Spatial representation diagonal elements

G. Constraints on Off-Diagonal Elements from Other Positive-Definite Hamiltonians Linear Inequalities from the Spatial Representation Linking the Orbital and Spatial Representations... 

Note that there is no simple method for converting the g-density from the spatial representation to the orbital representation and back. The g-density in the spatial representation depends on off-diagonal elements of the g-matrix in the orbital representation and the g-density in the orbital representation depends on off-diagonal elements of the g-matrix in the spatial representation. 

Recall that the spatial representation of the g-density actually depends on the off-diagonal elements of the density matrix in the orbital representation. (See Eqs. (18)-(21) and the surrounding discussion.) This suggests that some progress can be made by using the A -representabihty constraints for off-diagonal elements in the density matrix. If one chooses the one-electron Hamiltonian associated with the G condition to be a simple function, then one finds that [22, 28, 54]... 

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