Compact representation of helium wave functions in perimetric and hyperspherical coordinates

Abstract

Variational calculations of the ground-state energy of helium are performed using a basis set representation that includes an explicit treatment of the Fock expansion in hyperspherical coordinates. The construction of basis functions that have the correct cusp behavior at three-particle coalescence points and the evaluation of integrals containing these functions is discussed. The basis set in hyperspherical coordinates is added to a basis set consisting of products of Laguerre polynomials in perimetric coordinates. It is demonstrated that the use of Fock basis functions provides a substantial improvement in the convergence rate of the basis set expansion.