Calculation of theS1State of the Beryllium Atom in Hylleraas Coordinates

The ${}_{}{}^1{}_{}{}^{}S$ state of the Be atom is calculated in Hylleraas coordinates using a 25-term single-determinant wave function having the proper spin-angular-momentum symmetry. A ground-state energy of -29.3158 Ry is obtained, as compared with the experimentally observed value of -29.337 Ry and the best Hartree-Fock value of -29.145 96 Ry, indicating that the application of the procedure to larger systems should be fruitful. Suggestions are given to improve the accuracy of the present method and to extend it to atoms of higher atomic number. Solutions of the integrals and procedures for manipulating them in storage are presented.