Three-electron integral evaluation in the transcorrelated method using a frozen Gaussian geminal

Formulas are developed for evaluating the three-electron integrals, which a ppear in the transcorrelated method using a frozen Gaussian geminal. First, we derive expressions with intermediates, in which the angular momentum in dices of the inter-electronic operators are temporarily increased. Followin g the inspection on the factorization property, we further derive more stra ightforward recurrence relations corresponding to the Obara-Saika one for e lectron repulsion integrals. It is shown that the relations can be applied outside the contraction loops over geminal primitives by introducing three- indexed auxiliary integrals. (C) 2000 Elsevier Science B.V. All rights rese rved.