2-ELECTRON INTEGRALS AND INTEGRAL DERIVATIVES REVISITED

A new vertical recurrence relation (NVRR) for electron-repulsion integrals (ERIs) is introduced. NVRR connects the Cartesian Gaussian ERI with the auxiliary functions, introduced by McMurchie and Davidson. Aspects of NVRR were used by McMurchie and Davidson in their fundamental work of 1978, by Gill, Head-Gordon and Pople in their scaling method (1990) and by Hamilton and Schaefer in their algebra for moving angular momenta between electrons (1990). Here, NVRR is employed to obtain an efficient formulation for the ERI gradients. Also, a straightforward procedure for constructing two-electron integrals over general spherical tensor operators is outlined.