  The Raman intensity can be well described by the famous Albrecht equation
that consists of A and B terms. It is well known that the contribution from
Albrecht's A term can be neglected without loss of accuracy for far
off-resonant Raman scattering processes. However, as demonstrated in this
study, we have found that this widely accepted long-standing assumption fails
drastically for totally symmetric vibration modes of molecules in general
off-resonant Raman scattering. Perturbed first principles calculations for
water molecule show that strong constructive interference between the A and B
terms occurs for the Raman intensity of the symmetric O-H stretching mode,
which can account for about 40% of the total intensity. Meanwhile, a minor
destructive interference is found for the angle bending mode. The state to
state mapping between the Albrecht's theory and the perturbation theory allows
us to verify the accuracy of the widely employed perturbation method for the
dynamic/resonant Raman intensities. The model calculations rationalized from
water molecule with the bending mode show that the perturbation method is a
good approximation only when the absolute energy difference between the first
excited state and the incident light is more than five times of the vibrational
energy in ground state.
