  We propose a method to engineer the phonon thermal transport properties of
low dimensional systems. The method relies on introducing a predetermined
combination of molecular adsorbates, which give rise to antiresonances at
frequencies specific to the molecular species. Despite their dissimilar
transmission spectra, thermal resistances due to individual molecules remain
almost the same for all species. On the other hand, thermal resistance due to
combinations of different species are not additive and show large differences
depending on the species. Using a toy model, the physics underlying the
violation of resistance summation rule is investigated. It is demonstrated that
equivalent resistance of two scatterers having the same resistances can be
close to the sum of the constituents or $\sim$70\% of it depending on the
relative positions of the antiresonances. The relative positions of the
antiresonances determine the net change in transmission, therefore the
equivalent resistance. Since the entire spectrum is involved in phonon spectrum
changes in different parts of the spectrum become important. Performing
extensive first-principles based computations, we show that these distinctive
attributes of phonon transport can be useful to tailor the thermal transport
through low dimensional materials, especially for thermoelectric and thermal
management applications.
