Abstract
The non-Newtonian classical Lagrangian on parameters involved in a trial many-electron wave function such as linear-combination-of-atomic-orbitals coefficients, centers of the basis set of orbitals, and configuration interaction expansion coefficients is constructed. The corresponding equations of the constrained motion on the parameters manifold are obtained in the explicit form and their relationship with those of the Car-Parrinello Newton-type approach is under discussion.