Subotnik Joseph E, Sodt Alex, Head-Gordon Martin
Biophysics Program, University of California, Berkeley, California 94720, USA and School of Chemistry, Tel-Aviv University, 69978 Tel-Aviv, Israel.
J Chem Phys. 2008 Jan 21;128(3):034103. doi: 10.1063/1.2821124.
Local coupled-cluster theory provides an algorithm for measuring electronic correlation quickly, using only the spatial locality of localized electronic orbitals. Previously, we showed [J. Subotnik et al., J. Chem. Phys. 125, 074116 (2006)] that one may construct a local coupled-cluster singles-doubles theory which (i) yields smooth potential energy surfaces and (ii) achieves near linear scaling. That theory selected which orbitals to correlate based only on the distances between the centers of different, localized orbitals, and the approximate potential energy surfaces were characterized as smooth using only visual identification. This paper now extends our previous algorithm in three important ways. First, locality is now based on both the distances between the centers of orbitals as well as the spatial extent of the orbitals. We find that, by accounting for the spatial extent of a delocalized orbital, one can account for electronic correlation in systems with some electronic delocalization using fast correlation methods designed around orbital locality. Second, we now enforce locality on not just the amplitudes (which measure the exact electron-electron correlation), but also on the two-electron integrals themselves (which measure the bare electron-electron interaction). Our conclusion is that we can bump integrals as well as amplitudes, thereby gaining a tremendous increase in speed and paradoxically increasing the accuracy of our LCCSD approach. Third and finally, we now make a rigorous definition of chemical smoothness as requiring that potential energy surfaces not support artificial maxima, minima, or inflection points. By looking at first and second derivatives from finite difference techniques, we demonstrate complete chemical smoothness of our potential energy surfaces (bumping both amplitudes and integrals). These results are significant both from a theoretical and from a computationally practical point of view.
局域耦合簇理论提供了一种仅利用定域电子轨道的空间局域性来快速测量电子关联的算法。此前，我们已经证明[J. Subotnik等人，《化学物理杂志》125, 074116 (2006)]，可以构建一种局域耦合簇单双激发理论，该理论：(i) 产生平滑的势能面；(ii) 实现近线性标度。该理论仅根据不同定域轨道中心之间的距离来选择哪些轨道进行关联，并且仅通过视觉识别将近似势能表面表征为平滑的。本文现在从三个重要方面扩展了我们之前的算法。首先，现在局域性既基于轨道中心之间的距离，也基于轨道的空间范围。我们发现，通过考虑离域轨道的空间范围，可以使用围绕轨道局域性设计的快速关联方法来考虑具有一定电子离域的系统中的电子关联。其次，我们现在不仅对振幅（测量精确的电子 - 电子关联）施加局域性，而且对双电子积分本身（测量裸电子 - 电子相互作用）也施加局域性。我们的结论是，我们可以对积分以及振幅进行“碰撞”，从而极大地提高速度，并且反常地提高我们的LCCSD方法的精度。第三也是最后一点，我们现在对化学平滑性给出了一个严格的定义，即要求势能面不支持人为的极大值、极小值或拐点。通过查看有限差分技术的一阶和二阶导数，我们证明了我们势能面的完全化学平滑性（对振幅和积分都进行“碰撞”）。从理论和计算实际的角度来看，这些结果都具有重要意义。
