The completeness properties of Gaussian‐type orbitals in quantum chemistry,International Journal of Quantum Chemistry

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The completeness properties of Gaussian‐type orbitals in quantum chemistry
International Journal of Quantum Chemistry ( IF 2.3 ) Pub Date : 2020-06-19 , DOI: 10.1002/qua.26264
Robert A. Shaw _{1,

2}

Affiliation

In this work, I extend results on the convergence of Gaussian basis sets in quantum chemistry, previously shown for ground‐state hydrogenic wavefunctions, to orbitals of arbitrary angular momentum. I give rigorous proofs of their asymptotic behavior, and demonstrate for methods with regular potential operators—in particular, Hartree–Fock and Kohn–Sham density functional theory—that the assumption of completeness is correct under fairly lenient conditions. The final result under the correct norm is that the convergence in energy follows $urn:x-wiley:00207608:media:qua26264:qua26264-math-0001$ , where M is the number of Gaussians and k is a positive constant, generalizing previous results due to Kutzelnigg. This then yields prescriptions for accelerated convergence using even‐tempered Gaussians, which could be used as initial guesses in future basis set optimizations.

中文翻译：

量子化学中高斯型轨道的完整性

在这项工作中，我将量子化学中高斯基集收敛的结果扩展到任意角动量的轨道上，该结果在先前对基态氢波函数进行了展示的基础上进行了研究。我对它们的渐近行为进行了严格的证明，并针对具有常规潜在算子的方法（尤其是Hartree-Fock和Kohn-Sham密度泛函理论）进行了证明，在相当宽松的条件下，完整性的假设是正确的。正确规范下的最终结果是能量收敛 $缸：x-wiley：00207608：media：qua26264：qua26264-math-0001$ ，其中M是高斯数，k是是一个正常数，归因于库特兹尼格（Kutzelnigg）而得出的先前结果。然后，这产生了使用均匀回火的高斯加速收敛的处方，可用作未来基础集优化中的初步猜测。

更新日期：2020-07-20

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