Trends in structural, electronic properties and Fermi surface topology of 15 tetragonal ThCr2Si2-type phases AFe2Ch2, where A = Li, Na, K, Rb, and Cs; Ch = S, Se, and Te, as parent systems of new ternary iron-chalcogenide superconductors

► Systematic study of 15 tetragonal ThCr2Si2-type phases AFe2Ch2 was performed. ► The trends in the electronic properties and Fermi surface topology are analyzed. ► AFe2Se2 and AFe2Te2 phases are favorable for the search of new superconductors.