Nonadiabatic singer polymal wave functions for three‐particle systems

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AbstractA method for nonadiabatic many‐particle quantum‐mechanical calculations is described and illustrated for the special case of three particles. The method uses a basis of explicitly correlated Singer‐type exponential quadratic function (polymals) of the internal degrees of freedom. Rigorous symmetry states are projected from the basis: linear momentum of the center of mass, total angular momentum, and permutational symmetry under interchange of indistinguishable particles. The nonadiabatic wave functions are interpreted via purely quantum‐mechanical criteria of interparticle correlation as measured by average values of powers of interparticle distances and angles. The illustrations are made on H2+ which is easily treated in the Born–Oppenheimer and adiabatic approximations, on helium, muonic helium, and on (e+, e−, e+) which are poorly described in adiabatic methods. The ground and lowest bound excited states of these systems are studied with up to 256 tempered Singer polymals for which we find energies too high by 0.0011 a.u. in H2+, 0.0017 a.u. in muonic helium, 0.0009 a.u. in 4He, and 0.0002 a.u. in (e+, e−, e+); the corresponding relative errors are 1800, 4, 300, and 200 ppm, respectively.