The problem of the convergence of a sequence of Hartree—Fock—Roothaan wavefunctions and energy values to the true Hartree—Fock results is examined for N2(X1Σg+). This critical study is based on a hierarchy of Hartree—Fock—Roothaan wavefunctions which differ in the size and composition of the expansion basis set in terms of STO symmetry orbitals. The concluding basis set gives a total Hartree—Fock energy of −108.9956 hartree and Re(HF)=2.0132 bohr for N2(X1Σg+).
Results are also presented from direct calculations for three states of the N2+ molecular ion (X2Σg+, A2Πu, B2Σu+) which are also thought to be very close approximations to the true Hartree—Fock values. The results give EHF=−108.4079, −108.4320, and −108.2702 hartree and Re(HF)=2.0385, 2.134, and 1.934 bohr for the X2Σg+, A2Πu, and B2Σu+ states of N2+, respectively. Extensive calculations for various R values establish that the X2Σg+ and A2Πu states are reversed in order relative to experiment, a short‐coming ascribed to the Hartree—Fock approximation.