We present the vibrational spectral profile of the intrinsic cationic (N-H) and anionic (C-O) probe stretch modes in methylammonium formate (MAF) using first principles molecular dynamics simulations in conjunction with the density functional theory (DFT) approaches. All simulations were performed employing Becke-Lee-Yang-Parr (BLYP) and Perdew-Burke-Ernzerhof (PBE) functionals, using three types of van der Waals (vdW) dispersion-corrected representations (D2, D3, and dispersion-corrected atom-centered one-electron potentials) and two values of plane-wave cut-off (300 and 600 Ry). The long-range electrostatic interactions, directional hydrogen bonds and non-directional van der Waals (vdW) dispersion forces are required to accurately interpret the interionic interactions in the protic ionic liquid, MAF. We compute the 2D IR correlation spectra from the wavelet-derived instantaneous frequencies obtained at each timeframe applying the cumulant expansion truncated at the second order to measure the dynamics of vibrational spectral diffusion. Here, we investigate the effects of electronic structure parameters on the spectral bands of the 2D IR contour plot. The spectral bands for both the N-H and CO stretching vibrations attain a round shape by 1 ps, indicating the loss of frequency correlation irrespective of the type of BLYP or PBE-based functionals. Further, the diagonal linewidth of the 2D IR spectral band agrees with the FWHM (full width at half maxima) of the calculated normalized vibrational stretch frequency distribution. Moreover, this study also finds the reason behind the coalescence of the symmetric and antisymmetric C-O stretches in the computed 2D IR spectra. Besides, these computational results may attract the attention of the experimental spectroscopists as it provides molecular-level interpretation and detailed ultrafast time-resolved spectral information of the intrinsic stretching vibrations and associated dynamics of the protic ionic liquid (PIL). Herein, we inspect the quality of different density functionals along with vdW dispersion corrections. However, even though the experimental data is not available for direct comparison of the results, we finally conclude that the inclusion of the effects of dispersion interactions provides a better estimation of the spectroscopic properties. © 2021 Elsevier B.V.