The objective of this thesis is to compare the upper bound of the ground state energy of doubly ionized carbon (C⁺⁺) to the lower bound obtained by reduced density matrices.

To make a fair comparison, the number of orbitals used in both is the same, namely ten. The upper bound is obtained by use of the standard Rayleigh-Ritz Variational Principle which states ⟨Ψ|H|Ψ⟩ ≥ Eo(H) were Eo(H) is the exact ground state energy, H is the Hamiltonian, and Ψ is the trial wave function.