Why Electron Detachment Energy Calculations Were Wrong and How They Got Fixed ✛

Original: "Third-order Algebraic Diagrammatic Construction Renormalized by Particle-Particle Ladders"

arXiv:2608.28424v1 · 2026-08-28 · CC BY 4.0 · 1 min

A simple correction for electron crowding in a molecule makes calculations nearly four times more accurate.

To tear an electron away from a molecule, you need to put in energy, which is called the ionization potential. The old calculation method ADC(3) assumed that the electron leaves via an empty ladder, encountering no one else. But in reality, other electrons are already standing on the rungs, and they push back against the departing one, like passengers in a crowded subway car.

The new method, EN-ADC(3), adds this "crowdedness" to the calculation. Each rung of the ladder gets a correction: if an electron is already there, climbing costs more. This correction is not a one-off but an infinite chain of interactions, yet it can be computed without extra effort. As a result, the average error for 23 molecules drops from 0.326 eV to 0.09 eV, which is better than the more expensive EOM-CCSD method.

The correction acts like a fee for proximity: two electrons on the same orbital repel each other, and the detachment energy changes. For the BN molecule, a single such correction shifted the result by 0.15 eV.

The improvement is not uniform across all molecules. For open-shell molecules, where electrons are unpaired, the error decreases less. And for long chains, the method can even make results worse. This means the ladder needs to be extended further, but for most ordinary molecules, it is already good enough.

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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.

\tilde{t}^{ab(1)}_{ij} = \frac{\langle ab||ij\rangle}{\epsilon_i + \epsilon_j - \epsilon_a - \epsilon_b - \langle ij||ij\rangle - \langle ab||ab\rangle}

Transition amplitude from occupied orbitals i,j to virtual orbitals a,b, including the repulsion of two holes and two particles

L_{pq,pq}(\omega) = \frac{(1-n_p)(1-n_q)}{\omega - \epsilon_p - \epsilon_q - \langle pq||pq\rangle + i\eta} - \frac{n_p n_q}{\omega - \epsilon_p - \epsilon_q + \langle pq||pq\rangle - i\eta}

Propagator for a pair of particles or holes, including their interaction in the ladder approximation

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Edward Witten Juan Maldacena

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Why Electron Detachment Energy Calculations Were Wrong and How They Got Fixed ✛