Partitioning of helium atom’s correlation energy into radial and angular contributions, although of fundamental interest, has eluded critical scrutiny. Conventionally, radial and angular correlation energies of helium atom are defined for its ground state as deviations, from Hartree–Fock and exact values, of the energy obtained using a purely radial wavefunction devoid of any explicit dependence on the interelectronic distance. Here, we show this rationale to associate the contribution from radial-angular coupling entirely to the angular part underestimating the radial one, thereby also incorrectly predict non-vanishing residual radial probability densities. We derive analytic matrix elements for the high-precision Hylleraas basis set framework to seamlessly uncouple the angular correlation energy from its radial counterpart. The resulting formula agrees with numerical cubature yielding precise purely angular correlation energies for the ground as well as excited states. Our calculations indicate 60.2% of helium’s correlation energy to arise from strictly radial interactions; when excluding the contribution from the radial-angular coupling, this value drops to 41.3%.

将氦原子的相关能分成径向和角向贡献，尽管具有根本的意义，但仍未进行严格的审查。常规上，氦原子的径向和角相关能被定义为基态，这是与使用纯径向波函数获得的能量从Hartree-Fock和精确值的偏差无关，而该函数完全不依赖于电子间距离。在这里，我们显示了将径向角耦合完全与低估径向角部分的角部分相关联的基本原理，从而也错误地预测了不消失的残余径向概率密度。我们导出了高精度Hylleraas基集框架的解析矩阵元素，以将角度相关能量与其径向对应能量无缝地解耦。得出的公式与数值形式相符，可以为地面以及激发态产生精确的纯角度相关能量。我们的计算结果表明，氦的相关能的60.2％来自严格的径向相互作用。如果不考虑径向角耦合的影响，则该值降至41.3％。