  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, from which 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), which is the second largest electron
correlation contribution after CCSD. 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: apparently, replacing nZaPa basis
sets with truncations of 7ZaPa at 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.
