“…In the nonresonant case, the sum-frequency light ω is not resonant with molecular excited electronic states and μ k is the k ( k = x , y , z ) component of the electric dipole operator. The anti-Stokes Raman tensor M ij is written as , where n is the excited electronic state, δ is the corresponding vibrational state, ω ( n ,δ)( g , v ) ( v = 0, 1) is the energy difference between the excited vibronic state | n ,δ⟩ and the ground vibronic state | g , v ⟩, and Γ ( n ,δ)( g , v ) is the corresponding damping constant. M ij can be written as the sum of A and B terms The A term is from the electric dipole contribution, and the B term is due to the nonadiabatic effect.…”