AI 中文总结
本文提出投影q壳层（PQS）改进嵌套笛卡尔高斯基，可恢复多项式完备性、降低小分子计算误差，尤其适用于q较小的紧凑基组。
AI 中文摘要
电子结构计算需要对电子波函数及其库仑相互作用进行有限表示。传统紧凑基组会产生四索引相互作用，而高斯基组是少数能实现类似实空间网格的双索引相互作用、同时所需点数少得多的方法之一。其发展面临的持续挑战是在保持高精度的同时进一步减少所需函数数量。本文引入投影q壳层（PQS），这是对White和Lindsey提出的嵌套笛卡尔高斯基的改进。标准嵌套构造将连接壳层划分为不相交的面、边和角，使其多项式完备性从q阶降至q-2阶；PQS则近似恢复了这两个丢失的阶数。关于完备性，我们证明对于理想无畸变的母基，PQS基的张成等价于重叠补丁的超完备基；实际中始终使用的坐标畸变仅对该等价性造成轻微损害。即使无畸变，允许双索引相互作用的矩性质也会变得不精确，但我们表明阶数的提升足以弥补这种损失。在相似基组规模下，对于H₂⁺、H₂、C₂等小分子，PQS的单电子和相互作用误差均小于标准嵌套构造，且对于q更小的更紧凑基组，改进效果最显著。
英文摘要
Electronic-structure calculations require a finite representation of both the electronic wave functions and their Coulomb interaction. Conventional compact basis sets lead to a four-index interaction. Gausslet basis sets are one of a very small number of approaches that allow a much smaller two-index interaction, similar to a real-space grid, but with far fewer points. The continuing challenge in their development is reducing further the number of functions needed while maintaining high accuracy. Here we introduce projected q-shells (PQS), an improvement to the nested Cartesian gausslets of White and Lindsey. Their standard nesting construction divides a joining shell into disjoint faces, edges, and corners, reducing its polynomial completeness from order q to order q-2. PQS approximately restores the two lost orders. In terms of completeness, we prove that for an ideal, undistorted parent, the span of the PQS basis is equivalent to an overcomplete basis of overlapping patches. Coordinate distortions, which are always used in practice, harm this equivalence only slightly. The moment properties that allow two-index interactions also become inexact, even without distortion, but we show that the improvement in order more than makes up for this loss. For similar basis sizes, PQS gives smaller one-electron and interaction errors on small molecules, such as H2+, H2, and C2, than standard nesting. The improvement is largest for more compact bases with smaller q.
Comments12 pages, 5 figures, 3 tables
