The molecular hydrogen adsorption was investigated on additional frameworks with earth alkaline metal atoms (Be, Mg and Ca) in 24T ERI zeolite cluster model by means of Density Functional Theory study. HOMO and LUMO energy values, chemical potential, chemical hardness, electronegativity, adsorption energy and adsorption enthalpy values have been calculated in this study. Mg-ERI and Ca-ERI clusters have much lower chemical potentials with much lower adsorption energy values when compared to the value of Be-ERI cluster. Additionally, they are softer than Be-ERI cluster with respect to their lower chemical hardness values. Hydrogen adsorption enthalpy values were computed as - 3.6 and -3.9 kJ/mol on Mg-ERI and Ca-ERI clusters, respectively. These adsorption enthalpy values are significantly larger than the enthalpy value of liquefaction for hydrogen molecule. This consequently specifies that Mg-ERI and Ca-ERI zeolite structures which have higher chemical reactivity appear to be a promising candidate cryoadsorbent for hydrogen storage. (C) 2016 Elsevier B.V. All rights reserved.