Accuracy of basis-set extrapolation schemes for DFT-RPA correlation energies in molecular calculations

Abstract

We construct a reference benchmark set for atomic and molecular random phase approximation (RPA) correlation energies in a density functional theory framework at the complete basis-set limit. This set is used to evaluate the accuracy of some popular extrapolation schemes for RPA all-electron molecular calculations. The results indicate that for absolute energies, accurate results, clearly outperforming raw data, are achievable with two-point extrapolation schemes based on quintuple- and sextuple-zeta basis sets. Moreover, we show that results in good agreement with the benchmark can also be obtained by using a semiempirical extrapolation procedure based on quadruple- and quintuple-zeta basis sets. Finally, we analyze the performance of different extrapolation schemes for atomization energies.

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References

  1. 1.

    Bohm D, Pines D (1953) Phys Rev 92:609

    Article  CAS  Google Scholar 

  2. 2.

    Gell-Mann M, Brueckner KA (1957) Phys Rev 106:364

    Article  CAS  Google Scholar 

  3. 3.

    Langreth DC, Perdew JP (1977) Phys Rev B 15:2884

    Article  Google Scholar 

  4. 4.

    Furche F (2001) Phys Rev B 64:195120

    Article  Google Scholar 

  5. 5.

    Fuchs M, Gonze X (2002) Phys Rev B 65:235109

    Article  Google Scholar 

  6. 6.

    Furche F, Van Voorhis T (2005) J Chem Phys 122:164106

    Article  Google Scholar 

  7. 7.

    Dobson JF, Wang J, Dinte BP, McLennan K, Le HM (2005) Int J Quantum Chem 101:579

    Article  CAS  Google Scholar 

  8. 8.

    Scuseria GE, Henderson TM, Sorensen DC (2008) J Chem Phys 129:231101

    Article  Google Scholar 

  9. 9.

    Grüneis A, Marsman M, Harl J, Schimka L, Kresse G (2009) J Chem Phys 131:154115

    Article  Google Scholar 

  10. 10.

    Janesko BG, Scuseria GE (2009) J Chem Phys 131:154106

    Article  Google Scholar 

  11. 11.

    Janesko BG, Henderson TM, Scuseria GE (2009) J Chem Phys 130:081105

    Article  Google Scholar 

  12. 12.

    Toulouse J, Gerber IC, Jansen G, Savin A, Ángyán JG (2009) Phys Rev Lett 102:096404

    Article  Google Scholar 

  13. 13.

    Toulouse J, Zhu W, Ángyán JG, Savin A (2010) Phys Rev A 82:032502

    Article  Google Scholar 

  14. 14.

    Ruzsinszky A, Perdew JP, Csonka GI (2010) J Chem Theor Comput 6:127

    Article  CAS  Google Scholar 

  15. 15.

    Nguyen HV, Galli G (2010) J Chem Phys 132:044109

    Article  Google Scholar 

  16. 16.

    Paier J, Janesko BG, Henderson TM, Scuseria GE, Grüneis A, Kresse G (2010) J Chem Phys 132:094103

    Article  Google Scholar 

  17. 17.

    Eshuis H, Yarkony J, Furche F (2010) J Chem Phys 132:234114

    Article  Google Scholar 

  18. 18.

    Jansen G, Liu RF, Ángyán JG (2010) J Chem Phys 133:154106

    Article  Google Scholar 

  19. 19.

    Ren X, Tkatchenko A, Rinke P, Scheffler M (2011) Phys Rev Lett 106:153003

    Article  Google Scholar 

  20. 20.

    Eshuis H, Furche F (2011) J Phys Chem Lett 2:983

    Article  CAS  Google Scholar 

  21. 21.

    Ruzsinszky A, Perdew JP, Csonka GI (2011) J Chem Phys 134:114110

    Article  Google Scholar 

  22. 22.

    Ángyán JG, Liu RF, Toulouse J, Jansen G (2011) J Chem Theory Comput 7:3116

    Article  Google Scholar 

  23. 23.

    Heßelmann A (2011) J Chem Phys 134:204107

    Article  Google Scholar 

  24. 24.

    Eshuis H, Bates JE, Furche F (2012) Theor Chem Acc 131:1084

    Article  Google Scholar 

  25. 25.

    Paier J, Ren X, Rinke P, Scuseria GE, Grüneis A, Kresse G, Scheffler M (2012) New J Phys 14:043002

    Article  Google Scholar 

  26. 26.

    Ren X, Rinke P, Blum V, Wieferink J, Tkatchenko A, Sanfilippo A, Reuter K, Scheffler M (2012) New J Phys 14:053020

    Article  Google Scholar 

  27. 27.

    Ren X, Rinke P, Joas C, Scheffler M (2012) . J Mater Sci. doi:10.1007/s10853-012-6570-4

  28. 28.

    Heßelmann A, Görling A (2010) Mol Phys 108:359

    Article  Google Scholar 

  29. 29.

    Heßelmann A, Görling A (2011) Phys Rev Lett 106:093001

    Article  Google Scholar 

  30. 30.

    Heßelmann A, Görling A (2011) Mol Phys 109:2473

    Article  Google Scholar 

  31. 31.

    Godby RW, Schlüter M, Sham LJ (1986) Phys Rev Lett 56:2415

    Article  CAS  Google Scholar 

  32. 32.

    Kotani T (1998) J Phys Cond Matt 10:9241

    Article  CAS  Google Scholar 

  33. 33.

    Niquet YN, Fuchs M, Gonze X (2003) Phys Rev A 68:032507

    Article  Google Scholar 

  34. 34.

    Grüning M, Marini A, Rubio A (2006) J Chem Phys 124:154108

    Article  Google Scholar 

  35. 35.

    Hellgren M, von Barth U (2007) Phys Rev B 76:075107

    Article  Google Scholar 

  36. 36.

    Hellgren M, von Barth U (2010) J Chem Phys 132:044101

    Article  Google Scholar 

  37. 37.

    Hellgren M, Rohr DR, Gross EKU (2012) J Chem Phys 136:034106

    Article  Google Scholar 

  38. 38.

    Verma P, Bartlett RJ (2012) J Chem Phys 136:044105

    Article  Google Scholar 

  39. 39.

    Harl J, Kresse G (2008) Phys Rev B 77:045136

    Article  Google Scholar 

  40. 40.

    Eshuis H, Furche F (2012) J Chem Phys 136:084105

    Article  Google Scholar 

  41. 41.

    Janesko BG, Henderson TM, Scuseria GE (2009) J Chem Phys 131:034110

    Article  Google Scholar 

  42. 42.

    Zhu W, Toulouse J, Savin A, Ángyán JG (2010) J Chem Phys 132:244108

    Article  Google Scholar 

  43. 43.

    Schwartz C (1962) Phys Rev 126:1015

    Article  CAS  Google Scholar 

  44. 44.

    Schwartz C (1963) Methods Comput Phys 2:241

    Google Scholar 

  45. 45.

    Carroll DP, Silverstone HJ, Metzger RM (1979) J Chem Phys 71:4142

    Article  CAS  Google Scholar 

  46. 46.

    Schmidt HM, von Hirschhausen H (1983) Phys Rev A 28:3179

    Article  CAS  Google Scholar 

  47. 47.

    Hill RN (1985) J Chem Phys 83:1173

    Article  CAS  Google Scholar 

  48. 48.

    Kutzelnigg W, Morgan JD III (1992) J Chem Phys 96:4484

    Article  CAS  Google Scholar 

  49. 49.

    Schmidt HM, Linderberg J (1994) Phys Rev A 49:4404

    Article  CAS  Google Scholar 

  50. 50.

    Müller T (2006) Basis set accuracy and calibration in quantum chemistry. In: Grotendorst J, Blugel S, Marx D (eds) Computational nanoscience: do it yourself! John von Neumann Institute for Computing, Julich, NIC Series, vol 31, ISBN 3-00-017350-1, pp 19-43

  51. 51.

    Feller D, Peterson KA, Grant Hill J (2011) J Chem Phys 135:044102

    Article  Google Scholar 

  52. 52.

    Barkowies D (2007) J Chem Phys 127:084105

    Article  Google Scholar 

  53. 53.

    Barkowies D (2007) J Chem Phys 127:164109

    Article  Google Scholar 

  54. 54.

    Varandas AJC (2007) J Chem Phys 126:244105

    Article  CAS  Google Scholar 

  55. 55.

    Perdew JP, Burke K, Ernzerhof M (1996) Phys Rev Lett 77:3865

    Article  CAS  Google Scholar 

  56. 56.

    Dunning TH Jr (1989) J Chem Phys 90:1007

    Article  CAS  Google Scholar 

  57. 57.

    Woon DE, Dunning TH Jr (1994) J Chem Phys 100:2975

    Article  CAS  Google Scholar 

  58. 58.

    Feller D, Peterson KA (1999) J Chem Phys 110:8384

    Article  CAS  Google Scholar 

  59. 59.

    Feller D, Sordo JA (2000) J Chem Phys 113:485

    Article  CAS  Google Scholar 

  60. 60.

    Woon DE, Dunning TH Jr. (1995) J Chem Phys 103:4572

    Article  CAS  Google Scholar 

  61. 61.

    Peterson KA, Dunning TH Jr (2002) J Chem Phys 117:10548

    Article  CAS  Google Scholar 

  62. 62.

    Grant Hill J, Mazumder S, Peterson KA (2010) J Chem Phys 132:054108

    Article  Google Scholar 

  63. 63.

    Boyd DRJ (1955) J Chem Phys 23:922

    Article  CAS  Google Scholar 

  64. 64.

    Venkateswarlu P, Gordy W (1955) J Chem Phys 23:1200

    Article  CAS  Google Scholar 

  65. 65.

    Redington RL, Olson WB, Cross PC (1962) J Chem Phys 36:1311

    Article  CAS  Google Scholar 

  66. 66.

    Herzberg G (1966) Electronic spectra and electronic structure of polyatomic molecules. Van Nostrand, New York

    Google Scholar 

  67. 67.

    Sverdlov LM, Kovner MA, Krainov EP (1974) Vibrational spectra of polyatomic molecules. Wiley, New York

    Google Scholar 

  68. 68.

    Tsuboi M, Overend J (1975) J Mol Spec 52:256

    Article  Google Scholar 

  69. 69.

    Hirota E (1979) J Mol Spect 77:213

    Article  CAS  Google Scholar 

  70. 70.

    Hoy AR, Bunker PR (1979) J Mol Spect 74:1

    Article  CAS  Google Scholar 

  71. 71.

    Huber KP, Herzberg G (1979) Molecular spectra and molecular structure. IV. Constants of diatomic molecules. Van Nostrand Reinhold Co, New York

    Google Scholar 

  72. 72.

    Herbst E, Messer JK, DeLucia FC (1984) J Mol Spect 108:42

    Article  CAS  Google Scholar 

  73. 73.

    Junttila ML, Lafferty WJ, Burkholder JB (1994) J Mol Spect 164:583

    Google Scholar 

  74. 74.

    Gurvich LV, Veyts IV, Alcock CB (1989) Thermodynamic properties of individual substances, 4th edn. Hemisphere Pub Co, New York

    Google Scholar 

  75. 75.

    Kuchitsu, K (eds) (1998) Structure of free polyatomic molecules—basic data. Springer, Berlin

    Google Scholar 

  76. 76.

    NIST Diatomic Spectral Database. http://www.physics.nist.gov/PhysRefData/MolSpec/Diatomic/index.html

  77. 77.

    TURBOMOLE V6.2 2010, a development of University of Karlsruhe and Forschungszentrum Karlsruhe GmbH, 1989–2007, TURBOMOLE GmbH, since 2007; available from http://www.turbomole.com

  78. 78.

    Kutzelnigg W (1985) Theor Chem Acta 68:445

    Article  CAS  Google Scholar 

  79. 79.

    Helgaker T, Klopper W, Koch H, Noga J (1997) J Chem Phys 106:9639

    Article  CAS  Google Scholar 

  80. 80.

    Halkier A, Helgaker T, Jørgensen P, Klopper W, Koch H, Olsen J, Wilson AK (1998) Chem Phys Lett 286:243

    Article  CAS  Google Scholar 

  81. 81.

    Martin JML (1996) Chem Phys Lett 259:669

    Article  CAS  Google Scholar 

  82. 82.

    Truhlar DG (1998) Chem Phys Lett 294:45

    Article  CAS  Google Scholar 

  83. 83.

    Fast PL, Sanchez ML, Truhlar DG (1999) J Chem Phys 111:2921

    Article  CAS  Google Scholar 

  84. 84.

    Pitoňák M, Riley KE, Neogrády P, Hobza P (2008) Chem Phys Chem 9:1636

    Article  Google Scholar 

Download references

Acknowledgments

We thank TURBOMOLE GmbH for providing us with the TURBOMOLE program package, and M. Margarito for technical support. This work was funded by the ERC Starting Grant FP7 Project DEDOM, Grant Agreement No. 207441.

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Correspondence to E. Fabiano.

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Fabiano, E., Della Sala, F. Accuracy of basis-set extrapolation schemes for DFT-RPA correlation energies in molecular calculations. Theor Chem Acc 131, 1278 (2012). https://doi.org/10.1007/s00214-012-1278-8

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Keywords

  • RPA correlation
  • Basis-set extrapolation
  • Complete basis-set limit