The conical intersections between the 1(2)A' and 2(2)A' electronic states and the 2(2)A' and 3(2)A' electronic states of the H-2 + H system were characterized by line-integral calculations using ab initio non-adiabatic coupling terms. The calculations confirmed that when a contour surrounds the {1(2)A',2(2)A'} conical intersection but does not approach, too closely, the {22 A', 32 A'} conical intersections the line-integral produces for the topological phase, the expected pi-value [Chem. Phys. Lett., 319 (2000) 489]. Estimating the location of {2(2)A', 3(2)A'} conical intersection, the line-integral procedure was employed again - this time for the {2(2)A', 3(2)A'} system -confirming, in the same way, also the existence of the {2(2)A', 3(2)A'} conical intersections. (C) 2002 Published by Elsevier Science B.V.