On the Accuracy of the Discretization Techniques in Approximate Relativistic Methods |

D. Woźniak and A.J. SadlejDepartment 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 p^{2}
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 p^{2}
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 |