While the conventional variants of the algebraic-diagrammatic construction (ADC) scheme for the polarization propagator are generally incapable of correctly describing the topology of S/S conical intersections (CIs), its corresponding spin-flip (SF) variant of third-order ADC (ADC(3)) is herein demonstrated to successfully reproduce the S/S minimum-energy CI (MECI) of twisted formaldinium (HC═NH). Analytical nuclear excited-state gradients of ADC have been used in combination with the CIOpt program for the optimization of the MECI without the need for nonadiabatic-coupling vectors. For comparison, MS-CASPT2 calculations were performed via conventional CI optimization employing analytical nonadiabatic-coupling vectors. It is shown that SF-ADC(3) yields the correct dimensionality of the CI and overall compares very favorably to the MS-CASPT2 results.
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