量子动力学中并行算法的发展与应用
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摘要
本文针对量子动力学理论研究中并行算法问题,发展了Shepard插值方法的计算势能的GPU算法；研究了范德华体系振转光谱的束缚态理论计算的MPI/OpenMP并行算法；研究了X+NH3反应的七维量子动力学理论方法和MPI/OpenMP并行算法,并应用于研究Cl (2P)+NH3/ND3反应。本论文的研究工作如下：
1.采用改进的Shepard插值方法构造的势能面被广泛用于化学反应动力学研究,这种构造方法通过对从头算数据点进行插值来获得任意构型的能量,采用该方法构造的势能面精度高,能够更精准地研究化学反应动力学。但是在实际运用中,插值势能面计算量大,从而限制了该方法的应用。本工作基于GPU的强大计算能力和高度并行性特点,发展采用Shepard插值方法计算势能的GPU新算法。并以H+H2O? H2+OH, H+NH3?H2NH2,H+CH4?H2+CH3这3个反应的势能面为例对算法进行验证,发现GPU算法相对CPU算法具有明显的优越性,并且GPU加速比随着体系增大而增大,随着数据点增加而增加。
2.范德华体系振转光谱的束缚态理论计算需求精确求解Schrodinger方程,由于体系的波函数展开为各个坐标基函数的乘积,所以体系基函数的大小随原子数增加呈指数增加,计算时间和内存需求也随之增加。需要应用并行化计算方案使计算得以实现。我们针对线性分子-线性分子组成的范德华体系振转光谱的理论研究,开发了束缚态计算的并行算法,采用节点间采用MPI和节点内采用OpenMP的并行方案,并针对N2O-N2O体系验证了该并行算法,结果显示计算效率明显提高,加速比是1.67倍到8.6倍。
3. Cl+NH3在过渡态前后都有较深的势阱,对量子动力学理论计算提出了挑战。在动力学计算中,我们采用X+YCZ2类型的七维量子动力学模型,其中不参与反应的NH2基团在反应过程中保持不变,采用该模型我们对Cl+NH3和Cl+ND3两个反应进行了研究,计算结果显示Cl+NH3和Cl+ND3有相似的动力学行为,而且反应几率都是非常小,与实验观测一致。由于该反应Cl+ND3比较复杂,Cl原子有较重的质量,因此,基函数大小为3.175*109,势能格点的数目为3.78*1010,传播时间为是25000a.u,是当前量子动力学研究中计算量最大的工作之一。
For the problem of parallel algorithms of quantum dynamics, GPU algorithm of accelerating modified Shepard interpolated potential energy calculations is developed; the OpenMP and MPI parallel algorithms of bound state calculation of vibrational and rotational spectrum of van der Waals(vdW) system is investigated; the method of seven dimension quantum dynamics theory and MPI/OpenMP parallel algorithms of X+NH3reaction is investigated, and this method and algorithm is applied to study the reaction of Cl (2P)+NH3/ND3. The present thesis is organized as follows:
1. The potential energy surfaces constructed with the Modified Shepard interpolation scheme have been widely used in studies of chemical reaction dynamics. The energy of any configuration is obtained by interpolation of ab initio data points. The potential energy surface constructed using this method is high precision, more precise for research of chemical reaction dynamics. However, in practical application, the interpolation potential energy surface is computationally intensive, which limits the application of this method. This work is based on GPU computing power and highly parallel features, development of GPU algorithm of the Shepard interpolation method to calculate the potential energy. The algorithm is veritied through the potential energy surfaces of the three reactions of H+H2O(?)H2+OH, H+NH3(?)H2+NH2, H+CH4(?)H2+CH3. We find that the GPU algorithm has obvious advantages relative CPU algorithm, GPU speedup increases with the system size and speedup inceases with the increase of the number of data points in the PES(Potential Energy Surface).
2. The bound state calculation of vibrational and rotational spectrum of vdW system needs exact solution of the Schrodinger equation. Because the wave function of the system is expanded as the product of the basis function of each degree of freedom, so the size of basis set increase exponentially with the number of atoms. Computation time and memory requirements have increased. Computing can be achieved by application of parallel computing. Parallel algorithms of bound state calculation using MPI between nodes and OpenMP in node is developed for the research of linear molecules-linear molecular vibrational and rotational spectrum of vdW system, and the parallel algorithm is verified by using N2O-N2O system, the results show that the computational efficiency is significantly improved, the speedup is1.67times to8.6times.
3. That there are deep wells before and after the transition state is a challenge for theoretical calculation of quantum dynamics. In the calculation of dynamics, a seven-dimensional quantum dynamics model for the reaction X+YCZ2is employed. NH2group which does not participate in the reaction remains unchanged during the reaction, the two reactions of Cl+NH3and Cl+ND3are investigated by using this model. The calculated results show that C1+NH3and Cl+ND3have similar dynamic behavior and the reaction probabilities are small, consistent with the experiment observations. Because the reaction Cl+ND3is more complex and the Cl atom has heavy mass, so the size of the total basis function is3.175*109, the number of potential energy nodes is3.78*1010, the entire propagation time is25,000a. u. This is one of the largest computational work of current quantum dynamics study.
1.采用改进的Shepard插值方法构造的势能面被广泛用于化学反应动力学研究,这种构造方法通过对从头算数据点进行插值来获得任意构型的能量,采用该方法构造的势能面精度高,能够更精准地研究化学反应动力学。但是在实际运用中,插值势能面计算量大,从而限制了该方法的应用。本工作基于GPU的强大计算能力和高度并行性特点,发展采用Shepard插值方法计算势能的GPU新算法。并以H+H2O? H2+OH, H+NH3?H2NH2,H+CH4?H2+CH3这3个反应的势能面为例对算法进行验证,发现GPU算法相对CPU算法具有明显的优越性,并且GPU加速比随着体系增大而增大,随着数据点增加而增加。
2.范德华体系振转光谱的束缚态理论计算需求精确求解Schrodinger方程,由于体系的波函数展开为各个坐标基函数的乘积,所以体系基函数的大小随原子数增加呈指数增加,计算时间和内存需求也随之增加。需要应用并行化计算方案使计算得以实现。我们针对线性分子-线性分子组成的范德华体系振转光谱的理论研究,开发了束缚态计算的并行算法,采用节点间采用MPI和节点内采用OpenMP的并行方案,并针对N2O-N2O体系验证了该并行算法,结果显示计算效率明显提高,加速比是1.67倍到8.6倍。
3. Cl+NH3在过渡态前后都有较深的势阱,对量子动力学理论计算提出了挑战。在动力学计算中,我们采用X+YCZ2类型的七维量子动力学模型,其中不参与反应的NH2基团在反应过程中保持不变,采用该模型我们对Cl+NH3和Cl+ND3两个反应进行了研究,计算结果显示Cl+NH3和Cl+ND3有相似的动力学行为,而且反应几率都是非常小,与实验观测一致。由于该反应Cl+ND3比较复杂,Cl原子有较重的质量,因此,基函数大小为3.175*109,势能格点的数目为3.78*1010,传播时间为是25000a.u,是当前量子动力学研究中计算量最大的工作之一。
For the problem of parallel algorithms of quantum dynamics, GPU algorithm of accelerating modified Shepard interpolated potential energy calculations is developed; the OpenMP and MPI parallel algorithms of bound state calculation of vibrational and rotational spectrum of van der Waals(vdW) system is investigated; the method of seven dimension quantum dynamics theory and MPI/OpenMP parallel algorithms of X+NH3reaction is investigated, and this method and algorithm is applied to study the reaction of Cl (2P)+NH3/ND3. The present thesis is organized as follows:
1. The potential energy surfaces constructed with the Modified Shepard interpolation scheme have been widely used in studies of chemical reaction dynamics. The energy of any configuration is obtained by interpolation of ab initio data points. The potential energy surface constructed using this method is high precision, more precise for research of chemical reaction dynamics. However, in practical application, the interpolation potential energy surface is computationally intensive, which limits the application of this method. This work is based on GPU computing power and highly parallel features, development of GPU algorithm of the Shepard interpolation method to calculate the potential energy. The algorithm is veritied through the potential energy surfaces of the three reactions of H+H2O(?)H2+OH, H+NH3(?)H2+NH2, H+CH4(?)H2+CH3. We find that the GPU algorithm has obvious advantages relative CPU algorithm, GPU speedup increases with the system size and speedup inceases with the increase of the number of data points in the PES(Potential Energy Surface).
2. The bound state calculation of vibrational and rotational spectrum of vdW system needs exact solution of the Schrodinger equation. Because the wave function of the system is expanded as the product of the basis function of each degree of freedom, so the size of basis set increase exponentially with the number of atoms. Computation time and memory requirements have increased. Computing can be achieved by application of parallel computing. Parallel algorithms of bound state calculation using MPI between nodes and OpenMP in node is developed for the research of linear molecules-linear molecular vibrational and rotational spectrum of vdW system, and the parallel algorithm is verified by using N2O-N2O system, the results show that the computational efficiency is significantly improved, the speedup is1.67times to8.6times.
3. That there are deep wells before and after the transition state is a challenge for theoretical calculation of quantum dynamics. In the calculation of dynamics, a seven-dimensional quantum dynamics model for the reaction X+YCZ2is employed. NH2group which does not participate in the reaction remains unchanged during the reaction, the two reactions of Cl+NH3and Cl+ND3are investigated by using this model. The calculated results show that C1+NH3and Cl+ND3have similar dynamic behavior and the reaction probabilities are small, consistent with the experiment observations. Because the reaction Cl+ND3is more complex and the Cl atom has heavy mass, so the size of the total basis function is3.175*109, the number of potential energy nodes is3.78*1010, the entire propagation time is25,000a. u. This is one of the largest computational work of current quantum dynamics study.
引文
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