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 quantum dot edge. This effect is nonuniversal depending on the shape and the size of the dot. It may provide insight into recent experiments on statistics of Coulomb blockade peak spacings.