Determination of the collective modes from the quantum-mechanical time-correlation functions

Theoretical characterization of vibrational spectra for large molecular systems often comes from the normal modes analysis derived from the quadratic approximation of the potential energy surface near its minimum. The normal modes of motion provide accurate representation of low-energy collective motion within a system near equilibrium, but they may be inadequate at high energies or for strongly anharmonic systems. In this article, the collective modes of motion are examined from the time-dependent perspective. It is shown that the imaginary part of the quantum-mechanical position-position correlation functions contains all the information about the collective modes of motion without the harmonic approximation on the potential energy of a system.