The third-order algebraic diagrammatic construction method (ADC(3)) for the polarization propagator for closed-shell molecules: Efficient implementation and benchmarking

Abstract

The implementation of an efficient program of the algebraic diagrammatic construction method for the polarisation propagator in third-order perturbation theory (ADC(3)) for the computation of excited states is reported. The accuracies of ADC(2) and ADC(3) schemes have been investigated with respect to Thiel's recently established benchmark set for excitation energies and oscillator strengths. The calculation of 141 vertical excited singlet and 71 triplet states of 28 small to medium-sized organic molecules has revealed that ADC(3) exhibits mean error and standard deviation of 0.12 ± 0.28 eV for singlet states and -0.18 ± 0.16 eV for triplet states when the provided theoretical best estimates are used as benchmark. Accordingly, the ADC(2)-s and ADC(2)-x calculations revealed accuracies of 0.22 ± 0.38 eV and -0.70 ± 0.37 eV for singlets and 0.12 ± 0.16 eV and -0.55 ± 0.20 eV for triplets, respectively. For a comparison of CC3 and ADC(3), only non-CC3 benchmark values were considered, which comprise 84 singlet states and 19 triplet states. For these singlet states CC3 exhibits an accuracy of 0.23 ± 0.21 eV and ADC(3) an accuracy of 0.08 ± 0.27 eV, and accordingly for the triplet states of 0.12 ± 0.10 eV and -0.10 ± 0.13 eV, respectively. Hence, based on the quality of the existing benchmark set it is practically not possible to judge whether ADC(3) or CC3 is more accurate, however, ADC(3) has a much larger range of applicability due to its more favourable scaling of O(N(6)) with system size.

Performance of SOPPA-based methods in the calculation of vertical excitation energies and oscillator strengths

“…Compared with the three popular alternatives, B3LYP, CC2 and ADC(2), we can see that the mean deviation for the same benchmark set is −0.46 ± 0.29 eV for SOPPA, −0.29 ± 0.46 eV for B3LYP [45], 0.13 ± 0.26 eV for CC2 [18] and 0.01 ± 0.27 eV [15] or −0.03 ± 0.54 eV [16] for ADC (2) (in the latter case, using two slightly smaller subsets of the standard benchmark set). SOPPA thus underestimates vertical excitation energies more strongly than B3LYP but does so more consistently (as indicated by the standard deviations) and both are outperformed by CC2 and ADC (2).…”

“…The performance of these methods in the calculation of vertical electronic excitation energies or even 0-0 transitions is well documented for ADC (2) [10][11][12][13][14][15][16] and CC2 [10,11,[17][18][19][20][21][22][23][24] but not for SOPPA. Vertical electronic excitation energies * Corresponding author.…”

The IPEA dilemma in CASPT2

“…Furthermore, the Thiel set was employed in a recent benchmark by Dreuw and co-workers who performed excited-state calculations using second and third-order algebraic diagrammatic construction (ADC). 104,105 Of the above available results, we consider here only those that made use of the TZVP basis set.…”

Communication: Exciton analysis in time-dependent density functional theory: How functionals shape excited-state characters

“…However, an almost constant shift towards higher correlation values is observed with a shift of +0.02 for B3LYP and an even larger shift of +0.05 for CAM-B3LYP. The R eh values were recomputed at the ab initio level using the algebraic-diagrammatic construction method for the polarization propagator to third order (ADC(3)/SV(P)), 41 showing excellent agreement with the TDA/CAM-B3LYP level.…”