Transition state geometry in radical abstraction reactions: comparison of interatomic distances in the intersecting parabolas and Morse curves models with quantum-chemical calculations

Interatomic distances in the transition state were estimated for the reactions of radical abstraction: H^· + H₂, H^· + HCl, H^· + CH₄, N^·H₂ + NH₃, HO^· + H₂O, HO₂ ^· + HOOH, and C^·H₃ + SiH₄. The calculation was performed by the quantum-chemical density functional method or coupled clusters method (QCH), as well as by the methods of intersecting parabolas (IPM) and Morse curves (IMM), using experimental data (activation energies and reaction enthalpies). The results of the latter two methods are close to the quantum-chemical calculation and differ only by the increment a: r(IPM or IMM) = a + r(QCH), where a = –4.5·10^–12 m for IPM and a = +1.9·10^–12 m for IMM.     

氮原子在Ni平坦和缺陷表面上的吸附和振动

 构造了氮－镍相互作用的5－参数Morse势，研究了氮原子在Ni（\r\n100），Ni（110）和Ni（111）平坦表面的吸附和振动，获得了氮原子\r\n在三个低指数表面的吸附位、吸附构型、结合能和本征振动等数据，计\r\n算结果与实验结果非常吻合．同时，与Ni（100）表面对比，系统研究\r\n了氮原子在Ni（510）台阶面的吸附和扩散．计算结果表明，氮原子在\r\n台阶下部形成最稳定的吸附态，台阶对下台面上扩散的氮原子形成捕获\r\n势，对上台面上扩散的氮原子形成反射势．     

Wigner function of the rotating Morse oscillator

We present an analytical expression of the Wigner distribution function (WDF) for the bound eigenstates of the rotating Morse oscillator (RMO). The effect of rotational excitation on the WDF on the quantum phase space has been demonstrated. This effect has been visualized by a series of contour diagrams for given rovibrational quantum states. Rotations of the molecule have been proved to qualitatively and quantitatively change the Wigner function. As a result, the most probable distance between atoms in a rotating molecule changes, and depends on the parity of the vibrational quantum number. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

Morse Index of Multiple Blow-up Solutions to the Two-Dimensional Sinh-Poisson Equation

In this paper we consider the Dirichlet problemwhere $\rho$ is a small parameter and $\Omega$ is a $C^2$ bounded domain in $\mathbb{R}^2$. In [1], the author proves the existence of a $m$-point blow-up solution $u_\rho$ jointly with its asymptotic behaviour. We compute the Morse index of $u_\rho$ in terms of the Morse index of the associated Hamilton function of this problem. In addition, we give an asymptotic estimate for the first $4m$ eigenvalues and eigenfunctions.     

原子氧在Ru低指数面及(110),(111)台阶面上的吸附

利用原子与表面簇合物相互作用的5参数Morse势方法(简称5-MP)系统地研究了O-Ru低指数面及Ru(1120),(1121)台阶面体系,获得了吸附几何、结合能、振动频率等临界点特性,所得相关数据与实验结果非常吻合.并且通过理论计算及原子吸附态振动指纹的遗传、遗变特性预言了氧原子在Ru(1121)台阶面的吸附.本文认为氧原子在HCP晶格的金属表面上的吸附倾向于三重位.     

Spectral density distribution moments of a Hamiltonian of N coupled Morse oscillators: The large‐N limit

The expressions for moments of spectral density distribution of a Hamiltonian representing a system of N coupled Morse oscillators are reduced to the large‐N limit. The effect of the values of coupling constants on the spectral density distribution is analyzed. For the values of coupling constants within the pertinent range for real molecules, the relations between moments appear to be close to those for a Gaussian distribution. Outside this range, the deviations from the normal distribution are substantial. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002     

E ⊗ ϵ Jahn–Teller anharmonic coupling for an octahedral system

The coupling between doubly degenerate electronic states and doubly degenerate vibrations is analyzed for an octahedral system on the basis of the introduction of an anharmonic Morse potential for the vibronic part. The vibrations are described by anharmonic coherent states and their linear coupling with the electronic states is considered. The matrix elements of the vibronic interaction are built and the energy levels corresponding to the interaction Hamiltonian derived. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002     

Nontrivial Solutions for p-Laplace Equations with Right-Hand Side Having p-Linear Growth at Infinity

ABSTRACT

The existence of a nontrivial solution for quasi-linear elliptic equations involving the p-Laplace operator and a nonlinearity with p-linear growth at infinity is proved. Techniques of Morse theory are employed.     

Topological conjugacy of constant length substitution dynamical systems

Primitive constant length substitutions generate minimal symbolic dynamical systems. In this article we present an algorithm which can produce the list of injective substitutions of the same length that generate topologically conjugate systems. We show that each conjugacy class contains infinitely many substitutions which are not injective. As examples, the Toeplitz conjugacy class contains three injective substitutions (two on two symbols and one on three symbols), and the length two Thue–Morse conjugacy class contains twelve substitutions, among which are two on six symbols. Together, they constitute a list of all primitive substitutions of length two with infinite minimal systems which are factors of the Thue–Morse system.