Lower-Bound Method for Atomic Calculations

In the reduced-density-matrix variational method, a trial density matrix Γₜ⁽²⁾ is varied subject to physical realizability conditions in order to calculate the ground-state energy E₀=1/2N min TrH⁽²⁾Γₜ⁽²⁾. Here we expand Γₜ⁽²⁾ in a finite basis of Hartree-Fock geminals and apply a number of equalities to reduce the parameter space of Γₜ⁽²⁾. The method is completely general, but application is made only to the C⁺⁺ ion, where a six-geminal expansion coupled with positivity of Γₜ⁽²⁾ recovers the Hartree-Fock result.