Efficiently Calculating Anharmonic Frequencies of Molecular Vibration by Molecular Dynamics Trajectory Analysis

Two efficient methods, the Eckart frame algorithm and the multiorder derivative algorithm, for vibrational frequency calculation directly based on the raw data of atomic trajectory from the state-of-the-art first-principles molecular dynamics simulation are presented. The Eckart frame approach is robust to retrieve the full set of anharmonic fundamental frequencies of any molecule from the atomic trajectory for a sufficiently long molecular dynamics simulation at a temperature close to 0 K. In addition to the fundamental vibrational frequencies, the multiorder derivative approach is universal for the calculations of vibrational frequencies based on the molecular dynamics result in a wide range of temperatures. The accuracy, efficiency, and applicability of these two methods are demonstrated through several successful examples in calculating the anharmonic fundamental vibrational frequencies of methane, ethylene, water, and cyclobutadiene.