Implementation of analytical first derivatives for evaluation of the many-body nonadiabatic wave function with explicitly correlated Gaussian functions

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Abstract
A nonadiabatic many-particle wave function is generated using an expansion in terms of explicitly correlated Gaussian-type basis functions. In this approach, motions of all particles are correlated at the same time, and electrons and nuclei are distinguished via permutational symmetry. We utilize our newly proposed nonadiabatic variational approach [P. M. Kozlowski and L. Adamowicz, J. Chem. Phys. 95, 6681 (1991)], which does not require the separation of the internal and external motions. The analytical first derivative of the variational functional with respect to the nonlinear parameters appearing in the basis functions are derived and implemented to find the minimum. Numerical examples for the ground state of the hydrogen molecule are presented.