Zhang Tianyuan, Evangelista Francesco A
Department of Chemistry and Cherry L. Emerson Center for Scientific Computation, Emory University , Atlanta, Georgia 30322, United States.
J Chem Theory Comput. 2016 Sep 13;12(9):4326-37. doi: 10.1021/acs.jctc.6b00639. Epub 2016 Aug 16.
In this work we propose a novel approach to solve the Schrödinger equation which combines projection onto the ground state with a path-filtering truncation scheme. The resulting projector configuration interaction (PCI) approach realizes a deterministic version of the full configuration interaction quantum Monte Carlo (FCIQMC) method [Booth, G. H.; Thom, A. J. W.; Alavi, A. J. Chem. Phys. 2009, 131, 054106]. To improve upon the linearized imaginary-time propagator, we develop an optimal projector scheme based on an exponential Chebyshev expansion in the limit of an infinite imaginary time step. After writing the exact projector as a path integral in determinant space, we introduce a path filtering procedure that truncates the size of the determinantal basis and approximates the Hamiltonian. The path filtering procedure is controlled by one real threshold that determines the accuracy of the PCI energy and is not biased toward any determinant. Therefore, the PCI approach can equally well describe static and dynamic electron correlation effects. This point is illustrated in benchmark computations on N2 at both equilibrium and stretched geometries. In both cases, the PCI achieves chemical accuracy with wave functions that contain less than 0.5% determinants of full CI space. We also report computations on the ground state of C2 with up to quaduple-ζ basis sets and wave functions as large as 200 million determinants, which allow a direct comparison of the PCI, FCIQMC, and density matrix renormalization group (DMRG) methods. The size of the PCI wave function grows modestly with the number of unoccupied orbitals, and its accuracy may be tuned to match that of FCIQMC and DMRG.
在这项工作中，我们提出了一种求解薛定谔方程的新方法，该方法将基态投影与路径过滤截断方案相结合。由此产生的投影算符组态相互作用（PCI）方法实现了全组态相互作用量子蒙特卡罗（FCIQMC）方法[布斯，G. H.；汤姆，A. J. W.；阿拉维，A. J. 《化学物理杂志》2009年，131卷，054106]的确定性版本。为了改进线性化虚时传播子，我们在无限虚时步长的极限下，基于指数切比雪夫展开开发了一种最优投影算符方案。在将精确投影算符写为行列式空间中的路径积分后，我们引入了一种路径过滤程序，该程序截断行列式基的大小并近似哈密顿量。路径过滤程序由一个实阈值控制，该阈值决定了PCI能量的精度，并且不偏向任何行列式。因此，PCI方法能够同样好地描述静态和动态电子关联效应。这一点在N₂平衡和拉伸几何构型的基准计算中得到了说明。在这两种情况下，PCI方法都能以包含不到全CI空间0.5%行列式的波函数达到化学精度。我们还报告了使用高达四重ζ基组和波函数行列式多达2亿的C₂基态计算结果，这使得能够直接比较PCI、FCIQMC和密度矩阵重整化群（DMRG）方法。PCI波函数的大小随未占据轨道数适度增长，其精度可以调整以匹配FCIQMC和DMRG的精度。
