Skip to main content
Log in

Permanent electric dipole moment of diatomic molecules using relativistic extended–coupled–cluster method

  • Research
  • Published:
Theoretical Chemistry Accounts Aims and scope Submit manuscript

Abstract

We employ the four-component relativistic extended–coupled–cluster (ECC) method, a variational coupled–cluster (CC) approach, to compute the permanent electric dipole moment (PDM) of open-shell diatomic molecules (CaH, CaF, SrH and SrF) in their ground electronic state. The ECC results are compared with the PDM values estimated by the experiments as well as other single-reference CC-based approaches (the Z-vector technique, the expectation value method and the finite field approach) within the four-component relativistic framework to test the efficacy of the employed method. Our study reveals that the relativistic ECC method can yield reliable results for the PDMs of the considered molecular systems. We also observe that the computed results of the dipole moment improve upon the augmentation of diffused functions to the basis set.

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

Similar content being viewed by others

Data availability

No datasets were generated or analysed during the current study.

References

  1. Cizek J (1966) J Chem Phys 45:4256

    Article  CAS  Google Scholar 

  2. Cizek J (1969) Adv Quantum Chem 14:35

    CAS  Google Scholar 

  3. Mukherjee D, Pal S (1989) Use of cluster expansion methods in the open-shell correlation problem. In: Advances in quantum chemistry, Elsevier, vol 20, pp 291–373, Amsterdam,

  4. Löwdin P-O (1959) Adv Chem Phys 2:270

    Google Scholar 

  5. Helgaker TU, Almlöf J (1984) Int J Quantum Chem 26:275

    Article  CAS  Google Scholar 

  6. Bartlett RJ, Kucharski SA, Noga J (1989) Chem Phys Lett 155:133

    Article  CAS  Google Scholar 

  7. Pal S (1984) Theor Chim Acta 66:207

    Article  CAS  Google Scholar 

  8. Bartlett RJ, Noga J (1988) Chem Phys Lett 150:29

    Article  CAS  Google Scholar 

  9. Pal S (1984) Theor Chim Acta 66:151

    Article  CAS  Google Scholar 

  10. Arponen J (1983) Ann Phys (NY) 151:311

    Article  CAS  Google Scholar 

  11. Bishop R, Arponen J, Pajanne P (1989) Aspects of many-body effects in molecules and extended systems. Springer, Berlin

    Google Scholar 

  12. Pal S (1986) Phys Rev A 34:2682

    Article  CAS  Google Scholar 

  13. Koch H, Jensen HA, Jorgensen P, Helgaker T, Scuseria GE, Schaefer III HF (1990) J Chem Phys 92:4924

  14. Ilyabaev E, Kaldor U (1992) J Chem Phys 97:8455

    Article  CAS  Google Scholar 

  15. Visscher L, Dyall KG, Lee TJ (1995) Int J Quantum Chem Symp 29:441

    Google Scholar 

  16. Visscher L, Lee TJ, Dyall KG (1996) J Chem Phys 105:8769

    Article  CAS  Google Scholar 

  17. Visscher L, Eliav E, Kaldor U (2001) J Chem Phys 115:9720

    Article  CAS  Google Scholar 

  18. Lee HS, Han YK, Kim MC, Bae C, Lee YS (1998) Chem Phys Lett 293:97

    Article  CAS  Google Scholar 

  19. Eliav E, Kaldor U, Ishikawa Y (1994) Phys Rev A 50:1121

    Article  CAS  PubMed  Google Scholar 

  20. Eliav E, Kaldor U, Ishikawa Y, Pyykko P (1996) Phys Rev Lett 77:5350

    Article  CAS  PubMed  Google Scholar 

  21. Eliav E, Kaldor U, Ishikawa Y (1995) Phys Rev A 51:225

    Article  CAS  PubMed  Google Scholar 

  22. Petrov AN, Mosyagin NS, Isaev TA, Titov AV, Ezhov VF, Eliav E, Kaldor U (2002) Phys Rev Lett 88:073001

    Article  CAS  PubMed  Google Scholar 

  23. Chaudhuri RK, Panda PK, Das B, Mahapatra US, Mukherjee D (1999) Phys Rev A 60:246

    Article  CAS  Google Scholar 

  24. Chaudhuri RK, et al. (2000) J Phys B At, Mol Opt Phys 33:5129

  25. Cheng L, Wang F, Stanton JF, Gauss J (2018) J Chem Phys 148:044108

    Article  PubMed  Google Scholar 

  26. Cao Z, Wang F, Yang M (2016) J Chem Phys 145:154110

    Article  PubMed  Google Scholar 

  27. Wang Z, Hu S, Wang F, Guo J (2015) J Chem Phys 142:144109

    Article  PubMed  Google Scholar 

  28. Wang Z, Tu Z, Wang F (2014) J Chem Theory Comput 10:5567

    Article  CAS  PubMed  Google Scholar 

  29. Shee A, Visscher L, Saue T (2016) J Chem Phys 145:184107

    Article  PubMed  Google Scholar 

  30. Shee A, Saue T, Visscher L, Severo Pereira Gomes A (2018) J Chem Phys 149:174113

  31. Liu J, Cheng L (2021) Wiley Interdiscip Rev Comput Mol Sci 11(6):e1536

    Article  Google Scholar 

  32. Zhang C, Zheng X, Cheng L (2021) Phys Rev A 104:012814

    Article  CAS  Google Scholar 

  33. Sunaga A, Saue T (2018) Mol Phys 119(21–22):e1974592

    Google Scholar 

  34. Zhang C, Zheng X, Liu J, Asthana A, Cheng L (2023) J Chem Phys 159:244113

    Article  CAS  PubMed  Google Scholar 

  35. Chamoli S, Surjuse K, Jangid B, Nayak MK, Dutta AK (2022) J Chem Phys 156:204120

    Article  CAS  PubMed  Google Scholar 

  36. Denis M et al (2020) J Chem Phys 152:084303

    Article  CAS  PubMed  Google Scholar 

  37. Pathak H, Sahoo B, Das B, Vaval N, Pal S (2014) Phys Rev A 89:042510

    Article  Google Scholar 

  38. Pathak H, Sasmal S, Nayak MK, Vaval N, Pal S (2016) Comput Theor Chem 94:1076

  39. Pathak H, Sasmal S, Nayak MK, Vaval N, Pal S (2016) J Chem Phys 145:074110

    Article  PubMed  Google Scholar 

  40. Pathak H, Sasmal S, Talukdar K, Nayak MK, Vaval N, Pal S (2020) J Chem Phys 152(10):104302

    Article  CAS  PubMed  Google Scholar 

  41. Sasmal S, Pathak H, Nayak MK, Vaval N, Pal S (2015) Phys Rev A 91:022512

    Article  Google Scholar 

  42. Sasmal S, Pathak H, Nayak MK, Vaval N, Pal S (2016) Phys Rev A 93:062506

    Article  Google Scholar 

  43. Sasmal S, Pathak H, Nayak MK, Vaval N, Pal S (2015) Phys Rev A 91:030503(R)

    Article  Google Scholar 

  44. Talukdar K, Sasmal S, Nayak MK, Vaval N, Pal S (2018) Phys Rev A 98:022507

    Article  CAS  Google Scholar 

  45. Sasmal S, Talukdar K, Nayak MK, Vaval N, Pal S (2016) J Chem Sci 128:1671

    Article  CAS  Google Scholar 

  46. Sasmal S (2017) Phys Rev A 96:012510

    Article  Google Scholar 

  47. Sasmal S, Pathak H, Nayak MK, Vaval N, Pal S (2016) J Chem Phys 144:124307

    Article  PubMed  Google Scholar 

  48. Talukdar K, Nayak MK, Vaval N, Pal S (2020) J Phys B At Mol Opt Phys 53:135102

    Article  CAS  Google Scholar 

  49. Sasmal S, Talukdar K, Nayak MK, Vaval N, Pal S (2017) Mol Phys 115:2807

    Article  CAS  Google Scholar 

  50. Talukdar K, Nayak MK, Vaval N, Pal S (2020) J Chem Phys 153:184306

    Article  CAS  PubMed  Google Scholar 

  51. Talukdar K, Nayak MK, Vaval N, Pal S (2019) Phys Rev A 99:032503

    Article  CAS  Google Scholar 

  52. Talukdar K, Nayak MK, Vaval N, Pal S (2019) J Chem Phys 150:084304

    Article  PubMed  Google Scholar 

  53. Haldar S, Talukdar K, Nayak MK, Pal S (2021) Int J Quantum Chem 121:26764

    Article  Google Scholar 

  54. Talukdar K, Buragohain H, Nayak MK, Vaval N, Pal S (2023) Theoret Chem Acc 142:15

    Article  CAS  Google Scholar 

  55. Fazil NM, Prasannaa VS, Latha KVP, Abe M, Das BP (2018) Phys Rev A 98:032511

    Article  CAS  Google Scholar 

  56. Abe M, Prasannaa VS, Das BP (2018) Phys Rev A 97:032515

    Article  CAS  Google Scholar 

  57. Sasmal S, Pathak H, Nayak MK, Vaval N, Pal S (2015) J Chem Phys 143:084119

    Article  PubMed  Google Scholar 

  58. Talukdar K, Nayak MK, Vaval N, Pal S (2020) Phys Rev A 101:032505

    Article  CAS  Google Scholar 

  59. Trefzger C, Menotti C, Capogrosso-Sansone B, Lewenstein M (2011) J Phys B At Mol Opt Phys 44:193001

    Article  Google Scholar 

  60. Mishra T, Pai RV, Ramanan S, Luthra MS, Das BP (2009) Phys Rev A 80:43614

    Article  Google Scholar 

  61. Altman E, Brown KR, Carleo G, Carr LD, Demler E, Chin C, DeMarco B, Economou SE, Eriksson MA, Fu KMC, Greiner M, Hazzard KR, Hulet RG, Kollaer AJ, Lev BL, Lukin MD, Ma R, Mi X, Misra S, Monroe C, Murch K, Nazario Z, Ni KK, Potter AC, Roushan P, Saffman M, Schleier-Smith M, Siddiqi I, Simmonds R, Singh M, Spielman I, Temme K, Weiss DS, Vuckovic J, Vuletic V, Ye J, Zwierlein M (2021) PRX Quantum 2:017003

    Article  Google Scholar 

  62. DeMille D (2002) Phys Rev Lett 88:67901

    Article  CAS  Google Scholar 

  63. Toerring T, Ernst WE, Kindt S (1984) J Chem Phys 81:4614

    Article  CAS  Google Scholar 

  64. Rice SF, Martin H, Field RW (1985) J Chem Phys 82:5023

    Article  CAS  Google Scholar 

  65. Buckingham AD, Olegario RM (1993) Chem Phys Lett 212:253

    Article  CAS  Google Scholar 

  66. Buendgen P, Engels B, Peyerimhoff SD (1991) Chem Phys Lett 176:407

    Article  CAS  Google Scholar 

  67. Kobus J, Moncrieff D, Wilson S (2000) Phys Rev A 62:62503

    Article  Google Scholar 

  68. Langhoff SR, Bauschlicher CW Jr, Partridge H, Ahlrichs R (1986) J Chem Phys 84:5025

    Article  CAS  Google Scholar 

  69. Joshi SP, Vaval N (2013) Chem Phys Lett 568–569:170

    Article  Google Scholar 

  70. DIRAC, a relativistic ab initio electronic structure program, Release DIRAC10 (2010), written by Saue T, Visscher L, Jensen HJ with contributions from Bast R, Dyall KG, Ekström U, Eliav E, Enevoldsen T, Fleig T, Gomes ASP, Henriksson J, Iliaš M, Jacob ChR, Knecht S, Nataraj HS, Norman P, Olsen J, Pernpointner M, Ruud K, Schimmelpfennig B, Sikkema J, Thorvaldsen A, Thyssen J, Villaume S, Yamamoto S (see http://www.diracprogram.org)

  71. Saue T et al (2020) J Chem Phys 152:204104

    Article  CAS  PubMed  Google Scholar 

  72. Visscher L, Dyall K (1997) At Data Nucl Data Tables 67:207

    Article  CAS  Google Scholar 

  73. Faegri K Jr, Dyall KG (2007) Introduction to relativistic quantum chemistry. Oxford University Press, Oxford

    Google Scholar 

  74. Sucher J (1980) Phys Rev A 22:348

    Article  CAS  Google Scholar 

  75. Almoukhalalati A, Knecht S, Jensen HJA, Dyall KG, Saue T (2016) J Chem Phys 145:074104

    Article  PubMed  Google Scholar 

  76. https://cccbdb.nist.gov/

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

  78. Dyall KG (2004) Theor Chem Acc 112:403

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  80. Saue T, Faegri K, Helgaker T, Gropen O (1997) Mol Phys 91:937

    Article  CAS  Google Scholar 

  81. Steimle TC, Chen J, Gengler J (2004) J Chem Phys 121:829

    Article  CAS  PubMed  Google Scholar 

  82. Childs WJ, Goodman LS, Nielsen U, Pfeufer V (1984) J Chem Phys 80:2283

    Article  CAS  Google Scholar 

  83. Ernst WE, Kandler J, Kindt S, Torring T (1985) Chem Phys Lett 113:351

    Article  CAS  Google Scholar 

  84. Holka F, Urban M (2006) Chem Phys Lett 426:252

    Article  CAS  Google Scholar 

  85. Kerkines ISK, Mavridis A (2007) J Phys Chem A 111:371

    Article  CAS  PubMed  Google Scholar 

  86. Kutzelnigg W, Liu W (2005) J Chem Phys 123:241102

    Article  PubMed  Google Scholar 

  87. Iliaš M, Saue T (2007) J Chem Phys 126:064102

    Article  PubMed  Google Scholar 

Download references

Acknowledgements

The authors are grateful to Prof. Sourav Pal (Ashoka University, India) for providing the motivation of the present work and to Dr. Sudip Sasmal (University of Heidelberg, Germany) for his contribution to the implementation of the relativistic extended–coupled–cluster method. The authors also thank Dr. Nayana Vaval (CSIR-NCL, Pune, India) for providing access to necessary computational facilities. K.T. acknowledges the Department of Science and Technology (DST), India, for the DST-INSPIRE Faculty Fellowship Research Grant.

Author information

Authors and Affiliations

Authors

Contributions

H.B. and K.T. performed calculations, curated data and wrote the main manuscript text. H.B. prepared the figure, and M.K.N. contributed to the implementation of the methodology. K.T. and M.K.N. conceptualized the work, and all authors reviewed the manuscript.

Corresponding authors

Correspondence to Kaushik Talukdar or Malaya K. Nayak.

Ethics declarations

Conflict of interest

The authors have no Conflict of interest to declare that are relevant to the content of this article.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Buragohain, H., Talukdar, K. & Nayak, M.K. Permanent electric dipole moment of diatomic molecules using relativistic extended–coupled–cluster method. Theor Chem Acc 143, 43 (2024). https://doi.org/10.1007/s00214-024-03117-w

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s00214-024-03117-w

Keywords

Navigation