Variational low-energy subspaces for chemically accurate excited states

Accurate electronic excited states are essential for photochemistry, spectroscopy and non-adiabatic molecular dynamics, but high-level calculations often scale steeply and require prior knowledge of the target state's character or symmetry. Here we show that variational excited-state optimization can be reformulated as an iterated ground-state-like problem for a low-energy subspace of the electronic Hamiltonian. Applying this variational principle to non-orthogonal Slater determinants leads to EXIDOS, an automatic method for excited state calculations controlled only by the number of states and determinants per state. EXIDOS optimizes multiple excited states simultaneously, without explicit orthogonality constraints or imposed spin and point-group symmetries. Benchmarks against FCI and state-of-the-art quantum chemistry methods show chemical accuracy for a multitude of states in N₂ and CO, charge-transfer states in HCl, Rydberg states in NH₃, double excitations and extended potential-energy curves in C₂, and avoided crossings and conical intersections in ethylene. These results establish EXIDOS as a low-scaling, fully variational route to chemically accurate excited states.