Relationships among derivatives of the integrals in the calculation of the gradient of the electronic energy with respect to the nuclear coordinates

The use of the translational invariance property of molecular integrals is extended by its combination with the closely related transformation properties under infinitesimal rotations. This further reduces the number of truly linearly independent derivatives of the molecular integrals that require calculation in obtaining the gradient of the electronic energy. The detailed linear equations that yield the linearly dependent derivatives in terms of the ''independent'' derivatives are presented.