We are interested in multi-physics observed in biomolecules such as deoxyribonucleic acids (DNAs). Phenomena in biomolecules should be understood in multi-scale. The role of charge transfer in DNA base molecules is one of the hottest topics. In this study, propagation of electron wave functions in DNA base molecules has been investigated. The calculations have been examined for the highest occupied molecular orbital (HOMO) on an adenine molecule and the lowest unoccupied molecular orbital (LUMO) on a guanine molecule. Wave functions in each initial state propagate along the external electric field and diffuse from the base molecules. Hopping propagations via hydrogen bonds between base molecules have not been induced although diffusions between base pairs along the DNA axis have been observed. A numerical method for wavepacket dynamics is suggested and that is efficient for long time dynamics simulations which require conservation of quantities.