jj-Coupling-based atomic self-consistent-field calculations with relativistic effective core potentials and two-component spinors

A self-consistent-field (SCF) program for the calculation of atomic energies and wave functions defined in jj-coupling using two-component atomic spinors and relativistic effective core potentials (RECPs) is described. The code is based on the linear combination of atomic orbitals SCF algorithm for atomic states defined in LS-coupling developed by Roothaan and Bagus. Hamiltonian matrix elements with respect to one- and two-electron operators, including RECPs, are calculated for two-component atomic spinor basis functions of either Gaussian-type orbitals (GTOs) or Slater-type orbitals (STOs). Electronic states are defined as eigenfunctions of the total angular momentum squared operator and tables of the required vector coupling coefficients that define such pure states are provided. In addition, one or more GTO expansions of large- and small-core RECPs and their corresponding GTO basis sets are supplied for all elements Z=3 through Z=118. Optimized two-component basis sets of STOs or GTOs can be calculated for use in molecular structure codes based on RECPs and relativistic electronic structure theory. Atomic asymptotic state energies at the SCF level of theory for analysis of molecular dissociation limits can be studied.

本文描述了一款采用二分量原子旋量与相对论有效核势（relativistic effective core potentials，RECPs），用于计算jj耦合下原子能量与波函数的自洽场（self-consistent-field，SCF）程序。该程序基于罗特汉（Roothaan）与巴古斯（Bagus）提出的、针对LS耦合原子态的原子轨道线性组合自洽场算法。针对高斯型轨道（Gaussian-type orbitals，GTOs）或斯莱特型轨道（Slater-type orbitals，STOs）的二分量原子旋量基函数，程序会计算包含相对论有效核势在内的单电子与双电子算符对应的哈密顿矩阵元。电子态被定义为总角动量平方算符的本征函数，同时提供了定义此类纯态所需的矢量耦合系数表格。此外，针对原子序数Z=3至Z=118的所有元素，均提供了大核与小核相对论有效核势的单组或多组高斯型轨道展开式，以及与之对应的GTO基组。可基于相对论有效核势与相对论电子结构理论，计算得到优化后的斯莱特型轨道或高斯型轨道二分量基组，供分子结构程序使用。还可开展自洽场理论层面的原子渐近态能量研究，用于分析分子解离极限。