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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
  • 105 Downloads

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 (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.

Keywords

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

Notes

Acknowledgments

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)

References

  1. 1.
    Marggraf AS, Miscell Berolin 1740, 6.Google Scholar
  2. 2.
    Stock A (1909). Ber Dtsch Chem Ges 42:2062CrossRefGoogle Scholar
  3. 3.
    Cowley AH (1964). J Chem Educ 41:530CrossRefGoogle Scholar
  4. 4.
    Stock A (1908). Ber Dtsch Chem Ges 41:558CrossRefGoogle Scholar
  5. 5.
    Stock A (1910). Ber Dtsch Chem Ges 43:414CrossRefGoogle Scholar
  6. 6.
    Stock A (1910). Ber Dtsch Chem Ges 43:1223CrossRefGoogle Scholar
  7. 7.
    Stock A (1910). Ber Dtsch Chem Ges 43:150CrossRefGoogle Scholar
  8. 8.
    Meisel M, Grunze H (1969). Z Anorg Allg Chem 366:152CrossRefGoogle Scholar
  9. 9.
    Bjorholm T, Jakobsen HJ (1991). J Am Chem Soc 113:27CrossRefGoogle Scholar
  10. 10.
    Nowottnick H, Blachnik R (1999). Z Anorg Allg Chem 625:1966CrossRefGoogle Scholar
  11. 11.
    Blachnik R, Peukert U, Czediwoda A, Engelen B, Boldt K (1995). Z Anorg Allg Chem 621:1637CrossRefGoogle Scholar
  12. 12.
    Rödl T, Pfitzner A (2011). Z Anorg Allg Chem 637:1507CrossRefGoogle Scholar
  13. 13.
    Brevard C, Demarcq M (1981). Chem Phys Lett 82:167CrossRefGoogle Scholar
  14. 14.
    Andrew ER, Vennart W, Bonnard G, Croiset RM, Demarcq M, Mathieu E (1976). Chem Phys Lett 43:317CrossRefGoogle Scholar
  15. 15.
    Griffin AM, Minshall PC, Sheldrick GM (1976). J Chem Soc Chem Commun:809Google Scholar
  16. 16.
    Jason ME, Ngo T, Rahman S (1997). Inorg Chem 36:2633CrossRefGoogle Scholar
  17. 17.
    Jason ME, Ngo T, Rahman S (1996). Phosphorus Research Bulletin 6:127CrossRefGoogle Scholar
  18. 18.
    Blachnik R, Hoppe A (1979). Z Anorg Allg Chem 457:91CrossRefGoogle Scholar
  19. 19.
    Ozturk T, Ertas E, Mert O (2010). Chem Rev 110:3419CrossRefGoogle Scholar
  20. 20.
    Berzelius J (1843). Liebigs Ann 46:129CrossRefGoogle Scholar
  21. 21.
    Schlesinger ME (2002). Chem Rev 102:4267CrossRefGoogle Scholar
  22. 22.
    Cueilleron J, Vincent H (1970). Bull Soc Chim Fr 6:2118Google Scholar
  23. 23.
    Cueilleron J, Vincent H (1970). Bull Soc Chim Fr 4:1296Google Scholar
  24. 24.
    Treadwell WD, Beeli C (1935). Helv Chim Acta 18:1161CrossRefGoogle Scholar
  25. 25.
    Hartley SB, Holmes WS, Jacques JK, Mole MF, McCoubrey JC (1963). Q Rev Chem Soc 17:204CrossRefGoogle Scholar
  26. 26.
    Ystenes M, Brockner W, Menzel F (1993). Vib Spectrosc 5:195CrossRefGoogle Scholar
  27. 27.
    Ystenes M, Menzel F, Brockner W (1994). Spectrochim Acta A: Molecular Spectroscopy 50:225CrossRefGoogle Scholar
  28. 28.
    Jones RO, Seifert G (1992). J Chem Phys 96:2942CrossRefGoogle Scholar
  29. 29.
    Seifert G, Jones RO (1992). J Chem Phys 96:2951CrossRefGoogle Scholar
  30. 30.
    Császár AG (1997). J Phys Chem A 101(2):201CrossRefGoogle Scholar
  31. 31.
    Karton A, Martin JML (2012). J Chem Phys 136:124114CrossRefGoogle Scholar
  32. 32.
    Karton A, Kaminker I, Martin JML (2009). J Phys Chem A 113:7610CrossRefGoogle Scholar
  33. 33.
    Karton A (2016). Wiley Interdiscip Rev Comput Mol Sci 6:292CrossRefGoogle Scholar
  34. 34.
    Karton A, Daon S, Martin JML (2011). Chem Phys Lett 510:165CrossRefGoogle Scholar
  35. 35.
    Karton A, Sylvetsky N, Martin JML (2017). J Comput Chem 38:2063CrossRefGoogle Scholar
  36. 36.
    Hättig C, Klopper W, Köhn A, Tew DP (2012). Chem Rev 112:4CrossRefGoogle Scholar
  37. 37.
    Sylvetsky N, Peterson KA, Karton A, Martin JML (2016). J Chem Phys 144:214101CrossRefGoogle Scholar
  38. 38.
    Peterson KA, Adler TB, Werner H-J (2008). J Chem Phys 128:084102CrossRefGoogle Scholar
  39. 39.
    Noga J, Kedžuch S, Šimunek J (2007). J Chem Phys 127:034106CrossRefGoogle Scholar
  40. 40.
    Knizia G, Werner H-J (2008). J Chem Phys 128:154103CrossRefGoogle Scholar
  41. 41.
    Adler TB, Knizia G, Werner H-J (2007). J Chem Phys 127:221106CrossRefGoogle Scholar
  42. 42.
    Martin JML, Oliveira G (1999). J Chem Phys 111:1843CrossRefGoogle Scholar
  43. 43.
    Dunning TH (1989). J Chem Phys 90:1007CrossRefGoogle Scholar
  44. 44.
    Kendall RA, Dunning TH, Harrison RJ (1992). J Chem Phys 96:6796CrossRefGoogle Scholar
  45. 45.
    Ten-no S, Noga J (2012). WIREs Comput Mol Sci 2:114CrossRefGoogle Scholar
  46. 46.
    Ten-no S (2004). Chem Phys Lett 398:56CrossRefGoogle Scholar
  47. 47.
    Werner H-J, Adler TB, Manby FR (2007). J Chem Phys 126:164102CrossRefGoogle Scholar
  48. 48.
    Knizia G, Adler TB, Werner H-J (2009). J Chem Phys 130:054104CrossRefGoogle Scholar
  49. 49.
    Peterson KA, Dunning TH (2002). J Chem Phys 117:10548CrossRefGoogle Scholar
  50. 50.
    Douglas M, Kroll NM (1974). Ann Phys 82:89CrossRefGoogle Scholar
  51. 51.
    Hess BA (1986). Phys Rev A 33:3742CrossRefGoogle Scholar
  52. 52.
    de Jong WA, Harrison RJ, Dixon DA (2001). J Chem Phys 114:48CrossRefGoogle Scholar
  53. 53.
    CFOUR (2015). a quantum chemical program package written by J. F. Stanton, J. Gauss, M. E. Harding, P. G. Szalay, with contributions from A. A. Auer, R. J. Bartlett, U. Benedikt, C. Berger, D. E. Bernholdt, Y. J. Bomble, O. Christiansen, et al. See: http://www.cfour.de.
  54. 54.
    MOLPRO (2012). is a package of ab initio programs written by H.-J. Werner, P. J. Knowles, G. Knizia, F. R. Manby, M. Schütz, P. Celani, T. Korona, R. Lindh, A. Mitrushenkov, G. Rauhut, et al. See: http://www.molpro.net.
  55. 55.
    Rolik Z, Szegedy L, Ladjanszki I, Ladoczki B, Kallay M (2013). J Chem Phys 139:094105CrossRefGoogle Scholar
  56. 56.
    Lee C, Yang W, Parr RG (1988). Phys Rev B 37:785CrossRefGoogle Scholar
  57. 57.
    Becke AD (1993). J Chem Phys 98:5648CrossRefGoogle Scholar
  58. 58.
    Stephens PJ, Devlin FJ, Chabalowski CF, Frisch MJ (1994). J Phys Chem 98:11623CrossRefGoogle Scholar
  59. 59.
    Grimme S, Ehrlich S, Goerigk L (2011). J Comput Chem 32:1456CrossRefGoogle Scholar
  60. 60.
    Weigend F, Ahlrichs R (2005). Phys Chem Chem Phys 7:3297CrossRefGoogle Scholar
  61. 61.
    Grimme S, Antony J, Ehrlich S, Krieg H (2010). J Chem Phys 132:154104CrossRefGoogle Scholar
  62. 62.
    Grimme S (2011). WIREs Comput Mol Sci 1:211CrossRefGoogle Scholar
  63. 63.
    Johnson ER, Becke AD (2006). J Chem Phys 124:174104CrossRefGoogle Scholar
  64. 64.
    Karton A, Yu L-J, Kesharwani MK, Martin JML (2014). Theor Chem Accounts 133:1483CrossRefGoogle Scholar
  65. 65.
    Kesharwani MK, Brauer B, Martin JML (2015). J Phys Chem A 119:1701CrossRefGoogle Scholar
  66. 66.
    Frisch MJ, Trucks GW, Schlegel HB, Scuseria GE, Robb MA, Cheeseman JR, Scalmani G, Barone V, Mennucci B, Petersson GA, et al. Gaussian 09, Revision D.01; Gaussian, Inc.: Wallingford CT, 2009.Google Scholar
  67. 67.
    Curtiss LA, Redfern PC, Raghavachari K (2011). WIREs Comput Mol Sci 1:810CrossRefGoogle Scholar
  68. 68.
    Montgomery JA, Frisch MJ, Ochterski JW, Petersson GA (2000). J Chem Phys 112:6532CrossRefGoogle Scholar
  69. 69.
    Peterson KA, Feller D, Dixon DA (2012). Theor Chem Accounts 131:1079CrossRefGoogle Scholar
  70. 70.
    Helgaker T, Klopper W, Tew DP (2008). Mol Phys 106:2107CrossRefGoogle Scholar
  71. 71.
    Curtiss LA, Redfern PC, Raghavachari K (2007). J Chem Phys 126:084108CrossRefGoogle Scholar
  72. 72.
    Curtiss LA, Redfern PC, Raghavachari K (2007). J Chem Phys 127:124105CrossRefGoogle Scholar
  73. 73.
    Chan B, Deng J, Radom L (2011). J Chem Theory Comput 7:112CrossRefGoogle Scholar
  74. 74.
    Curtiss LA, Raghavachari K, Redfern PC, Rassolov V, Pople JA (1998). J Chem Phys 109:7764CrossRefGoogle Scholar
  75. 75.
    Curtiss LA, Redfern PC, Raghavachari K, Rassolov V, Pople JA (1999). J Chem Phys 110:4703CrossRefGoogle Scholar
  76. 76.
    Baboul AG, Curtiss LA, Redfern PC, Raghavachari K (1999). J Chem Phys 110:7650CrossRefGoogle Scholar
  77. 77.
    Montgomery Jr JA, Frisch MJ, Ochterski JW, Petersson GA (1999). J Chem Phys 110:2822CrossRefGoogle Scholar
  78. 78.
    Ochterski JW, Petersson GA, Montgomery Jr JA (1996). J Chem Phys 104:2598CrossRefGoogle Scholar
  79. 79.
    Karton A, Rabinovich E, Martin JML, Ruscic B (2006). J Chem Phys 125:144108CrossRefGoogle Scholar
  80. 80.
    Karton A, Martin JML (2010). J Chem Phys 133:144102CrossRefGoogle Scholar
  81. 81.
    Fogueri UR, Kozuch S, Karton A, Martin JML (2013). Theor Chem Accounts 132:1291CrossRefGoogle Scholar
  82. 82.
    Karton A (2018). J Chem Phys 149:034102CrossRefGoogle Scholar
  83. 83.
    Ruscic B (2014). Int J Quantum Chem 114:1097CrossRefGoogle Scholar
  84. 84.
    Karton A, Martin JML (2007). Mol Phys 105:2499CrossRefGoogle Scholar
  85. 85.
    Cox JD, Wagman DD, Medvedev VA, CODATA key values for thermodynamics; Hemisphere Publishing Corp.: New York, 1989.Google Scholar
  86. 86.
    Izgorodina EI, Coote ML, Radom L (2005). J Phys Chem A 109:7558CrossRefGoogle Scholar
  87. 87.
    Grimme S (2006). Angew Chem Int Ed 45:4460CrossRefGoogle Scholar
  88. 88.
    Wodrich MD, Corminboeuf C, Schleyer P v R (2006). Org Lett 8:3631CrossRefGoogle Scholar
  89. 89.
    Wodrich MD, Corminboeuf C, Schreiner PR, Fokin AA, Schleyer PVR (2006). Org Lett 9:1851CrossRefGoogle Scholar
  90. 90.
    Schreiner PR (2007). Angew Chem Int Ed 46:4217CrossRefGoogle Scholar
  91. 91.
    Grimme S, Steinmetz M, Korth M (2007). J Organomet Chem 72:2118CrossRefGoogle Scholar
  92. 92.
    Wheeler SE, Houk KN, Schleyer PVR, Allen WD (2009). J Am Chem Soc 131:2547CrossRefGoogle Scholar
  93. 93.
    Karton A, Gruzman D, Martin JML (2009). J Phys Chem A 113:8434CrossRefGoogle Scholar
  94. 94.
    Grimme S (2010). Org Lett 12:4670CrossRefGoogle Scholar
  95. 95.
    Ramabhadran RO, Raghavachari K (2011). J Chem Theory Comput 7:2094CrossRefGoogle Scholar
  96. 96.
    Ramabhadran RO, Raghavachari K (2012). J Phys Chem A 116:7531CrossRefGoogle Scholar
  97. 97.
    O’Reilly RJ, Karton A, Radom L (2012). Int J Quantum Chem 112:1862CrossRefGoogle Scholar
  98. 98.
    Karton A, Martin JML (2012). Mol Phys 110:2477CrossRefGoogle Scholar
  99. 99.
    Wodrich MD, Corminboeuf C, Wheeler SE (2012). J Phys Chem A 116:3436CrossRefGoogle Scholar
  100. 100.
    Wheeler SE (2012). WIREs Comput Mol Sci 2:204CrossRefGoogle Scholar
  101. 101.
    Yu LJ, Karton A (2014). Chem Phys 441:166CrossRefGoogle Scholar
  102. 102.
    Karton A, Chan B, Raghavachari K, Radom L (2013). J Phys Chem A 117:1834CrossRefGoogle Scholar
  103. 103.
    Karton A (2017). J Comput Chem 38:370CrossRefGoogle Scholar
  104. 104.
    Karton A, Schreiner PR, Martin JML (2016). J Comput Chem 37:49CrossRefGoogle Scholar
  105. 105.
    Ruscic B, Pinzon RE, Morton ML, von Laszewski G, Bittner SJ, Nijsure SG, Amin KA, Minkoff M, Wagner AF (2004). J Phys Chem A 108:9979CrossRefGoogle Scholar

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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

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

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