We theoretically study the influence of the second-order electric transition dipole moment derivatives on antisymmetric nonresonant vibrational Raman polarizabilities and the sum-frequency vibrational spectroscopy off electronic resonance. Time-dependent density functional theory computation for limonene chiral liquids indicates that the contribution from the second-order derivatives may be detectable in experiments. (C) 2011 Elsevier B.V. All rights reserved.