Jakobsen Philip, Jensen Frank
Department of Chemistry, Aarhus University, Langelandsgade 140, DK-8000 Aarhus, Denmark.
J Chem Theory Comput. 2021 Jan 12;17(1):269-276. doi: 10.1021/acs.jctc.0c01029. Epub 2020 Dec 8.
The premise for Kohn-Sham density functional theory is that the exact electron density can be generated by a set of orbitals in a single Slater determinant. While this is ensured in a complete basis set, it has been shown that it cannot hold in small basis sets. The present work probes how accurately a reference electron density of the full-CI type can be reproduced by a set of orbitals in a single Slater determinant, as a function of the basis set used for the fitting electron density. The key finding is that the fitting error may be significant for basis sets of double- or triple-ζ quality. It is also shown that it is important that the fitting basis set includes the same basis functions as used for generating the reference electron density. The main limitation in a given basis set is the lack of higher order polarization functions. The error for practical purposes becomes insignificant for basis sets of quadruple-ζ or better quality, and this should be the choice when assessing the accuracy of exchange-correlation functionals by comparing electron densities to accurate reference results generated by wave function methods. The methodology in the present work can be used to transform an electron density from a multideterminant wave function into a set of orbitals in a single Slater determinant, and this may be useful for developing and testing new exchange-correlation functionals.
科恩-沈（Kohn-Sham）密度泛函理论的前提是，精确的电子密度可以由单个斯莱特行列式中的一组轨道生成。虽然在完备基组中这是可以保证的，但已经表明在小基组中它并不成立。本工作探究了作为用于拟合电子密度的基组的函数，单个斯莱特行列式中的一组轨道能够多精确地重现全组态相互作用（full-CI）类型的参考电子密度。关键发现是，对于双ζ或三ζ质量的基组，拟合误差可能很大。还表明拟合基组包含与用于生成参考电子密度相同的基函数很重要。给定基组中的主要限制是缺乏高阶极化函数。对于四重ζ或更高质量的基组，实际应用中的误差变得微不足道，当通过将电子密度与波函数方法生成的精确参考结果进行比较来评估交换关联泛函的准确性时，这应该是首选。本工作中的方法可用于将多行列式波函数中的电子密度转换为单个斯莱特行列式中的一组轨道，这对于开发和测试新的交换关联泛函可能有用。
