The binding energies and other properties of the excitonic complexes ͑bound systems of electrons and holes͒ in two and three dimensions ͑2D and 3D͒ are calculated by a precise variational method. The mass ratios for the limit of the stability of X 3 ϩ (eehhh) are determined in both 2D and 3D cases. Two excited states of the biexciton are found to remain bound for any mass ratio.

The positronium molecule (Ps 2 ) has not been experimentally observed yet because its tiny (4.

A new, hitherto unknown bound state of the positronium molecule, with orbital angular momentum L 1 and negative parity, is reported. This state is stable against autodissociation even if the masses of the positive and negative charges are not equal. The existence of a similar state in two dimensions has also been investigated. The fact that the biexcitons have a second bound state may aid in the better understanding of their binding mechanism. [S0031-9007(98)

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A new formulation is presented for a variational calculation of N -body systems on a correlated Gaussian basis with arbitrary angular momenta. The rotational motion of the system is described with a single spherical harmonic of the total angular momentum L, and thereby needs no explicit coupling of partial waves between particles. A simple generating function for the correlated Gaussian is exploited to derive the matrix elements. The formulation is applied to various Coulomb three-body systems such as e − e − e + , ttµ, tdµ, and αe − e − up to L = 4 in order to show its usefulness and versatility. A stochastic selection of the basis functions yields good results for various angular momentum states.