  We investigate the influence of interactions and geometry on ground states of
clean chaotic quantum dots using the self-consistent Hartree-Fock method. We
find two distinct regimes of interaction strength: While capacitive energy
fluctuations $\delta \chi$ follow approximately a random matrix prediction for
weak interactions, there is a crossover to a regime where $\delta \chi$ is
strongly enhanced and scales roughly with interaction strength. This
enhancement is related to the rearrangement of charges into ordered states near
the dot edge. This effect is non-universal depending on dot shape and size. It
may provide additional insight into recent experiments on statistics of Coulomb
blockade peak spacings.
