Benchmark atomization energy of ethane: Importance of accurate zero-point vibrational energies and diagonal Born-Oppenheimer corrections for a 'simple' organic molecule

A benchmark calculation of the atomization energy of the 'simple' organic molecule C2H6 (ethane) has been carried out by means of W4 theory. While the molecule is straightforward in terms of one-particle and n-particle basis set convergence, its large zero-point vibrational energy (and anharmonic correction thereto) and nontrivial diagonal Born-Oppenheimer correction (DBOC) represent interesting challenges. For the W4 set of molecules and C2H6, we show that DBOCs to the total atomization energy are systematically overestimated at the SCF level, and that the correlation correction converges very rapidly with the basis set. Thus, even at the CISD/cc-pVDZ level, useful correlation corrections to the DBOC are obtained. When applying such a correction, overall agreement with experiment was only marginally improved, but a more significant improvement is seen when hydrogen-containing systems are considered in isolation. We conclude that for closed-shell organic molecules, the greatest obstacles to highly accurate computational thermochemistry may not lie in the solution of the clamped-nuclei Schrödinger equation, but rather in the zero-point vibrational energy and the diagonal Born-Oppenheimer correction.