Development Of Efficient Wavepacket Approach For State-to-state Quantum Dynamic

Product-resolved reactive scattering theory can provide the most accurate and detailed description of a chemical reaction.Only the accurate product-resolved theoretical results can be quantificationally compared with the product state-resolved differential cross sections(DCSs)measured in a molecular cross beam experiment and reveal the detailed microscopic mechanism of chemical reactions further.For describing a reactive scattering within quantum mechanics principles,basically there are two kinds of methods:the time-independent method and the time-dependent wavepacket method.A lot of basis functions will be used for accurately describing the reaction process of complicated reaction,which can be solved by the time-independent method difficultly.While the results can be obtained by the time-dependent wavepacket method easily due to its better numerical scaling.However,the time-dependent method can't solve any reaction efficiently at present,such as,the reaction with low translation energy or long-range interaction potential in both reactant and product channels.The reason is that the long-standing coordinate problem in wavepacket calculation has not been completely solved and there is no coordinate system which can efficiently describe reactant and product channel simultaneously.Based on these facts,the key of this thesis is continuously developing product state-resolved reactive scattering theory and computational method,writing corresponding computation progarm,solving the coordinate problem and efficiently calculating state-to-state dynamic of complicated reaction.The achievements in this work are summarized as follows:In previous time dependent method based on hyperspherical coordinate,the state-to-state calculation with J>0 was difficult to realize as the hyperradial degree of freedom was used as state-to-state matching position.For solving this problem,the radial degree of freedom in product Jacobi coordinate is adopted as state-to-state matching position,the intermediate coordinate technique was applied to realize the state-to-state calculation with all total angular momentum J and product-resolved quantum wavepacket method based on APH(adiabatically adjusting,principal axes hyperspherical)coordinate was developed.In this method,the product-resolved scattering matrix element in all product arrangement channels could be extracted with single propagation.Moreover,for the reaction with linear transition states,the number of magnetic quantum numbers used in calculation could be effectively saved.While the method was similar with the product-resolved quantum wavepacket method based on reactant coordinate and this hyperspherical coordinate system could't efficiently describe reactant and product channel simultaneously.For efficiently describing reactant and product channel simultaneously,an interaction-asymptotic region decomposition(IARD)method was proposed,in which the boundary conditions of overlap of different regions were fulfilled.In the method,the interaction region and asymptotic regions were applied with the local optimal coordinate system,i.e.,APH coordinate in the interaction region,and the corresponding Jacobi coordinates in the asymptotic regions.The coordinate problem could be solved by this way.The IARD method was capable of efficiently and accurately accomplishing a calculation with a grid box for the Jacobi coordinate R extending several hundred or even thousands bohrs for both reactant and product arrangements.We demonstrated the effectiveness of the IARD method with the reaction of H+HD,which was the simplest direct reaction,and F+HD,which was a typical reaction involving resonances with products of extremely slow translational energy and required extremely long absorbing potential in all channels.Moreover,the total propagation time is 20 000 000 au for latter reaction,thus F+HD reaction can't be accurately calculated by previous quantum wavepacket method.The above-mentioned IARD method was appropriate for a general triatomic reactive scattering A+BC.While for a triatomic reaction A+B₂ with symmetry,it was unnecessary to explicitly include all three channels in the calculation.Therefore,the symmetrical IARD method was put forward to reduce the numerical effort of A+B₂ reaction.The computer effort could be significant reduced when dealing with the reaction of A+B₂ type using symmetry adoption.For illustration of the power of the symmetric IARD method,the numerical performance for calculating the state-to-state reaction probabilities of the ¹⁶O+³⁶O_2,¹⁸O+³²O₂,F+H₂ and D⁺+H₂ reactions in the cold reaction region were discussed.The results of these reactions were in good agreement with those obtained by the ABC code,which indicated that IARD method was not only appropriate for direct reaction,but also suitable for complicate reaction.The previous IARD method was inefficient for describing the insertion-type reaction S(¹D)+H₂ due to the singularity problem of APH coordinate.To deal with this issue,the channel-dependent Delves hyperspherical(DH)coordinate was proposed to describe the interaction region using the IARD method,which was called as DH-IARD method.The DH-IARD method was applied to calculate the differential and integral cross sections of the typical insertion reaction S(¹D)+H₂.It was found that the new DH-IARD method was much more efficient than the previous APH-IARD method for dealing with insertion reactions.The partial wave resonance structures were observed in the integral cross section.