For H2O, CCSD(T)(FC) energies in hartrees at the optimized geometry for each basis set for the aug-cc-pVnZ basis sets are -76.363588 for n = 4, -76.370298 for n = 5, -76.372559 for n = 6, and -76.373672 for n = 7 [D. Feller and K. A. Peterson, J. Chem. Phys., 131, 154306 (2009)]. (The n = 7 basis set exists for only a few elements.)
(a) Use the equation following (16.32) to derive a formula that expresses E in terms of En and En-1.
(b) Use this formula with n and n - 1 being 5 and 4 to estimate the CCSD(T)(FC) CBS limit for H2O. Repeat for the values 6 and 5 and then for 7 and 6. Your estimates will not be close to the true nonrelativistic energy -76.438 listed in Table 16.2 mainly because of the frozen-core approximation. A CCSD(T)(full)/aug-cc-pCV5Z calculation gives -76.432 hartrees [M. Cortez et al., J. Chem. Theory Comput., 3, 1267 (2007)].