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A relativistic 4-component general-order multi-reference coupled cluster method: initial implementation and application to HBr

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An Erratum to this article was published on 31 July 2007

Abstract

We present the initial implementation of a determinant-based general-order coupled cluster method which fully accounts for relativistic effects within the four-component framework. The method opens the way for the treatment of multi-reference problems through a state-selective expansion of the model space. The evaluation of the coupled cluster vector function is carried out via relativistic configuration interaction expansions. The implementation is based on a large-scale configuration interaction technique, which may efficiently treat long determinant expansions of more than 108 terms. We demonstrate the capabilities of the new method in calculations of complete potential energy curves of the HBr molecule. The inclusion of spin–orbit interaction and higher excitations than coupled cluster double excitations, either by multi-reference model spaces or the inclusion of full iterative triple excitations, lead to highly accurate results for spectral constants of HBr.

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References

  1. Abrams ML, Sherrill CD (2005) General-order single and multi-reference configuration interaction and coupled- cluster theory: symmetric dissociation of water. Chem Phys Lett 404:284

    Article  CAS  Google Scholar 

  2. Andersson K, Barysz M, Bernhardsson A, Blomberg MRA, Cooper DL, Fleig T, Fülscher MP, de~Graaf C, Hess BA, Karlström G, Lindh R, Malmqvist På, Neogrády P, Olsen J, Roos BO, Sadlej AJ, Schütz M, Schimmelpfennig B, Seijo L, Serrano-Andrés L, Siegbahn PEM, Stålring J, Thorsteinsson T, Veryazov V, Widmark PO (2000) \({\mathcal{MOLCAS}}\) version 5. Lund University, Sweden

  3. Barysz M, Sadlej A, Snijders JG (1997) Nonsingular two/one-component relativistic Hamiltonians accurate through arbitrary high order in α. Int J Quantum Chem 65:225

    Article  CAS  Google Scholar 

  4. Dyall KG (1994) An exact separation of the spin-free and spin-dependent terms of the Dirac–Coulomb–Breit Hamiltonian. J Chem Phys 100:2118

    Article  CAS  Google Scholar 

  5. Fan P, Hirata S (2006) Active-space coupled-cluster methods through connected quadruple excitations. J Chem Phys 124:104,108

    Google Scholar 

  6. Fleig T, Sørensen LK (2006) A relativistic 4-component multi-reference coupled cluster method. Application to the CsLi molecule. In: Münster G, Wolf D, Kremer M (eds) NIC Symposium 2006, vol 32, NIC series. ISBN 3-00-017351-X, pp 91–98

  7. Fleig T, Visscher L (2005) Large-scale electron correlation calculations in framework of the spin-free Dirac formalism. The Au2 molecule revisited. Chem Phys 311:113

    Google Scholar 

  8. Fleig T, Olsen J, Marian CM (2001) The generalized active space concept for the relativistic treatment of electron correlation. I. Kramers-restricted two-component configuration interaction. J Chem Phys 114:4775

    Article  CAS  Google Scholar 

  9. Fleig T, Olsen J, Visscher L (2003) The generalized active space concept for the relativistic treatment of electron correlation. II: Large-scale configuration interaction implementation based on relativistic 2- and 4-spinors and its application. J Chem Phys 119:2963

    Article  CAS  Google Scholar 

  10. Fleig T, Jensen HJAa, Olsen J, Visscher L (2006) The generalized active space concept for the relativistic treatment of electron correlation. III: Large-scale configuration interaction and multi-configuration self-consistent-field four-component methods with application to UO2. J Chem Phys 124:104–106

  11. DIRAC04, a relativistic ab initio electronic structure program, release dirac04.0 (2004) written by Jensen HJAa, Saue T, Visscher L with contributions~from Bakken V, Eliav E, Enevoldsen T, Fleig T, Fossgaard O, Helgaker T, Laerdahl J, Larsen CV, Norman P, Olsen J, Pernpointner M, Pedersen JK, Ruud K, Salek P, van Stralen JNP, Thyssen J, Visser O, Winther T

  12. Hanrath M (2005) An exponential multireference wave- function ansatz. J Chem Phys 123:084,102

    Article  Google Scholar 

  13. Helgaker T, Ruden TA, Jørgensen P, Olsen J, Klopper W (2004) A priori calculation of molecular properties to chemical accuracy. J Phys Org Chem 17:913

    Article  CAS  Google Scholar 

  14. Heß BA (1985) Applicability of the no-pair equation with free-particle projection operators to atomic and molecular structure calculations. Phys Rev A 32:756

    Article  Google Scholar 

  15. Heß BA (1986) Relativistic electronic-structure calculations employing a two-component no-pair formalism with external field projection operators. Phys Rev A 33:3742

    Article  Google Scholar 

  16. Hirata S (2004) Higher-order equation-of-motion coupled-cluster methods. J Chem Phys 121:51

    Article  CAS  Google Scholar 

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

    Google Scholar 

  18. Jensen HJAa, Iliaš M (2006) Two-component relativistic methods based on the quaternion modified dirac equation: from the Douglas–Kroll to the Barysz–Sadlej–Snijders infinite order (to be published)

  19. Jeziorski B, Monkhorst HJ (1981) Coupled-cluster method for multideterminantal reference states. Phys Rev A 24:1668

    Article  CAS  Google Scholar 

  20. Kowalski K, Piecuch P (2004) New classes of non-iterative energy corrections to multi-reference coupled-cluster energies. Mol Phys 102:2425

    Article  CAS  Google Scholar 

  21. Kállay M, Gauss J (2005) Approximate treatment of higher excitations in coupled-cluster theory. J Chem Phys 123:214,105

    Article  Google Scholar 

  22. Kállay M, Surján P (2001) Higher excitations in coupled- cluster theory. J Chem Phys 115:2945

    Article  Google Scholar 

  23. Kállay M, Szalay P, Surján P (2002) A general state- selective multireference coupled-cluster algorithm. J Chem Phys 117:980

    Article  Google Scholar 

  24. Krogh JW, Olsen J (2001) A general coupled cluster study of the {N2 molecule. Chem Phys Lett 344:578

    Article  CAS  Google Scholar 

  25. Landau A, Eliav E, Kaldor U (1999) Intermediate Hamiltonian Fock-space coupled-cluster method. Chem Phys Lett 313:399

    Article  CAS  Google Scholar 

  26. Lévy-Leblond JM (1967) Nonrelativistic particles and wave equations. Commun Math Phys 6:286

    Article  Google Scholar 

  27. Oliphant N, Adamowicz L (1991) The implementation of the multireference coupled-cluster method based on the single-reference formalism. J Chem Phys 96:3739

    Article  Google Scholar 

  28. Oliphant N, Adamowicz L (1991) Multireference coupled-cluster method using a single-reference formalism. J Chem Phys 94:1229

    Article  CAS  Google Scholar 

  29. Olsen J (2000) The initial implementation and applications of a general active space coupled cluster method. J Chem Phys 113:7140

    Article  CAS  Google Scholar 

  30. Olsen J, Roos BO, Jørgensen P, Jensen HJAa (1988) Determinant based configuration interaction algorithms for complete and restricted configuration interaction spaces. J Chem Phys 89:2185

    Article  CAS  Google Scholar 

  31. Ruden TA, Helgaker T, Jørgensen P, Olsen J (2004) Coupled-cluster connected quadruples and quintuples corrections to the harmonic vibrational frequencies and equilibrium bond distances of HF, N2, F2, and CO. J Phys Chem 121: 5874

    Article  CAS  Google Scholar 

  32. Saue T, Jensen HJAa (1999) Quaternion symmetry in relativistic molecular calculations: the Dirac–Hartree–Fock method. J Chem Phys 111:6211

    Article  CAS  Google Scholar 

  33. Sørensen LK, Fleig T, Olsen J (2006) Implementation of a four-component spin–orbit free multi-reference coupled cluster method with application to CsLi, Chem Phys Lett (in preparation)

  34. Styszyński J (2000) Relativistic core–valence correlation effects on molecular properties of the hydrogen halide molecules. Chem Phys Lett 317:351

    Article  Google Scholar 

  35. Thyssen J, Jensen HJAa, Fleig T (2006) A four-component relativistic multi-configuration self-consistent-field method for molecules. J Chem Phys (submitted, under revision)

  36. Visscher L, Dyall KG, Lee TJ (1995) Kramers-restricted closed-shell CCSD theory. Int J Quantum Chem Quantum Chem Symp 29:411

    Article  CAS  Google Scholar 

  37. Visscher L, Lee TJ, Dyall KG (1996) Formulation and implementation of a relativistic unrestricted coupled-cluster method including noniterative connected triples. J Chem Phys 105:8769

    Article  CAS  Google Scholar 

  38. Visscher L, Styszyński J, Nieuwpoort WC (1996) Relativistic and correlation effects on molecular properties. 2. The hydrogen halides HF, HCl, HBr, HI, and HAt. J Chem Phys 105:1987

    Article  CAS  Google Scholar 

  39. Visscher L, Eliav E, Kaldor U (2001) Formulation and implementation of the relativistic Fock-space coupled- cluster method for molecules. J Chem Phys 115:9720

    Article  CAS  Google Scholar 

  40. Wolf A, Reiher M, Hess BA (2002) The generalized Douglas–Kroll transformation. J Chem Phys 117:9215

    Article  CAS  Google Scholar 

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Authors and Affiliations

  1. Department of Theoretical Chemistry, building 26.32, Heinrich Heine University Düsseldorf, Universitätsstraß e 1, 40225, Düsseldorf, Germany

    Timo Fleig & Lasse K. Sørensen

  2. Theoretical Chemistry, Langelandsgade 140, Aarhus University, 8000, Århus C, Denmark

    Jeppe Olsen

Authors
  1. Timo Fleig
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  2. Lasse K. Sørensen
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  3. Jeppe Olsen
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Correspondence to Timo Fleig.

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An erratum to this article can be found at http://dx.doi.org/10.1007/s00214-007-0381-8

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Fleig, T., Sørensen, L.K. & Olsen, J. A relativistic 4-component general-order multi-reference coupled cluster method: initial implementation and application to HBr. Theor Chem Account 118, 347–356 (2007). https://doi.org/10.1007/s00214-007-0265-y

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