Department of Chemistry, Virginia Tech, 107 Davidson Hall, Blacksburg, Virgina 24061, USA.
J Chem Phys. 2010 Jun 7;132(21):214104. doi: 10.1063/1.3417984.
Combinations of explicitly correlated R12 wave functions with relativistic Douglas-Kroll-Hess (DKH) Hamiltonians are discussed. We considered several ways to incorporate the relativistic terms into the second-order Moller-Plesset R12 method and applied them to the helium isoelectronic series to investigate their accuracy and numerical stability. Among the approaches are the evaluation of the relativistic terms via double resolution-of-the-identity and the explicit evaluation of all terms up to O(c(-4)) using the Pauli Hamiltonian. Numerical collapse of the latter can be avoided if the R12 amplitudes are determined by Kato's cusp condition. Closed formulas for new two-electron integrals that include the mass-velocity term have been derived and implemented into the LIBINT2 integral library. The proposed approaches are not restricted to DKH and can be combined with other one- and two-component relativistic Hamiltonians.
讨论了明确相关的 R12 波函数与相对论道格拉斯-克罗尔-海斯（DKH）哈密顿量的组合。我们考虑了几种将相对论项纳入二阶莫勒-普莱塞特 R12 方法的方法，并将它们应用于氦等电子系列，以研究它们的准确性和数值稳定性。这些方法包括通过双分辨率身份评估相对论项，以及使用 Pauli 哈密顿量显式评估高达 O(c(-4))的所有项。如果通过 Kato 的角点条件确定 R12 幅度，则可以避免后者的数值崩溃。已经推导出了包含质量速度项的新双电子积分的封闭公式，并将其实现到 LIBINT2 积分库中。所提出的方法不仅限于 DKH，并且可以与其他单分量和双分量相对论哈密顿量结合使用。
