Jensen Stig Rune, Flå Tor, Jonsson Dan, Monstad Rune Sørland, Ruud Kenneth, Frediani Luca
Centre for Theoretical and Computational Chemistry, Department of Chemistry, University of Tromsø - The Arctic University of Norway, N-9037 Tromsø, Norway.
High-Performance Computing Group, University of Tromsø - The Arctic University of Norway, N-9037 Tromsø, Norway.
Phys Chem Chem Phys. 2016 Aug 3;18(31):21145-61. doi: 10.1039/c6cp01294a.
Multiwavelets are emerging as an attractive alternative to traditional basis sets such as Gaussian-type orbitals and plane waves. One of their distinctive properties is the ability to reach the basis set limit (often a chimera for traditional approaches) reliably and consistently by fixing the desired precision ε. We present our multiwavelet implementation of the linear response formalism, applied to static magnetic properties, at the self-consistent field level of theory (both for Hartree-Fock and density functional theories). We demonstrate that the multiwavelets consistently improve the accuracy of the results when increasing the desired precision, yielding results that have four to five digits precision, thus providing a very useful benchmark which could otherwise only be estimated by extrapolation methods. Our results show that magnetizabilities obtained with the augmented quadruple-ζ basis (aug-cc-pCVQZ) are practically at the basis set limit, whereas absolute nuclear magnetic resonance shielding tensors are more challenging: even by making use of a standard extrapolation method, the accuracy is not substantially improved. In contrast, our results provide a benchmark that: (1) confirms the validity of the extrapolation ansatz; (2) can be used as a reference to achieve a property-specific extrapolation scheme, thus providing a means to obtain much better extrapolated results; (3) allows us to separate functional-specific errors from basis-set ones and thus to assess the level of cancellation between basis set and functional errors often exploited in density functional theory.
多小波正成为高斯型轨道和平面波等传统基组的一种有吸引力的替代方案。它们的一个独特性质是能够通过固定所需精度ε，可靠且一致地达到基组极限（这对于传统方法来说往往是一种幻想）。我们展示了线性响应形式的多小波实现，将其应用于自洽场理论水平（包括哈特里－福克理论和密度泛函理论）下的静态磁性。我们证明，当提高所需精度时，多小波能持续提高结果的准确性，得到具有四到五位数字精度的结果，从而提供了一个非常有用的基准，否则只能通过外推法来估计。我们的结果表明，使用增强四重ζ基（aug-cc-pCVQZ）获得的磁化率实际上已达到基组极限，而绝对核磁共振屏蔽张量则更具挑战性：即使使用标准外推法，准确性也没有显著提高。相比之下，我们的结果提供了一个基准，它：（1）证实了外推假设的有效性；（2）可作为实现特定性质外推方案的参考，从而提供一种获得更好外推结果的方法；（3）使我们能够将特定泛函的误差与基组误差分开，从而评估密度泛函理论中经常利用的基组误差和泛函误差之间的抵消程度。
