Recently the quantum chemistry program can provide the anharmonic potentials for polyatomic molecules and clusters. It makes the quantum calculation of intramlecular vibrational redistribution (IVR) rates and intramolecular vibrational energy transfer possible. In the present paper, we apply the adiabatic approximation method to treat these two intramolecular energy redistribution processes. Using this method, we calculate the IVR rates of the dipeptides (glycyl tyrosine (GlyTyr) and leucyl tyrosine (LeuTyr)) and their cation radicals from the high frequency modes to the low frequency modes. Our theoretical results of the IVR lifetimes of the high frequency modes, like C-H, N-H, and O-H stretching modes, for both GlyTyr and LeuTyr molecules and their cation radicals are about 1 ps, 10 ps, and 100 ps, respectively. It provides theoretical support for the claim that IVR takes place prior to dissociation and the IVR rates are determined by the functional group rather than the degrees of freedom of the system. Thus the Rice-Ramsperger-Kassel- Marcus (RRKM) theory is suitable for investigating the photodissociation process of dipeptides. In addition, the calculated intramolecular energy transfer rate from O-H stretching mode of the C-termius of dipeptides to N-H mode of N-terminus is close to IVR rate.