Institute of Physical and Theoretical Chemistry, University of Regensburg, Universitätsstraße 31, D-93040 Regensburg, Germany.
J Chem Phys. 2013 Nov 21;139(19):194101. doi: 10.1063/1.4829898.
Theory and implementation of the periodic local MP2-F12 method in the 3*A fixed-amplitude ansatz is presented. The method is formulated in the direct space, employing local representation for the occupied, virtual, and auxiliary orbitals in the form of Wannier functions (WFs), projected atomic orbitals (PAOs), and atom-centered Gaussian-type orbitals, respectively. Local approximations are introduced, restricting the list of the explicitly correlated pairs, as well as occupied, virtual, and auxiliary spaces in the strong orthogonality projector to the pair-specific domains on the basis of spatial proximity of respective orbitals. The 4-index two-electron integrals appearing in the formalism are approximated via the direct-space density fitting technique. In this procedure, the fitting orbital spaces are also restricted to local fit-domains surrounding the fitted densities. The formulation of the method and its implementation exploits the translational symmetry and the site-group symmetries of the WFs. Test calculations are performed on LiH crystal. The results show that the periodic LMP2-F12 method substantially accelerates basis set convergence of the total correlation energy, and even more so the correlation energy differences. The resulting energies are quite insensitive to the resolution-of-the-identity domain sizes and the quality of the auxiliary basis sets. The convergence with the orbital domain size is somewhat slower, but still acceptable. Moreover, inclusion of slightly more diffuse functions, than those usually used in the periodic calculations, improves the convergence of the LMP2-F12 correlation energy with respect to both the size of the PAO-domains and the quality of the orbital basis set. At the same time, the essentially diffuse atomic orbitals from standard molecular basis sets, commonly utilized in molecular MP2-F12 calculations, but problematic in the periodic context, are not necessary for LMP2-F12 treatment of crystals.
本文提出了在 3*A 定振幅假设下周期性局域 MP2-F12 方法的理论和实现。该方法在直接空间中构建，使用占据轨道、虚拟轨道和辅助轨道的局域表示形式，分别为 Wannier 函数（WFs）、投影原子轨道（PAOs）和原子中心高斯型轨道。引入了局域近似，将显式相关对的列表以及强正交投影中的占据轨道、虚拟轨道和辅助空间限制在基于各自轨道空间接近度的对特定域中。出现在形式中的四索引双电子积分通过直接空间密度拟合技术进行近似。在此过程中，拟合轨道空间也限制在围绕拟合密度的局部拟合域中。该方法的构建和实现利用了 WF 的平移对称性和点群对称性。在 LiH 晶体上进行了测试计算。结果表明，周期性 LMP2-F12 方法极大地加速了总相关能量的基组收敛，对相关能量差的加速作用更大。得到的能量对身份分解域大小和辅助基组的质量不太敏感。与轨道域大小的收敛速度稍慢，但仍可接受。此外，包含比周期性计算中通常使用的稍微弥散的函数，可以改善 LMP2-F12 相关能量的收敛性，无论是 PAO 域大小还是轨道基组的质量。同时，标准分子基组中通常用于分子 MP2-F12 计算但在周期性环境中存在问题的本质弥散原子轨道，对于晶体的 LMP2-F12 处理并不是必需的。
