The two-dimensional vibrational spectroscopy involving two infrared (IR) pulses and a single optical pulse, which was theoretically proposed recently [J. Chem. Phys. 109, 10559 (1998)], is studied by using the ab initio calculation method for CHCl3. By obtaining the first- and second-order derivatives of the molecular dipole moment as well as the polarizability, the coherent 2D IR response function and its spectrum are calculated with an assumption that the vibrational dynamics can be described by the Brownian oscillator model. The origin of each peak in the entire coherent 2D IR spectrum is discussed in detail, and is directly compared with the coherent 2D Raman scattering spectrum of CHCl3. This comparison demonstrates the complementary nature between the coherent 2D IR and Raman spectroscopies. A brief discussion on the coupling patterns is also presented.