Abstract
Wave functions of a new functional kind has been proposed in this work for helium-like atoms. These functions depend explicitly on interelectronic and hyperspherical coordinates.
The best ground state energy for the helium atom -2.903724376677 a.u. has been calculated using the variational method with a basis including a single exponential parameter. To our knowledge, this is the best result so far using of hyperspherical coordinates.
Comparable result has been obtained for the hydrogen anion. For helium atom, our best wave functions matched the Kato cusp conditions within an accuracy below 6.10(-4).
An important feature of proposed wave functions is the inclusion of negative powers of R = root(r1(2) + r2(2)) in combination with positive powers of r(12) into the wave function. We showed that this is necessary condition for proposed wave function to be a formal solution of Schrodinger equation.