Structural Chemistry

, Volume 30, Issue 5, pp 1665–1675 | Cite as

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

  • Asja A. Kroeger
  • Amir KartonEmail author
Original Research


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 (ε-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.


Phosphorus sulfide cages Thermochemistry CCSD(T) CCSDT(Q) G4 theory 



This research was undertaken with the assistance of resources from the National Infrastructure (NCI), which is supported by the Australian Government. We also acknowledge the system administration support provided by the Faculty of Science at the University of Western Australia to the Linux cluster of the Karton group. We gratefully acknowledge the provision of a Forrest Research Foundation Scholarship and an Australian Government Research Training Program Stipend (to A.A.K.), and an Australian Research Council (ARC) Future Fellowship (to A.K.).

Funding information

This research was funded by an Australian Research Council (ARC) Future Fellowship (awarded to A.K.; Project No. FT170100373).

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

Supplementary material

11224_2019_1352_MOESM1_ESM.pdf (565 kb)
ESM 1 (PDF 565 kb)


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Authors and Affiliations

  1. 1.School of Molecular SciencesThe University of Western AustraliaPerthAustralia

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