dftatom：一个用于原子结构计算的鲁棒通用薛定谔和狄拉克解算器
dftatom: A robust and general Schrödinger and Dirac solver for atomic structure calculations
摘要：
本文提出了一种求解径向薛定谔方程、狄拉克方程和Kohn-Sham方程的鲁棒通用方法。该公式承认一般的潜力和网格：均匀，指数，或其他定义的节点分布和导数函数。对于给定的网格类型，可以通过增加网格点的数量来系统地控制收敛。径向积分进行了渐近形式，龙格-库塔和隐式亚当斯方法的组合。特征函数的确定，结合二分法和扰动法的鲁棒性和速度。一个向外的泊松积分，以增加在核心区域的准确性，允许$10^{-8}$ Hartree的绝对精度，以达到重原子，如铀的总能量。详细的收敛性研究和计算参数提供，以实现在实践中通常需要的精度。原子序数$Z$ = 1- 92的分析和当前基准密度泛函结果的比较，验证并提供了一个完善的当前基准。一个有效的，模块化的Fortran 95实现，\ttt{dftatom}，提供作为开放源代码，包括示例，测试，和包装接口到其他语言，其中特别强调的独立性（无全局变量），可重用性，和一般性的个人例程。
英文摘要：
A robust and general solver for the radial Schrödinger, Dirac, and Kohn--Sham equations is presented. The formulation admits general potentials and meshes: uniform, exponential, or other defined by nodal distribution and derivative functions. For a given mesh type, convergence can be controlled systematically by increasing the number of grid points. Radial integrations are carried out using a combination of asymptotic forms, Runge-Kutta, and implicit Adams methods. Eigenfunctions are determined by a combination of bisection and perturbation methods for robustness and speed. An outward Poisson integration is employed to increase accuracy in the core region, allowing absolute accuracies of $10^{-8}$ Hartree to be attained for total energies of heavy atoms such as uranium. Detailed convergence studies are presented and computational parameters are provided to achieve accuracies commonly required in practice. Comparisons to analytic and current-benchmark density-functional results for atomic number $Z$ = 1--92 are presented, verifying and providing a refinement to current benchmarks. An efficient, modular Fortran 95 implementation, \ttt{dftatom}, is provided as open source, including examples, tests, and wrappers for interface to other languages; wherein particular emphasis is placed on the independence (no global variables), reusability, and generality of the individual routines.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
