分子电子态跃迁偶极矩解析表达式构建研究

The precise measurement and manipulation of molecular electronic states and their changes with external field are attracting much attention and in-depth research in the frontier of atomic and molecular physics. In recent years, the experimental research has achieved significant progress, but theoretical research lags behind. One reason is lack of enough development for the new method to calculate dynamics relative to the coupled electronic states, however, the main thing is that no method with high computational efficiency to express the transition dipole moments of the interaction between the molecular electronic states. The present project will build high-precision analytical expressions for the transition dipole moment. With the characteristics of the molecular transition dipole moment changing with the coordinates in mind, we will construct the analytical function with some fitting parameters based on the idea of many-body expansion and particularly emphasising on the obvisouly undulating area of transition dipole moment. We will achieve rapid fitting of the complex problem by combining the constructed function, the non-linear least square fitting and the acceleration method with GPU parallel. After determining the specific typical molecules for photoassociation and photodissociation researches, we will establish the calculation scheme of single-point collection which is able to satisfactory reflect the characteristics of transition dipole moment interaction between the electronic states of molecule. Then, a sufficient number of single-point values can be obtained using the scheme. With the non-linear least square fitting and the obtained collection of single point transition dipole moment, the parameters in the constructed analytical expression can be determined. So far, the analytical function of the transition dipole moment, which can be served as photoassociation or photodissociation studies, has been obtained. It is expected that the new constructed analytical functions could enhance the computational simulation level of the photoassociation and photodissociation dynamics.

利用外场精确测量和操控分子的电子状态及其变化是倍受关注和正在深入研究的原子与分子物理前沿领域。近年来实验研究进展明显，但理论研究严重滞后。原因之一是针对多电子态耦合的动力学计算新方法发展不足，但更主要的是缺少高精度和高计算效率的表达电子态间相互作用跃迁偶极矩方法。本项目将构建高精度跃迁偶极矩解析表达式。根据分子跃迁偶极矩随坐标变化的特点，以多体展式思想为基础、特别注重跃迁偶极矩变化起伏较大区域的描述，构建出带拟合参数的解析函数表达式。将所构建的表达式、最小二乘拟合方和GPU并行方法相结合，实现复杂拟合快速化。选定光缔合和光离解研究的典型分子，确立能够全面反映分子的电子态间相互作用特点的跃迁偶极矩单点集合计算方案，获得足够数量的单点值。利用单点集合进行非线性拟合确定所构建表达式中的参数，从而获得能够用于光缔合或光离解研究的跃迁偶极矩的解析函数表达式，提升光缔合和光离解动力学过程计算模拟水平。

分子电子态间跃迁偶极矩是研究利用外场操控分子的电子状态必不可少的信息。由于它随分子几何结构变化而变化，而不同光激发或光离解动力学过程中涉及分子结构又是随时间或外场而变化的，因此需要构建跃迁偶极矩解析表达式才能进行光激发或光离解过程模拟。但是一直缺少高精度和高计算效率的表达电子态间相互作用跃迁偶极矩方法，严重制约了外场操控分子动力学的理论研究。根据分子跃迁偶极矩随坐标变化的特点，本项目对于双原子分子采用Aguado and Paniagua(AP)函数,而对三原子分子则采用对称化的结构坐标作为输入层、以跃迁偶极矩为输出层，基于神经网络，针对不同体系分别采用了不同的神经元组合，构建了带拟合参数的解析表达式。对H3+分子使用10*15神经元，对应有221个待定参数；而对HeH2+分子则使用15*15神经元，共有316个待定常数。将所构建的表达式、最小二乘拟合方法和多核心并行方法相结合，实现了复杂拟合快速化。确定了能够比较全面反映分子电子态间相互作用特点的单点集合计算方案，基于从头计算获得了光激发和光离解研究的典型分子XBe（X=LiRb, Cs）、MH±（M=B,N Ga,In）、H3+，HeH2+的势能面和跃迁偶极矩足够数量的单点值。通过对各个结构进行分析，去除了一些存在收敛问题或明显与整体变化趋势不符的点，最终确定势能面每个电子态约45000个结构，跃迁偶极矩的x和y方向各42000个点参与拟合确定所构建表达式中的参数，从而获得能够用于光激发或光离解研究的跃迁偶极矩解析函数表达式，为提升这类研究水平提供了不可或缺的基础。为了考察基于神经网络表达式的效果，我们也用它拟合了H3+，HeH2+分子的基态和激发态的势能面，并与基于AP函数的H3+拟合结果进行了比较，发现基于神经网络的表达式拟合方均根误差小了一个数量级。.利用本团队的计算资源和第一性原理计算程序，还开展了一些分子光谱、团簇结构与反应、复杂体系的力、光、电性质与其微观结构关系研究。结果可增进人们对激光冷却、光与物质相互作用、分子电子器件和发展氢能及利用太阳能等方面的理解和认识。