W4 theory for computational thermochemistry: in pursuit of confident sub-kJ/mol predictions

In an attempt to improve on our earlier W3 theory [J. Chem. Phys. {\bf 120}, 4129 (2004)] we consider such refinements as more accurate estimates for the contribution of connected quadruple excitations ($\hat{T}_4$), inclusion of connected quintuple excitations ($\hat{T}_5$), 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 ATcT (Active Thermochemical Tables) Thermochemical Network. 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 $\hat{T}_4$ contribution. The largest $\hat{T}_5$ contribution found in the present work is on the order of 0.5 kcal/mol (for ozone). DBOC corrections are significant at the 0.1 kcal/mol level in hydride systems. . 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. Our W4 atomization energies for a number of key species are in excellent agreement (better than 0.1 kcal/mol on average, 95% confidence intervals narrower than 1 kJ/mol) with the latest experimental data obtained from Active Thermochemical Tables. A simple {\em 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.