三原子分子光解动力学的理论研究
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摘要
光解反应动力学是光化学的一部分,也是分子反应动力学的一个重要分支。由于含时波包方法的简单性,容易实现,能够得到详细的动力学信息等优点,它被广泛地应用于光解动力学研究中。本论文中我们应用含时波包方法研究了三原子分子的光解过程。
为了解含时的Schr?dinger方程,我们要给出初始条件,也就是初始波包。我们应用三维分离变量表象方法编写了求解三原子分子振动光谱的程序,应用到H2O和H2S体系,都得到了与实验结果符合的很好的振动能级。
我们研究了J′=1特殊情况下三原子光解动力学。以O3在Hartley波段的光解为例,同以前J′= 0的研究结果比较,发现J′=1的处理对于自相关函数和吸收谱的影响比较小,而对转动态分布影响较大。
非绝热效应在光解动力学中是一个很普遍的现象。我们研究了总角动量J =0情况下发生在多个非绝热电子态的光解过程,用分裂算符方法给出相应的含时波包理论。以CH_3I光解为例验证我们的程序,发现由于1~Q_1(A′)和1~Q_1(A")态之间耦合的存在,影响了I通道中甲基的振动分布和转动分布,它们随两个态之间的耦合程度的变化而变化。
Photodissociation is at the heart of photochemistry, also is animportant embranchment in molecular reaction dynamics. Because of itssimplicity, ease of implementation and the detailed physical insight intothe dynamics obtained, time-dependent wave packet method is generallyused in photodissociation study.
In order to solve time-dependent schrodinger equation, we must represent theinitial wave function on finite grids. The modified DVR3D method is applied to thedetermination of the vibrational energy levels of triatomic molecules. This method issuccessfully used in H_2O and H_2S systems, and the results are similar to theexperimental one.
The photodissociation of triatomic system for the special case of J′= 1 isinvestigated. We discuss the photodissociation of O_3 in the Hartley band. Comparedwith previous results, the treatment with J′= 1 is less likely to be valid forphotodissociation cross section and autocorrelation function, but is likely to be mostvalid for rotational state populations.
It is well known that non-adiabatic effects occur in many photodissociationprocesses. We study photodissociation dynamics of triatomic molecules in severalcoupled electronic states for total angular momentum quantum number J = 0, andtime-dependent wave packet method with split-operator scheme is presented. As anexample to test our program validity, the photodissociation of CH3I is studied. Thecoupling between 1~Q_1 ( A′) and 1~Q_1 ( A′′) states has more effect on the vibrational
and rotational populations in the I channel, and the populations are changed as theeffect of coupling strength.
为了解含时的Schr?dinger方程,我们要给出初始条件,也就是初始波包。我们应用三维分离变量表象方法编写了求解三原子分子振动光谱的程序,应用到H2O和H2S体系,都得到了与实验结果符合的很好的振动能级。
我们研究了J′=1特殊情况下三原子光解动力学。以O3在Hartley波段的光解为例,同以前J′= 0的研究结果比较,发现J′=1的处理对于自相关函数和吸收谱的影响比较小,而对转动态分布影响较大。
非绝热效应在光解动力学中是一个很普遍的现象。我们研究了总角动量J =0情况下发生在多个非绝热电子态的光解过程,用分裂算符方法给出相应的含时波包理论。以CH_3I光解为例验证我们的程序,发现由于1~Q_1(A′)和1~Q_1(A")态之间耦合的存在,影响了I通道中甲基的振动分布和转动分布,它们随两个态之间的耦合程度的变化而变化。
Photodissociation is at the heart of photochemistry, also is animportant embranchment in molecular reaction dynamics. Because of itssimplicity, ease of implementation and the detailed physical insight intothe dynamics obtained, time-dependent wave packet method is generallyused in photodissociation study.
In order to solve time-dependent schrodinger equation, we must represent theinitial wave function on finite grids. The modified DVR3D method is applied to thedetermination of the vibrational energy levels of triatomic molecules. This method issuccessfully used in H_2O and H_2S systems, and the results are similar to theexperimental one.
The photodissociation of triatomic system for the special case of J′= 1 isinvestigated. We discuss the photodissociation of O_3 in the Hartley band. Comparedwith previous results, the treatment with J′= 1 is less likely to be valid forphotodissociation cross section and autocorrelation function, but is likely to be mostvalid for rotational state populations.
It is well known that non-adiabatic effects occur in many photodissociationprocesses. We study photodissociation dynamics of triatomic molecules in severalcoupled electronic states for total angular momentum quantum number J = 0, andtime-dependent wave packet method with split-operator scheme is presented. As anexample to test our program validity, the photodissociation of CH3I is studied. Thecoupling between 1~Q_1 ( A′) and 1~Q_1 ( A′′) states has more effect on the vibrational
and rotational populations in the I channel, and the populations are changed as theeffect of coupling strength.
引文
1. Balakrishnan N, Kalyanaraman C, Sathyamurthy N. Time-dependent quantum mechanical approach to reactive scattering and related processes. Physics Reports 1997, 280: 79-144.
2. Manthe U. Quantum Molecular Dynamics with wave packets. John Von Neumann Institute for Computing, NIC Series 2002, 10: 361-375.
3. Mohan V, Sathyamurthy N. Quantal wavepacket calculations of reactive scattering. Computer Physics Reports 1988, 7: 213-258.
4. Kosloff R. Time-dependent quantum-mechanical for molecular dynamics. J. Phys. Chem. 1988, 92: 2087-2100.
5. Schinke R. Photodissociation dynamics Cambridge University Press: Cambridge, 1993.
6. McCullough E A, Wyatt R E. Quantum dynamics of the collinear (H, H_2) reaction. J. Chem. Phys. 1969, 51: 1253-1254.
7. Feit M D, Fleck J A. Solution of the schr?dinger equation by a spectral method II: Vibrational energy levels of triatomic molecules. J. Chem. Phys. 1983, 78: 301- 308.
8. Kosloff D, Kosloff R. A Fourier method solution for the time dependent schr?dinger equation as a tool in molecular dynamics. J. Comput. Phys. 1983, 52: 35-53.
9. Light J C, Hamilton I P, Lill J V. Generalized discrete variable approximation in quantum mechanics. J. Chem. Phys. 1985, 82: 1400-1409.
10. Bacic Z, Light J C. Theoretical methods for rovibrational states of floppy molecules. Annu. Rev. Phys. Chem. 1989, 40: 469-498.
11. Askar A, Cakmak A S. Explicit integration method for the time-dependent schrodinger equation for collision problems. J. Chem. Phys. 1978, 68: 2794 -2798.
12. Feit M D, Fleck, Jr J A. Wave packet dynamics and chaos in the henon-heiles system. J. Chem. Phys. 1984, 80: 2578-2584.
13. Halcomb L L, Diestler D J. Hemiquantal mechanics. I. Vibrational predissociation of Van der Waals molecules. J. Chem. Phys. 1986, 84: 3130-3137.
14. Tal-Ezer H, Kosloff R. An accurate and efficient scheme for propagating the time dependent schr?dinger equation. J. Chem. Phys. 1984, 81: 3967-3971.
15. Lanczos C. An iteraction method for the solution of the eigenvalue problem of linear differential and entergral operators. J. Res. Natl. Bur. Stand. 1950, 45: 255-282.
16. Park T J, Light J C, Unitary quantum time evolution by iterative lanczos reduction. J. Chem. Phys. 1986, 85: 5870-5876.
17. Chen R, Guo H. A sigle Lanczos propagation method for calculating transition amplitudes. II. Modified QL and symmetry adaptation. J. Chem. Phys. 2001, 114: 1467-1472.
18. Wang X-G, Carrington, Jr. T. Contracted basis Lanczoa methods for computing numerically exact rovibrational levels of methane. J. Chem. Phys. 2004, 121: 2937-2954.
19. Bisseling R H, Kosloff R, Manz J. Dynamics of hyperspherical and local mode resonance decay studied by time dependent wave packet propagation. J. Chem. Phys. 1985, 83: 993-1004.
20. Neuhauser D, Baer M. Wave-packet approach to treat low energy reactive systems: accurate probabilities for hydrogen atom + hydrogen J. Phys. Chem. 1989, 93: 2872-2873.
21. Child M S. Analysis of a complex absorbing barrier. Mol. Phys. 1991, 72: 89-93.
22. Vibok A, Balint-Kurti G G. Reflection and transmission of waves by a complex potential—a semiclassical Jeffreys–Wentzel–Kramers–Brillouin treatment J. Chem. Phys. 1992, 96: 7615-7622.
23. Vibok A, Balint-Kurti G G. Parametrization of complex absorbing potentials for time-dependent quantum dynamics. J. Phys. Chem. 1992, 96: 8712-8719.
24. Heller E J. Quantum corrections to classical photdissociation models. J. Chem. Phys. 1978, 68: 2066-2075
25. Balint-Kurti G G, Dixon R N, Marston C C. Time-dependent quantum dynamics of molecular photofragmentation process. J. Chem. Soc. Faraday Trans. 1990, 86: 1741-1749.
26. Balint-Kurti G G, Dixon R N, Marston C C. Grid methods for solving the schrodinge equation and time dependent quantum dynamics of molecular photofragmentation and reactive scattering processes. International Reviews in Physical Chemistry. 1992, 11: 317-344.
2. Manthe U. Quantum Molecular Dynamics with wave packets. John Von Neumann Institute for Computing, NIC Series 2002, 10: 361-375.
3. Mohan V, Sathyamurthy N. Quantal wavepacket calculations of reactive scattering. Computer Physics Reports 1988, 7: 213-258.
4. Kosloff R. Time-dependent quantum-mechanical for molecular dynamics. J. Phys. Chem. 1988, 92: 2087-2100.
5. Schinke R. Photodissociation dynamics Cambridge University Press: Cambridge, 1993.
6. McCullough E A, Wyatt R E. Quantum dynamics of the collinear (H, H_2) reaction. J. Chem. Phys. 1969, 51: 1253-1254.
7. Feit M D, Fleck J A. Solution of the schr?dinger equation by a spectral method II: Vibrational energy levels of triatomic molecules. J. Chem. Phys. 1983, 78: 301- 308.
8. Kosloff D, Kosloff R. A Fourier method solution for the time dependent schr?dinger equation as a tool in molecular dynamics. J. Comput. Phys. 1983, 52: 35-53.
9. Light J C, Hamilton I P, Lill J V. Generalized discrete variable approximation in quantum mechanics. J. Chem. Phys. 1985, 82: 1400-1409.
10. Bacic Z, Light J C. Theoretical methods for rovibrational states of floppy molecules. Annu. Rev. Phys. Chem. 1989, 40: 469-498.
11. Askar A, Cakmak A S. Explicit integration method for the time-dependent schrodinger equation for collision problems. J. Chem. Phys. 1978, 68: 2794 -2798.
12. Feit M D, Fleck, Jr J A. Wave packet dynamics and chaos in the henon-heiles system. J. Chem. Phys. 1984, 80: 2578-2584.
13. Halcomb L L, Diestler D J. Hemiquantal mechanics. I. Vibrational predissociation of Van der Waals molecules. J. Chem. Phys. 1986, 84: 3130-3137.
14. Tal-Ezer H, Kosloff R. An accurate and efficient scheme for propagating the time dependent schr?dinger equation. J. Chem. Phys. 1984, 81: 3967-3971.
15. Lanczos C. An iteraction method for the solution of the eigenvalue problem of linear differential and entergral operators. J. Res. Natl. Bur. Stand. 1950, 45: 255-282.
16. Park T J, Light J C, Unitary quantum time evolution by iterative lanczos reduction. J. Chem. Phys. 1986, 85: 5870-5876.
17. Chen R, Guo H. A sigle Lanczos propagation method for calculating transition amplitudes. II. Modified QL and symmetry adaptation. J. Chem. Phys. 2001, 114: 1467-1472.
18. Wang X-G, Carrington, Jr. T. Contracted basis Lanczoa methods for computing numerically exact rovibrational levels of methane. J. Chem. Phys. 2004, 121: 2937-2954.
19. Bisseling R H, Kosloff R, Manz J. Dynamics of hyperspherical and local mode resonance decay studied by time dependent wave packet propagation. J. Chem. Phys. 1985, 83: 993-1004.
20. Neuhauser D, Baer M. Wave-packet approach to treat low energy reactive systems: accurate probabilities for hydrogen atom + hydrogen J. Phys. Chem. 1989, 93: 2872-2873.
21. Child M S. Analysis of a complex absorbing barrier. Mol. Phys. 1991, 72: 89-93.
22. Vibok A, Balint-Kurti G G. Reflection and transmission of waves by a complex potential—a semiclassical Jeffreys–Wentzel–Kramers–Brillouin treatment J. Chem. Phys. 1992, 96: 7615-7622.
23. Vibok A, Balint-Kurti G G. Parametrization of complex absorbing potentials for time-dependent quantum dynamics. J. Phys. Chem. 1992, 96: 8712-8719.
24. Heller E J. Quantum corrections to classical photdissociation models. J. Chem. Phys. 1978, 68: 2066-2075
25. Balint-Kurti G G, Dixon R N, Marston C C. Time-dependent quantum dynamics of molecular photofragmentation process. J. Chem. Soc. Faraday Trans. 1990, 86: 1741-1749.
26. Balint-Kurti G G, Dixon R N, Marston C C. Grid methods for solving the schrodinge equation and time dependent quantum dynamics of molecular photofragmentation and reactive scattering processes. International Reviews in Physical Chemistry. 1992, 11: 317-344.