Efficient implementation of the pair atomic resolution of the identity approximation for exact exchange for hybrid and range- separated density functionals.
Efficient implementation of the pair atomic resolution of the identity approximation for exact exchange for hybrid and range- separated density functionals.
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DOI：
10.1021/ct5008586
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发表时间：
2015-02-10
影响因子：
5.5
通讯作者：
Head-Gordon, Martin
中科院分区：
文献类型：
--
作者：
Manzer, Samuel F.;Epifanovsky, Evgeny;Head-Gordon, Martin
报道了一种新的高效的分子轨道(MO)基算法，它实现了恒等式近似的对原子分辨(PARI)，以计算对杂化和距离分离杂化密度泛函等自洽场方法的精确交换贡献(K)。最近，Merlot等人研究了PARI近似，即原子轨道(AO)基函数对仅使用以其各自的两个原子为中心的辅助基函数来展开。访问数/每百万人：Reach for[J.化学.2013，34,1486].我们的算法比四次尺度RI-K快得多，混合泛函的渐近交换加速比为(1+X/N)，其中N和X是AO和辅助基的维度。对于包括短程和长程精确交换的距离分离杂交体，如CAM-B3LYP、ωB97X-D和ωB97X-V，渐近加速比为2+2X/N。在ωB97X-V中观察到的cc-pVTZ基础上的C68石墨烯片段的交换相对于RI-K的加速比为3.4。与传统的RI-K方法一样，我们的方法在大的基集上大大优于传统的积分计算；基于cc-pVQZ的方法在c54石墨烯片段上获得了19%的加速比。在键合和非键合相互作用的数据库上，相对于精确的积分评估，精度损失可以忽略不计。我们还从解析和数值两方面证明了PARI-K近似是变分稳定的。
An efficient new molecular orbital (MO) basis algorithm is reported implementing the pair atomic resolution of the identity approximation (PARI) to evaluate the exact exchange contribution (K) to self-consistent field methods, such as hybrid and range-separated hybrid density functionals. The PARI approximation, in which atomic orbital (AO) basis function pairs are expanded using auxiliary basis functions centered only on their two respective atoms, was recently investigated by Merlot et al. [J. Comput. Chem.2013, 34, 1486]. Our algorithm is significantly faster than quartic scaling RI-K, with an asymptotic exchange speedup for hybrid functionals of (1 + X/N), where N and X are the AO and auxiliary basis dimensions. The asymptotic speedup is 2 + 2X/N for range separated hybrids such as CAM-B3LYP, ωB97X-D, and ωB97X-V which include short- and long-range exact exchange. The observed speedup for exchange in ωB97X-V for a C68 graphene fragment in the cc-pVTZ basis is 3.4 relative to RI-K. Like conventional RI-K, our method greatly outperforms conventional integral evaluation in large basis sets; a speedup of 19 is obtained in the cc-pVQZ basis on a C54 graphene fragment. Negligible loss of accuracy relative to exact integral evaluation is demonstrated on databases of bonded and nonbonded interactions. We also demonstrate both analytically and numerically that the PARI-K approximation is variationally stable.
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