Direct approximation to the reduced density matrices: Calculation of the isoelectronic sequence of beryllium up to argon

The spin-adapted reduced Hamiltonian theory has been applied to calculate the energies and the first- and second-order reduced density matrices for the isoelectronic sequence of beryllium up to argon in the singlet symmetry. The projection on the spin symmetry has been performed in two ways: by considering the space spanned by the eigenfunctions of Ŝ ${}_{}{}^2{}_{}{}^{}$ and S${^}_z$ or by considering the space spanned by the S${^}_z$ eigenfunctions. Several approximations for calculating the reduced density matrices are analyzed and discussed in detail. The results obtained with two of the approximations considered are highly encouraging when compared both to experimental data and to the total energy values obtained with the full configuration-interaction method.