. 2022 Jan 13;18(2):865–882. doi: 10.1021/acs.jctc.1c01100

Table 1. XC Kernel Applied, Number of Independent Parameters, and Their Optimal Values Tuned for Singlet Excitations of the Gordon Training Set^62,135 for Different Functionals Using the aug-cc-pVTZ Basis Set with Corresponding Auxiliary Bases^a.

Functional	XC energy	Number of parameters	α_X^HF	α_C^MP2	α_C^DFT	μ (au)
PBE-P86/CIS(D)	eq 1	2^d	0.68	0.35	0.65	N/A
PBE-P86/ADC(2)	eq 1	2^d	0.68	0.35	0.65	N/A
ωPBEPP86^b	eq 3	4	0.70	0.48	0.68	0.18
LC-PBE-P86/CIS(D)	eq 4	2	0.70	0.49	0.51	0.18
LC-PBE-P86/ADC(2)	eq 4	2	0.70	0.49	0.51	0.19
RS-PBE-P86/CIS(D)^c	eq 5	2	0.50	0.25	0.75	0.70
RS-PBE-P86/ADC(2)	eq 5	2	0.50	0.25	0.75	0.70

For the LC- and RS-type functionals, the α_X^HF, α_C, and α_C^DFT values correspond, respectively, to λ, λ², and 1 – λ².

Taken from ref (98).

Taken from ref (89).

As α_C^MP2 + α_C = 1.

Table 1. XC Kernel Applied, Number of Independent Parameters, and Their Optimal Values Tuned for Singlet Excitations of the Gordon Training Set62,135 for Different Functionals Using the aug-cc-pVTZ Basis Set with Corresponding Auxiliary Basesa.