We have recently demonstrated that the second hyperpolarizability gamma of a selected vibrational mode of a molecule can be determined by using the computational Raman activity against an internal standard with a known Raman gamma value. This approach provides a convenient way for prediction of the gamma magnitude of DOVE four wave mixing spectroscopy, an optical analogue to two-dimensional (2D) NMR. Here, by using the Hartree-Fock (HF) method, the density functional theory (DFT) method, and the second-order Moller-Plesset perturbation theory (MP2) method, we extend our early work from the less anharmonic region <2000 cm(-1) into the more anharmonic region >2000 cm(-1) covering C-H, C-D, and C N stretching modes of benzene, deuterated benzene, acetonitrile, deuterated acetonitrile, and tetrahydrofuran. The computed Raman gamma values of these vibrational modes have been determined by using either the 992 cm(-1) Raman band of benzene or the compound's own Raman band (C-C stretch) around 800-1000 cm(-1) as an internal standard. In this more anharmonic region, the HF method with a larger basis set provides the best outputs and the predicted Raman gamma values agree well with experimental values for most of the vibrational modes studied. By choosing a suitable method and basis set, this facile approach could be applied to a broader spectral range for Raman gamma estimation of various materials.