Two-Component Relativistic Hamiltonians and the Douglas-Kroll Approximation |
| M. Barysz Department of Quantum Chemistry, Institute of Chemistry Nicolaus Copernicus University, 7, Gagarin St., 87-100 Toruń, Poland |
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| Received: November 15, 2001; in final form March 28, 2002 |
| 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. |
| DOI: 10.12693/APhysPolA.101.815 PACS numbers: 31.15.-p, 31.30.Jv |