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On the Accuracy of the Discretization Techniques in Approximate Relativistic Methods |
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D. Woźniak and A.J. Sadlej Department of Quantum Chemistry, Institute of Chemistry, Nicolaus Copernicus University, 7, Gagarin St., 87-100 Toruń, Poland |
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| Received: September 7, 2000; in final form November 27, 2000 |
| Several non-singular 2-component methods for relativistic calculations of the electronic structure of atoms and molecules lead to cumbersome operators which are partly defined in the coordinate representation and partly in the momentum representation. The replacement of the Fourier transform technique by the approximate resolution of identity in the basis set of approximate eigenvectors of the p2 operator is investigated in terms of the possible inaccuracies involved in this method. The dependence of the accuracy of the evaluated matrix elements on the composition of the subspace of these eigenvectors is studied. Although the method by itself appears to be quite demanding with respect to the faithfulness of the representation of the p2 operator, its performance in the context of the standard Gaussian basis sets is found to be encouragingly accurate. This feature is interpreted in terms of approximately even-tempered structure of the majority of Gaussian basis sets used in atomic and molecular calculations. |
| DOI: 10.12693/APhysPolA.98.673 PACS numbers: 31.15.-p, 31.30.Jv |