## Abstract

We present an efficient algorithm for evaluating a class of two-electron integrals of the form r_{12}r_{12}/r12n over one-electron Gaussian basis functions. The full Breit interaction in four-component relativistic theories beyond the Gaunt term is such an operator with n 3. Another example is the direct spin-spin coupling term in the quasi-relativistic Breit-Pauli Hamiltonian (n 5). These integrals have been conventionally evaluated by expensive derivative techniques. Our algorithm is based on tailored Gaussian quadrature, similar to the Rys quadrature for electron repulsion integrals (ERIs), and can utilize the so-called horizontal recurrence relation to reduce the computational cost. The CPU time for computing all six Cartesian components of the Breit or spin-spin coupling integrals is found to be only 3 to 4 times that of the ERI evaluation.

Original language | English (US) |
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Article number | 111101 |

Journal | Journal of Chemical Physics |

Volume | 138 |

Issue number | 11 |

DOIs | |

State | Published - Mar 21 2013 |

## ASJC Scopus subject areas

- Physics and Astronomy(all)
- Physical and Theoretical Chemistry