Calculating ionization potentials (the energies required to remove an electron) is a fundamental task in quantum chemistry, with applications in photoelectron spectroscopy, materials science, and astrochemistry. The standard ADC(3) method is based on Møller–Plesset perturbation theory and yields average errors around 0.3 eV for closed-shell molecules, which is often insufficient for interpreting experiments. Alongside this work on the archive are studies that improve the accuracy of excitation energy calculations through other perturbation theory variants (REPT, Brillouin–Wigner), as well as methods related to propagators and the T-matrix. This work stands somewhat apart: it does not introduce a new iterative apparatus but merely modifies the denominators in the existing ADC(3) formalism, preserving its computational cost.
The author replaces the standard Møller–Plesset denominators (differences of orbital energies) in the first- and second-order amplitude expressions with Epstein–Nesbet denominators that include diagonal Hamiltonian matrix elements for doubly excited configurations. From the full Epstein–Nesbet shift, only the 'particle-particle' and 'hole-hole' terms are kept, corresponding to the repulsion of two excited particles or two holes; the 'particle-hole' terms are discarded to avoid divergences. These shifts are equivalent to the diagonal elements of ladder diagrams in the particle-particle T-matrix approximation and can be computed without additional integrals. To adapt to spin symmetry, two spin-averaging schemes for the denominators are introduced: spin-summed (2J−K) and spin-averaged (J−K/2). All calculations are performed in the (aug-)cc-pVXZ basis (X = D, T, Q) using density fitting, with an implementation in Python using matrix-free operations and the Davidson solver from pySCF.
For 58 ionization potentials of 23 closed-shell molecules (sCI benchmark), standard ADC(3) yields a mean absolute deviation (MAD) of 0.326 eV. The EN-ADC(3) variant with spin-summed denominators and only doublet shifts (without the CIS shift) achieves a MAD of 0.09 eV, an improvement of nearly four times. This is better than EOM-CCSD (MAD 0.174 eV) and close to EOM-CCSDT (MAD 0.04 eV). The spin-averaged variant performs worse (MAD 0.11–0.13 eV). Including the CIS shift leads to problems for systems with strong electron-hole coupling (e.g., the second ionization potential of BN), where the error reaches -0.6 eV; screening this shift in the RPA approximation removes the outlier. For open shells, the improvements are more modest: for weakly spin-contaminated systems, the MAD drops from 0.16 to 0.07 eV (using the unrelaxed density), while for strongly contaminated systems it only drops from 0.17 to 0.15 eV, and EOM-CCSD remains more accurate. For acene and oligothiophene series, the EN shift reduces ionization potentials, improving agreement for small systems but worsening it for larger ones, where standard ADC(3) already underestimates the energies.
This work shows that a simple replacement of denominators in ADC(3) amplitudes with diagonal ladder diagram elements can radically improve accuracy without increasing computational cost. Unlike neighboring approaches such as REPT(2) or Brillouin–Wigner, which require iterative equation solving and increase formal complexity, EN-ADC(3) uses only already available integrals and retains the O($N^5$) scaling. This places the method on par with the best ADC variants for closed shells and makes it attractive for routine calculations. For open shells and extended systems, the gain is less obvious, which outlines the limits of applicability.
Promising directions include extending the approach to ADC for the polarization propagator (excitation energy calculations) and to ADC(4) for the self-consistent energy, though double-counting corrections will be needed there because the corresponding configurations are already included. More promising is the use of tensor hypercontraction or interpolative separable density fitting to solve the full pp-RPA (ladder CCD) equations while maintaining O($N^5$) or even O($N^4$) complexity, which would allow non-diagonal ladder terms to be included. Also of interest is combining pp-ladders with renormalization in the particle-hole channel (as in the work of Marie et al.) without double counting, in the spirit of parquet approximations.
The method can be directly implemented in existing quantum chemistry software packages to improve the accuracy of closed-shell ionization potential calculations at no extra cost. This will affect the interpretation of photoelectron spectra, prediction of redox potentials, and modeling of charge transfer processes in molecular electronics.
The immediate next steps are extended testing on broader molecular sets, including strongly correlated systems, and implementing full pp-ladders with tensor factorization to check whether the accuracy gain persists.
This work is directly related to the problem of describing many-body correlations within the single-particle picture of the self-consistent energy. For quantum chemistry, the question of systematically improving ADC methods without losing their computational efficiency remains open, especially for strongly correlated systems where Møller–Plesset perturbation theory diverges. This approach offers a partial solution through amplitude renormalization, but it does not eliminate the fundamental limitations of single-reference theory.
This section is addressed to the author of the paper and their colleagues. Neighbouring works were found by meaning-based search across our archive, not by word overlap. We do not review: we show the field around the work.
What the work does
This paper proposes a variant of ADC(3) in which the Møller–Plesset perturbation theory denominators are replaced by dressed Epstein–Nesbet denominators that account for ladder diagrams in the particle-particle T-matrix approximation. The method is tested on a set of 58 ionization potentials of 23 molecules and shows a reduction in mean absolute error from 0.33 eV to 0.09 eV for closed shells, outperforming EOM-CCSD and approaching EOM-CCSDT. For open shells, the improvements are more modest, and for long conjugated chains, a sign change in the error is observed.
Where its strength is
The strength of the work lies in maintaining the computational cost of ADC(3) while significantly improving accuracy through a simple modification of the denominators, making the method practical for a wide range of problems.
Where it could go next
Worth trying
Why this may matter
Improving the accuracy of ionization potential calculations while keeping the cost low could make the method valuable for interpreting photoelectron spectra and for high-throughput materials screening.
Nearby works in our archive
The archive is sparse around this work: the closest review is only 0.50, against a usual 0.64. It looks like few have drilled nearby.
The Epstein–Nesbet shift can be interpreted as adding the repulsion energy of two electrons that end up in the same orbital. For a pair of virtual orbitals, this shift is always positive, making the denominator more negative and preventing divergences when orbital energies are degenerate. In calculations for the BN molecule, the second ionization potential changed by 0.15 eV solely due to the inclusion or exclusion of one shift term, illustrating how sensitive the system is.