Thermochemistry of phosphorus sulfide cages: an extreme challenge for high-level ab initio methods

Abstract

The enthalpies of formation and isomerization energies of P4Sn molecular cages are not experimentally (or theoretically) well known. We obtain accurate enthalpies of formation and isomerization energies for P4Sn cages (n = 3, 4, 5, 6, and 10) by means of explicitly correlated high-level thermochemical procedures approximating the CCSD(T) and CCSDT(Q) energies at the complete basis set (CBS) limit. The atomization reactions have very significant contribution from post-CCSD(T) correlation effects and, due to the presence of many second-row atoms, the CCSD and (T) correlation energies converge exceedingly slowly with the size of the one-particle basis set. As a result, these cage structures are challenging targets for thermochemical procedures approximating the CCSD(T) energy (e.g., W1-F12 and G4). Our best enthalpies of formation at 298 K (∆fH°298) are obtained from thermochemical cycles in which the P4Sn cages are broken down into P2S2 and S2 fragments for which highly accurate ∆fH°298 values are available from W4 theory. For the smaller P4S3 and P4S4 cages, the reaction energies are calculated at the CCSDT(Q)/CBS level and for the larger P4S5, P4S6, and P4S10 cages, they are obtained at the CCSD(T)/CBS level. Our best ∆fH°298 values are − 94.5 (P4S3), − 108.4 (α-P4S4), − 98.7 (β-P4S4), − 126.2 (α-P4S5), − 126.1 (β-P4S5), − 112.7 (γ-P4S5), − 144.7 (α-P4S6), − 153.9 (β-P4S6), − 134.4 (γ-P4S6), − 136.3 (δ-P4S6), − 118.7 (e-P4S6), and − 215.4 (P4S10) kJ mol−1. Interestingly, we find a linear correlation (R2 = 0.992) between the enthalpies of formation of the most stable isomers of each molecular formula and the number of atoms in the P4Sn cages. We use our best ∆fH°298 values to assess the performance of a number of lower-cost composite ab initio methods. For absolute enthalpies of formation, G4(MP2) and G3(MP2)B3 result in the best overall performance with root-mean-square deviations (RMSDs) of 10.6 and 12.9 kJ mol−1, respectively, whereas G3, G3B3, and CBS-QB3 result in the worst performance with RMSDs of 27.0–38.8 kJ mol−1. In contrast to absolute enthalpies of formation, all of the considered composite procedures give a good-to-excellent performance for the isomerization energies with RMSDs below the 5 kJ mol−1 mark.