Skip to main content
Log in

Singlet–triplet energy gap for trimethylenemethane, oxyallyl diradical, and related species: single- and multireference computational results

  • Regular Article
  • Published:
Theoretical Chemistry Accounts Aims and scope Submit manuscript

Abstract

We have investigated the through-bond exchange interactions in three non-Kekulé hydrocarbon diradicals on the basis of single- and multireference coupled cluster and related broken-symmetry (BS) methods. The singlet–triplet energy gap (S-T gap) and diradical characters for these species are evaluated. It is found that the spin contamination involved in the BS solutions is non-negligible and the approximate spin-projection method greatly improves the usual BS solutions. As for Mukherjee’s state-specific multireference coupled cluster (MkMRCC) computations, the size-consistent correction with the UHF localized natural orbitals (ULO) is useful to obtain the qualitatively correct 2J values.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

References

  1. Salem L (1982) Electrons in chemical reactions: first principles. Wiley, New York

    Google Scholar 

  2. Borden WT (1982) Diradicals. Wiley, New York

    Google Scholar 

  3. Dowd P (1966) J Am Chem Soc 88:2587

    Article  CAS  Google Scholar 

  4. Chenier PJ (1978) J Chem Educ 55:286

    Article  CAS  Google Scholar 

  5. Osamura Y, Borden WT, Morokuma K (1984) J Am Chem Soc 106:5112

    Article  CAS  Google Scholar 

  6. Coolidge MB, Yamashita K, Morokuma K (1990) J Am Chem Soc 112:1751

    Article  CAS  Google Scholar 

  7. Hirano T, Kumagai T, Miyashi T (1991) J Org Chem 56:1907

    Article  CAS  Google Scholar 

  8. Wenthold PG, Hu J, Squires RR, Lineberger WC (1996) J Am Chem Soc 118:475

    Article  CAS  Google Scholar 

  9. Wenthold PG, Lineberger WC (1999) Acc Chem Res 32:597

    Article  CAS  Google Scholar 

  10. Cramer CJ, Smith BA (1996) J Phys Chem 100:9664

    Article  CAS  Google Scholar 

  11. Schalley CA, Blanksby S, Harvey JN, Schröder D, Zummack W, Bowie JH, Schwarz H (1998) Eur J Org Chem 987–1009

  12. Li J, Worthington SE, Cramer CJ (1998) J Chem Soc Perkin Trans 2:1045

    Google Scholar 

  13. Hess BA Jr, Eckart U, Fabian J (1998) J Am Chem Sco 120:12310

    Article  CAS  Google Scholar 

  14. Brown EC, Borden WT (2002) J Phys Chem A 106:2963

    Article  CAS  Google Scholar 

  15. Shipchenko LV, Krylov AI (2002) J Chem Phys 117:4694

    Article  Google Scholar 

  16. Shipchenko LV, Krylov AI (2005) J Chem Phys 123:084107

    Article  Google Scholar 

  17. Brabec J, Pittner J (2006) J Phys Chem A 110:11765

    Article  CAS  Google Scholar 

  18. Harmata M (2006) Adv Synth Catal 348:2297

    Article  CAS  Google Scholar 

  19. Demel O, Shamasundar KR, Kong L, Nooijen M (2008) J Phys Chem A 112:11895

    Article  CAS  Google Scholar 

  20. Li X, Paldus J (2008) J Chem Phys 129:174101

    Article  Google Scholar 

  21. Shen J, Fang T, Li S, Jiang Y (2008) J Phys Chem A 112:12518

    Article  CAS  Google Scholar 

  22. Ichino T, Villano SM, Gianola AJ, Goebbert DJ, Velarde L, Sanov A, Blanksby SJ, Zhou X, Hrovat DA, Borden WT, Lineberger WC (2009) Angew Chem Int Ed 48:8509

    Article  CAS  Google Scholar 

  23. Dong H, Hrovat DA, Quast H, Borden WT (2009) J Phys Chem A 113:895

    Article  CAS  Google Scholar 

  24. Bettinger HF (2010) Angew Chem Int Ed 49:670 (doi:10.1002/anie.200905482 for the English version. doi:10.1002/ange.200905482 for the German version.)

  25. Mozhayskiy V, Goebbert DJ, Velarde L, Sanov A, Krylov AI (2010) J Phys Chem A 114:6935

    Article  CAS  Google Scholar 

  26. Carsky P, Paldus J, Pittner J (2010) Recent progress in coupled cluster methods: theory and applications (challenging and advances in computational chemistry and physics). Springer, New York

    Google Scholar 

  27. Raghavachari K, Trucks GW, Pople JA, Head-Gordon M (1989) Chem Phys Lett 157:479

    Article  CAS  Google Scholar 

  28. Fukutome H (1968) Prog Theoret Phys 40:998

    Article  Google Scholar 

  29. Hirao K (1992) Chem Phys Lett 190:374

    Article  CAS  Google Scholar 

  30. Andersson K, Malmqvist P-A, Roos BO (1992) J Chem Phys 96:1218

    Article  CAS  Google Scholar 

  31. Maranzana A, Ghigo G, Tonachini G (2000) J Am Chem Soc 122:1414

    Article  CAS  Google Scholar 

  32. Park K, West A, Raheja E, Sellner B, Lischka H, Windus TL, Hase WL (2010) J Chem Phys 133:184306

    Article  Google Scholar 

  33. West AC, Kretchmer JS, Sellner B, Park K, Hase WL, Lischka H, Windus TL (2009) J Phys Chem A 113:12663

    Article  CAS  Google Scholar 

  34. Jeziorski B, Monkhorst HJ (1981) Phys Rev A 24:1668

    Article  CAS  Google Scholar 

  35. Mukherjee D, Pal S (1989) Adv Quant Chem 20:292

    Google Scholar 

  36. Balkova A, Bartlett RJ (1994) J Chem Phys 101:8972

    Article  CAS  Google Scholar 

  37. Mahapatra US, Datta B, Mukherjee D (1999) J Chem Phys 110:6171

    Article  CAS  Google Scholar 

  38. Pittner J, Nachtigall P, Cársky P, Másik J, Hubac I (1999) J Chem Phys 110:10275

    Article  CAS  Google Scholar 

  39. Evangelista FA, Allen WD, Schaefer HF III (2006) J Chem Phys 125:154113

    Article  Google Scholar 

  40. Evangelista FA, Allen WD, Schaefer HF III (2007) J Chem Phys 127:024102

    Article  Google Scholar 

  41. Bartlett RJ (1981) Ann Rev Phys 32:359

    Article  CAS  Google Scholar 

  42. Szabo A, Ostlund NS (1996) Modern quantum chemistry. Dover, New York

    Google Scholar 

  43. Yamaguchi K, Fukui H, Fueno T (1986) Chem Lett 625–628

  44. Yamaguchi K, Takahara Y, Fueno T (1986) In: Smith VH, Schaefer HF, Morokuma K (eds) Applied quantum chemistry, Boston, MA, US

  45. Yamaguchi K, Takahara Y, Fueno T, Houk KN (1988) Theor Chim Acta 73:377

    Article  Google Scholar 

  46. Purvis GD III, Bartlett RJ (1982) J Chem Phys 76:1910

    Article  CAS  Google Scholar 

  47. Handy NC, Pople JA, Head-Gordon M, Raghavachari K, Trucks GW (1989) Chem Phys Lett 164:185

    Article  CAS  Google Scholar 

  48. Nishihara S, Yamanaka S, Saito T, Kitagawa Y, Kawakami Y, Okumura M, Yamaguchi K (2010) Int J Quant Chem 110:3015

    Article  CAS  Google Scholar 

  49. Nishihara S, Saito T, Yamanaka S, Kitagawa Y, Kawakami T, Okumura M, Yamaguchi K (2010) Mol Phys 108:2559

    Article  CAS  Google Scholar 

  50. Saito T, Nishihara S, Yamanaka S, Kitagawa Y, Kawakami T, Okumura M, Yamaguchi K (2010) Mol Phys 108:2533

    Article  CAS  Google Scholar 

  51. Saito T, Nishihara S, Kitagawa Y, Kawakami T, Yamanaka S, Okumura M, Yamaguchi K (2010) Chem Phys Lett 498:253

    Article  CAS  Google Scholar 

  52. Purvis GD III, Sekino H, Bartlett RJ (1988) Collect Czech Chem Commun 53:2203

    Article  CAS  Google Scholar 

  53. Yamaguchi K (1975) Chem Phys Lett 30:330

    Article  Google Scholar 

  54. Yanai T, Tew D, Handy NC (2004) Chem Phys Lett 393:51

    Article  CAS  Google Scholar 

  55. Dinning TH Jr (1989) J Chem Phys 90:1007

    Article  Google Scholar 

  56. Becke AD (1988) Phys Rev A 38:3098

    Article  CAS  Google Scholar 

  57. Lee C, Yang W, Parr RG (1988) Phys Rev B 37:785

    Article  CAS  Google Scholar 

  58. Becke AD (1993) J Chem Phys 98:5648

    Article  CAS  Google Scholar 

  59. Iikura H, Tsuneda T, Yanai T, Hirao K (2001) J Chem Phys 115:3540

    Article  CAS  Google Scholar 

  60. Frisch MJ, Trucks GW, Schlegel HB, Scuseria GE, Robb MA, Cheeseman JR, Scalmani G, Barone V, Mennucci B, Petersson GA, Nakatsuji H, Caricato M, Li X, Hratchian HP, Izmaylov AF, Bloino J, Zheng G, Sonnenberg JL, Hada M, Ehara M, Toyota K, Fukuda R, Hasegawa J, Ishida M, Nakajima T, Honda Y, Kitao O, Nakai H, Vreven T, Montgomery JA Jr, Peralta JE, Ogliaro F, Bearpark M, Heyd JJ, Brothers E, Kudin KN, Staroverov VN, Kobayashi R, Normand J Raghavachari K, Rendell A, Burant JC, Iyengar SS, Tomasi J, Cossi M, Rega N, Millam NJ, Klene M, Knox JE, Cross JB, Bakken V, Adamo C, Jaramillo J, Gomperts R, Stratmann RE, Yazyev O, Austin AJ, Cammi R, Pomelli C, Ochterski JW, Martin RL, Morokuma K, Zakrzewski VG, Voth GA, Salvador P, Dannenberg JJ, Dapprich S, Daniels AD, Farkas Ö, Foresman JB, Ortiz JV, Cioslowski J, Fox DJ (2009) Gaussian 09, Revision A.2. Gaussian, Inc., Wallingford

  61. Schmidt MW, Baldridge KK, Boatz JA, Elbert ST, Gordon MS, Jensen JH, Koseki S, Matsunaga N, Nguyen KA, Su SJ, Windus TL, Dupuis M, Montgomery JA (1993) J Comput Chem 14:1347

    Article  CAS  Google Scholar 

  62. Crawford TD, Sherrill CD, Valeev EF, Fermann JT, King RA, Leininger ML, Brown ST, Janssen CL, Sedil ET, Kenny JP, Allen WD (2007) J Comput Chem 28:1610

    Article  CAS  Google Scholar 

  63. Li X, Paldus J (2009) J Chem Phys 131:114103

    Article  Google Scholar 

  64. Kendall RA, Dunning TH Jr, Harrison RJ (1992) J Chem Phys 96:6796

    Article  CAS  Google Scholar 

Download references

Acknowledgments

T. S. is grateful for the Research Fellowships from Japan Society for the Promotion of Science for Young Scientists (JSPS). This work has been supported by Grants-in-Aid for Scientific Research (KAKENHI) (Nos. 21550014, 19750046, 19350070) from JSPS and that on Grant-in-Aid for Scientific Research on Innovative Areas (“Coordination Programming” area 2170, No. 22108515) from the Ministry of Education, Culture, Sports, Science, and Technology (MEXT).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Toru Saito.

Additional information

Dedicated to Professor Akira Imamura on the occasion of his 77th birthday and published as part of the Imamura Festschrift Issue.

Electronic supplementary material

Below is the link to the electronic supplementary material.

Supplementary material 1 (DOC 1,763 kb)

Appendix

Appendix

Definitions of acronyms are given in Table 7.

Table 7 Acronyms used in the text

Rights and permissions

Reprints and permissions

About this article

Cite this article

Saito, T., Nishihara, S., Yamanaka, S. et al. Singlet–triplet energy gap for trimethylenemethane, oxyallyl diradical, and related species: single- and multireference computational results. Theor Chem Acc 130, 739–748 (2011). https://doi.org/10.1007/s00214-011-0914-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00214-011-0914-z

Keywords

Navigation