Exact decoupling of the Dirac Hamiltonian. II. The generalized Douglas-Kroll-Hess transformation up to arbitrary order
Journal Article
·
· Journal of Chemical Physics
- Lehrstuhl fuer Theoretische Chemie, Universitaet Bonn, Wegelerstrasse 12, D-53115 Bonn (Germany)
In order to achieve exact decoupling of the Dirac Hamiltonian within a unitary transformation scheme, we have discussed in part I of this series that either a purely numerical iterative technique (the Barysz-Sadlej-Snijders method) or a stepwise analytic approach (the Douglas-Kroll-Hess method) are possible. For the evaluation of Douglas-Kroll-Hess Hamiltonians up to a pre-defined order it was shown that a symbolic scheme has to be employed. In this work, an algorithm for this analytic derivation of Douglas-Kroll-Hess Hamiltonians up to any arbitrary order in the external potential is presented. We discuss how an estimate for the necessary order for exact decoupling (within machine precision) for a given system can be determined from the convergence behavior of the Douglas-Kroll-Hess expansion prior to a quantum chemical calculation. Once this maximum order has been accomplished, the spectrum of the positive-energy part of the decoupled Hamiltonian, e.g., for electronic bound states, cannot be distinguished from the corresponding part of the spectrum of the Dirac operator. An efficient scalar-relativistic implementation of the symbolic operations for the evaluation of the positive-energy part of the block-diagonal Hamiltonian is presented, and its accuracy is tested for ground-state energies of one-electron ions over the whole periodic table. Furthermore, the first many-electron calculations employing sixth up to fourteenth order DKH Hamiltonians are presented.
- OSTI ID:
- 20658126
- Journal Information:
- Journal of Chemical Physics, Journal Name: Journal of Chemical Physics Journal Issue: 22 Vol. 121; ISSN JCPSA6; ISSN 0021-9606
- Country of Publication:
- United States
- Language:
- English
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