A density functional representation of quantum chemistry. III. Rigorous realization of the program in lattice space

AbstractA mathematically rigorous reformulation of molecular quantum mechanics in terms of the particle density operator and a canonically conjugated phase field is given. Using a momentum cutoff, it is shown that the usual molecular Hamiltonian can be expressed in terms of the particle density operator and a rigorously defined phase operator. It is shown that this Hamiltonian converges strongly to the cutoff‐free Hamiltonian. In spite of the fact that this Hamiltonian is of second order in the phase operators, all hitherto published expressions are not correct. Unfortunately, the correct formulation destroys the intuitive appeal of using the particle density operator as a coordinate for the many‐body problems of quantum chemistry. Unless somebody provides an essential new and clever idea, we propose to resist the fascination of a local quantum field theory of molecular matter in terms of the particle density operator.