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).     

A dynamical Lie algebraic mehtod for quantum reactive scattering

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Quantum dynamics of dissociative adsorption of H_2 and D_2:The time-dependent wave packet method

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Quantum dynamics of dissociative adsorption of H2 and D2: The time-dependent wave packet method

A time-dependent quantum wave packet method was used to study the dynamics of dissociative adsorption of H₂ and D₂ on a flat and static surface. The molecule-surface interaction is described using a modified London-Eyring-Polanyi-Sato (LEPS) type potential for the H₂/Ni(100) system. The three-dimensional (3-D) dissociation probabilities were calculated for different initial rovibrational states as a function of initial incident energies. Our results show that the dissociation of the diatomic rotational states whose quantum numbers satisfyj+m = odd is forbidden at low energies for the homonuclear H_z and D₂ due to the selection rule. The effect of the rotational orientation of diatoms on adsorption predicts that the in-plane rotation (m = j) is more favorable for dissociation than the out-of-plane rotation (m = 0). Enhanced dissociation for vibrationally excited molecules and the significant enhancement of the dissociation probability of H2 when compared to D₂ were explained reasonably in terms of quantum mechanical zero-point energies, the tunneling effect and the reflection from an activation barrier. Project supported by the National Natural Science Foundation of China (Grant No. 19694033) and partially by the Science Foundation for Overseas Chinese Scholars and Students, administered by the State Education Commission of China (Grant No. 1992), by the State Key Laboratory of Theoretical and Computational Chemistry of Jilin University at Changchun (Grant No. 98011, and by the Natural Science Foundation of Shandong Province (Grant No. Y96B03022)     

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.     

D_2在Ni(100)表面离解吸附的量子动力学研究

用量子含时波包法研究了Ｄ２在镍表面顶－桥位上离解吸附量子动力学．计算了不同入射动能及初始振转态的离解几率．讨论了分子的同核对称性、转动取向和振动激发对离解几率的影响，并与其他理论计算结果做了比较．     

Rotationally inelastic molecule–surface scattering: dynamical lie algebraic method

The rotationally inelastic molecule–surface scattering is analyzed using dynamical Lie algebraic method. We treat, by example, the simple model of the scattering of NO from a rigid, flat Ag(111) surface. The explicit expressions of transition probability and the probability current density are obtained. It is proved that dynamical Lie algebraic method can be useful for describing the scattering problems. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 76: 500–510, 2000     

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     

Application of Lie algebraic method to the calculation of rotational spectra for linear triatomic molecules

The Hamiltonian describing rotational spectra of linear triatomic molecules has been derived by using the dynamical Lie algebra of symmetry group U1(4) U2(4). After rovibrational interactions being considered, the eigenvalue expression of the Hamiltonian has the form of term value equation commonly used in spectrum analysis. The molecular rotational constants can be obtained by using the expression and fitting it to the observed lines. As an example, the rotational levels of v2 band for transition (02°0-0110) of molecules N2O and HCN have been fitted and the fitting root-mean-square errors (RMS) are 0.00001 and 0.0014 cm-1, respectively.     

Theoretical analysis of dissociative adsorption of H2O on Ni(100)

In conclusion, let us note the principal results of the calculation.

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     

Quantum wave packet study of N(2D) + H2 reactive scattering

N(²D) + H₂ → NH + H reaction at zero total angular momentum is studied by using a time dependent quantum wave packet method. State‐to‐state and state‐to‐all reactive scattering probabilities for a broad range of energy are calculated. The probabilities show many sharp peaks that ascribed to reactive scattering resonances. The probabilities for J > 0 are estimated by using the J‐shifting method. The integral cross sections and thermal rate constants are then calculated. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2006     

Adsorption and dissociation of the methanethiol (CH3SH) molecule on the Fe(100) surface

These contributions explore interaction modes between the methanethoil (CH₃SH) molecule and the Fe(100) surface via implementing accurate density functional theory (DFT) calculations with the inclusion of van der Waals corrections. We consider three adsorption sites over the Fe(100) surface, namely, top(T), bridge (B), and hollow (H) sites as potential catalytic active sites for the molecular and dissociative adsorption of the CH₃SH molecule. The molecular adsorption structures are found to occupy either B or T sites with former sites holding higher stability by 0.17 eV. The inclusion of van der Waals corrections refound to slightly alter adsorption energies. For instance, adsorption energies increased by ~ 0.18 and ~ 0.21 eV for B and T structure, respectively, in reference to values obtained by the plain generalized gradient approximation (GGA) functional. A stability ordering of the dissociation products was found to follow the sequence (CH₄, S) > (CH₃, S, H) > (─SCH_3, H) > (─CH₃, SH). The differential charge density distributions were examined to underpin prominent electronic contributing factors. Direct fission of C─S bond in the CH₃SH molecule attains exothermic values in the range 2.0 to 2.1 eV. The most energetically favorable sites for the surface-mediated fission of the thiol's S─H bond correspond to the structure where the ─SCH₃ and H are both situated on hollow sites with an adsorption energy of −2.43 eV. Overall, we found that inclusion of van der Waals functional to change the binding energies more noticeably in case of dissociative adsorption structures. The results presented herein should be instrumental in efforts that aim to design stand-alone Fe desulfurization catalysts.     

Quantum dynamics of dissociative chemisorption of CH(4) on Ni(111): Influence of the bending vibration

Two-dimensional, three-dimensional, and four-dimensional quantum dynamic calculations are performed on the dissociative chemisorption of CH(4) on Ni(111) using the multiconfiguration time-dependent Hartree (MCTDH) method. The potential energy surface used for these calculations is 15-dimensional (15D) and was obtained with density functional theory for points which are concentrated in the region that is dynamically relevant to reaction. Many reduced dimensionality calculations were already performed on this system, but the molecule was generally treated as pseudodiatomic. The main improvement of our model is that we try to describe CH(4) as a polyatomic molecule by including a degree of freedom describing a bending vibration in our three-dimensional and four-dimensional models. Using a polyspherical coordinate system, a general expression for the 15D kinetic energy operator is derived, which discards all the singularities in the operator and includes rotational and Coriolis coupling. We use seven rigid constraints to fix the CH(3) umbrella of the molecule to its gas phase equilibrium geometry and to derive two-dimensional, three-dimensional, and four-dimensional Hamiltonians, which were used in the MCTDH method. Only four degrees of freedom evolve strongly along the 15D minimum energy path: the distance of the center of mass of the molecule to the surface, the dissociative C[Single Bond]H bond distance, the polar orientation of the molecule, and the bending angle between the dissociative C[Single Bond]H bond and the umbrella. A selection of these coordinates is included in each of our models. The polar rotation is found to be important in determining the mode selective behavior of the reaction. Furthermore, our calculations are in good agreement with the finding of Xiang et al. [J. Chem. Phys. 117, 7698 (2002)] in their reduced dimensional calculation that the helicopter motion of the umbrella symmetry axis is less efficient than its cartwheel motion for promoting the reaction. The effect of pre-exciting the bend modes is qualitatively incorrect at higher energies, suggesting the necessity of including additional rotational and vibrational degrees of freedom in the model.     

Time-dependent quantum study of the kinetics of the H(2S) + FO(2II) OH(2II) + F(2P) reaction

Quantum mechanical wave packet calculations are carried out for the H((2)S) + FO((2)II) --> OH((2)II) + F((2)P) reaction on the adiabatic potential energy surface of the ground (3)A' triplet state. The state-to-state and state-to-all reaction probabilities for total angular momentum J = 0 have been calculated. The probabilities for J > 0 have been estimated from the J = 0 results by using J-shifting approximation based on a capture model. Then, the integral cross sections and initial state-selected rate constants have been calculated. The calculations show that the initial state-selected reaction probabilities are dominated by many sharp peaks. The reaction cross section does not manifest any sharp oscillations and the initial state-selected rate constants are sensitive to the temperature.     

Six-dimensional quantum dynamics of H2 dissociative adsorption on the Pt(211) stepped surface

Results of experimental studies, and theoretical calculations utilizing classical trajectories, have shown that dissociation of H2 on the Pt(211) stepped surface is enhanced at low energies by a molecular trapping mechanism. Because quantum effects can play a large role at the low energies and long lifetimes that characterize molecular trapping, we have undertaken quantum dynamics calculations for this system, the first to treat all molecular degrees of freedom of a gas molecule reacting on a stepped metallic surface. The calculations show that molecular trapping persists in the quantum system, but only at much lower energies than experimentally seen, pointing to possible deficiencies in the potential energy surface. Classical and quasiclassical trajectory calculations on the same potential provide a reasonable picture of reaction overall, but many of the finer details are inaccurate, and certain classical reaction mechanisms are entirely invalid. We conclude that some skepticism should be shown toward any classical study for which long-lived trapping states play a role.     

Quantum wave packet calculation of reaction probabilities,cross sections,and rate constants for the C(1D) + HD reaction

The time‐dependent real wave packet method has been used to study the C(¹D) + HD reaction. The state‐to‐state and state‐to‐all reactive scattering probabilities for a broad range of energies are calculated at zero total angular momentum. The probabilities for J > 0 are estimated from accurately computed J = 0 probabilities by using the J‐shifting approximation. The integral cross sections for a large energy range, and thermal rate constants are calculated. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

噻吩在Ni(100),Cu(100),Co(100)表面吸附的密度泛函研究

采用密度泛函理论对噻吩分子在Ni(100),Cu(100)和Co(100)表面的吸附构型进行了GGA/PBE水平上的计算,通过比较吸附能及各结构参数,预测了各金属的脱硫活性.结果表明:噻吩在Ni表面发生了作用力较强的化学吸附,噻吩的S—C键有解离趋势;在Cu表面发生的是作用力较弱的物理吸附,噻吩分子构型并未发生较大变化;而噻吩在Co表面的吸附作用最强,噻吩的S—C键已经发生解离,和Co原子之间的距离已经达到甚至短于Co—S键的键长.这说明,金属的吸附脱硫活性为CoNiCu,与实验研究结果一致.此3种金属最稳定的分子吸附位均为hol45位.     

Six-Dimensional State-to-State Quantum Dynamics of H2/D2 Scattering from Cu(100): Validity of Site-Averaging Model

Six-dimensional quantum dynamics calculations for the state-to-state scattering of H\begin{document}$ _2 $\end{document}/D\begin{document}$ _2 $\end{document} on the rigid Cu(100) surface have been carried out using a time-dependent wave packet approach, based on an accurate neural network potential energy surface fit for thousands of density functional theory data computed with the optPBE-vdW density functional. The present results are compared with previous theoretical and experimental ones regarding to the rovibrationally (in)elastic scattering of H\begin{document}$ _2 $\end{document} and D\begin{document}$ _2 $\end{document} from Cu(100). In particular, we test the validity of the site-averaging approximation in this system by which the six-dimensional (in)elastic scattering probabilities are compared with the weighted average of four-dimensional results over fifteen fixed sites. Specifically, the site-averaging model reproduces vibrationally elastic scattering probabilities quite well, though less well for vibrationally inelastic results at high energies. These results support the use of the site-averaging model to reduce computational costs in future investigations on the state-to-state scattering dynamics of heavy diatomic or polyatomic molecules from metal surfaces, where full-dimensional calculations are too expensive.