A quantum mechanical derivation is presented for the circular intensity differential scattering (CIDS) of a molecule of arbitrary size. Expressions for the special case where the scattering system is composed of a collection of independent scatterers are derived and the relationship is shown between the quantum mechanical expressions and previous expressions obtained using classical electrodynamics. The differences between elastic and inelastic CIDS are then discussed, as well as the differences between the CIDS due to large and small scattering systems. © 1984 American Institute of Physics.