Excited-state machine-learned potentials get a local Hamiltonian: two molecules 10 Å apart keep exactly the union of their levels
Excited-state energies, unlike ground-state energies, are not sums of atomic contributions, so multistate readouts that pool atomic terms drift when molecules grow larger or two molecules appear together. LEH-MACE instead assembles a symmetric matrix from one diagonal block per atom and coupling blocks for atom pairs, and takes its eigenvalues as the singlet excitation energies, so the spectrum of two molecules beyond the cutoff is exactly the union of their spectra. On TD-DFT data for about 303,000 geometries of 106,933 molecules, the advantage grew away from the training distribution, and only this construction kept single-molecule accuracy for molecule pairs.