Fig. 2
From: Theoretical analysis of spectral lineshapes from molecular dynamics
Convergence properties for graphene treated using ab initio molecular dynamics with a temperature of around 50 K and the velocity auto-correlation method. The E2g symmetry modes are isolated at the Γ-point by projections. The convergence is studied using two approaches, which are denoted by “|FFT|2 + Lorentzian” and “Re{FT} + Analytical”. In both cases, the effective velocities at the Γ-point were obtained using Eq. (5) and the velocity auto-correlation was subsequently calculated with Eq. (15). In the “|FFT|2 + Lorentzian” method, which is the standard procedure and assumes infinite simulation time, the spectrum is calculated as the modulus squared of the fast Fourier transform of the velocity auto-correlation and the resulting peaks are subsequently fit using Lorentzian functions (Eq. (25)). In the “Re{FT} + Analytical” method, which is the new approach and is valid at all simulation times based on our analytical derivations, the spectra are evaluated with Eq. (16) and the vibrational frequencies and half-linewidths are extracted by fitting with Eq. (23). a Convergence of the vibrational frequency with the number of configurations (=NC). Convergence is indicated by the vertical lines with NC = 14,501 for the Lorentzian fit and NC = 2,461 for the analytical model, with improvement by a factor of about 5.9. b Convergence of the half-linewidth Γ with the number of configurations. Convergence is indicated by the vertical lines with NC = 27,301 for the Lorentzian fit and NC = 12,301 for the analytical model, with improvement by a factor of about 2.2. The developed method results in a significant reduction in the required simulation time to obtain converged properties
