Low lattice thermal conductivity(L)is a key parameter for high efficient thermoelectric materials.There are generally several strategies for low L,such as stronger low sound velocity,phonon-phonon interaction,which are in-cell strategies,and nano-to meso-structure,which are out-of-cell strategies and scatter long-wavelength phonons.Another in-cell strategy is the introduction of low-lying optic phonons and interacting with heat-carrying acoustic ones.A particular case of this kind is caged compounds with foreign guest fillers;by examining more low-L thermoelectric compounds,we can find that those with multinary components and complex structures all have the acoustic-optic interaction(AOI).The origin of the AOI is various,depending on the structural uniqueness.On the other hand,the influence to L reduction is similar,i.e.,introducing multiple phonons and increasing the scattering channels after the threshold of AOI.In order to quantify the AOI to L,a cutoff frequency is thus introduced,combining with ab initio phonon calculations and the Callaway model.The simulation package is applied to the evaluations of Ls for over 10 materials with values covering over three orders of magnitude.The agreement between our predictions and experiments is fairly good;this is because both the 2nd and 3rd interatomic force constants have been calculated explicitly.Our method is faster than the accurate three-phonon calculations by at least two orders of magnitude,well balanced in the speed and accuracy,and could be served as a L descriptor for high throughput purpose.The large impact of AOI on L is emphasized by the calculations.Based on the results,an ideal architecture of low L in TE materials are proposed,and confirmed experimentally by our work on an early transition metal chalcogenide.