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In this letter the conceptual and computational implications of the Hartreeproduct type nuclear wavefunction introduced recently within the context of theab initio non-Born-Oppenheimer Nuclear-electronic orbital (NEO) methodology areconsidered. It is demonstrated that this wavefunction may imply apseudo-adiabatic separation of the nuclei and electrons and each nucleus isconceived as a quantum oscillator while a non-Coulombic effective Hamiltonianis deduced for electrons. Using the variational principle this Hamiltonian isemployed to derive a modified set of single-component Hartree-Fock equationswhich are equivalent to the multi-component version derived previously withinthe context of the NEO and, easy to be implemented computationally.

Some implications of the Hartree product treatment of the quantum nuclei in the ab initio Nuclear-electronic orbital methodology