An Accurate Classical Simulation of a Two-Dimensional Vibrational Spectrum: OD Stretch Spectrum of a Hydrated HOD Molecule

Abstract

An accurate computational method for the classical simulation of the two-dimensional vibrational spectra is presented. The method refines our previous computational method for the third order vibrational response function in the classical limit, and it enables capturing the diagonal elongation and its waiting time (T) dependence widely observed in experimental two-dimensional infrared (2D IR) spectra of intramolecular modes. The improvement is achieved by a series of new developments including (i) a block algorithm for the stability matrix computation, (ii) new equations of motion for the position perturbed molecular dynamics (MD) trajectory, and (iii) enhanced sampling efficiency by exploiting the time-reversal invariance of MD trajectories. The method is applied to the simulation of 2D IR spectra of the OD stretch mode in a hydrated HOD molecule, employing a hybrid quantum mechanical/molecular mechanical force field. The simulated spectra exhibit diagonal elongation of the 2D IR signal at small T, reflecting the correlation of individual transitions among the inhomogeneously broadened ensemble. The slopes of the nodal lines of the elongated signals are found to decay with a time scale of 1.6 ps as T increases, in reasonable agreement with the frequency correlation decay time of 1.2 ps. The amplitudes of the positive and negative peaks also decay as T increases, due to vibrational population relaxation and molecular rotation. The peak positions tend to blue shift with increasing T, reflecting the different relaxation rates of the strongly and weakly solvated HOD species. These results indicate that the present method can reliably predict the waiting-time-dependent changes of 2D IR spectra of a single vibrational chromophore in solution.