Dear Subham,

finding the correct LJ pair coefficients for materials, especially those with multiple atom types, can be challenging when such parameters are not readily available in the literature or databases. When the Lorentz-Berthelot mixing rules are applied and the results still fall short of experimental thermal conductivity values, several factors could be contributing to the discrepancy.

Potential Reasons for Discrepancy - Limitations of the mixing rulkes:

LB mixing rules are an approximation and may not always yield accurate parameters for interactions between different types of atoms, especially in complex materials. This can lead to an underestimation of the interaction strength, affecting thermal conductivity calculations.

Accuracy of Lj parameters - LJ potential might not fully capture the interactions in your material, especially for materials with complex bonding, directional interactions, or significant electronic effects. LJ parameters are often fitted for specific systems, and they might need refinement or alternative potentials like EAM, MEAM, Tersoff etc. to better represent the interactions.

Take into account cuttoff. If the cutoff distances in your simulations are not appropriately chosen, it can lead to inaccuracies in the calculated forces, and hence, the thermal conductivity. Simulation box&time as well - the size of the simulation box and the length of the simulation time can significantly impact the accuracy of the Green-Kubo results. Insufficiently large systems or short simulation times can lead to poor convergence.

At low temperatures, quantum effects might need to be considered, which classical MD using the LJ potential cannot capture.

If the atoms in the material are polarizable or the interactions are anisotropic, the LJ potential may not capture these effects adequately. This can also lead to discrepancies in calculated thermal conductivity.

Consider fitting the LJ parameters (ε and σ) to reproduce known thermodynamic or mechanical properties (e.g., lattice constants, elastic constants) from experiments or quantum mechanical calculations.

Explore using more sophisticated potentials like EAM, MEAM, S-W .... potentials if they exist for your material.

Perform first-principles calculations like DFT to obtain interatomic potentials or directly calculate thermal conductivity using methods like the Boltzmann Transport Equation or MD with ab initio forces.

Search for experimentally fitted L-J parameters or force fields specifically developed for your material in the literature. Materials Project, OpenKIM, or other similar databases might have data relevant to your material.

Apply corrective scaling to the obtained thermal conductivity based on known discrepancies between experimental and calculated values. This should be done carefully and with an understanding of the underlying causes.

Hope it helps.