Benchmark theoretical study on the dissociation energy of chlorine

The currently accepted D(0)((35)Cl(2)) is 239.221 ± 0.001 kJ/mol, whereas popular theoretical model chemistries provide values in the range of 233-247 kJ/mol, and even the so-called high-accuracy protocols can yield values as low as 237.9 kJ/mol and as high as 240.1 kJ/mol for D(0)((35)Cl(2)). The aim of this study was to uncover the sources of error inherent in the theoretical approaches. Therefore, a coupled-cluster-based composite model chemistry was utilized that included contributions of up to pentuple excitations, as well as corrections beyond the nonrelativistic and Born-Oppenheimer approximations. In our calculations, correlation consistent basis set families were used up to octuple-ζ basis sets. It was found that the following factors, in order of significance, can be identified as the most important error sources: (i) the considerably large relativistic contributions carrying large uncertainties, (ii) the very slow convergence of the M?ller-Plesset (MP2) correlation energy (with the octuple-ζ basis set, it still contains an error of a few tenth of a kJ/mol), (iii) the slow convergence of the coupled-cluster singles and doubles (CCSD) contribution (it needs a octuple-ζ basis set to converge within 0.1 kJ/mol), and (iv) the relatively large basis set (quadruple-ζ) needed in the calculation of an accurate perturbative quadruples contribution. It is also notable that, for chlorine, the use of a quintuple-ζ basis set for the Hartree-Fock energy, the MP2 correlation energy, and for the CCSD and perturbative triples contributions, which is the usual treatment in almost every high-accuracy model chemistry, resulted in the overestimation of all of these contributions (altogether about by 1.8 kJ/mol). However, this overestimation is accidentally compensated by (i) using an inappropriate, small basis set for the valence electron contribution due to quadruple excitations (～1.2 kJ/mol), (ii) neglecting the effects of core electron contributions due to quadruple excitations (～0.2 kJ/mol), and (iii) neglecting relativistic effects beyond the scalar relativistic treatment (～0.3 kJ/mol). The most reliable theoretical estimate for D(0)((35)Cl(2)) obtained in this study, 239.27 ± 1.30 kJ/mol, differs by only 0.05 kJ/mol from the most accurate experimental result. This study also underpins the effect of relativistic contributions, which precludes current model chemistries to enter the range of sub-kJ/mol accuracy for second-row systems.