In an attempt to improve on our earlier W3 theory [A. D. Boese et al., J. Chem. Phys. 120, 4129 (2004)] we consider such refinements as more accurate estimates for the contribution of connected quadruple excitations (T̂4), inclusion of connected quintuple excitations (T̂5), diagonal Born-Oppenheimer corrections (DBOC), and improved basis set extrapolation procedures. Revised experimental data for validation purposes were obtained from the latest version of the Active Thermochemical Tables thermochemical network. The recent CCSDT(Q) method offers a cost-effective way of estimating T̂4, but is insufficient by itself if the molecule exhibits some nondynamical correlation. The latter considerably slows down basis set convergence for T̂4, and anomalous basis set convergence in highly polar systems makes two-point extrapolation procedures unusable. However, we found that the CCSDTQ−CCSDT(Q) difference converges quite rapidly with the basis set, and that the formula 1.10[CCSDT(Q)∕cc-pVTZ+CCSDTQ∕cc-pVDZ-CCSDT(Q)∕cc-pVDZ] offers a very reliable as well as fairly cost-effective estimate of the basis set limit T̂4 contribution. The T̂5 contribution converges very rapidly with the basis set, and even a simple double-zeta basis set appears to be adequate. The largest T̂5 contribution found in the present work is on the order of 0.5kcal∕mol (for ozone). DBOCs are significant at the 0.1kcal∕mol level in hydride systems. Post-CCSD(T) contributions to the core-valence correlation energy are only significant at that level in systems with severe nondynamical correlation effects. Based on the accumulated experience, a new computational thermochemistry protocol for first- and second-row main-group systems, to be known as W4 theory, is proposed. Its computational cost is not insurmountably higher than that of the earlier W3 theory, while performance is markedly superior. Our W4 atomization energies for a number of key species are in excellent agreement (better than 0.1kcal∕mol on average, 95% confidence intervals narrower than 1kJ∕mol) with the latest experimental data obtained from Active Thermochemical Tables. Lower-cost variants are proposed: the sequence W1→W2.2→W3.2→W4lite→W4 is proposed as a converging hierarchy of computational thermochemistry methods. A simple a priori estimate for the importance of post-CCSD(T) correlation contributions (and hence a pessimistic estimate for the error in a W2-type calculation) is proposed.

In an attempt to extend the applicability of the W1 and W2 ab initio computational thermochemistry methods, we propose explicitly correlated versions thereof, denoted W1-F12 and W2-F12. In W2-F12, we can “save” one cardinal number (viz., angular momentum) in the basis set sequences without loss in accuracy; in W1-F12, we can do so for first-row compounds but not for second-row compounds. At a root mean square deviation (RMSD) = 0.19 kcal/mol for the first-row molecules in the W4-11 benchmark dataset, W1-F12 is in fact superior to ordinary W1 theory. For the entire W4-11 set, W2-F12 yields a RMSD = 0.20 kcal/mol, comparable to 0.19 kcal/mol from ordinary W2 theory. The extended applicability ranges of W1-F12 and W2-F12 are not just due to the lower computational cost but also to greatly reduced memory and especially storage requirements. They are illustrated through applications to nucleic acids and to polyacenes (with up to four rings), for which the following revised gas-phase heats of formation are found: \documentclass[12pt]{minimal}\begin{document}$\Delta _fH^\circ _{298}$\end{document}ΔfH298∘ = 19.6 (benzene), 34.94 (naphthalene), 53.9, (anthracene), 73.9 (naphthacene/tetracene), 54.9 (adenine), −16.3 (cytosine), 5.1 (guanine), −80.6 (thymine), and −71.6 (uracil) kcal/mol. Our theoretical values for the DNA/RNA bases largely confirm recent predictions based on much lower-level calculations. The W1-F12 theoretical values for benzene, naphthalene, and anthracene are in very good to reasonable agreement with experiment. However, both W1-F12 and other computational estimates show that the accepted experimental value for naphthacene cannot be reconciled with those for the lower acenes: we suggest that \documentclass[12pt]{minimal}\begin{document}$\Delta _f H^\circ _{298}$\end{document}ΔfH298∘[naphthacene(g)] = 74.25 ± 1 kcal/mol is a more realistic estimate.