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 (T ˆ 4 ) (T̂4) , inclusion of connected quintuple excitations (T ˆ 5 ) (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 thermochemicalnetwork. The recent CCSDT(Q) method offers a cost-effective way of estimating T ˆ 4 T̂4 , but is insufficient by itself if the molecule exhibits some nondynamical correlation. The latter considerably slows down basis set convergence for T ˆ 4 T̂4 , and anomalous basis set convergence in highly polar systems makes two-point extrapolation procedures unusable. However, we found that the CCSDTQ−CCSDT(Q) 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] 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 T ˆ 4 T̂4 contribution. The T ˆ 5 T̂5 contribution converges very rapidly with the basis set, and even a simple double-zeta basis set appears to be adequate. The largest T ˆ 5 T̂5 contribution found in the present work is on the order of 0.5kcal∕mol 0.5kcal∕mol (for ozone). DBOCs are significant at the 0.1kcal∕mol 0.1kcal∕mol level in hydride systems. Post-CCSD(T) contributions to the core-valence correlationenergy 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 0.1kcal∕mol on average, 95% confidence intervals narrower than 1kJ∕mol 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 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.