Compton scattering is often dubbed "scattering on a free electron", and the scattering process determines energies and angles of the scattered photon and the electron.
This is not true for bound electrons. There you can either have the phtotoeffect or the transmission of energy from a photon to an electron (or vice versa), according to the atomic or molecular electronic levels. But this would be Raman scattering, not Compton scattering. Sloppily speaking, you might call Raman scattering as "Quantum limited Compton scattering on bound electrons" , but this is probably not a very helpful nomenclature.
The Compton effect is an ionizing effect. Visible light does not have sufficient energy to effect ionization of an atom. Visible light does engage in photochemical reactions which might lead to ionization. A photon may be adsorbed in a photochemical reaction and a lower energy photon may be emitted in the process. One might call the photon absorption- emission process as Compton like, but the process is only superficially similar.
Compton scattering is often dubbed "scattering on a free electron", and the scattering process determines energies and angles of the scattered photon and the electron.
This is not true for bound electrons. There you can either have the phtotoeffect or the transmission of energy from a photon to an electron (or vice versa), according to the atomic or molecular electronic levels. But this would be Raman scattering, not Compton scattering. Sloppily speaking, you might call Raman scattering as "Quantum limited Compton scattering on bound electrons" , but this is probably not a very helpful nomenclature.
The photoelectric effect with visible light requires charging the substrate. The electrons scattered are those in the band gap of the charged compound or crystal.
There are two reasons we don't see the Compton effect with visible light.
First, the effect is too small. When light (x-rays or other) scatters off a free electron, the wavelength is shifted by at most 2h/mec = 0.005 nm. That's measurable if the starting wavelength is 0.050 nm (25 keV x-rays). But it would be difficult to confirm that visible light had shifted from 500 nm to 500.005 nm.
Second, Compton scattering applies to free electrons. Of course, those electrons being hit by x-rays were part of some sort of atom, but atomic bonding energies are on the order of 20 eV, which is easily overcome by a 25keV x-ray. Visible light photons don't have the energy to knock an electron off an atom.