  The total atomization energy of a molecule is the thermochemical cognate of
the heat of formation in the gas phase, its most fundamental thermochemical
property. We decompose it into different components and provide a survey of
them. It emerges that the connected triple excitations contribution is the
third most important one, about an order of magnitude less important than the
"big two" contributions (mean-field Hartree-Fock and valence CCSD correlation),
but 1-2 orders of magnitude more important than the remainder. For the 200
total atomization energies of small molecules in the W4-17 benchmark, we have
investigated the basis set convergence of the connected triple excitations
contribution (T). Achieving basis set convergence for the valence triple
excitations energy is much easier than for the valence singles and doubles
correlation energy. Using reference data obtained from spdfghi and spdfghik
basis sets, we show that extrapolation from quintuple-zeta and sextuple-zeta
yields values within about 0.004 kcal/mol RMS. Convergence to within about 0.01
kcal/mol is achievable with quadruple- and quintuple-zeta basis sets, and to
within about 0.05 kcal/mol with triple- and quadruple-zeta basis sets. It
appears that radial flexibility in the basis set is more important here than
adding angular momenta L: apparently, replacing nZaPa basis sets with
truncations of 7ZaPa at L=n gains about one angular momentum for small values
of n. We end the article with a brief outlook for the future of accurate
electronic structure calculations.
