A new computational benchmark has found that Dyson and non-Dyson versions of ADC(3) can give meaningfully different molecular ionization potentials. In a matched comparison using the same static density matrix, the two formulations differed by 0.09 to 0.10 electronvolt on average. The gap was about 0.2 eV for CS and exceeded 0.25 eV for C2.
An ionization potential is the energy a calculation assigns to removing an electron from a molecule. For researchers choosing among electronic-structure methods, the practical point is that the non-Dyson approximation was not numerically negligible in this benchmark; the authors describe the discrepancy as substantial.
What was tested
The preprint addresses a missing direct benchmark of multi-channel Dyson equation, or MCDE, and algebraic diagrammatic construction, or ADC, methods for molecules. The implemented approximations included ADC(2), ADC(2)-X/(3,1)-MCDE and ADC(3), alongside Dyson, non-Dyson and screened formulations.
The test covered 58 ionization potentials from 23 small molecules. The calculations were judged against selected-configuration-interaction, or selected-CI, theoretical estimates. At the aug-cc-pVQZ basis set, 56 values were shown because two CO2 selected-CI reference values were missing.
The paper also notes that (3,1)-MCDE and ADC(2)-X share the same working equations.
The approximation changed the result
At aug-cc-pVQZ, the difference persisted across ionization order. The mean absolute deviation—the average size of the gap without regard to direction—was 0.093 eV for 23 first ionization potentials, 0.085 eV for 22 second ionization potentials and 0.127 eV for 11 third-or-higher ionization potentials. The largest deviations in those groups were 0.267, 0.288 and 0.262 eV, respectively.
The broader accuracy comparison exposed a separate weakness in ADC(2)-X. The method substantially underestimated the reference ionization potentials: its best reported mean absolute error was 0.628 eV for the Σ(1) variant, while ADC(2)-X-Σ(CCSD) had a mean absolute error of 0.870 eV.
ADC(3) reduced the mean absolute errors compared with ADC(2)-X. Its best reported variant, ADC(3)-Σ(4), had a mean absolute error of 0.264 eV, but the authors report that it still did not reach the accuracy of EOM-CCSD or state-of-the-art vertex-corrected GW methods.
A tighter spread of errors
The screened (3,1)-MCDE showed less systematic underestimation than ADC(2)-X. Its σ_MAE, a measure of how widely errors are dispersed around their average, was smaller for the Σ(3), Σ(3+) and Σ(CCSD) variants, and slightly better than the best ADC(3) variant on that dispersion measure.
The authors interpret this narrower distribution as a reason screening may be useful for molecular photoemission calculations and describe sMCDE as potentially cost-efficient.
Accuracy also did not track ionization order in a simple way. Across valence, semi-valence and semi-core groups, ADC(3) performance remained largely unchanged. ADC(2)-X and sMCDE showed nearly flat mean-absolute-error distributions, even though their absolute errors were larger for deeper, more tightly bound ionization potentials, and their Z-factors, numbers used to characterize calculated states, were not indicative of accuracy.
Where the comparison becomes less certain
Basis-set convergence—the effect of changing the mathematical functions used to represent the electrons—was molecule-dependent. In slowly converging systems, the spread between approximations to the correlation contribution of the static self-energy fell from 0.69 eV with aug-cc-pVDZ to 0.39 eV with aug-cc-pVQZ.
In another static-self-energy comparison, the Σ(3+) approximation closely tracked the CCSD reference for the three states shown.
The scope is narrow: the benchmark contains 58 ionization potentials from 23 small molecules, and its reference set is selected-CI theoretical estimates. The result is therefore a comparison within this molecular test set, not a universal ranking of computational methods.
One comparison was also incomplete. The nD-ADC(2)-X calculation for CH2O converged only three physical quasiparticle roots instead of four, so the fourth ionization potential was omitted from those comparisons.
The reported figures are descriptive summaries, and no confidence intervals were given. They should be read as comparisons within this benchmark rather than as a universal ranking of molecular methods.
Preprint status and access
The document is an arXiv preprint, arXiv:2608.25669v1, dated 26 August 2026. The study reports that its data are available in the article and Supplementary Material, including a CSV file, while the Python calculation code is provided through the stated GitHub repository. AMS input requires a modified developer code version available to licensed AMS developers or on reasonable request.
The acknowledgments report support from NWO, use of SURFsara supercomputer facilities and a VENI grant under agreement VI.Veni.232.013. The authors declared no conflict of interest.
Paper data and sources
Original title: Benchmark of Multi-Channel Dyson Equation and Algebraic Diagrammatic Construction Methods for molecules
Authors: Mike Keizer, Stefano Paggi, J. Arjan Berger et al.
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-08-26
DOI: Not available
Original paper · Full text