Lagrange function method for energy optimization directly in the space of natural orbitals

We propose a Lagrange method to obtain the electronic energy directly in the space of natural orbitals. The Lagrange function contains constraints to force the off-diagonal elements of the one-particle density matrix to zero, so the molecular orbitals converge to the natural orbitals simultaneously while the energy minimizes. The recently discovered “generalized Pauli conditions” for the occupation numbers are invoked to generate an initial approximation. As a demonstration of this approach, we study the system of three electrons in six orbitals which has become a paradigm for investigating multi-particle entanglement.