Humboldt-Universität zu Berlin, Unter den Linden 6, 10099 Berlin, Germany.
J Chem Phys. 2012 Sep 14;137(10):104103. doi: 10.1063/1.4747538.
We present an approach to compute accurate correlation energies for atoms and molecules using an adaptive discontinuous spectral-element multiresolution representation for the two-electron wave function. Because of the exponential storage complexity of the spectral-element representation with the number of dimensions, a brute-force computation of two-electron (six-dimensional) wave functions with high precision was not practical. To overcome the key storage bottlenecks we utilized (1) a low-rank tensor approximation (specifically, the singular value decomposition) to compress the wave function, and (2) explicitly correlated R12-type terms in the wave function to regularize the Coulomb electron-electron singularities of the Hamiltonian. All operations necessary to solve the Schrödinger equation were expressed so that the reconstruction of the full-rank form of the wave function is never necessary. Numerical performance of the method was highlighted by computing the first-order Møller-Plesset wave function of a helium atom. The computed second-order Møller-Plesset energy is precise to ~2 microhartrees, which is at the precision limit of the existing general atomic-orbital-based approaches. Our approach does not assume special geometric symmetries, hence application to molecules is straightforward.
我们提出了一种使用双电子波函数的自适应不连续谱元多分辨率表示来计算原子和分子精确相关能量的方法。由于谱元表示的存储复杂度随维度呈指数增长，因此使用高精度的暴力计算双电子（六维）波函数是不切实际的。为了克服关键的存储瓶颈，我们利用（1）低秩张量逼近（具体来说，奇异值分解）来压缩波函数，以及（2）波函数中显式相关的 R12 型项来正则化哈密顿量的库仑电子-电子奇点。所有求解薛定谔方程所需的操作都被表示出来，因此永远不需要重建波函数的满秩形式。通过计算氦原子的一阶 Møller-Plesset 波函数来突出该方法的数值性能。计算得到的二阶 Møller-Plesset 能量精确到约 2 微哈特里，这达到了现有基于原子轨道的通用方法的精度极限。我们的方法不假设特殊的几何对称性，因此可以直接应用于分子。
