The quantum mechanics (QM) method and grand canonical Monte Carlo (GCMC) simulations are used to study the effect of lithium cation doping on the adsorption and separation of CO , CH , and H on a twofold interwoven metal-organic framework (MOF), Zn (NDC) (diPyNI) (NDC=2,6-naphthalenedicarboxylate; diPyNI=N,N'-di-(4-pyridyl)-1,4,5,8-naphthalenetetracarboxydiimide). Second-order Moller-Plesset (MP2) calculations on the (Li -diPyNI) cluster model show that the energetically most favorable lithium binding site is above the pyridine ring side at a distance of 1.817 Å from the oxygen atom. The results reveal that the adsorption capacity of Zn (NDC) (diPyNI) for carbon dioxide is higher than those of hydrogen and methane at room temperature. Furthermore, GCMC simulations on the structures obtained from QM calculations predict that the Li -doped MOF has higher adsorption capacities than the nondoped MOF, especially at low pressures. In addition, the probability density distribution plots reveal that CO , CH , and H molecules accumulate close to the Li cation site. The selectivity results indicate that CO /H selectivity values in Zn (NDC) (diPyNI) are higher than those of CO /CH . The selectivity of CO over CH on Li -doped Zn (NDC) (diPyNI) is improved relative to the nondoped MOF.