Fig. 3. Deep VMC obtains highly accurate excited-state energies and wavefunctions for small molecules.

a PauliNet recovers the same amount of correlation energy as high-order CC methods³⁶. (CH⁺: No better reference energy to compare with.) b Lowest triplet (0 → 1) and singlet (0 → 2) excitation energies obtained using PauliNet (with (red) and without (yellow) variance matching), CC, and TDDFT, with the TBE given. (BH and CH⁺ exhibit degeneracy for the triplet state; CC is CCSD or higher, except for the triplet state of BH which includes CC2.) c Oscillator strengths computed for the 0 → 2 transitions. PauliNet compares well to experiment in all systems and matches the accuracy of (MR−)CC results, demonstrating the quality of few-determinant PauliNet wavefunctions. (We have omitted a factor of two linked to degeneracy in BH and CO.) Refs: exact correlation energies^36,60,61; excitation energies from CC^{41–43,62–66}, TDDFT^65–68 and TBE^{41,42,44,62,69}; oscillator strengths from (MR-)CC^{41 -- 43,70,71}, TDDFT⁷² and experiment^73–77. (The numerical data can be found in Supplementary Table III; source data are provided as a Source Data file).