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Two new alkaline earth metal–organic frameworks (AE-MOFs) containing Sr(II) (UPJS-15) or Ba(II) (UPJS-16) cations and extended tetrahedral linker (MTA) were synthesized and characterized in detail (UPJS stands for University of Pavol Jozef Safarik). Single-crystal X-ray analysis (SC-XRD) revealed that the materials are isostructural and, in their frameworks, one-dimensional channels are present with the size of ~11 × 10 Å2. The activation process of the compounds was studied by the combination of in situ heating infrared spectroscopy (IR), thermal analysis (TA) and in situ high-energy powder X-ray diffraction (HE-PXRD), which confirmed the stability of compounds after desolvation. The prepared compounds were investigated as adsorbents of different gases (Ar, N2, CO2, and H2). Nitrogen and argon adsorption measurements showed that UPJS-15 has SBET area of 1321 m2 g−1 (Ar) / 1250 m2 g−1 (N2), and UPJS-16 does not adsorb mentioned gases. From the environmental application, the materials were studied as CO2 adsorbents, and both compounds adsorb CO2 with a maximum capacity of 22.4 wt.% @ 0 °C; 14.7 wt.% @ 20 °C and 101 kPa for UPJS-15 and 11.5 wt.% @ 0°C; 8.4 wt.% @ 20 °C and 101 kPa for UPJS-16. According to IAST calculations, UPJS-16 shows high selectivity (50 for CO2/N2 10:90 mixture and 455 for CO2/N2 50:50 mixture) and can be applied as CO2 adsorbent from the atmosphere even at low pressures. The increased affinity of materials for CO2 was also studied by DFT modelling, which revealed that the primary adsorption sites are coordinatively unsaturated sites on metal ions, azo bonds, and phenyl rings within the MTA linker. Regarding energy storage, the materials were studied as hydrogen adsorbents, but the materials showed low H2 adsorption properties: 0.19 wt.% for UPJS-15 and 0.04 wt.% for UPJS-16 @ −196 °C and 101 kPa. The enhanced CO2/H2 selectivity could be used to scavenge carbon dioxide from hydrogen in WGS and DSR reactions. The second method of applying samples in the area of energy storage was the use of UPJS-15 as an additive in a lithium-sulfur battery. Cyclic performance at a cycling rate of 0.2 C showed an initial discharge capacity of 337 mAh g−1, which decreased smoothly to 235 mAh g−1 after 100 charge/discharge cycles.