A very accurate variational expansion is suggested for calculation of nonre
lativistic energies of the metastable antiprotonic helium atoms He+(p) over
bar. This expansion reflects the dual atomic-molecular nature of the syste
m. Convergence of the results as a function of the increasing sets of basis
functions shows an accuracy better than 10(-10) a.u., two orders of magnit
ude better than in our previous calculations. [S1050-2947(99)50802-0].