XVIth International Workshop on
Quantum Systems in
Chemistry and Physics
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Relativistic Quantum Theory for Large Systems
Hiromi Nakai1 2 3
1Department of Chemistry and Biochemistry, Waseda University, Tokyo, Japan
2Research Institute for Science and Engineering, Waseda University, Tokyo, Japan
3CREST, Japan Science and Technology Agency, Tokyo, Japan
A number of relativistic quantum-chemical methods are available to treat compounds containing heavy elements. The four-component relativistic theory using Dirac–Coulomb or Dirac–Coulomb–Breit Hamiltonian [1] is sufficiently accurate for describing various chemical phenomena and is therefore a good reference for examining approximate two-component schemes. The infinite-order Douglas–Kroll (IODK) method [2-5] gives an exact description of the large component for the one-electron Dirac Hamiltonian. The IODK/IODK method [6], which transforms two-electron Coulomb operator by using the one-electron IODK unitary transformation, can reproduce the total energies for the four-component Dirac–Coulomb Hamiltonian even including superheavy elements. However, the computational costs for the IODK/IODK method are extremely expensive from a practical point of view.

The purpose of the present study is to propose a practical scheme for two-component relativistic quantum-chemical calculations based on the accurate IODK/IODK method, in which the unitary transformation in a whole system is a bottle neck. We assume the locality of relativistic effect and define the local unitary transformation (LUT) [7]. The numerical tests clarify that the LUT scheme enables to reduce the computational scaling without any loss of accuracy.

In the presentation, I will explain the background of the present study, and show the formulation of the LUT scheme and the numerical results. I will also discuss the further direction of the practical relativistic quantum theory for large systems.

[1] I. P. Grant, in: S. Wilson (Ed.), Methods in Computational Chemistry, Vol. 2, Plenum Press, New York, p. 1 (1987).
[2] M. Douglas and N. M. Kroll, Ann. Phys. (Leipzig) 82, 89 (1974).
[3] B. A. Hess, Phys. Rev. A 32, 756 (1985).
[4] M. Barysz, A. J. Sadlej, and J. G. Snijders, Int. J. Quant. Chem. 65, 225 (1997).
[5] M. Barysz and A. J. Sadlej, J. Chem. Phys. 116, 2696 (2002).
[6] J. Seino and M. Hada, Chem. Phys. Lett. 461, 327 (2008).
[7] J. Seino and H. Nakai, in preparation.


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