Optimization of Complex Slater-type Functions with Analytic Derivative Methods for Describing Photoionization Differential Cross Sections
Optimization of Complex Slater-type Functions with Analytic Derivative Methods for Describing Photoionization Differential Cross Sections
复制标题
用解析导数方法优化复斯莱特型函数来描述光电离微分截面
DOI：
10.1002/jcc.24766
复制
发表时间：
2017
影响因子：
3
通讯作者：
S.Yabushita
中科院分区：
文献类型：
--
作者：
R.Matsuzaki;S.Yabushita
复基函数（CBF）方法应用于各种原子和分子的光电离问题，可以解释为一个 方法来解决驱动型（非齐次）薛定谔方程，其驱动项是偶极算子乘以初始状态波函数。然而，有效的基函数表示的解决方案还没有得到充分的研究。此外，它们的解与普通薛定谔方程的解之间的关系一直不清楚。由于这些原因，大多数以前的应用已被限制到总横截面。为了检验CBF方法对微分截面和非对称性参数的适用性，我们证明了通过优化频率相关极化率的复试探函数，可以变分地获得驱动型薛定谔方程的复值解。用解析导数法对具有5个或6个复斯莱特型轨道（cSTO）的氢光电离问题进行了实验计算，优化了它们的复值展开系数和轨道指数.在覆盖典型分子区域的宽范围内，精确地求得了解的真实的和虚部。通过使用WKB方法将CBF解从内匹配区域外推到渐进区域，成功地获得了它们的相移和不对称参数。基于CBF方法和驱动型方程方法之间的密切联系，解释了优化轨道指数在复平面中的分布。所获得的信息是必不可少的，在未来的分子应用中构建适当的基组。© 2017 Wiley Periodicals，Inc.
The complex basis function (CBF) method applied to various atomic and molecular photoionization problems can be interpreted as an method to solve the driven‐type (inhomogeneous) Schrödinger equation, whose driven term being dipole operator times the initial state wave function. However, efficient basis functions for representing the solution have not fully been studied. Moreover, the relation between their solution and that of the ordinary Schrödinger equation has been unclear. For these reasons, most previous applications have been limited to total cross sections. To examine the applicability of the CBF method to differential cross sections and asymmetry parameters, we show that the complex valued solution to the driven‐type Schrödinger equation can be variationally obtained by optimizing the complex trial functions for the frequency dependent polarizability. In the test calculations made for the hydrogen photoionization problem with five or six complex Slater‐type orbitals (cSTOs), their complex valued expansion coefficients and the orbital exponents have been optimized with the analytic derivative method. Both the real and imaginary parts of the solution have been obtained accurately in a wide region covering typical molecular regions. Their phase shifts and asymmetry parameters are successfully obtained by extrapolating the CBF solution from the inner matching region to the asymptotic region using WKB method. The distribution of the optimized orbital exponents in the complex plane is explained based on the close connection between the CBF method and the driven‐type equation method. The obtained information is essential to constructing the appropriate basis sets in future molecular applications. © 2017 Wiley Periodicals, Inc.