An analytic configuration interaction method based on variationally optimized inteally orthogonalized modified Laguerre orbitals is presented. We have developed the corresponding computer code. For application, we study the ls2s 1S isoelectronic sequence from helium to neon, and compare with other methods. By taking into account the Eckart upper-bound theorem, we obtained more accurate and more intuitively understandable results than Hartree-Fock and multi-configuration Hartree-Fock reported results.