Abstract: With a variational method and a modified arrangmement channel quantum mechanics(MACQM) method, the energies of a equilateral triangle H₃ and a tetrahedron H₄ system are calculated. The result shows that as α=1.03 and R=1.74a₀, the H₃ system has a minimal energy of -1.58161 a.u.; as α=1.07 and R=1.60 a₀, the H₄ system has a minimal energy of -2.28097 a.u.. It shows that both structures could exist.

Key words: variational method, arrangement channel, structure and energy equilateral, triangle, tetrahedron