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Vibrational assignment, which establishes the correspondence between vibrational modes and spectral frequencies, is a key step in any spectroscopic study. Due to the lack of experimental technique to directly observe the thermal vibration of atoms, the assignment is usually done by empirical trial-and-error method with considerable uncertainty. Here we demonstrate a successful study of intrinsic molecular vibration property based on first-principles molecular dynamics trajectory. A unified approach for calculating and assigning vibrational frequencies is developed and applied to solve some historical issues of benzene vibration. As a major achievement, the experimental frequencies of benzene  a   2g   and  b   2u   vibrations are reassigned, which breaks a deadlock in contemporary spectroscopic science and removes a cloud over the application of density-functional theory in organic chemistry. This work paves the way for the comprehensive realization of the first-principles spectroscopic research, and provides crucial clues to solve the century-old problems of Kekule resonance, π-deformation, and aromaticity.

Intrinsic molecular vibration and rigorous vibrational assignment of benzene by first-principles molecular dynamics