The nonrelativistic electronic energy of Be(S1) is computed by a generalization of the method of Brueckner, through the variational solution of generalized Bethe-Goldstone equations. These equations describe clusters of two, three, or four electrons interacting with the remainder of an N-electron system. The three- and four-particle terms are found to be very small, but the sum of three-particle terms is nearly 0.001 atomic units (a. u.). The computed correlation energy is -0.0921 a. u., or 98.1% of the difference between experimental total energy and computed Hartree-Fock and relativistic energies. © 1967 The American Physical Society.