Hartree–Fock energy derivatives with respect to basis set exponents. Integral derivatives using Rys polynomials

The Rys polynomial method has been used to evaluate the first derivatives of the two electron integrals and the nuclear electron attraction integrals with respect to the Gaussian exponents. Gradients for the sulfur 6-31 G(d) basis set in HS−, H2S, H3S+, H2S2, H3CSH, H2CS, CS, H2SO, SO2 and SO3 have been evaluated to illustrate the effect of charge, multiple bonding and hypervalency on the basis set exponents.