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The extra electron occupies the lowest unoccupied molecular orbital of the neutral molecule, the $B_{3g}$ orbital at the middle root ${\lambda }_L=0.25410169\dots$ of ${\lambda }^3-4\lambda +1=0$. WriteThe first and third rows of the $B_{3g}$ block giveChoosing the overall phase so that site 1 is positive gives $(a,b,c)\simeq (0.664623,-0.495741,-0.559033)$. In the original site order,The squared coefficients sum to one. Within this fixed-orbital Hückel orbital charge density approximation, the added electron contributes site populationsThus the oxygen sites $\boxed{1\text{ and }8}$ receive the largest added negative charge, each receiving an increment of approximately $-0.221e$. Including the four doubly occupied neutral orbitals gives an anion $\pi$ population of about $1.621$ on each oxygen, $0.870$ on sites 2 and 7, and $1.005$ on each remaining carbon. Thus oxygen also has the largest total $\pi$ population in this model. A coefficient's sign is an orbital phase, not the sign of its electric charge. Predicting an actual charge density would additionally require orbital relaxation and a population-analysis convention; the stated result is the requested orbital model.

Each site has a pi-electron population $4/3$, and each adjacent pi bond order is $2/3$. The two carbon sites supply one pi electron each and the nitrogen lone pair supplies two, giving four electrons in two occupied molecular orbitals. Orthogonality to the given Homo and LUMO fixes the remaining occupied normalized orbital, up to overall sign, asFor doubly occupied orbitals, the Hückel orbital charge density and Hückel pi bond order follow fromThe diagonal sums to four electrons. The negative $P_{13}$ is an off-diagonal density-matrix element between nonadjacent sites, not an additional directly connected chemical bond.

Relative to neutral pi contributions $(1,2,1)$, the pi-system charges are $(-e/3,+2e/3,-e/3)$: electron density has moved from nitrogen toward the two carbon sites. Thus the physical electric dipole moment vector points from the midpoint of the carbon pair toward nitrogen along the molecular symmetry bisector. The conventional chemical dipole arrow, with a crossed positive tail, points oppositely: from nitrogen toward the carbon pair. This is only the pi contribution, not a prediction of the full sigma-plus-pi molecular dipole.

The Hückel orbital charge density and Hückel pi bond order giveEach site receives $1/2$ electron from the lowest orbital and one from the occupied nonbonding subspace, so $n_i=3/2$ at every carbon, summing to six. Relative to one neutral pi electron per carbon this is a pi charge of $-e/2$ at each site.

For adjacent sites, only the lowest orbital contributes, giving $p_{12}=p_{23}=p_{34}=p_{41}=1/2$. For opposite sites the nonbonding contribution reverses the sign: $p_{13}=p_{24}=-1/2$. These non-neighbour negative density-matrix entries are not extra sigma bonds or extra resonance integrals in the Hamiltonian. If only skeletal nearest-neighbour pi bond orders are requested, the four values $1/2$ are the relevant ones.