Computing many-body wave functions with guaranteed precision: The first-order Moller-Plesset wave function for the ground state of helium atom
Computing many-body wave functions with guaranteed precision: The first-order Moller-Plesset wave function for the ground state of helium atom
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DOI：
10.1063/1.4747538
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发表时间：
2012-09-14
影响因子：
4.4
通讯作者：
Valeev, Edward F.
中科院分区：
文献类型：
--
作者：
Bischoff, Florian A.;Harrison, Robert J.;Valeev, Edward F.
我们提出了一种方法来计算精确的原子和分子的相关能使用自适应不连续谱元多分辨率表示的两个电子波函数。由于谱元表示的存储复杂度与维数成指数关系，用蛮力法计算高精度的双电子（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）低秩张量近似（特别是奇异值分解）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-电子奇异性。所有必要的操作来解决薛定谔方程表示，使重建的满秩形式的波函数是没有必要的。通过对氦原子一阶Moller-Plesset波函数的计算，验证了该方法的数值性能。计算得到的二阶Moller-Plesset能量的精度接近2微哈特树，达到了现有一般原子轨道方法的精度极限。我们的方法不假设特殊的几何对称性，因此应用到分子是简单的。(C)2012年美国物理学会。[http：//dx.doi.org/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 Schrodinger 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 Moller-Plesset wave function of a helium atom. The computed second-order Moller-Plesset energy is precise to similar 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. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4747538]