Materials displaying anomalous quantum confinement effects (aqce) comprise the significant materials for recent optoelectronics, two-dimensional (2D) heterojunctions and band-gap engineering. Although available literature involves numerous works for regular 2D materials, there is still a lack of the key physical properties of aqce materials. So, in this work, density functional theory (DFT) calculations have been performed for the electronic, optical, phonon and thermoelectric properties of bulk and monolayered counterparts of recently introduced RbLiS and RbLiSe (aqce) compounds. The bulk RbLiS demonstrated a bandgap of 2.53 eV, whereas its monolayer has a lower bandgap of 1.20 eV. In addition, the bulk bandgap of RbLiSe was determined to be 2.10 eV being higher than the 1.26 eV of its monolayered counterpart. The optical properties of the addressed compounds are reported to be complex in nature, where bulk RbLiS and monolayers of RbLiS and RbLiSe can be intended as low -dielectric materials. Also, both bulk and monolayered RbLiS and RbLiSe compounds may be used as demanded photoconductors for possible UV purposes. In addition, both bulk RbLiS and RbLiSe exhibit high-refractive indices and are determined to be feasible for practical IR goals in contrast to their monolayer counterparts. Also, both bulk and monolayered RbLiS and RbLiSe compounds can be used as effective optical absorbers in ultraviolet (UV) applications. Phonon dispersions indicated dynamical stability of both bulk and monolayered structures of RbLiS and RbLiSe, which means the possibility of their experimental synthesis. Bulk and mono -layered structures of RbLiS and RbLiSe compounds with high Seebeck coefficients suggest the possibility of new thermoelectric materials from bulk (3000 mu V/K) and monolayered (2200 mu V/K) RbLiS and RbLiSe compounds.