Department of Chemistry and Biochemistry, University of California, Los Angeles, California 90095, USA.
Department of Chemistry, University of California and Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA.
J Chem Phys. 2019 Nov 7;151(17):174115. doi: 10.1063/1.5110226.
Over this past decade, we combined the idea of stochastic resolution of identity with a variety of electronic structure methods. In our stochastic Kohn-Sham density functional theory (DFT) method, the density is an average over multiple stochastic samples, with stochastic errors that decrease as the inverse square root of the number of sampling orbitals. Here, we develop a stochastic embedding density functional theory method (se-DFT) that selectively reduces the stochastic error (specifically on the forces) for a selected subsystem(s). The motivation, similar to that of other quantum embedding methods, is that for many systems of practical interest, the properties are often determined by only a small subsystem. In stochastic embedding DFT, two sets of orbitals are used: a deterministic one associated with the embedded subspace and the rest, which is described by a stochastic set. The method agrees exactly with deterministic calculations in the limit of a large number of stochastic samples. We apply se-DFT to study a p-nitroaniline molecule in water, where the statistical errors in the forces on the system (the p-nitroaniline molecule) are reduced by an order of magnitude compared with nonembedding stochastic DFT.
在过去的十年中，我们将随机身份分辨思想与各种电子结构方法相结合。在我们的随机 Kohn-Sham 密度泛函理论（DFT）方法中，密度是多个随机样本的平均值，随机误差随采样轨道数的平方根倒数减小。在这里，我们开发了一种选择性降低所选子系统（多个）的随机误差（特别是在力上）的随机嵌入密度泛函理论方法（se-DFT）。其动机与其他量子嵌入方法类似，对于许多实际感兴趣的系统，性质通常仅由一小部分子系统决定。在随机嵌入 DFT 中，使用了两组轨道：与嵌入子空间相关的确定轨道和其余的由随机集描述的轨道。该方法在大量随机样本的极限下与确定性计算完全一致。我们将 se-DFT 应用于研究水中的对硝基苯胺分子，与非嵌入随机 DFT 相比，系统（对硝基苯胺分子）上的力的统计误差减小了一个数量级。
