Convergence of the ADC hierarchy to full configuration interaction

Establish whether the algebraic diagrammatic construction (ADC) hierarchy converges reliably to full configuration interaction (FCI), including by determining whether higher-order ADC approximations provide conclusive convergence beyond the currently benchmarked non-Dyson ADC(4) level.

Background

The paper benchmarks Dyson-ADC(3), non-Dyson ADC(3), ADC(2)-X, and screened (3,1)-MCDE approximations for molecular ionization potentials. Although higher-order ADC calculations, particularly non-Dyson ADC(4), have shown improvement over non-Dyson ADC(3), the available implementations and benchmarks do not establish systematic convergence toward full configuration interaction. The authors therefore identify the reliability of convergence of the ADC hierarchy to FCI as unresolved, especially because no variant beyond non-Dyson ADC(4) had, to their knowledge, been implemented and benchmarked and existing results were inconclusive.

References

It is also yet to be established whether the ADC hierarchy converges reliably to FCI.

— Benchmark of Multi-Channel Dyson Equation and Algebraic Diagrammatic Construction Methods for molecules  (2608.25669 - Keizer et al., 26 Aug 2026) in Section Conclusions

Whether this crossover behavior holds generally is an interesting open question that broader benchmarks will need to address.

— Third-order Algebraic Diagrammatic Construction Renormalized by Particle-Particle Ladders  (2608.28424 - Förster, 28 Aug 2026) in Section 3.3, “π-Conjugated Molecules”; Conclusions