溶液中电子转移反应速率的理论研究
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摘要
对于扩散控制的溶液中的电子转移反应,分子内振动模的运动比溶剂运动快很多,Sumi-Marcus理论提出用反应扩散方程(reaction-diffusion equation)处理溶剂的扩散运动,而分子内的振动用sink函数来表示,我们基于此理论发展了用虚时间分裂算符的方法(imaginary-time Split operator approach)解反应扩散方程,并将其应用于嗪1(oxazine 1,OX1)和N,N-二甲基苯胺(DMA)分子之间的电子转移反应,Sink函数采用几种不同的微扰表达式,通过计算得到给体几率衰减的两种平均速率和长时间极限下的速率常数,揭示了该体系电子转移过程中的一些动力学性质。
为了处理任意耦合强度时的电子转移反应,我们发展了R-matrix方法处理sink函数,与虚时间分裂算符方法一起研究了从弱到强电子耦合区域内分子内高频振动模对扩散控制的电子转移反应速率的量子效应。研究的模型体系电子转移反应处于Marcus反转区,结果显示R-matrix方法得到的绝热抑制比Laudau-Zener理论得到的要小,微扰理论没有预测到绝热抑制现象。模拟过程中还研究了电子耦合强度和溶剂弛豫时间对电子转移反应速率的影响。
上述两种方法还用于计算双肼自由基阳离子体系的电子转移速率。所用到的参数电子耦合强度和重组能用从头算方法计算得到。最后得到的速率常数发现与体系的结构有很大关系,与实验上的数据吻合得较好,这也说明了从头算方法得到的电子转移参数的正确性。
在谐振子近似失效的情况下,我们考虑了势能面为Morse势时,溶剂化方向和分子内振动方向的非谐性对电子转移速率的影响。结果显示:(1)溶剂化方向的非谐性使电子转移速率减小,而分子振动方向的非谐性增大电子转移速率,这两种效应的相对大小取决于体系参数的设置;(2)因核隧道效应的影响,电子转移速率与溶剂化弛豫时间之间不符合幂定律。
For intramolecular electron transfer(ET) reactions in solution,the fluctuations of the intramolecular vibrational modes are much faster than that of solvent mode.Thus,the reaction-diffusion equation is commonly used to describe the motion of solvent,with a sink function to treat the vibrational high-frequency mode.Based on this theory-so -called the Sumi-Marcus theory,we proposed an imaginary-time split operator approach to solve the reaction-diffusion equation.The approach is applied to evaluate the intermolecular ET rate between oxazine 1 and N,N-dimethlaniline.By measuring the two average survival times of the donor state probability and the rate constant in long time limit,the full kinetics of the ET is revealed with a variety of sink functions.
In order to deal with the ET reaction in wide electronic coupling regions,we introduced the R-matrix method to treat the sink function. Together with the imaginary-time split operator approach,we investigated the quantum effect of intramolecular high-frequency vibrational modes in the Marcus inverted region.The numerical results illustrate that the adiabatic suppression obtained from the R-matrix approach is much smaller than that from the Laudau-Zener theory whereas it cannot be predicted by the perturbation theory.The jointed effects of the electronic coupling and solvent relaxation time on the rates are also explored.
The proposed ET approaches are extended to investigate realistic systems together with ab initio calculations.The bis(hydrazine) radical cations are taken as examples.The predicted rates are in good agreement with the the experiments.Meanwhile,we also revealed the isomeric effects on ET.
When the harmonic approximation is breakdown,the Morse potential is taken as the free energy surface to study the anharmonic effects of solvent mode and vibrational mode.The results show:(1) the anharmonicity of the intramolecular modes always enhances the rate while the solvent anharminicity decreases the rate,compared with the harmonic modes.(2) the relation between the ET rate and the solvent relation time does not satisfy the power law for the nuclear tunneling effect.
为了处理任意耦合强度时的电子转移反应,我们发展了R-matrix方法处理sink函数,与虚时间分裂算符方法一起研究了从弱到强电子耦合区域内分子内高频振动模对扩散控制的电子转移反应速率的量子效应。研究的模型体系电子转移反应处于Marcus反转区,结果显示R-matrix方法得到的绝热抑制比Laudau-Zener理论得到的要小,微扰理论没有预测到绝热抑制现象。模拟过程中还研究了电子耦合强度和溶剂弛豫时间对电子转移反应速率的影响。
上述两种方法还用于计算双肼自由基阳离子体系的电子转移速率。所用到的参数电子耦合强度和重组能用从头算方法计算得到。最后得到的速率常数发现与体系的结构有很大关系,与实验上的数据吻合得较好,这也说明了从头算方法得到的电子转移参数的正确性。
在谐振子近似失效的情况下,我们考虑了势能面为Morse势时,溶剂化方向和分子内振动方向的非谐性对电子转移速率的影响。结果显示:(1)溶剂化方向的非谐性使电子转移速率减小,而分子振动方向的非谐性增大电子转移速率,这两种效应的相对大小取决于体系参数的设置;(2)因核隧道效应的影响,电子转移速率与溶剂化弛豫时间之间不符合幂定律。
For intramolecular electron transfer(ET) reactions in solution,the fluctuations of the intramolecular vibrational modes are much faster than that of solvent mode.Thus,the reaction-diffusion equation is commonly used to describe the motion of solvent,with a sink function to treat the vibrational high-frequency mode.Based on this theory-so -called the Sumi-Marcus theory,we proposed an imaginary-time split operator approach to solve the reaction-diffusion equation.The approach is applied to evaluate the intermolecular ET rate between oxazine 1 and N,N-dimethlaniline.By measuring the two average survival times of the donor state probability and the rate constant in long time limit,the full kinetics of the ET is revealed with a variety of sink functions.
In order to deal with the ET reaction in wide electronic coupling regions,we introduced the R-matrix method to treat the sink function. Together with the imaginary-time split operator approach,we investigated the quantum effect of intramolecular high-frequency vibrational modes in the Marcus inverted region.The numerical results illustrate that the adiabatic suppression obtained from the R-matrix approach is much smaller than that from the Laudau-Zener theory whereas it cannot be predicted by the perturbation theory.The jointed effects of the electronic coupling and solvent relaxation time on the rates are also explored.
The proposed ET approaches are extended to investigate realistic systems together with ab initio calculations.The bis(hydrazine) radical cations are taken as examples.The predicted rates are in good agreement with the the experiments.Meanwhile,we also revealed the isomeric effects on ET.
When the harmonic approximation is breakdown,the Morse potential is taken as the free energy surface to study the anharmonic effects of solvent mode and vibrational mode.The results show:(1) the anharmonicity of the intramolecular modes always enhances the rate while the solvent anharminicity decreases the rate,compared with the harmonic modes.(2) the relation between the ET rate and the solvent relation time does not satisfy the power law for the nuclear tunneling effect.
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