  We present calculations of the fluorescence-detected coherent two-dimensional
(F-2DES) spectra of a molecular heterodimer. We compare how the F-2DES
technique differs from the standard coherently detected two-dimensional (2DES)
spectroscopy in measuring exciton delocalization. We analyze which processes
contribute to cross-peaks in the zero-waiting-time spectra obtained by the two
methods. Based strictly on time-dependent perturbation theory, we study how in
both methods varying degree of cancellation between perturbative contributions
gives rise to cross-peaks, and identify exciton annihilation and exciton
relaxation contributions to the cross-peak in the zero-waiting-time F-2DES. We
propose that time-gated fluorescence detection can be used to isolate the
annihilation contribution to F-2DES both to retrieve information equivalent to
2DES spectroscopy and to study annihilation contribution itself.
