多通道多位井速率常数的计算 Rate Constants for Multi-Channel, Multi-Well Reactions

1. 多通道多位井速率常数的计算 Rate Constants for Multi-Channel, Multi-Well Reactions 张绍文 北京理工大学

2. 化学反应速率理论 • 碰撞理论（经典碰撞理论，轨线法，量子散射理论） • 过渡状态理论（传统过渡状态理论，变分过渡状态理论）

3. 过渡状态理论的基本假设 • 玻恩-奥本海默近似 • 反应物微观状态保持玻尔兹曼分布 • 不返回假定 • 运动分离假定

4. 化学反应速率常数的计算 • 正则系综速率常数的计算 • 传统过渡态理论 • 正则变分过渡态理论

5. 考虑到量子隧道效应时

6. 微正则系综速率常数的计算 • 传统过渡态理论

7. 微正则变分过渡态理论

8. 隧道穿透系数的计算 BWK近似

9. Master Equation Method • Why Use Master Equation • Calculate pressure dependence of rate constants • Calculate branching ratios of multi-channel reactions • High accuracy

10. B + C A D + E F + G Single Well Multi-channel Case

11. A B + C E ni • Methodology Ei k(Ei) Rji Ej nj E0 B+C A • niis the population of reactant molecules at energy Ei. • [M] is the concentration of bath gas. • Rij is the rate of collision-induced excitation from EjtoEi of the reactant molecule on collision with a bath gas molecule (Energy transfer coefficient). • k(Ei) is the microcanonical rate constant of the reaction at energy Ei • Gilbert, R. G.; Smith, S. C. Theory of Unimolecular and Recombination Reactions; Blackwell: London, 1990. • Klippenstein, S. J., Harding, L. B. J. Phys. Chem. 1999, 103, 9388. • Diau, E. W. G, Lin M. C. J. Phys. Chem. 1995, 99, 6589. • Robertson, S. H., Pilling, M. J., Baulch, D. L., Green, N. J. B. J. Phys. Chem. 1995, 99, 13452.

12. Z: collision number per unit time, collision frequency, (time-1) Pi(E,E’): probability of energy transferred per collision, (energy-1)

13. kuniis pressure dependent thermal rate constants

14. E Energy Transfer Rate Coefficient Ej Exponential down model Rji Pij=c(Ej)exp[-(Ej-Ei)/], Ei < Ej Ei Pji f(Ei) = Pij f(Ej) f(Ei) = [(Ei) exp(- Ei/kBT)]/Q c(E) is normalization coefficient;  is energy transfer constant; f(E) is distribution function; (E) is density of state; Q is partition function.

15. Microcanonical Rate Constant NGTS(E,S) is the sum of states of the Generalized Transition State (GTS). R(E) is the density of states of the reactant. 1. Garrett, B. C.; Truhlar, D. G.; Grev, R. S.; Magnuson, A. W. J. Phys. Chem. 1980, 84, 1370. 2. Hase, W. L. Acc. Chem. Res. 1998, 31, 659. 3. Forst, W. Theory of Unimolecular Reactions; Academic: London, 1973. 4. Baer, T.; Hase, W. L. Unimolecular Reaction Dynamics. Theory and Experiment; Oxford: New York, 1996. 5. Gilbert, R. G.; Smith, S. C. Theory of Unimolecular and Recombination Reactions; Blackwell: London, 1990.

16. B + C A D + E F + G Rate Constants for Multi-channel Reaction Sum over channels

17. Rate Constants for Multi-Well Multi-channel Reaction

18. Z: collision number per unit time, collision frequency, (time-1) Pi(E,E’): probability of energy transferred per collision, (energy-1) • J. A. Miller, S. J. Klippenstein, S. H. Robertson, J. Phys. Chem. A 2000, 104, 7525-7536 • S. J. Klippenstein, J. A. Miller, J. Phys. Chem. A 2002, 106, 9267-9277

19. Pi(E’,E)fi(E) = Pi(E,E’)fi(E’) kij(E)j(E)=kji(E)i(E)

21. Solution to the Master Equation • Finding the eigenvalue and eigenvectors ? • Solving the stiff ordinary differential equations ?

22. C2H5+O2=C2H4+HO2 的产物产率 理论 实验

23. + I O O N O O N O O N II N N O H H O N N N H H H H P H H Master Equation Study of HMX decomposition

24. Potential energy profile of the HONO elimination and NO2 fission chnnels

25. Pressure dependent rate constants NO2 fission HONO elimination a b

26. Branching ratios vs pressure

27. Branching ratios vs temperature