The time correlator formalism was used to calculate the absolute resonance Raman cross sections for the aromatic amino acids based on density functional theory calculations of the ground-state potential energy surfaces combined with projection along normal mode eigenvectors in the excited state. The geometric difference between the minima of the around and excited states along each normal mode was calculated to provide inputs for the time correlator in the linear approximation. The calculated dimensionless nuclear displacements, Delta(i), provide the electron-phonon coupling constants, S-i = Delta(2)(i)/2, for the corresponding Raman active mode of frequency omega(t). The method is generally applicable to molecules that are Franck-Condon active. As an example we have chosen to calculate the absolute resonance Raman cross sections of models of the aromatic amino acids phenylalanine, tyrosine, and tryptophan. We discuss the role played by substituents on the aromatic ring that decrease vibronic activity to a level that permits application of the time correlator. While the method may have limitations for molecules of high symmetry, the current stud of excited-state displacements and electronic structure indicates that the L-a,L-b states are Franck-Condon active in the aromatic molecules studied.