  Classical molecular dynamics (MD) has been shown to be effective in
simulating heat conduction in certain molecular junctions since it inherently
takes into account some essential methodological components which are lacking
with quantum Landauer-type transport model, such as many-body full force-field
interactions, anharmonicity effects and nonlinear responses for large
temperature biases. However, the classical mechanics reaches its limit in the
environments where the quantum effects are significant (e.g. with
low-temperatures substrates, presence of extremely high frequency molecular
modes). Here, we present an atomistic simulation methodology for molecular heat
conduction that incorporates the quantum Bose-Einstein statistics into an
effective temperature in the form of modified Langevin equation. We show that
the results from such a quasi-classical effective temperature (QCET) MD method
deviates drastically when the baths temperature approaches zero from classical
MD simulations and the results converge to the classical ones when the bath
approaches the high-temperature limit, which makes the method suitable for full
temperature range. In addition, we show that our quasi-classical thermal
transport method can be used to model the conducting substrate layout and
molecular composition (e.g. anharmonicities, high-frequency modes). Anharmonic
models are explicitly simulated via the Morse potential and compared to pure
harmonic interactions, to show the effects of anharmonicities under quantum
colored bath setups. Finally, the chain length dependence of heat conduction is
examined for one-dimensional polymer chains placed in between quantum augmented
baths.
