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In the present study, we have devised the G4(MP2)-XK composite method that covers species with up to fifth-row main-group elements (i.e., up to Rn). This new protocol is based on the previously published G4(MP2)-6X method, which has a general accuracy of ∼5 kJ mol-1 for a diverse range of first- and second-row systems. The main difference between G4(MP2)-6X and G4(MP2)-XK is that the Pople-type basis sets in the former are replaced by Karlsruhe-type basis sets, with adjustments to the standard Karlsruhe basis sets to mimic the ones that they replace. Generally, G4(MP2)-XK is comparable in accuracy to G4(MP2)-6X. It is somewhat computationally more efficient than G4(MP2)-6X for the larger species that we have examined (e.g., a pentaglycine peptide). Importantly, the accuracy of G4(MP2)-XK for heavier elements is similar to that for first- and second-row species, even though it contains parameters that are fitted only to systems of the first two rows. This is indicative of the transferability of G4(MP2)-XK, and it paves the way for further expansion of its scope in future studies.