Benchmark Theoretical Study on the Dissociation Energy of Chlorine

The currently accepted D0(35Cl2) 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 D0(35Cl2). 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 Møller–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 D0(35Cl2) 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.