Relativistic radial electron density functions and natural orbitals from GRASP2018

A new module, RDENSITY, of the GRASP2018 package [1] is presented for evaluating the radial electron density function of an atomic state described by a multiconfiguration Dirac-Hartree-Fock or configuration interaction wave function in the fully relativistic scheme. The present module is the relativistic version of DENSITY [2] that was developed for the ATSP2K package [3]. The calculation of the spin-angular factors entering in the expression of the expectation value of the density operator is performed using the angular momentum theory in orbital, spin, and quasispin spaces, adopting a generalized graphical technique [4]. The natural orbitals (NOs) are evaluated from the diagonalization of the density matrix, taking advantage of its κ-block structure. The features of the code are discussed in detail, focusing on the advantages and properties of the NOs and on the electron radial density picture as a mean for investigating electron correlation and relativistic effects.本文提出了GRASP2018软件包[1]的全新模块RDENSITY，用于在全相对论框架下，计算由多组态狄拉克-哈特里-福克（multiconfiguration Dirac-Hartree-Fock）或组态相互作用（configuration interaction）波函数所描述的原子态的径向电子密度函数。本模块是文献[2]中为ATSP2K软件包[3]开发的DENSITY模块的相对论版本。密度算符期望值表达式中包含的自旋角因子，借助广义图形技术[4]，采用轨道、自旋与准自旋空间中的角动量理论完成计算。自然轨道（natural orbitals, NOs）可通过密度矩阵的对角化求得，并利用其κ分块结构进行计算。本文详细讨论了该代码的各项特性，重点围绕自然轨道的优势与性质，以及将电子径向密度图景作为研究电子关联与相对论效应的手段展开论述。