Minimization of the energy of a molecule with respect to nonlinear parameters of the basis set

We study characteristic features of minimization of the Hartree-Fock-Roothaan energy with respect to nonlinear parameters of the Gaussian basis set. We describe and apply regularization of the discrete Newton-Raphson method based on the analysis of eigenvalues of the Hessian matrix. We discuss results of groundstate energy calculations for the molecules LiH, CH⁺, CH^–, He₃ ²⁺, BH₂ ⁺, and H₂O in optimal ls-Gaussian basis sets. We find that, for molecules with four to six electrons, good accuracy is obtained with small basis sets consisting of ls-functions only.Translated from Teoreticheskaya i Éxperimental'naya Khimiya, Vol. 24, No. 2, pp. 215–218, March–April, 1988.