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=12N 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.