Molecular dynamics simulation study of N-methylacetamide in water. II. Two-dimensional infrared pump–probe spectra

A theoretical description of two-dimensional (2D) IR pump–probe spectroscopy of a three-level system is presented by taking into account the system–bath interaction. By using the correlation function of the fluctuating amide I mode frequency of $N$ -methylacetamide in ${\mathrm{D}}_2\mathrm{O},$ which was obtained by carrying out both ab initio calculations and MD simulations, the time-resolved 2D pump–probe spectra as a function of pump–probe pulse delay time are calculated and compared with experiment. We found that the vibrational dephasing becomes homogeneous on the 2 ps time scale, which is a bit faster than the experimental result. It is theoretically shown that the degree of slant of 2D contours is linearly proportional to the correlation function of the fluctuating amide I mode frequency. Consequently, it is suggested that the 2D IR pump–probe spectroscopy can provide a direct information on the vibrational frequency fluctuation dynamics and on the magnitude of static inhomogeneity.