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Excited states in molecules can be difficult to investigate and generallyrequire methods that are either computationally expensive or are notuniversally accurate. Recent research has focused on using higher-energy Slaterdeterminants as mean-field representations of excited states, which can then beused to define reference states for electron correlation techniques such asM{\o}ller-Plesset theory. However, the convergence behaviour of theseexcited-state perturbation series has not yet been explored, limiting ourunderstanding into the systematic improvability and reliability of suchmethods. Here, we present a systematic analysis of the M{\o}ller-Plessetperturbation series for closed-shell excited states using higher-energyreference determinants identified with, and without, state-specific orbitaloptimisation. We combine numerical calculations with complex analysis to showthat the excited-state M{\o}ller-Plesset theory diverges almost universally forthe stereotypical $\mathrm{H}_2$, $\mathrm{H}_2\mathrm{O}$, and $\mathrm{CH}_2$molecules. Our results cast doubt on the suitability of higher-energy Slaterdeterminants as reference states for perturbative treatments of electroncorrelation.

Convergence of M{\o}ller-Plesset perturbation theory for excited reference states