Department of Physics, The University of Tokyo, Tokyo 113-0033, Japan.
J Chem Phys. 2012 Mar 7;136(9):094108. doi: 10.1063/1.3689440.
The transcorrelated (TC) method is one of the promising wave-function-based approaches for the first-principles electronic structure calculations. In this method, the many-body wave function is approximated as the Jastrow-Slater type and one-electron orbitals in the Slater determinant are optimized with a one-body self-consistent-field equation such as that in the Hartree-Fock (HF) method. Although the TC method has yielded good results for both molecules and solids, its computational cost in solid-state calculations, being of order O(N(k)(3)N(b)(3)) with N(k) and N(b) the respective numbers of k-points and bands, has for some years hindered its wide application in condensed matter physics. Although an efficient algorithm was proposed for a Gaussian basis set, that algorithm is not applicable to a plane-wave basis that is suited to and widely used in solid-state calculations. In this paper, we present a new efficient algorithm of the TC method for the plane-wave basis or an arbitrary basis function set expanded in terms of plane waves, with which the computational cost of the TC method scales as O(N(k)(2)N(b) (2)). This is the same as that of the HF method. We applied the TC method with the new algorithm to obtain converged band structure and cell parameters of some semiconductors.
关联（TC）方法是基于波函数的第一性原理电子结构计算的有前途的方法之一。在该方法中，多体波函数被近似为 Jastrow-Slater 型，Slater 行列式中的单电子轨道通过类似于 Hartree-Fock（HF）方法中的单自洽场方程进行优化。尽管 TC 方法已在分子和固体中取得了良好的结果，但由于其在固态计算中的计算成本为 O(N(k)(3)N(b)(3))，其中 N(k)和 N(b)分别是 k 点和能带的数量，多年来一直阻碍了其在凝聚态物理中的广泛应用。尽管已经为高斯基集提出了一种有效的算法，但该算法不适用于适合且广泛用于固态计算的平面波基。在本文中，我们提出了一种新的平面波基或任意基于平面波展开的基函数集的 TC 方法的有效算法，其中 TC 方法的计算成本为 O(N(k)(2)N(b)(2))。这与 HF 方法相同。我们应用具有新算法的 TC 方法来获得一些半导体的收敛能带结构和晶胞参数。
