Ab initio thermochemistry using optimal-balance models with isodesmic corrections: The ATOMIC protocol

Abstract

A theoretical composite approach, termed ATOMIC for Ab initio Thermochemistry using Optimal-balance Models with Isodesmic Corrections, is introduced for the calculation of molecular atomization energies and enthalpies of formation. Care is taken to achieve optimal balance in accuracy and cost between the various components contributing to high-level estimates of the fully correlated energy at the infinite-basis-set limit. To this end, the energy at the coupled-cluster level of theory including single, double, and quasiperturbational triple excitations is decomposed into Hartree-Fock, low-order correlation (MP2, CCSD), and connected-triples contributions and into valence-shell and core contributions. Statistical analyses for 73 representative neutral closed-shell molecules containing hydrogen and at least three first-row atoms (CNOF) are used to devise basis-set and extrapolation requirements for each of the eight components to maintain a given level of accuracy. Pople's concept of bond-separation reactions is implemented in an ab initio framework, providing for a complete set of high-level precomputed isodesmic corrections which can be used for any molecule for which a valence structure can be drawn. Use of these corrections is shown to lower basis-set requirements dramatically for each of the eight components of the composite model. A hierarchy of three levels is suggested for isodesmically corrected composite models which reproduce atomization energies at the reference level of theory to within 0.1 kcal/mol (A), 0.3 kcal/mol (B), and 1 kcal/mol (C). Large-scale statistical analysis shows that corrections beyond the CCSD(T) reference level of theory, including coupled-cluster theory with fully relaxed connected triple and quadruple excitations, first-order relativistic and diagonal Born-Oppenheimer corrections can normally be dealt with using a greatly simplified model that assumes thermoneutral bond-separation reactions and that reduces the estimate of these corrections to the simple task of adding up bond increments. Preliminary validation with experimental enthalpies of formation using the subset of neutral closed-shell (HCNOF) species contained in the G3/99 test set indicates that the ATOMIC protocol performs slightly better than the popular G3 approach. The newly introduced protocol does not require empirical calibration, however, and it is still efficient enough to be applied routinely to molecules with 10 or 20 nonhydrogen atoms.

Can incremental expansions cope with high-order coupled-cluster contributions?

“…Finally, the very different T-(T) contribution for C-H and C-C reported in Ref. [13] (-0.021 kcal/mol and -0.221 kcal/mol, respectively) is in contrast to our observation that one-, two-, and three-body increments …”

“…A decomposition of higher-order coupled-cluster contributions to atomization energies into bond increments has recently been suggested by Bakowies [13]. His suggestion differs from that of the present work in that the increments are taken from larger entities, i.e., the bond increment for C-H is taken from a full calculation for CH 4 , that for C-C is calculated from full calculations for C 2 H 6 and CH 4 .…”

“…It is interesting to note that inclusion of diffuse functions (aug-cc-pVDZ basis) significantly change the coupled-cluster correlation contributions, by 5% and 13% for D and (T), respectively, and even change sign for T-(T); such augmented basis sets have not been considered in Refs. [11,12,13]. In the same vein, as before, we consider an incremental expansion starting with the sp part of the aug-cc-pVDZ basis and leading eventually to the full aug-cc-pVDZ set, cf.…”

“…The O 3 molecule is among those with the largest high-order coupled-cluster corrections of the molecules considered in Refs. [11,12,13], due to its multi-reference character. Our results to be discussed in the following refer to the experimental geometry (r O−O = 1.272Å, θ = 116.8 0 ).…”

“…[10,11,12,13]. The approach used in the present work is the incremental scheme (see, e.g., [14,15]) which consists in a many-body expansion of the correlation energy in terms of local corrections.…”