Ferenc Dávid, Jeszenszki Péter, Mátyus Edit
Institute of Chemistry, ELTE, Eötvös Loránd University, Pázmány Péter sétány 1/A, Budapest H-1117, Hungary.
J Chem Phys. 2022 Sep 7;157(9):094113. doi: 10.1063/5.0105355.
Variational and perturbative relativistic energies are computed and compared for two-electron atoms and molecules with low nuclear charge numbers. In general, good agreement of the two approaches is observed. Remaining deviations can be attributed to higher-order relativistic, also called non-radiative quantum electrodynamics (QED), corrections of the perturbative approach that are automatically included in the variational solution of the no-pair Dirac-Coulomb-Breit (DCB) equation to all orders of the α fine-structure constant. The analysis of the polynomial α dependence of the DCB energy makes it possible to determine the leading-order relativistic correction to the non-relativistic energy to high precision without regularization. Contributions from the Breit-Pauli Hamiltonian, for which expectation values converge slowly due the singular terms, are implicitly included in the variational procedure. The α dependence of the no-pair DCB energy shows that the higher-order (αE) non-radiative QED correction is 5% of the leading-order (αE) non-radiative QED correction for Z = 2 (He), but it is 40% already for Z = 4 (Be), which indicates that resummation provided by the variational procedure is important already for intermediate nuclear charge numbers.
计算并比较了低核电荷数双电子原子和分子的变分相对论能量和微扰相对论能量。总体而言，观察到两种方法有良好的一致性。剩余的偏差可归因于微扰方法的高阶相对论修正（也称为非辐射量子电动力学（QED）修正），在无对狄拉克 - 库仑 - 布赖特（DCB）方程的变分解中自动包含了α精细结构常数所有阶次的此类修正。对DCB能量的多项式α依赖性分析使得无需正则化就能高精度地确定非相对论能量的主导阶相对论修正。由于奇异项，布赖特 - 泡利哈密顿量的期望值收敛缓慢，其贡献隐含在变分过程中。无对DCB能量的α依赖性表明，对于Z = 2（氦），高阶（αE）非辐射QED修正为一阶（αE）非辐射QED修正的5%，但对于Z = 4（铍）已经是40%，这表明变分过程提供的求和对于中等核电荷数已经很重要。
