激光诱导光化学反应模拟与半经验MRCI及其解析梯度程序化研究
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摘要
首先我们概述了分子动力学的理论基础,包括波恩-奥本海默近似(或绝热近似)、半经典近似及两种非绝热动力学近似方法—Ehrenfest动力学和系间窜越(SurfaceHopping近似)。在此基础上我们介绍了一种半经典非绝热动力学模拟方法—半经典的电子-辐射-离子动力学(SERID),此种方法具有以下几个特点:
1.在电子Hamiltonian中通过时间有关的Peierls替代引入了辐射场的矢势A(x,t),即在模型中引入了激光与电子的相互作用。
2.动力学过程采用半经典模型。电子运动用电子波函数描述,而电子波函数的更新需要求解含时Schr(o|¨)dinger方程。核运动轨迹借求解牛顿运动方程获得,求解时采用了一种辛算法(velocity Verlet algorithm),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 tight-binding method)方法计算。DFTB计算提供了模拟过程中体系的各种能量的变化,电子在轨道之间的跃迁等。
4.是一种直接动力学计算方案,即不需预先构建势能面,能量和力的计算采用了即用即算(on the fly)方案。
在这一章我们还简要剖析了SERID程序(由我们的合作者豆育升教授提供),给出了程序的流程图。并指出了该程序的优点和某些不足之处。
其次我们采用SERID方法模拟了环丁烷光解离生成两个乙烯分子的非绝热动力学过程。模拟结果表明环丁烷光解离是一个两步过程,首先环丁烷一个C-C键断裂形成一个四亚甲基中间体,接着这个中间体解离生成两个乙烯分子。这个结果与以前报道的实验结果一致。为了将模拟结果与以前报道的ab initio结果进行对比,我们采用CASSCF/MRPT2(complete active space self-consistent field/multi-reference secondorder perturbation)方法沿着模拟的反应路径构造了解离过程中基态和低能激发态的势能曲线,还构造了给定C—C键长后各电子态的最小能量路径。这些计算结果表明,环丁烷光解离过程中四亚甲基中间体确实存在,但是却出现在1~3A的势能曲线上,因为此时1~3A的能量比基态的低,而且基态与1~3A的势能曲线发生了两次相交,其中第一次相交对应于四亚甲基中间体的形成,而经过第二次相交后,1~3A的能量比基态的高,从而体系又回到了基态。同样我们采用SERID方法模拟了腺嘌昤非辐射去活化的非绝热动力学过程。应用两个不同波长的激光模拟得到了两条不同的反应路径,分别对应于氨基的平面外扭转和C_2-H键的平面外扭转。为了与以前报道的ab initio结果进行对比,我们采用CASSCF方法沿着两条模拟的反应路径构造了解离过程中基态以及能量较低激发态的势能曲线。结果表明两条反应路径中都存在第一激发态(~1ππ~*(~1L_α))与基态(S_0)的相交,导致电子从激发态回到基态,即活化过程中是从~1ππ~*(~1L_α)到S_0的衰减过程,这与前人的ab initio计算结果不同;他们的计算认为氨基平面外扭转的反应路径是从~1nπ~*到S_0的衰减过程。另外通过对各电子态主组态的分析,我们得到的激发态寿命与实验结果基本一致。
鉴于SERID方法中DFTB的缺点,我们拟采用半经验MRCI(multi-referenceconfiguration interaction)方法来改进电子结构计算。为了将改进方法应用于非绝热动力学中,半经验MRCI的解析梯度也是重要的。因此在第四章中我们概述了半经验MRCI及其解析梯度的理论基础。首先简要介绍了半经验方法的基本原理及发展现状,其中重点介绍了NDDO(neglect of diatomic differential overlap)方法及其参量改进方法。然后重点讨论我们的基于图形酉群的MRCISD算法。我们讨论了酉群不可约表示的基与自旋匹配的组态函数(CSF)的对应关系;给出了Shavitt建议的用于记录CSF的不同行表(DRT)的构造方式;描述了如何搜寻DRT中的Loop,从而计算生成元和生成元乘积的矩阵元以及哈密顿矩阵元。在此基础上简要介绍了最新发展的基于空穴粒子对应的MRCISD算法及其近似算法—双收缩CI(DCCI)的基本原理。在空穴粒子对应的MRCISD算法中,我们重新定义了不同行表(DRT),将空穴空间域外空间的完成Loop和未完成Loop预先计算出来,使得不同行表只包括活性空间的子DRT,这样大大降低了Loop搜索的计算量。作为近似算法,DCCI充分应用了空穴粒子对应的原理,将空穴空间和外空间都收缩为单一步矢,这样大大降低了参与变分的CI系数的数目。在本章的最后,我们介绍了半经验MRCISD解析梯度的理论基础。其中解析梯度的计算可以分为两部分,第一部分计算积分梯度的贡献,称为静态部分;第二部分计算分子轨道系数梯度的贡献,称为响应部分。静态部分需要CI约化密度矩阵与积分梯度相结合,响应部分需要计算Lagrangian矩阵元与求解CPRHF(restricted coupled perturb Hartree-Fock)方程。基于此我们讨论了半经验MRCI及其解析梯度程序的实现过程。半经验MRCI程序将MOPAC 7.0与我们小组发展的XIAN-CI程序包中的基于空穴粒子对应的MRCISD和DCCI程序相结合。从MOPAC 7.0中的MNDO(modified neglect differential overlap)计算得到原子轨道积分及分子轨道系数,完成积分变换得到CI计算所需的分子轨道积分,接着采用MRCISD或DCCI程序计算CI能量。计算过程中我们根据冻结轨道的特点,分开计算冻结轨道和CI轨道对能量的贡献以减少计算量。在半经验MRCI解析梯度程序的实现过程中,首先需要从CI系数和耦合系数确定约化密度矩阵,接着需要将MNDO计算得到的原子轨道积分梯度及分子轨道系数作为输入,计算解析梯度静态部分的贡献;然后计算Lagrangian矩阵元和Z向量,最后计算解析梯度响应部分的贡献。其中CI密度矩阵的计算量最大,直接决定计算瓶颈及计算效率。我们不仅采用直接CI的算法避免了传统CI中需要保存耦合系数或哈密顿矩阵元所带来的计算瓶颈,而且应用空穴粒子对应提高了计算效率。同时针对冻结轨道的特点,应用了许多简化算法以提高计算效率。测试结果显示,我们的半经验MRCI及其解析梯度程序无论从计算规模还是计算效率上都比以前报道的程序优越。
The dissertation can be divided into two parts.One part includes chapter 1,2 and 3.In this part,we introduce a semiclassical nonadiabatic molecular dynamic simulation--a semiclassical electron-radiation-ion dynamic approach(SERID) with its applications into the research of the laser induced photochemical reactions,which involve the photodissociation of cyclobutane and the nonradiative deactivation of adenine.The other part includes chapter 4 and 5.In this part,we present a new implementation of a semiempirical multireference configuration interaction with single and double excitations (MRCISD) with analytic gradients.First of all,We briefly show the theoretical background of molecular dynamic and point out the merit and demerit of SERID.In addition,we display the flow chart of a SERID program,which is provided by R.E.Allen and Yusheng Dou.Secondly,we report the SERID simulations for the photodissociation of cyclobutane into two molecules of ethylene.The results clearly show that the reaction processes by two steps.The first step is the C -C bond breaking of Cyclobutane and form the intermediate, tetramethylene diradical,then in the second step,the C-C bond in tetramethylene breaks and two ethylenes move away from each other.The reaction path is in a good agreement with experimental observation.In order to explain the results,the CASSCF/MRPT2 methods are employed to calculate the potential energy curves(PECs) of the ground state and some low-lying excited states along the path determined from the simulation.On the other hand,the PECs are constructed as a function of C-C bond distance but optimizing remaining internal coordinates by employing CASSCF/MRCISD method.These results reveal that the tetramethylene intermediate diradical is actually formed,but on the PECs of 1~3A state.Thirdly,a realistic dynamics simulation study of the ultrafast radiationless deactivation of 9H-adenine is performed employing the SERID.The simulation finds that the excited molecule decays to the electronic ground state through two different radiationless pathways:one decay channel involves the out-of-plane vibration of the amino group while the other decay strongly associates with the deformation of the pyrimidine at the C_2 atom.In order to explain the results,the CASSCF methods are employed to calculate the potential energy curves(PECs) of the ground state and four low-lying excited states along the path determined from the simulation.These calculations reveal that the excited molecule decays to the electronic ground state from the lowest excited state ~1ππ~*(~1L_α) on both two paths.In addition,the determined lifetime of the excited state obtained is in agreement with the experimental observation.
On the other hand,we introduce the theoretical background of semiempirical MRCI and analytic gradients.Firstly,we briefly show the semiempirical methods and recent implementations,focus on the NDDO method and its parameter improvement.Secondly, the graphical unitary group approach(GUGA) has been introduced to calculate MRCISD and its approximation,double contracted CI(DCCI),including the hole-particle symmetry and a mixed driven model for computing coupling coefficients.In addition,the theoretical background of analytic gradient is also briefly presented.After that we first report the improved algorithms,and then employ them to implement the programs of semiempirical MRCI and analytic gradients.The reduced CI density matrices are very crucial to the implementation of analytic gradients,because they are difficult to calculate.Therefore we use the new algorithms based on the hole-particle symmetry to reduce the calculating time. Our benchmark calculations indicate that our program is not only efficient but also without bottleneck.
1.在电子Hamiltonian中通过时间有关的Peierls替代引入了辐射场的矢势A(x,t),即在模型中引入了激光与电子的相互作用。
2.动力学过程采用半经典模型。电子运动用电子波函数描述,而电子波函数的更新需要求解含时Schr(o|¨)dinger方程。核运动轨迹借求解牛顿运动方程获得,求解时采用了一种辛算法(velocity Verlet algorithm),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 tight-binding method)方法计算。DFTB计算提供了模拟过程中体系的各种能量的变化,电子在轨道之间的跃迁等。
4.是一种直接动力学计算方案,即不需预先构建势能面,能量和力的计算采用了即用即算(on the fly)方案。
在这一章我们还简要剖析了SERID程序(由我们的合作者豆育升教授提供),给出了程序的流程图。并指出了该程序的优点和某些不足之处。
其次我们采用SERID方法模拟了环丁烷光解离生成两个乙烯分子的非绝热动力学过程。模拟结果表明环丁烷光解离是一个两步过程,首先环丁烷一个C-C键断裂形成一个四亚甲基中间体,接着这个中间体解离生成两个乙烯分子。这个结果与以前报道的实验结果一致。为了将模拟结果与以前报道的ab initio结果进行对比,我们采用CASSCF/MRPT2(complete active space self-consistent field/multi-reference secondorder perturbation)方法沿着模拟的反应路径构造了解离过程中基态和低能激发态的势能曲线,还构造了给定C—C键长后各电子态的最小能量路径。这些计算结果表明,环丁烷光解离过程中四亚甲基中间体确实存在,但是却出现在1~3A的势能曲线上,因为此时1~3A的能量比基态的低,而且基态与1~3A的势能曲线发生了两次相交,其中第一次相交对应于四亚甲基中间体的形成,而经过第二次相交后,1~3A的能量比基态的高,从而体系又回到了基态。同样我们采用SERID方法模拟了腺嘌昤非辐射去活化的非绝热动力学过程。应用两个不同波长的激光模拟得到了两条不同的反应路径,分别对应于氨基的平面外扭转和C_2-H键的平面外扭转。为了与以前报道的ab initio结果进行对比,我们采用CASSCF方法沿着两条模拟的反应路径构造了解离过程中基态以及能量较低激发态的势能曲线。结果表明两条反应路径中都存在第一激发态(~1ππ~*(~1L_α))与基态(S_0)的相交,导致电子从激发态回到基态,即活化过程中是从~1ππ~*(~1L_α)到S_0的衰减过程,这与前人的ab initio计算结果不同;他们的计算认为氨基平面外扭转的反应路径是从~1nπ~*到S_0的衰减过程。另外通过对各电子态主组态的分析,我们得到的激发态寿命与实验结果基本一致。
鉴于SERID方法中DFTB的缺点,我们拟采用半经验MRCI(multi-referenceconfiguration interaction)方法来改进电子结构计算。为了将改进方法应用于非绝热动力学中,半经验MRCI的解析梯度也是重要的。因此在第四章中我们概述了半经验MRCI及其解析梯度的理论基础。首先简要介绍了半经验方法的基本原理及发展现状,其中重点介绍了NDDO(neglect of diatomic differential overlap)方法及其参量改进方法。然后重点讨论我们的基于图形酉群的MRCISD算法。我们讨论了酉群不可约表示的基与自旋匹配的组态函数(CSF)的对应关系;给出了Shavitt建议的用于记录CSF的不同行表(DRT)的构造方式;描述了如何搜寻DRT中的Loop,从而计算生成元和生成元乘积的矩阵元以及哈密顿矩阵元。在此基础上简要介绍了最新发展的基于空穴粒子对应的MRCISD算法及其近似算法—双收缩CI(DCCI)的基本原理。在空穴粒子对应的MRCISD算法中,我们重新定义了不同行表(DRT),将空穴空间域外空间的完成Loop和未完成Loop预先计算出来,使得不同行表只包括活性空间的子DRT,这样大大降低了Loop搜索的计算量。作为近似算法,DCCI充分应用了空穴粒子对应的原理,将空穴空间和外空间都收缩为单一步矢,这样大大降低了参与变分的CI系数的数目。在本章的最后,我们介绍了半经验MRCISD解析梯度的理论基础。其中解析梯度的计算可以分为两部分,第一部分计算积分梯度的贡献,称为静态部分;第二部分计算分子轨道系数梯度的贡献,称为响应部分。静态部分需要CI约化密度矩阵与积分梯度相结合,响应部分需要计算Lagrangian矩阵元与求解CPRHF(restricted coupled perturb Hartree-Fock)方程。基于此我们讨论了半经验MRCI及其解析梯度程序的实现过程。半经验MRCI程序将MOPAC 7.0与我们小组发展的XIAN-CI程序包中的基于空穴粒子对应的MRCISD和DCCI程序相结合。从MOPAC 7.0中的MNDO(modified neglect differential overlap)计算得到原子轨道积分及分子轨道系数,完成积分变换得到CI计算所需的分子轨道积分,接着采用MRCISD或DCCI程序计算CI能量。计算过程中我们根据冻结轨道的特点,分开计算冻结轨道和CI轨道对能量的贡献以减少计算量。在半经验MRCI解析梯度程序的实现过程中,首先需要从CI系数和耦合系数确定约化密度矩阵,接着需要将MNDO计算得到的原子轨道积分梯度及分子轨道系数作为输入,计算解析梯度静态部分的贡献;然后计算Lagrangian矩阵元和Z向量,最后计算解析梯度响应部分的贡献。其中CI密度矩阵的计算量最大,直接决定计算瓶颈及计算效率。我们不仅采用直接CI的算法避免了传统CI中需要保存耦合系数或哈密顿矩阵元所带来的计算瓶颈,而且应用空穴粒子对应提高了计算效率。同时针对冻结轨道的特点,应用了许多简化算法以提高计算效率。测试结果显示,我们的半经验MRCI及其解析梯度程序无论从计算规模还是计算效率上都比以前报道的程序优越。
The dissertation can be divided into two parts.One part includes chapter 1,2 and 3.In this part,we introduce a semiclassical nonadiabatic molecular dynamic simulation--a semiclassical electron-radiation-ion dynamic approach(SERID) with its applications into the research of the laser induced photochemical reactions,which involve the photodissociation of cyclobutane and the nonradiative deactivation of adenine.The other part includes chapter 4 and 5.In this part,we present a new implementation of a semiempirical multireference configuration interaction with single and double excitations (MRCISD) with analytic gradients.First of all,We briefly show the theoretical background of molecular dynamic and point out the merit and demerit of SERID.In addition,we display the flow chart of a SERID program,which is provided by R.E.Allen and Yusheng Dou.Secondly,we report the SERID simulations for the photodissociation of cyclobutane into two molecules of ethylene.The results clearly show that the reaction processes by two steps.The first step is the C -C bond breaking of Cyclobutane and form the intermediate, tetramethylene diradical,then in the second step,the C-C bond in tetramethylene breaks and two ethylenes move away from each other.The reaction path is in a good agreement with experimental observation.In order to explain the results,the CASSCF/MRPT2 methods are employed to calculate the potential energy curves(PECs) of the ground state and some low-lying excited states along the path determined from the simulation.On the other hand,the PECs are constructed as a function of C-C bond distance but optimizing remaining internal coordinates by employing CASSCF/MRCISD method.These results reveal that the tetramethylene intermediate diradical is actually formed,but on the PECs of 1~3A state.Thirdly,a realistic dynamics simulation study of the ultrafast radiationless deactivation of 9H-adenine is performed employing the SERID.The simulation finds that the excited molecule decays to the electronic ground state through two different radiationless pathways:one decay channel involves the out-of-plane vibration of the amino group while the other decay strongly associates with the deformation of the pyrimidine at the C_2 atom.In order to explain the results,the CASSCF methods are employed to calculate the potential energy curves(PECs) of the ground state and four low-lying excited states along the path determined from the simulation.These calculations reveal that the excited molecule decays to the electronic ground state from the lowest excited state ~1ππ~*(~1L_α) on both two paths.In addition,the determined lifetime of the excited state obtained is in agreement with the experimental observation.
On the other hand,we introduce the theoretical background of semiempirical MRCI and analytic gradients.Firstly,we briefly show the semiempirical methods and recent implementations,focus on the NDDO method and its parameter improvement.Secondly, the graphical unitary group approach(GUGA) has been introduced to calculate MRCISD and its approximation,double contracted CI(DCCI),including the hole-particle symmetry and a mixed driven model for computing coupling coefficients.In addition,the theoretical background of analytic gradient is also briefly presented.After that we first report the improved algorithms,and then employ them to implement the programs of semiempirical MRCI and analytic gradients.The reduced CI density matrices are very crucial to the implementation of analytic gradients,because they are difficult to calculate.Therefore we use the new algorithms based on the hole-particle symmetry to reduce the calculating time. Our benchmark calculations indicate that our program is not only efficient but also without bottleneck.
引文
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