A journey from generalized valence bond theory to the full CI complete basis set limit

A qualitative examination of generalized valence bond pair correlation ener gies leads us to a quantitative relationship (interference effect) between basis set truncation errors in MP2 energies and basis set truncation errors in CCSD(T) energies. Thus, a knowledge of the MP2 complete basis set limit can be combined (for example) with CCSD(T)/[5s4p3d2f/4s3p2d] calculations to estimate the CCSD(T) limit to within +/-0.46 kcal/mol. Explicit MP2-R12 calculations are then compared to three extrapolation schemes employing cc- pVnZ correlation consistent basis sets in an attempt to find an inexpensive route to the required MP2 limit. The first employs the N-1 asymptotic conv ergence of pair natural orbital (PNO) expansions to extrapolate to the comp lete basis set (CBS2) Limit. The second employs (l + 1/2)(-3) extrapolation s of more than one MP2/cc-pVnZ calculation to estimate this MP2 limit. The third method combines the PNO extrapolations with a linear and thus size-co nsistent (l + 1/2)(-3) extrapolation. This linear (l + 1/2)(-3) extrapolati on of first CBS2/cc-pVDZ and CBS2/cc-pVTZ then CBS2/cc-pVDZ and CBS2/cc-pVQ Z energies gives the absolute MP2-R12 limit to within +/-0.86 and +/-0.49 k cal/mol respectively for a test set of 12 small closed shell molecules, whi ch represents a new level of accuracy for calculations fast enough to be ro utinely applied to molecules as large as naphthalene. Combining these MP2 l imits with the interference corrected CCSD(T)/cc-pVDZ and CCSD(T)/cc-pVTZ e nergies respectively, gives the absolute CCSD(T) basis set limit to within +/-1.74 and +/-0.93 kcal/mol.