Dissociation of LiH in the cc-pVDZ basis. NRHFB is equivalent to AGP and offers sizable improvement over RHF and UHF.
Top panel: Dissociation of C2H4 to two CH2 fragments, in the cc-pVDZ basis. Symmetry-broken AGP (i.e., NUHFB) offers significant variational improvements. Bottom panel: Spin contamination in UHF and NUHFB as a function of C–C bond length.
Torsion of C2H4 about the C–C double bond, in the cc-pVDZ basis. Breaking spatial and spin symmetry offers significant amounts of static correlation at both the HF and projected HFB levels.
Dissociation of N2 in the STO-3G basis. Restoring the broken spin symmetry provides significant correlation and eliminates the instability in the NRHFB wave function.
Dissociation of equally spaced linear H4 in the STO-3G basis. Only by breaking symmetry can projected HFB reach the correct dissociation limit.
Comparison of KNHFB and SNHFB to full CI for the dissociation of equally spaced linear H4. Restoring these symmetries leads to results almost equal to full CI. In particular, SNGHFB appears to be energetically identical to full CI for the points at which we successfully converged the equations.
Dissociation of He2 in the 3-21G basis. We have broken the energy axis several times as the solutions are well separated in energy and the binding is minimal. The full CI results exactly match the KNRHFB curve shown in the figure. The labels “s” and “bs” on the NRHFB indicate whether spatial symmetry is preserved (“s”) or broken (“bs”) in the underlying HFB determinant.
Correlation energies in the four-electron series. We compare the NRHFB results in the aug-cc-pVTZ basis to the exact results of Ref. 57. Note that we correctly recover the linear behavior of the correlation energy as a function of nuclear charge Z.
Nomenclature defining our various projected and unprojected HFB states.
Errors associated with the discretization of the particle number projection operator in NRHFB calculations of hydrogen atom rings (r H-H = 1.80 bohrs, STO-3G basis). The reference energy is taken to be that with N grid = 9.
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