Non-adiabatic excited-state molecular dynamics is used to study the ultrafast intramolecular energy transfer between two-, three-, and four-ring linear polyphenylene ethynylene chromophore units linked through meta-substitutions. Twenty excited-state electronic energies, with their corresponding gradients and nonadiabatic coupling vectors were included in the simulations. The initial laser excitation creates an exciton delocalized between the different absorbing two-ring linear PPE units. Thereafter, we observe an ultrafast directional change in the spatial localization of the transient electronic transition density. The analysis of the intramolecular flux of the transition density shows a sequential through-bond two-ring→three- ring→four-ring transfer as well as an effective through-space direct two-to-four ring transfer. The vibrational excitations of C≡C stretching motions change according to that. Finally, a mechanism of unidirectional energy transfer is presented based on the variation of the energy gaps between consecutive electronic excited states in response to the intramolecular flux of the transition density. The mechanism resembles a Shishiodoshi Japanese bamboo water fountain where, once the electronic population has been transferred to the state directly below in energy, the two states decouple thereby preventing energy transfer in the opposite direction.