Why do some absorbing compounds fluoresce but others do not?

When a molecule absorbs sufficient radiant energy, the electron is excited to the excited state. If the electron returns to the ground state through vibrational relaxation, the compound fluoresces. However, many compounds cannot fluoresce because they return to the ground state by nonradiative processes, such as transferring excess energy to other molecules, decaying to a close but a little lower energy state without any emission, or reacting with surrounding molecules to form new products.