To calculate the correlation energy of an atom with N electrons we suggest the wave function
where Ã is the antisymmetrizer operator, φ1, φ2, ..., φN are one electron wave functions, and Wjk are correlation functions of the following form:
where the constants c j km, n, l are variational parameters. The function (a) is a generalization of the
wave function of Hylleraas for He. After a discussion of the properties of our function, an energy expression is derived. Numerical calculation is made for the ground state of the Be atom with the function
where φ1 and φ2 are ls wave functions, φ3 and φ4 are 2s wave functions, r1, r2, r3 and r4 are the radial coordinates of the four electrons, r12 and r34 are the distances between the corresponding electrons, and C1 and c2 are variational parameters. Using the one electron wave functions calculated by Roothaan and coll. with the Roothaan procedure, we got the energy value E= -14.624 a. u. while the Hartree-Fock and experimental values are EH,F= -14.570 a. u. and Eexp= -14.668 a. u. respectively. Thus the function (c) gives about one-half of the correlation energy of the Be atom.