing the statistical mechanics of the gas-surface scattering.     

A dynamical Lie algebraic mehtod for quantum reactive scattering

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Quantum dynamics of dissociative adsorption of H_2 on Ni(100) using the dynamical Lie algebraic method

A dynamical Lie algebraic method has been applied to treating the quantum dynamics of dissociative adsorption of H_2 on a static flat metal surface. An LEPS potential energy surface has been used to describe the interaction of H_2 with Ni(100) surface. The dependence of the initial state-selected dissociation probability was obtained analytically on the initial kinetic energy and time. A comparison with other theoretical calculations and experiments is made. The results show that the method can be effectively used to describe the dynamics of reactive gas-surface scattering.     

Quantum dynamics of dissociative adsorption of H2 on Ni(100) using the dynamical Lie algebraic method

A dynamical Lie algebraic method has been applied to treating the quantum dynamics of dissociative adsorption of H₂ on a static flat metal surface. An LEPS potential energy surface has been used to describe the interaction of H₂ with Ni(100) surface. The dependence of the initial state-selected dissociation probability was obtained analytically on the initial kinetic energy and time. A comparison with other theoretical calculations and experiments is made. The results show that the method can be effectively used to describe the dynamics of reactive gas-sdace scattering. Project supported by the National Natural Science Foundation of China (Grant No. 19694033) and partially by the State Key Laboratory of Theoretical and Computational Chemistry of Jilin University (Grant No. 9801).     

将A-L理论推广到无限维李代数

为使由Alhassid与Levine所提出的动力学李代数方法（简称A－L理论）能适用于更多的散射体系，在h(∞)中引入了有效集合C（有限维）的概念．按照微扰理论的意义，C中的代数元所对应的群参量是较低次微扰的结果，而不属于C的代数元所对应的群参量则相当于较高次做扰所产生的修正结果．因此可以近似地利用C来代替h(∞)．这样，不仅简化了计算程序并且对于很多具有现实意义的散射过程的计算成为可能．     

Application of dynamical Lie algebraic method to atom–diatomic molecule scattering

The dynamical Lie algebraic approach developed by Alhassid and Levine combined with intermediate picture is applied to the study of translational–vibrational energy transfer in the collinear collision between an atom and an anharmonic oscillator. We find that the presence of the anharmonic terms indeed has an effect on the vibrational probabilities of the oscillator. The computed probabilities are in good agreement with those obtained using exact quantum method. It is shown that the approach of dynamical Lie algebra combining with intermediate picture is reasonable in the treating of atom–anharmonic oscillator scattering.     

An application of the dynamical Lie algebraic method to energy transfer of the collinear scattering system AB+CD

The dynamical Lie algebraic method has been applied to treat the V–V and T–V energy transfers in the collinear scattering system AB+CD. The expression for the vibrational transition probability, which contains the main dynamical parameters, is given analytically. By using this expression we probe into the V–V resonance and T–V resonance phenomena appearing in the process of energy transfer. We find that the transition probability of V–V resonance is in good agreement with that obtained using the resonant exchange hypothesis. Then the reliability of the resonant exchange hypothesis is confirmed. This revised version was published online in July 2006 with corrections to the Cover Date.     

反应碰撞的动力学李代数描述

提出一种李代数方法描述分子反应碰撞问题．给出了含有主要动力学参量的S-矩阵元、分子碰撞跃迁几率以及反应体系能量统计平均值随时间演化的解析表达式．讨论了一个简单排斥势场中的原子-双原子分子共线反应体系，以阐明这种新方法的要点。     

Dynamical Lie algebraic treatment for the A+BC scattering

We report the study of translational‐vibrational energy transfer in the A+BC scattering using the dynamical Lie algebraic approach combined with the intermediate picture. The rotational sudden approximation is applied to treat the rotational motion of the BC molecule, which is regarded as an anharmonic oscillator. The calculated results show that the transition probabilities increase with increasing rotational quantum number. Comparison with those obtained in the collinear collision of system A+BC manifests that the transition probabilities here increase indeed. © 2001 John Wiley & Sons, Inc. Int J Quant Chem 81: 214–221, 2001     

A+BC共线碰撞能量传递的动力学李代数结合中间绘景研究

在半经典近似下将动力学李代数方法和中间绘景结合应用于原子-双原子分子(非谐振子)共线碰撞中的平动-振动传能的研究。在群参量的一级近似下求解群参量的运动方程,进而确定时间演化算符。并以散射体系H₂+He为例,计算了H₂分子的振动跃迁几率,计算结果与精确量子力学计算结果符合得较好。     

Dissociative chemisorption of H2 on the Cu(110) surface: a quantum and quasiclassical dynamical study

Six-dimensional quantum dynamical and quasiclassical trajectory (QCT) calculations are reported for the reaction and vibrationally inelastic scattering of (v = 0,1,j = 0) H(2) scattering from Cu(110), and for the reaction and rovibrationally elastic and inelastic scattering of (v = 1,j = 1) H(2) scattering from Cu(110). The dynamics results were obtained using a potential energy surface obtained with density functional theory using the PW91 functional. The reaction probabilities computed with quantum dynamics for (v = 0,1,j = 0) were in excellent agreement with the QCT results obtained earlier for these states, thereby validating the QCT approach to sticking of hydrogen on Cu(110). The vibrational de-excitation probability P(v=1,j = 0 --> v = 0) computed with the QCT method is in remarkably good agreement with the quantum dynamical results for normal incidence energies E(n) between 0.2 and 0.6 eV. The QCT result for the vibrational excitation probability P(v = 0,j = 0 --> v = 1) is likewise accurate for E(n) between 0.8 and 1 eV, but the QCT method overestimates vibrational excitation for lower E(n). The QCT method gives probabilities for rovibrationally (in)elastic scattering, P(v = 1,j = 1 --> v('),j(')), which are in remarkably good agreement with quantum dynamical results. The rotationally averaged, initial vibrational state-selective reaction probability obtained with QCT agrees well with the initial vibrational state-selective reaction probability extracted from molecular beam experiments for v = 1, for the range of collision energies for which the v=1 contribution to the measured total sticking probability dominates. The quantum dynamical probabilities for rovibrationally elastic scattering of (v = 1,j = 1) H(2) from Cu(110) are in good agreement with experiment for E(n) between 0.08 and 0.25 eV.     

取代苯体系的二阶非线性光学性质:动力学李代数方法

提出了一种动力学李代数方法来研究取代苯体系的非线性光学性质. 对于给定的PPP模型(Pariser-Parr-Pople)哈密顿量, 生成了一个动力学李代数. 依据这些代数元构造出演化算子作为群参数的函数, 通过求解一组非线性微分方程能够得到这些群参数. 再按照统计力学中的密度算子公式给出取代苯分子体系偶极矩的统计平均值. 于是导出二阶极化率的表达式. 与其他量子力学计算结果比较, 表明这种动力学李代数方法在预言有机共轭分子的非线性光学性质上同样有用.     

Lie algebraic approach to the collinear collisions between two diatomic molecules

We present the quantum mechanical studies on the vibrational energy transfer in the inelastic collinear collision between two diatomic molecules using a dynamic Lie algebraic method of Alhassid and Levine [Phys. Rev. A 18 , 89 (1978)] within the semiclassical approximations. A dynamical algebra h₁₅ is formed and used for calculating the transition probabilities and the expectation values of the interaction potential. Under the first-order approximation of the group parameters, the selection rules for the transitions among the vibrational levels have been obtained. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 65 : 159–165, 1997     

Theoretical study of nonlinear triatomic molecular potential energy surfaces: Lie algebraic method

Triatomic molecular potential energy surfaces (PES) are obtained by using coherent state to take the classical limits of algebraic Hamiltonian. The algebraic Hamiltonian for bent tria-tomic molecules can be obtained using Lie algebraic method (the expansion coefficients are obtained by fitting spectroscopic data). This PES is applied to H2O molecule, and good results are obtained.     

Transformation of phase size distribution into scattering intensity

A practical method of calculating the small-angle scattering intensity and the density correlation function from the phase size distribution is presented for a sample with a random two-phase morphology. The correlation function can be calculated in terms of joint probability distribution functions of the phase size distributions of the two individual phases with information from the chord length distribution. The phase size distribution is approximated as a weighted sum of exponentials, which is then transformed analytically into the correlation function and hence the small-angle scattering for any combination of phase size distributions of the two phases. This represents an extension of the Debye method for materials with more complex phase size distributions. The inverse problem of calculating the phase size distributions from the small-angle scattering requires a thermodynamic model or simplifying approximation. An example of the reverse transformation is given for a nanoporous polymer thin film. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 3070–3080, 2004     

Commutator perturbation method in the study of vibrational–rotational spectra of diatomic molecules

The commutator perturbation method, an algebraic version of the Van Vleck–Primas perturbation method, expressed in terms of ladder operators, has been applied to solving the eigenvalue problem of the Hamiltonian describing the vibrational–rotational motion of a diatomic molecule. The physical model used in this work is based on Dunham's approach. The method facilitates obtaining both energies and eigenvectors in an algebraic way. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 77: 721–726, 2000     

Algebraic approach to the asymmetric rigid rotor

A pure algebraic treatment of the eigenvalue equation corresponding to the asymmetric top is presented. The algebraic method employs the Holstein–Primakoff bosonic realization of the angular momentum algebra. Explicit determination of the linear boson transformation coefficients of the eigenstates is carried out by means of the coherent states formalism. No reference to special functions is needed and a completely algebraic approach is achieved. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 77: 704–709, 2000