激光诱导偶氮苯异构化反应的动力学模拟
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摘要
偶氮苯(Azobenzene，Ab)是一个典型的光致变色分子，在不同波长光照射下，会可逆地实现顺式(?)反式异构化。两种构型的偶氮苯分子具有明显不同的紫外可见吸收光谱：在光触发开关，全息数据擦写，图像存储、光调控材料以及生物学等诸多领域有着广泛的应用前景。基于此，偶氮苯光致异构化反应机理引起人们强烈的兴趣，成为近几十年来理论化学界的一个热点。
Rau提出了偶氮苯光致异构化的两种机理：n→π~*激发下的反转机制和π→π~*激发下的旋转机制，引起了关于偶氮苯分子光致异构化机理的争论。高水平的量子化学计算为研究该反应的机理提供了大量的理论依据。但是该反应机理的确定更需要动力学的计算。本文采用半经典的电子-辐射-离子动力学(Semiclassical electron radiation iondynamics，SERID)方法从反式偶氮苯出发模拟了n→π~*激发及π→π~*激发下的异构化反应。
SERID模型是一种半经典、非绝热动力学模拟方法，所谓半经典方法是指电子运动由求解含时Schr(?)dinger方程确定，而辐射场和核运动则由经典力学处理，即电子结构的量子力学计算提供核运动的力场，核的运动轨迹由求解经典的Newton方程(或对应的Ehrenfest方程)获得。这种模拟方法考虑激光场对电子结构的作用，并采用非绝热动力学的近似方法(Ehrenfest动力学)和紧束缚近似来建立模型。该方法有以下主要特点：
(1)在电子Hamiltonian中通过时间有关的Peierls替代引入了辐射场与分子的相互作用。计算中引入此种相互作用使我们能够研究激光脉冲对光化学反应结果的影响，这是激光控制化学反应的一个重要课题。
(2)核运动被半经典处理。含时Schr(?)dinger方程采用了一种基于时间演化算符的酉算法迭代方案求解。核运动方程采用了一种辛算法(velocity Verletalgorithm)求解，由解经典方程获得。这一算法能够保持能量、动量和几率守恒，并满足Pauli原理。
(3)电子结构采用半经验的DFTB(Density Functional based Tight Binding)方法计算。基函数取定域在原子上的非正交基。仅处理价电子，内层电子和核一起构成惰性的原子实(离子)，原子实之间的排斥采用参量化处理，因此能量以及力的计算有很高的效率。
(4)是一种直接动力学计算方案，即不需预先构建势能面，能量和力采用即用即算(on the fly)方案。
这些特点保证了SERID可以进行足够大体系的动力学模拟，但是此方法也有如下缺点：(a)模型使用的DFTB方法中，交换相关泛函应用了非常粗略的局域密度近似，不能正确地处理化学键的断裂问题。(b)由于没有明确的电子态和多重度，其模拟结果很难以和其它方法，特别是高相关电子结构计算结果相比较。
模拟过程中通过选择激光脉冲频率、波形、流量和持续时间等完成了近千条反应轨迹的计算，结果显示：
1．频率为1．75eV，持续时间为100fs的激光脉冲可以导致n→π~*激发，S_1在势能的驱动下随时间演化，最后通过无辐射非绝热跃迁衰变至基态S_0，S_1激发态寿命约1450～1650飞秒。频率为2．15eV和2．2eV，持续时间为100fs的激光脉冲作用于反式偶氮苯分子，皆可导致分子从基态激发到S_2态(π→π~*激发)。30飞秒以内发生S_2(ππ~*)／S_3(π~2π~(*2))弛豫，S_3(π~2π~(*2))寿命极短，只有几个飞秒，然后弛豫到S_1态(nπ~*激发态)。2．15eV脉冲作用下，S_1的寿命约800～1000飞秒；2．2eV脉冲作用下，S_1的寿命约500～600飞秒。
2．无论是n→π~*激发还是π→π~*激发，当激光脉冲使电子激发以后，N=N键级变小，键长伸长；反式偶氮苯分子都是通过围绕中心“-N=N-”键的旋转实现异构化；在旋转的同时，两个CNN键角同时增大约15°～20°，并未出现半线型结构，说明模拟结果不支持反转机制。
3．无论是n→π~*激发还是π→π~*激发，当反式偶氮苯分子处在或衰减至S_1激发态时，N-N键长与LUMO能量密切相关，CNN键角与HOMO能量密切相关，而CNNC二面角与LUMO和HOMO之间的能隙密切相关。
4．无论是n→π~*激发还是π→π~*激发，CNN键角开始增大时分子处在在S_1激发态，此时伴随着NN键长的强烈收缩，我们认为这是振动态改变所致。
5．无论是n→π~*激发还是π→π~*激发，发生非绝热跃迁时都可能形成苯环相互垂直的中间体结构。此结构下两个与N原子相连的C原子所受力的方向决定了产物的类型，即可能形成顺式产物或反式产物。
6．π→π~*激发下，非绝热跃迁时的分子结构除了第4条中所述“垂直构型”以外，还存在CNNC二面角约为140°的“扭曲构型”。在“扭曲构型”下的衰减将导致反式产物的形成。因为n→π~*激发下未发现“扭曲构型”的存在，故n→π~*激发生成反式产物的可能性低于π→π~*激发，解释了π→π~*激发下异构化反应量子产率低于n→π~*激发的实验现象。
7．π→π~*激发下，激发态分子发生S(ππ~*)／S(π~2π~(*2))衰减后，CNN的弯曲振动有明显加强。当衰减通道为“扭曲构型”时，CNN的弯曲振动对激发态衰减做出重要贡献。
8．1)多条模拟轨迹表明，在1．75eV的频率下，脉冲辐射通量密度较小时，形成顺式异构体的可能性较大；脉冲辐射通量密度较大时，形成反式构型的可能性较大。2)多轨迹的模拟发现：脉冲频率为2．15eV，形成顺式构型的可能性较大，脉冲频率为2．2eV，形成反式构型的可能性越大。
Azobenzene is a prototype chromophoric molecule and undergoes trans (?) cis isomerization under ultraviolet or visible radiation. The two isomers display clearly different UV absorption spectra. These make azobenzene and its derivatives become good candidates for many applications, including light-triggered switches, constituents of erasable holographic data, image storage devices and in biology. For this reason, the photochemical and photophysical features of azobenzene has attracted extensive research interests for many years.
The proposal by Rau that the azobenzene molecule takes inversion path from the reactant to the product for the nπ~* excitation and rotation path for theππ~* excitation opens a debate on the photoisomerization mechanism of the azobenzene molecule. Many high level quantum chemical calculations have been applied to study the mechanism and provided valuable information in understanding this important process. In this thesis, we present a realistic dynamics simulation study of the trans-azobenzene photoisomerization under nπ~* andππ~* excitations by semiclassical electron radiation ion dynamics (SERID) approach.
In the SERID approximation, the state of the valence electrons is calculated by the time-dependent Schrddinger equation, but the radiation field and the motion of the nuclei are treated classically. In other words, the forces for driving nuclear motion are calculated by quantum chemical calculations but nuclear trajectories are updated by solving Newton's motion equation (or Ehrenfest equation). The most important characteristic of SERID is the direct inclusion of a laser pulse that interacts with the molecule. SERID has following features:
(1) The laser pulse is characterized by the vector potential A that is coupled to the Hamiltonian through the time-dependent Peierls substitution. This explicitly incorporates the interaction between laser field and electrons and allows us to investigate the effects of laser pulses on the products of a photochemical reaction. This is an important topic in the laser control of chemical reactions.
(2) The time-dependent Schrodinger equation is solved using a unitary algorithm obtained from the equation for the time evolution operator. Nuclear positions are updated by numerically integrating Newton's motion equation with the velocity Verlet algorithm which preserves phase space and satisfies the Pauli principle.
(3) Electronic structure is calculated by the density functional based tight-binding (DFTB) method. The basis functions are the non-orthogonal basis set and only valence electrons are calculated. Nuclei and core electrons together are treated as an ion. Hamiltonian matrix elements and ion-ion repulsive interaction are calculated by the density functional method and then tabulated as a function of distance of two ions for time-dependent calculations. This allows an effective calculation of forces and energies.
(4) The model calculates the forces on-the-fly. This is in contrast to the Molecular Dynamics simulation in which the potential energy surface is constructed before any simulation is conducted.
These features make the model as a realistic technique for simulating large systems. Its shortcomes are described below: (A) DFTB is a decent from DFT at LDA level, which may not be suitable for the description of the breaking of chemical bonds. (B) Electronic states and spin multiplicity are not clearly defined and therefore it is not always possible to directly compare our simulation results to high level quantum chemical calculations.
We have carried out several hundreds simulation calculations by adjusting frequency, flux, and duration of the laser pulse and obtained the following conclusions:
1. For trans-azobenzene, if the laser pulse with frequency of 1.75 eV and duration of 100 fs is used the simulation will lead to nπ~* (S_1) excitation and then the S_1 state evolves with time and decays to the ground state S_0 through the drive of the potential energy. The lifetime of S_1 state is about 1450 fs-1650 fs. Laser pulse with frequency of 2.15 eV and 2.2 eV and duration of 100 fs will lead toππ~* excitation. The excited molecule decays from the S (ππ~*) state to the S((π)~2(π~*)~2) state within 30 fs and immediately relax to a S_1 state. The S_1 state evolves with time and decays to the ground state S_0. The lifetime of S_1 state induced by pulse of 2.15eV and 2.2eV is about 800 fs-1000 fs and 500 fs-600 fs, respectively.
2. The N=N bond stretching soon after laser pulse react to azobenzene molecule and rotary motion around central "-N=N-" group company with two CNN angles concerted expanding to 15°-20°are observed either nπ~*orππ~*excited. Without finding semi-linear structure indicates the "inversion mechanism" is not supported by simulation results.
3. Both nπ~*andππ~*excitation in which closely relation between N-N bondlength versus LUMO energy, CNN angles versus HOMO energy and CNNC dihedral versus energy between HOMO and LUMO are observed when azobenzene molecule locates in S_1 excited state.
4. The S_1 state can occur either from nπ~* orππ~* excitations. When its CNN angles increase the N-N bond shorten sharply, which might be brought about owing to change of vibrational states.
5. Decay channels from the S_1 state to the S_0 state at about the perpendicular structure of two phenyl rings in azobenzene. "Perpendicular structure" will lead to formation either trans or cis isomer according to orientation of the force on the two carbon atoms which are adjacent to the nitrogen atom.
6. There is an "twisted structure" with 140°dihedral onππ~*excitation besides the above-mentioned "perpendicular structure". Decay channel at "twisted structure" onππ~* excitation will only result in the formation of trans-product. The existence of a decay channel at geometry far from the "perpendicular structure" accounts for the poor E-Z photoisomerization quantum yield forππ~* excitation.
7. The bending vibration of the CNN bond are significantly enhanced after the S_2 (ππ~*)/S_3 ((π)~2(π~*)~2 ) decay. The energy for this excitation comes from internal energy conversion at the S(ππ~*)/S((π)~2(π~*)~2) decay. This excitation promotes the CNN bond angles expansion that makes significant contribution to the decay channel at the geometry of "twisted structure."
8. Results of Multiple trajectory simulations show :
1) For nπ~* excitation at pulse frequency of 1.75eV, the smaller fluence will bring larger possibility of the formation of cis-structure, and vice versa.
2) Forππ~* excitation at pulse frequency of 2.15eV, the formation of cis-isomer has larger possibility, while at pulse frequency of 2.2eV, trans-isomer has larger possibility.
Rau提出了偶氮苯光致异构化的两种机理：n→π~*激发下的反转机制和π→π~*激发下的旋转机制，引起了关于偶氮苯分子光致异构化机理的争论。高水平的量子化学计算为研究该反应的机理提供了大量的理论依据。但是该反应机理的确定更需要动力学的计算。本文采用半经典的电子-辐射-离子动力学(Semiclassical electron radiation iondynamics，SERID)方法从反式偶氮苯出发模拟了n→π~*激发及π→π~*激发下的异构化反应。
SERID模型是一种半经典、非绝热动力学模拟方法，所谓半经典方法是指电子运动由求解含时Schr(?)dinger方程确定，而辐射场和核运动则由经典力学处理，即电子结构的量子力学计算提供核运动的力场，核的运动轨迹由求解经典的Newton方程(或对应的Ehrenfest方程)获得。这种模拟方法考虑激光场对电子结构的作用，并采用非绝热动力学的近似方法(Ehrenfest动力学)和紧束缚近似来建立模型。该方法有以下主要特点：
(1)在电子Hamiltonian中通过时间有关的Peierls替代引入了辐射场与分子的相互作用。计算中引入此种相互作用使我们能够研究激光脉冲对光化学反应结果的影响，这是激光控制化学反应的一个重要课题。
(2)核运动被半经典处理。含时Schr(?)dinger方程采用了一种基于时间演化算符的酉算法迭代方案求解。核运动方程采用了一种辛算法(velocity Verletalgorithm)求解，由解经典方程获得。这一算法能够保持能量、动量和几率守恒，并满足Pauli原理。
(3)电子结构采用半经验的DFTB(Density Functional based Tight Binding)方法计算。基函数取定域在原子上的非正交基。仅处理价电子，内层电子和核一起构成惰性的原子实(离子)，原子实之间的排斥采用参量化处理，因此能量以及力的计算有很高的效率。
(4)是一种直接动力学计算方案，即不需预先构建势能面，能量和力采用即用即算(on the fly)方案。
这些特点保证了SERID可以进行足够大体系的动力学模拟，但是此方法也有如下缺点：(a)模型使用的DFTB方法中，交换相关泛函应用了非常粗略的局域密度近似，不能正确地处理化学键的断裂问题。(b)由于没有明确的电子态和多重度，其模拟结果很难以和其它方法，特别是高相关电子结构计算结果相比较。
模拟过程中通过选择激光脉冲频率、波形、流量和持续时间等完成了近千条反应轨迹的计算，结果显示：
1．频率为1．75eV，持续时间为100fs的激光脉冲可以导致n→π~*激发，S_1在势能的驱动下随时间演化，最后通过无辐射非绝热跃迁衰变至基态S_0，S_1激发态寿命约1450～1650飞秒。频率为2．15eV和2．2eV，持续时间为100fs的激光脉冲作用于反式偶氮苯分子，皆可导致分子从基态激发到S_2态(π→π~*激发)。30飞秒以内发生S_2(ππ~*)／S_3(π~2π~(*2))弛豫，S_3(π~2π~(*2))寿命极短，只有几个飞秒，然后弛豫到S_1态(nπ~*激发态)。2．15eV脉冲作用下，S_1的寿命约800～1000飞秒；2．2eV脉冲作用下，S_1的寿命约500～600飞秒。
2．无论是n→π~*激发还是π→π~*激发，当激光脉冲使电子激发以后，N=N键级变小，键长伸长；反式偶氮苯分子都是通过围绕中心“-N=N-”键的旋转实现异构化；在旋转的同时，两个CNN键角同时增大约15°～20°，并未出现半线型结构，说明模拟结果不支持反转机制。
3．无论是n→π~*激发还是π→π~*激发，当反式偶氮苯分子处在或衰减至S_1激发态时，N-N键长与LUMO能量密切相关，CNN键角与HOMO能量密切相关，而CNNC二面角与LUMO和HOMO之间的能隙密切相关。
4．无论是n→π~*激发还是π→π~*激发，CNN键角开始增大时分子处在在S_1激发态，此时伴随着NN键长的强烈收缩，我们认为这是振动态改变所致。
5．无论是n→π~*激发还是π→π~*激发，发生非绝热跃迁时都可能形成苯环相互垂直的中间体结构。此结构下两个与N原子相连的C原子所受力的方向决定了产物的类型，即可能形成顺式产物或反式产物。
6．π→π~*激发下，非绝热跃迁时的分子结构除了第4条中所述“垂直构型”以外，还存在CNNC二面角约为140°的“扭曲构型”。在“扭曲构型”下的衰减将导致反式产物的形成。因为n→π~*激发下未发现“扭曲构型”的存在，故n→π~*激发生成反式产物的可能性低于π→π~*激发，解释了π→π~*激发下异构化反应量子产率低于n→π~*激发的实验现象。
7．π→π~*激发下，激发态分子发生S(ππ~*)／S(π~2π~(*2))衰减后，CNN的弯曲振动有明显加强。当衰减通道为“扭曲构型”时，CNN的弯曲振动对激发态衰减做出重要贡献。
8．1)多条模拟轨迹表明，在1．75eV的频率下，脉冲辐射通量密度较小时，形成顺式异构体的可能性较大；脉冲辐射通量密度较大时，形成反式构型的可能性较大。2)多轨迹的模拟发现：脉冲频率为2．15eV，形成顺式构型的可能性较大，脉冲频率为2．2eV，形成反式构型的可能性越大。
Azobenzene is a prototype chromophoric molecule and undergoes trans (?) cis isomerization under ultraviolet or visible radiation. The two isomers display clearly different UV absorption spectra. These make azobenzene and its derivatives become good candidates for many applications, including light-triggered switches, constituents of erasable holographic data, image storage devices and in biology. For this reason, the photochemical and photophysical features of azobenzene has attracted extensive research interests for many years.
The proposal by Rau that the azobenzene molecule takes inversion path from the reactant to the product for the nπ~* excitation and rotation path for theππ~* excitation opens a debate on the photoisomerization mechanism of the azobenzene molecule. Many high level quantum chemical calculations have been applied to study the mechanism and provided valuable information in understanding this important process. In this thesis, we present a realistic dynamics simulation study of the trans-azobenzene photoisomerization under nπ~* andππ~* excitations by semiclassical electron radiation ion dynamics (SERID) approach.
In the SERID approximation, the state of the valence electrons is calculated by the time-dependent Schrddinger equation, but the radiation field and the motion of the nuclei are treated classically. In other words, the forces for driving nuclear motion are calculated by quantum chemical calculations but nuclear trajectories are updated by solving Newton's motion equation (or Ehrenfest equation). The most important characteristic of SERID is the direct inclusion of a laser pulse that interacts with the molecule. SERID has following features:
(1) The laser pulse is characterized by the vector potential A that is coupled to the Hamiltonian through the time-dependent Peierls substitution. This explicitly incorporates the interaction between laser field and electrons and allows us to investigate the effects of laser pulses on the products of a photochemical reaction. This is an important topic in the laser control of chemical reactions.
(2) The time-dependent Schrodinger equation is solved using a unitary algorithm obtained from the equation for the time evolution operator. Nuclear positions are updated by numerically integrating Newton's motion equation with the velocity Verlet algorithm which preserves phase space and satisfies the Pauli principle.
(3) Electronic structure is calculated by the density functional based tight-binding (DFTB) method. The basis functions are the non-orthogonal basis set and only valence electrons are calculated. Nuclei and core electrons together are treated as an ion. Hamiltonian matrix elements and ion-ion repulsive interaction are calculated by the density functional method and then tabulated as a function of distance of two ions for time-dependent calculations. This allows an effective calculation of forces and energies.
(4) The model calculates the forces on-the-fly. This is in contrast to the Molecular Dynamics simulation in which the potential energy surface is constructed before any simulation is conducted.
These features make the model as a realistic technique for simulating large systems. Its shortcomes are described below: (A) DFTB is a decent from DFT at LDA level, which may not be suitable for the description of the breaking of chemical bonds. (B) Electronic states and spin multiplicity are not clearly defined and therefore it is not always possible to directly compare our simulation results to high level quantum chemical calculations.
We have carried out several hundreds simulation calculations by adjusting frequency, flux, and duration of the laser pulse and obtained the following conclusions:
1. For trans-azobenzene, if the laser pulse with frequency of 1.75 eV and duration of 100 fs is used the simulation will lead to nπ~* (S_1) excitation and then the S_1 state evolves with time and decays to the ground state S_0 through the drive of the potential energy. The lifetime of S_1 state is about 1450 fs-1650 fs. Laser pulse with frequency of 2.15 eV and 2.2 eV and duration of 100 fs will lead toππ~* excitation. The excited molecule decays from the S (ππ~*) state to the S((π)~2(π~*)~2) state within 30 fs and immediately relax to a S_1 state. The S_1 state evolves with time and decays to the ground state S_0. The lifetime of S_1 state induced by pulse of 2.15eV and 2.2eV is about 800 fs-1000 fs and 500 fs-600 fs, respectively.
2. The N=N bond stretching soon after laser pulse react to azobenzene molecule and rotary motion around central "-N=N-" group company with two CNN angles concerted expanding to 15°-20°are observed either nπ~*orππ~*excited. Without finding semi-linear structure indicates the "inversion mechanism" is not supported by simulation results.
3. Both nπ~*andππ~*excitation in which closely relation between N-N bondlength versus LUMO energy, CNN angles versus HOMO energy and CNNC dihedral versus energy between HOMO and LUMO are observed when azobenzene molecule locates in S_1 excited state.
4. The S_1 state can occur either from nπ~* orππ~* excitations. When its CNN angles increase the N-N bond shorten sharply, which might be brought about owing to change of vibrational states.
5. Decay channels from the S_1 state to the S_0 state at about the perpendicular structure of two phenyl rings in azobenzene. "Perpendicular structure" will lead to formation either trans or cis isomer according to orientation of the force on the two carbon atoms which are adjacent to the nitrogen atom.
6. There is an "twisted structure" with 140°dihedral onππ~*excitation besides the above-mentioned "perpendicular structure". Decay channel at "twisted structure" onππ~* excitation will only result in the formation of trans-product. The existence of a decay channel at geometry far from the "perpendicular structure" accounts for the poor E-Z photoisomerization quantum yield forππ~* excitation.
7. The bending vibration of the CNN bond are significantly enhanced after the S_2 (ππ~*)/S_3 ((π)~2(π~*)~2 ) decay. The energy for this excitation comes from internal energy conversion at the S(ππ~*)/S((π)~2(π~*)~2) decay. This excitation promotes the CNN bond angles expansion that makes significant contribution to the decay channel at the geometry of "twisted structure."
8. Results of Multiple trajectory simulations show :
1) For nπ~* excitation at pulse frequency of 1.75eV, the smaller fluence will bring larger possibility of the formation of cis-structure, and vice versa.
2) Forππ~* excitation at pulse frequency of 2.15eV, the formation of cis-isomer has larger possibility, while at pulse frequency of 2.2eV, trans-isomer has larger possibility.
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