Double-Hybrid Density Functional Theory for Core Excitations: Theory and Benchmark Calculations

The double-hybrid (DH) time-dependent density functional
theory
is extended to core excitations. Two different DH formalisms are presented
utilizing the core–valence separation (CVS) approximation.
First, a CVS-DH variant is introduced relying on the genuine perturbative
second-order correction, while an iterative analogue is also presented
using our second-order algebraic-diagrammatic construction [ADC(2)]-based
DH ansatz. The performance of the new approaches is tested for the
most popular DH functionals using the recently proposed XABOOM [J. Chem. Theory Comput.2021, 17, 1618] benchmark
set. In order to make a careful comparison, the accuracy and precision
of the methods are also inspected. Our results show that the genuine
approaches are highly competitive with the more advanced CVS-ADC(2)-based
methods if only excitation energies are required. In contrast, as
expected, significant differences are observed in oscillator strengths;
however, the precision is acceptable for the genuine functionals as
well. Concerning the performance of the CVS-DH approaches, the PBE0-2/CVS-ADC(2)
functional is superior, while its spin-opposite-scaled variant is
also recommended as a cost-effective alternative. For these approaches,
significant improvements are realized in the error measures compared
with the popular CVS-ADC(2) method.