The reagent rotational excitation effect on the stereodynamics of H+LiF→HF+Li is calcu-lated by means of the quasi-classical trajectory method on the Aguado-Paniagua2-potential energy surface (AP2-PES) constructe...The reagent rotational excitation effect on the stereodynamics of H+LiF→HF+Li is calcu-lated by means of the quasi-classical trajectory method on the Aguado-Paniagua2-potential energy surface (AP2-PES) constructed by Aguado et al. [J. Chem. Phys. 106, 1013 (1997)]. The angular distributions of vector correlations between products and reactants, P(?r) and P(Φr) are presented. Meanwhile, the four polarization-dependent generalized differential cross sections are computed. The results indicate that the reagent rotational quantum num-bers have impact on the vector properties of the title reaction. In addition, the reaction probability has been calculated as well.展开更多
The quasi-classical trajectory calculations O++DH(v=0,j=0)→OD++H reactions on the RODRIGO potential energy surface have been carried out to study the isotope effect on stereo-dynamics at the collision energies ...The quasi-classical trajectory calculations O++DH(v=0,j=0)→OD++H reactions on the RODRIGO potential energy surface have been carried out to study the isotope effect on stereo-dynamics at the collision energies of 1.0, 1.5, 2.0, and 2.5 eV. The distributions of dihedral angle P(~r) and the distributions of P(Or) are discussed. Furthermore, the angular distributions of the product rotational vectors in the form of polar plot in θr and φr are calculated. The differential cross section shows interesting phenomenon that the reaction is dominated by the direct reaction mechanism. Reaction probability and reaction cross section are also calculated. The calculations indicate that the stereo-dynamics properties of the title reactions are sensitive to the collision energy.展开更多
Electronically non-adiabatic processes are essential parts of photochemical process, collisions of excited species, electron transfer processes, and quantum information processing. Various non-adiabatic dynamics metho...Electronically non-adiabatic processes are essential parts of photochemical process, collisions of excited species, electron transfer processes, and quantum information processing. Various non-adiabatic dynamics methods and their numerical implementation have been developed in the last decades. This review summarizes the most significant development of mixed quantum-classical methods and their applications which mainly include the Liouville equa- tion, Ehrenfest mean-field, trajectory surface hopping, and multiple spawning methods. The recently developed quantum trajectory mean-field method that accounts for the decoherence corrections in a parameter-free fashion is discussed in more detail.展开更多
We present a general formalism for setting up unitary transform operators from classical transforms via the technique of integration within an ordered product of operators, their normally ordered form can be obtained ...We present a general formalism for setting up unitary transform operators from classical transforms via the technique of integration within an ordered product of operators, their normally ordered form can be obtained too.展开更多
The Weil's integrality condition of prequantization is generalized to two-dimensional phase space with boundaries. It is shown that in the prequantization condition a term related to the symplectic potential on th...The Weil's integrality condition of prequantization is generalized to two-dimensional phase space with boundaries. It is shown that in the prequantization condition a term related to the symplectic potential on the boundary appears. The necessity of the generalized condition is proved by analyzing the isolated singularities of the Hermitian bundle while the sufficiency of the condition is proved via geometric construction on the space of equivalence class.展开更多
For the standard Lagrangian in classical mechanics, which is defined as the kinetic energy of the system minus its potential energy, we study the rate of convergence of the corresponding Lax-Oleinik semigroup. Under t...For the standard Lagrangian in classical mechanics, which is defined as the kinetic energy of the system minus its potential energy, we study the rate of convergence of the corresponding Lax-Oleinik semigroup. Under the assumption that the unique global minimum point of the Lagrangian is a degenerate fixed point, we provide an upper bound estimate of the rate of convergence of the semigroup.展开更多
基金ACKNOWLEDGMENTS This work was supported by the Jilin University, China (No.419080106440), the Chinese National Fusion Project for ITER (No.2010GB104003), and the National Natural Science Foundation of China (No.10974069). Many thanks to Prof. Ke-li Han for providing the stereodynamics program.
文摘The reagent rotational excitation effect on the stereodynamics of H+LiF→HF+Li is calcu-lated by means of the quasi-classical trajectory method on the Aguado-Paniagua2-potential energy surface (AP2-PES) constructed by Aguado et al. [J. Chem. Phys. 106, 1013 (1997)]. The angular distributions of vector correlations between products and reactants, P(?r) and P(Φr) are presented. Meanwhile, the four polarization-dependent generalized differential cross sections are computed. The results indicate that the reagent rotational quantum num-bers have impact on the vector properties of the title reaction. In addition, the reaction probability has been calculated as well.
文摘The quasi-classical trajectory calculations O++DH(v=0,j=0)→OD++H reactions on the RODRIGO potential energy surface have been carried out to study the isotope effect on stereo-dynamics at the collision energies of 1.0, 1.5, 2.0, and 2.5 eV. The distributions of dihedral angle P(~r) and the distributions of P(Or) are discussed. Furthermore, the angular distributions of the product rotational vectors in the form of polar plot in θr and φr are calculated. The differential cross section shows interesting phenomenon that the reaction is dominated by the direct reaction mechanism. Reaction probability and reaction cross section are also calculated. The calculations indicate that the stereo-dynamics properties of the title reactions are sensitive to the collision energy.
基金supported by the National Key R&D Program of China(No.2017YFB0203405)the National Natural Science Foundation of China(No.21421003)
文摘Electronically non-adiabatic processes are essential parts of photochemical process, collisions of excited species, electron transfer processes, and quantum information processing. Various non-adiabatic dynamics methods and their numerical implementation have been developed in the last decades. This review summarizes the most significant development of mixed quantum-classical methods and their applications which mainly include the Liouville equa- tion, Ehrenfest mean-field, trajectory surface hopping, and multiple spawning methods. The recently developed quantum trajectory mean-field method that accounts for the decoherence corrections in a parameter-free fashion is discussed in more detail.
基金The project supported by National Natural Science Foundation of China under Grant No. 10475056
文摘We present a general formalism for setting up unitary transform operators from classical transforms via the technique of integration within an ordered product of operators, their normally ordered form can be obtained too.
文摘The Weil's integrality condition of prequantization is generalized to two-dimensional phase space with boundaries. It is shown that in the prequantization condition a term related to the symplectic potential on the boundary appears. The necessity of the generalized condition is proved by analyzing the isolated singularities of the Hermitian bundle while the sufficiency of the condition is proved via geometric construction on the space of equivalence class.
基金supported by National Natural Science Foundation of China (Grant No. 11001100)China Postdoctoral Science Foundation (Grant No.20100470645)+3 种基金Shanghai Postdoctoral Science Foundation (Grant No. 11R21412100)the Young Fund of the College of Mathematics at Jilin Universitysupported by National Natural Science Foundation of China(Grant No. 10971093)National Basic Research Program of China (973 Program) (Grant No. 2007CB814800)
文摘For the standard Lagrangian in classical mechanics, which is defined as the kinetic energy of the system minus its potential energy, we study the rate of convergence of the corresponding Lax-Oleinik semigroup. Under the assumption that the unique global minimum point of the Lagrangian is a degenerate fixed point, we provide an upper bound estimate of the rate of convergence of the semigroup.