Full Configuration Interaction Excitations of Ethene and Butadiene: Resolution of an Ancient Question

We employ the recently developed full configuration interaction quantum Monte Carlo (FCIQMC) method to compute the π → π* vertical excitation energies of ethene and all-trans butadiene. These excitations have been the subject of extensive theoretical studies, and their location with respect to the corresponding absorption band maximum is the source of a long lingering debate. Here, we reliably estimate the vertical excitations of ethene and butadiene by performing FCIQMC calculations for spaces as large as 10(18) and 10(29) Slater determinants, respectively. For ethene, we obtain a vertical excitation energy in the range 7.89-7.96 eV, depending on the particular equilibrium ground-state geometry employed, and definitely higher than the absorption maximum located at 7.66 eV. For the computationally more challenging case of butadiene, our calculations provide a robust estimate of about 6.3 eV for this excitation, that is, 0.4 eV higher than the corresponding absorption band maximum. Our FCIQMC excitation energies represent a reliable benchmarking reference for future calculations.