[eng] Quantum calculations at several levels of theory have been used to examine complexes between halides (and pseudohalides) and three calix[4]pyrrole derivatives, including DFT-D3 and ab initio (RI-MP2) methods combined with def2-SVP, TZVP and def2-TZVP basis set. The receptors have been substituted at the mesocarbon atom by either methyl or trifluorosilyl groups in order to provide additional C-H X or F3- Si X interactions that enhance the anion binding ability of the receptors. We have computed the interaction energies and analyzed the contribution of the different interactions. As a result, the anion binding ability of the receptors is considerably enhanced by the r-hole tetrel bonds in the smaller anions. We have also characterized the interactions using the NCI (Non Covalent Interaction) plot that is based on the electron density and its derivatives and enables identification and visualization of non-covalent interactions efficiently. We have designed for the first time a calix[4]pyrrole-based anion receptor that uses supplementary binding facility from tetrel bonding.