Complex Gaussian functions for four-particle systems

A new type of basis function is suggested for precision variational calculations of many-particle atomic-molecular systems—the Gaussian functions with complex exponential parameters in the form of combinations of exponential-trigonometric functions of the squared interparticle separations. With these basis functions, all required many-particle integrals are evaluated explicitly. The method is applied to totally nonadiabatic calculations of ten four-particle molecules and mesomolecules ranging from the tritium molecule t+t+e−e− to the positronium molecule e+e+e−e−. The dissociation energies of these systems calculated by using 20 complex basis functions coincide with the exact values to within 1%; therefore, their inaccuracy is several times smaller than the inaccuracy of calculations with the basis sets of ordinary real Gaussian functions. This increase in accuracy is attained due to a more correct description of the vibrational part of wave functions of molecular systems by using oscillating complex Gaussian functions as compared to their nodeless real counterparts.