We are proposing a new computational thermochemistry protocol denoted W3 theory, as a successor to W1 and W2 theory proposed earlier [Martin and De Oliveira, J. Chem. Phys. 111, 1843 (1999)]. The new method is both more accurate overall (error statistics for total atomization energies approximately cut in half) and more robust (particularly towards systems exhibiting significant nondynamical correlation) than W2 theory. The cardinal improvement rests in an approximate account for post-CCSD(T) correlation effects. Iterative T-3 (connected triple excitations) effects exhibit a basis set convergence behavior similar to the T-3 contribution overall. They almost universally decrease molecular binding energies. Their inclusion in isolation yields less accurate results than CCSD(T) nearly across the board: It is only when T-4 (connected quadruple excitations) effects are included that superior performance is achieved. T-4 effects systematically increase molecular binding energies. Their basis set convergence is quite rapid, and even CCSDTQ/cc-pVDZ scaled by an empirical factor of 1.2532 will yield a quite passable quadruples contribution. The effect of still higher-order excitations was gauged for a subset of molecules (notably the eight-valence electron systems): T-5 (connected quintuple excitations) contributions reach 0.3 kcal/mol for the pathologically multireference X (1)Sigma(g)(+) state of C-2 but are quite small for other systems. A variety of avenues for achieving accuracy beyond that of W3 theory were explored, to no significant avail. W3 thus appears to represent a good compromise between accuracy and computational cost for those seeking a robust method for computational thermochemistry in the kJ/mol accuracy range on small systems. (C) 2004 American Institute of Physics.