Electron correlation effects are entirely ignored at the single determinant (Hartree-Fock) level. The traditional density functional approach utilizes nonlinear semiempirical density dependent functionals to account for the correlation effects. We show that a natural alternative is a linear correlation operator which modifies the Hartree-Fock Hamiltonian and yields correlation energy for the single determinant wave function. The form of the correlation operator is suggested by the analysis of the energy contributions and from the electron gas correlation hole. Using this operator we calculate the correlation correction to the energies of a number of atoms and atomic ions. This correction is considerably more accurate than standard density functional theory approximations. The new approach might represent an effective way to deal with correlation problems in the framework of linear operators acting in Hilbert space.