Two-Component Relativistic Hamiltonians and the Douglas-Kroll Approximation

• Authors: M. Barysz
• Languages of publication: EN

Abstracts

EN

The iterative solutions of the previously derived operator equation which defines an open-ended formalism for the reduction of the 4-component Dirac Hamiltonian to 2-component "electronic" operators of arbitrarily high accuracy, are discussed. It is shown that by departing from the approach based solely on the operator algebra one can define the initial iterative solution which leads to the 2-component Douglas-Kroll Hamiltonian. The present derivation reveals the origin of the success of methods based on the Douglas-Kroll Hamiltonian. It also shows that among relatively simple 2-component Hamiltonians, which are exact through the fourth power of the fine structure constant, the Douglas-Kroll operator is the most complete one. Also a computationally convenient and highly compact formula for matrix elements of the Douglas-Kroll Hamiltonian is obtained as a by-product of this investigation.

Keywords

EN

31.15.-p; 31.30.Jv

Discipline

• 31.15.-p: Calculations and mathematical techniques in atomic and molecular physics(see also 02.70.-c Computational techniques, in mathematical methods in physics)

• Publisher: Institute of Physics, Polish Academy of Sciences
• Journal: Acta Physica Polonica A
• Year: 2002
• Volume: 101
• Issue: 6
• Pages: 815-823

Dates

published

2002-06

received

2001-11-15

(unknown)

2002-03-28

Contributors

author

M. Barysz

• Department of Quantum Chemistry, Institute of Chemistry, Nicolaus Copernicus University, 7, Gagarin St., 87-100 Toruń, Poland

References

• 1. R.E. Moss, Advanced Molecular Quantum Mechanics, Chapman and Hall, London 1973
• 2. L.L. Foldy, S.A. Wouthuysen, Phys. Rev., 78, 29, 1950
• 3. M. Douglas, N.M. Kroll, Ann. Phys., 82, 1989, 1974
• 4. B.A. Hess, Phys. Rev. A, 33, 3742, 1986
• 5. G. Jansen, B.A. Hess, Phys. Rev A, 39, 6016, 1989
• 6. R. Samzow, B.A. Hess, G. Jansen, J. Chem. Phys., 96, 1227, 1992
• 7. E. van Lenthe, E.J. Baerends, J.G. Snijders, J. Chem. Phys., 99, 4597, 1993
• 8. A.J. Sadlej, J.G. Snijders, E. van Lenthe, E.J. Baerends, J. Chem. Phys., 102, 1758, 1995
• 9. E. van Lenthe, R. van Leeuwen, E.J. Baerends, J.G. Snijders, Int. J. Quantum Chem., 57, 281, 1996
• 10. M. Barysz, A.J. Sadlej, J.G. Snijders, Int. J. Quantum Chem., 65, 225, 1997
• 11. M. Barysz, J. Chem. Phys., 114, 9315, 2001
• 12. V. Kello, A.J. Sadlej, Int. J. Quantum. Chem., 68, 159, 1998
• 13. W. Kutzelnigg, Z. Phys. D, 11, 15, 1989
• 14. W. Kutzelnigg, Z. Phys. D, 15, 27, 1990
• 15. W. Kutzelnigg, Chem. Phys., 225, 203, 1990
• 16. G. Hardekopf, J. Sucher, Phys. Rev. A, 30, 703, 1984
• 17. J.-L. Heully, I. Lindgren, E. Lindroth, S. Lundqvist, A.J.-M. Martensson-Pendril, J. Phys. B, 19, 2799, 1986
• 18. B.A. Hess, Phys. Rev. A, 22, 756, 1985
• 19. J. Almlof, K. Feegri, Jr., H.H. Grelland, Chem. Phys. Lett., 114, 53, 1985
• 20. B.A. Hess, R.J. Buenker, P. Chandra, Int. J. Quantum Chem., 29, 737, 1986
• 21. D. Woźniak, A.J. Sadlej, Acta Phys. Pol. A, 98, 673, 2000
• 22. R.J. Bartlett, in: Methods in Computational Chemistry, Advanced Series in Physical Chemistry, Ed. D.R. Yarkony, Vol. 2, World Scientific, Singapore 1995, p. 1047 and references therein
• 23. J.D. Bjorken, S.D. Drell, Relativistic Quantum Fields, McGraw-Hill, New York 1965
• 24. T. Nakajima, K. Hirao, J. Chem. Phys., 113, 7786, 2000

Identifiers

DOI

10.12693/APhysPolA.101.815