In quantum-field chemistry approach computing simulation of high reversible hydrogen sorption in carbon nanotube is presented. It is shown that hydrogen molecules accumulation is coursed by strong spin-dependent exchange interactions between activated hydrogen bi-radical H2* and carbone nanotube’s surfaces. Investigation of the interaction between the hydrogen atoms and molecules and atoms of carbon are carried out by density functional method in non-local density approximation. Our results are in accordance with experimental data, which are corresponding with “super”- Van der Waals forces or “weak” covalent bonds in other works. Thus, it has been marked, that interaction energy between hydrogen and carbon nanostructure (20 - 40 кJ/mol) exceed interaction (distraction) energy of Van-der-Waals bonds in ten times, which is characteristic for physical hydrogen adsorption by carbon materials, Potentials of strong spin-dependent exchange interactions is ten times lower than distracting energies of covalent C-H bonds, which are characteristic for chemisorptions. We examine the self-assembling hydrogen adsorption both on internal, and on external surfaces of carbone nanotube. It is shown that thermodynamically stability of hydrogen bi-radical H2* adsorbate set in at mass-concentrations of hydrogen amount above 3%. Inside carbon nanotube the stabilization occurs easier. Computer experiment reveals thermodynamic stability of some self-assembly spiral nanostructure forms in the hydrogen bi-radical H2* adsorbate aggregation distribution. In case of exothermic processes of self-assembling adsorption on internal surface of nanotube, when concentrations of hydrogen amounts spontaneously increasing from initial 3% up to 7,7 mass. %, a thermal effect increases, as follows: 7 кJ/mol (3.7%), 27 кJ/mol (5.6%), 36 кJ/mol (7.7%). That provides both a thermodynamic stability of adsorbate with high hydrogen concentration and an easy reversibility of hydrogen sorption and desorption.