In order for computational chemistry to become a viable alternative to experiment and become a true predictor for science and industry,1 high accuracy must be attainable in a timeframe that does not exceed the time spent on experiment, Current methods are either hampered by a lack of accuracy (e.g., Hartree-Fock theory) or, in the worst case, insurmountable computational efforts for anything but the simplest problems (i.e. full configuration inter-action [FCI]). The working equation of quantum chemistry, the Schrodinger equation, relies on two-body operators only. This simplicity is deceiving in that the boundary conditions enforced by the nature of electrons, which are fermions, links these two-body operators in a very complex manner. The exact solution given by FCI results in a computational cost which is exponential in the size of the computed molecule. Due to the simple nature of the contracted Hamiltonian (K = nh + (n2) 1/r12 ),which is a two-electron operator, the computational complexity of the Schrodinger equation should be bounded by O(n6). this work shows that the ground state of a molecule can be expressed very accurately in terms of a geminal g in the form of Ag (l, 2)f(3 ... ), where A is the anti-symmetrizer and f is some n - 2-electron function. Using this result, the generalized antisymrnetric geminal product (GAGP) combines the ideas of geminal functional theory and Hartree-Fock theory to several geminals. GAGP lays the groundwork for the highest accuracy at a cost that scales with 0(n6). The GAGP approach wits further tested on sample 4-electron systems, Li- , Be, B+, as well as LiH, BeH+, He2, H3-l and their respective dissociated species, with the moderately large basis set cc-pVDZ. The calculations confirmed the theoretical results and rendered excellent accuracy.