Xizhang Yi

Lie algebraic method for vibrational and rotational transitions in inelastic collisions of a molecule with a solid surface

Abstract The vibrational and rotational transitions of a diatomic molecule in inelastic gas-surface scattering have been studied using the Lie algebraic approach of Alhassid and Levine [Phys. Rev. A 18 (1978) 89]. We have build a Hamiltonian describing the molecule-surface scattering and used it to construct a dynamical Lie algebra h 6 . The expressions for the wavefunction of the system near the surface ( z 2~ 0) are explicitly obtained. All the internal rotational and vibrational modes of a diatomic molecule and their coupling have been taken into account in the theoretical model. This wavefunction is applied to compute analytically the transition probabilities from an initial-vibrational state to another final one, for a model problem of H 2 scattering from the LiF(001) surface. The computed probabilities are in good agreement with those obtained using an accurate coupled-channel method.

A functional theoretical approach to the electrical double layer of a spherical colloid particle

Abstract By employing the iterative method in functional analysis, the governing Poisson–Boltzmann equation of a spherical colloid particle that is based on the so-called Gouy–Chapman–Stern model has been solved under general potential condition. The solution of the potential in the second iteration is a function of the distance from the center of the particle with the concentration of ions, the temperature of system and the particle charge as parameters. From this solution the radius and the surface potential of a particle have been defined and the corresponding values have been estimated with the help of the Newtons iterative method. Based on the equivalent condenser model with the same center of the particle, the correlation among the electric double layer thickness, the radius and the surface potential has been established. The analysis of the quartic equation of the thickness shows that it has a sole positive real root which is much more reasonable than the Debye reciprocal length from the Debye–Huchel approximation to represent the thickness. The calculation of the thickness can be much simplified in case of a higher concentration of ions or a higher particle charge.

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.

A dynamical Lie algebraic mehtod for quantum reactive scattering

The dynamical Lie algebraic method is used to describe the quantum reactive scattering. For the collinear exchange reaction A+BC→AB+C, an analytical expression for the reactive transition probability, which involves the main dynamic parameters of the system, is explicitly given. Numerical test calculations are carried out for the collinear reaction scattering H+H2 (n = 0)→H2 (n’ = 0)+H. The results show that the dynamical Lie algebraic method is very efficient for computing reaction probabilities.

Dynamical Lie algebraic approach to rotationally inelastic scattering of molecules from surfaces

Abstract This paper describes a dynamical Lie algebraic method that we have developed in the application of the theory of Alhassid and Levine [Phys. Rev. A 18 (1978) 89] to rotationally inelastic molecule–surface scattering. Transition probabilities and their dependence on main dynamics variables of the collision system can be given analytically. An application of the method to direct rotationally inelastic scattering of NO molecules from a static, flat Ag(111) surface is made. Calculations performed for this model system yield snapshots of the probability current density and those of the rate of change of probability density that provide an insight into the intimate details of the scattering dynamics in time. The results show that this method is efficient and more useful to the inelastic scattering problems.

Statistical mechanics of rotationally inelastic molecule–surface scattering in the dynamical Lie algebraic method

The dynamical Lie algebraic method is used for the description of statistical mechanics of rotationally inelastic molecule–surface scattering. A main advantage of this method is that it can not only give the expression for evolution operator in terms of the group parameters, but also provide the expression for the density operator for a given system. The group parameters may then be determined by solving a set of coupled nonlinear differential equations. Thus, the expressions of the statistical average values of the translational-to-rotational energy transfer, the interaction potential, and their dependence on the main dynamic variables for the system are derived in terms of the density operator formalism in statistical mechanics. The method is applied to the scattering of NO molecules from a static, flat Ag(111) surface to illustrate its general procedure. The results demonstrate that the dynamical Lie algebraic method can be useful for describing statistical dynamics of gas–surface scattering.

Statistical dynamics in rotationally inelastic gas-surface scattering: dynamical Lie algebraic method

Abstract A dynamical Lie algebraic approach to statistical dynamics of the rotationally inelastic gas-surface scattering is described. This method is applied to the study of the scattering of NO from Ag( 1 1 1 ) surface. Statistical average values of some physical observables, such as the translational-to-rotational (T→R) energy transfer and the interaction potential, and their dependence on various dynamic variables of the system are given analytically. The calculations predict a strong dependence of the average energy transfer and average interaction potential on temperature and the incident translational energy. The results imply that the dynamical Lie algebraic method appears to have a wide range of validity for describing the statistical dynamics of gas-surface scattering.

An Application of Functional Analysis Method to the Potential of Electrical Double Layer for Spherical Micelles

With the help of the iterative method in functional analysis theory based on the Gouy–Chapman model in the colloid and interface chemistry an analytic solution of the potential of electrical double layer of spherical micelles has been obtained. This method has eliminated the restriction that the Poisson–Boltzmann equation, which represents the distribution of the potential in the double layer, can be solved only under the condition of zeψ≪kT so far. The connections between the present results and those from Verwey and Overbeeks previous work have also been discussed. Our approach provides a simple but effective method for the calculation of the potential of electrical double layer under general potential condition.

A THEORETICAL TREATMENT FOR THE DYNAMICS OF NEAR-RESONANT CHARGE EXCHANGE IN GAS-SURFACE SCATTERING

Abstract A new approach for solving the problem of the dynamics of near-resonant charge exchange occurring in gas-surface collisions is presented for two electronic state system. This theory is based on Michas common eikonal formalism which gives the evolution of the transition amplitudes and the nuclear trajectories. In this new theoretical treatment, the quadratic forms method in linear analysis is used for calculating the electronic transition amplitudes. The results show that a large part of the calculation can be carried out analytically. Since such a calculation only requires a small computational efforts, it is thus possible to carry out extensive parameter variation in an assumed potential function in order to fit calculations to experiments. This method was applied to scattering of Na atom from W(110) surface. The oscillatory behavior of transition probability with angular frequency w ( t ) is also analysed in detail and discussed.

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.