Perturbative-variational approximation of the ground state of two-electron atoms

Here, we study the applicability of the perturbative variational method (PVM) to obtain the ground-state energy and wavefunction of the two-electron atoms. The convergence of the method has been studied with different bases and we have checked whether it is faster if we work with an orthogonal or quasi-orthogonal basis. We have focused our attention on the polynomial basis and our best results are very close to the best results provided for other calculations that include non-analytical terms in the basis. However, we have to use a number of states in a basis ten times larger than that used in other calculations.