  Equilibrium molecular dynamics (EMD) simulations through Green-Kubo formula
(GKF) have been widely used in the study of thermal conductivity of various
materials. However, there exist controversial simulation results which have
huge discrepancies with experimental ones in literatures. In this paper, we
demonstrate that the fluctuation in calculated thermal conductivity is due to
the uncertainty in determination of the truncation time, which is related to
the ensemble and size dependent phonon relaxation time. We thus propose a new
scheme in the direct integration of heat current autocorrelation function
(HCACF) and a nonzero correction in the double-exponential-fitting of HCACF to
describe correctly the contribution to thermal conductivity from low frequency
phonons. By using crystalline Silicon (Si) and Germanium (Ge) as examples, we
demonstrate that our method can give rise to the values of thermal conductivity
in an excellent agreement with experimental ones.
