Newton-Raphson optimization of the many-body nonadiabatic wave function expressed in terms of explicitly correlated Gaussian functions

A nonadiabatic many-body wave function is represented in terms of explicitly correlated Gaussian-type basis functions. Motions of all particles (nuclei and electrons) are treated equally and particles are distinguished via permutational symmetry. The nonadiabatic wave function is determined in a variational calculation with the use of the method proposed recently [P. M. Kozlowski and L. Adamowicz, J. Chem. Phys. 95, 6681 (1991)]. In this approach no direct separation of the center-of-mass motion from the internal motion is required. The theory of analytical first and second derivatives of the variational functional with respect to the Gaussian exponents and its computational implementation in conjunction with the Newton-Raphson optimization technique is described. Finally, some numerical examples are shown.