Physisorption of molecular hydrogen based on neutral and negatively charged aromatic molecular systems has been evaluated using A initio calculations to estimate the binding energy, Delta H, and Delta G at 298 (similar to 77 bar) and 77 K (45 bar) in order to compare calculated results with experimental measurements of hydrogen adsorption. The molecular systems used in this study were corannulene (C20H10), dicyclopenta[def, jkl]triphenylene (C20H10), 5,8-dioxo-5,8-dihydroindeno[2,1-c]fluorene (C20H10O2), 6-hexyl-5,8-dioxo-5,8-dihydroindeno[2,1-c]fluorene (C26H22O2), coronene (C24H12), dilithium phthalocyanine (LiPc, C32H16Li2N8), tetrabutylammonium lithium phthalocyanine (TBA-LiPc, C48H52LiN9), and tetramethylammonium lithium phthalocyanine (TMA-LiPc, C36H28LiN9). It was found (a) that the calculated term that corrects 0 K electronic energies to give Gibbs energies (thermal correction to Gibbs energy, TCGE) serves as a good approximation of the adsorbent binding energy required in order for a physisorption process to be thermodynamically allowed and (b) that the binding energy for neutral aromatic molecules varies as a function of curvature (e.g., corannulene versus coronene) or if electron-withdrawing or -donating groups are part of the adsorbent. A negatively charged aromatic ring, the lithium phthalocyanine complex anion, [LiPc](-), introduces charge-induced dipole interactions into the adsorption process, resulting in a doubling of the binding energy of Li2Pc relative to corannulene. Experimental hydrogen adsorption results for Li2Pc, which are consistent with MD simulation results using chi-Li2Pc to simulate the adsorbent, suggest that only one side of the phthalocyanine ring is used in the adsorption process. The introduction of a tetrabutylammonium cation as a replacement for one lithium ion in Li2Pc has the effect of increasing the number of hydrogen molecules adsorbed from 10 (3.80 wt %) for Li2Pc to 24 (5.93 wt %) at 77 K and 45 bar, suggesting that both sides of the phthalocyanine ring are available for hydrogen adsorption. MD simulations of layered tetramethylammonium lithium phthalocyanine molecular systems illustrate that doubling the wt % H-2 adsorbed is possible via such a system. Ab initio calculations also suggest that layered or sandwich structures can result in significant reductions in the pressure required for hydrogen adsorption.